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may be aided in his task of revision, from time to time, 
by the kindly criticism of his readers. 


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WORKS OF WILLIAM KENT 


PUBLISHED BY 


JOHN WILEY & SONS. 


The Mechanical Engineers’ Pocket=Book. 


A Reference Book of Rules, Tables, Data, and 
Formule, for the Use of Engineers, Mechanics, 
and Students. xxxii-++ 1100 pages, 16mo, morocco, 
$5.00, 


Steam=Boiler Economy. 


A Treatise on the Theory and Practice of Fuel 
Economy in the Operation of Steam-Boilers, 
xiv + 45g pages, 136 figures, 8vo, cloth, $4.00. 





THE 


MECHANICAL ENGINEER'S 
POCKET-BOOK, | 


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A REFERENCE-BOOK OF RULES» TADLHS:, DATA, 
| AND FORMULA, FOR TH USE OF 
ENGINEERS, MECHANICS, 
AND STUDENTS. 


By 
WILLIAM KENT, A.M., M.E., 


Dean and Professor of Mechanical Engineering in the L. C. Smith 
College of Applied Science, Syracuse University, 
Member Amer. Soc’y Mechl. Engrs. and Amer. Inst. Mining Engrs. 


SEVENTH EDITION, REVISED AND ENLARGED 


TWENTY-FIFTH THOUSAND. 
TOTAL ISSUE SIXTY THOUSAND. 


NEW YORK: 
JOHN WILEY & SONS. 
Lonpon: CHAPMAN & HALL,, Liuirep. 
1908, 


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CoPyYRIGHT, 1895, 1902, 
BY 
WILLIAM KENT, 


PRESS OF 
BRAUNWORTH & CO, 
BOOKBINDERS AND PRINTERS 
BROOKLYN, N. Y. 


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PREF AOE. 


wlORE than twenty years ago the author began to follow 
the advice given by Nystrom: ‘‘Every engineeer should 
make his own pocket-book, as he proceeds in study and 
practice, to suit his particular business.” The manuscript 
pocket-book thus begun, however, soon gave place to more 
modern means for disposing of the accumulation of engi- 
neering facts and figures, viz., the index rerum, the scrap- 
book, the collection of indexed envelopes, portfolios and 
boxes, the card catalogue, etc. Four years ago, at the re- 
quest of the publishers, the labor was begun of selecting 
from this accumulated mass such matter as pertained to 
mechanical engineering, and of condensing, digesting, and 
arranging it in form for publication. In addition to this, a 
careful examination was made of the transactions of engi- 
neering societies, and of the most important recent works 
on mechanical engineering, in order to fill gaps that might 
be left in the original collection, and insure that no impor- 
tant facts had been overlooked. 

Some ideas have been kept in mind during the prepara- 
tion of the Pocket-book that will, it is believed, cause it to 
differ from other works of its class. In the first place it 
was considered that the field of mechanical engineering was 
so great, and the literature of the subject so vast, that as 
little space as possible should be given to subjects which 


especially belong to civil engineering. While the mechan- 
‘ical engineer must continually deal with problems which 


belong properly to civil engineering, this latter branch is 
so well covered by Trautwine’s ‘‘ Civil Engineer’s Pocket- 
book” that any attempt to treat it exhaustively would not 
only fill no ‘‘long-felt want,” but would occupy space 
which should be given to mechanical engineering. 
Another idea prominently kept in view by the author has 
been that he would not assume the position of an ‘‘au- 
thority” in giving rules and formule for designing, but 
only that of compiler, giving not only the name of the 
originator of the rule, where it was known, but also the 
volume and page from which it was taken, so that its 


iii 


L277 


avon & PREFACE. 


derivation may be traced when desired. When different 
. formule for the same problem have bee> found they have 
been given in contrast, and in many cases examples have 
been calculated by each to show the difference between 
them. In some cases these differences are quite remark- 
able, as will be seen under Safety-valves and Crank-pins. 
Occasionally the study of these differences has led to the 
author’s devising a new formula, in which case the deriva 
tion of the formula is given. 

Much attention has been paid to the abstracting of data 
of experiments from recent periodical literature, and numer- 
ous references to other data are given. In this respect 
the present work will be found to differ from other Pocket- 
books. 

The author desires to express his obligation to the many 
persons who have assisted him in the preparation of the 
work, to manufacturers who have furnished their cata- 
logues and given permission for the use of their tables, 
and to many engineers who have contributed original data 
and tables. The-names of these persons are mentioned in 
their proper places in the text, and in all cases it has been 
endeavored to give credit to whom credit is due. The 
thanks of the author are also due to the following gentle- 
men who have given assistance in revising manuscript or 
proofs of the sections named: Prof. De Volson Wood, 
mechanics and turbines; Mr. Frank Richards, compressed 
air; Mr. Alfred R. Wolff, windmilis; Mr. Alex. C. 
Humphreys, illuminating gas; Mr. Albert E. Mitchell, 
locomotives; Prof. James E. Denton, refrigerating-ma. 
chinery; Messrs. Joseph Wetzler and Thomas W. Varley, 
electrical engineering ; and Mr. Walter S. Dix, for valuable 
contributions on several subjects, and suggestions as to their 


treatment. WILLIAM KENT. 
Passaic, N. J., 4fr22, 1895. 


FIFTH EDITION, MARCH, 1900. 


Some typographical and other errors discovered in the fourth 
edition have been corrected. New tables and some additions 
have been made under the head of Compressed Air. The new 
(1899) code of the Boiler Test Committee of the American 
Society of Mechanical Engineers has been substituted for the 
gld (1885) code, W. Ky 





PREFACE TO FOURTH EDITION. 


In this edition many extensive alterations have been made, 
Much obsolete matter has been cut out and fresh matter substi- 
tuted. In the first 170 pages but few changes have been found 
necessary, but a few typographical and other minor errors have 
been corrected. The tables of sizes, weight, and strength of 
materials (pages 172 to 282) have been thoroughly revised, many 
entirely new tables, kindly furnished by manufacturers, having 
been substituted. Especial attention is called to the new matter 
on Cast-iron Columns (pages 250 to 253). In the remainder of 
the book changes of importance have been made in more than 100 
pages, and all typographical errors reported to date have been 
corrected. Manufacturers’ tables have been revised by reference 
to their latest catalogues or from tables furnished by the manufac- 
turers especially for this work. Much new matter is inserted 
under the heads of Fans and Blowers, Flow of Air in Pipes, and 
Compressed Air. The chapter on Wire-rope Transmission (pages 
QI7 to 922) has been entirely rewritten. The chapter on Electrical 
Engineering has been improved by the omission of some matter 
that has become out of date and the insertion of some new matter. 

It has been found necessary to place much of the new matter of 
this edition in an Appendix, as space could not conveniently be 
made for it in the body of the book. It has not been found possi- 
ple to make in the body of the book many of the cross-references 
which should be made to the items in the Appendix. Users of the 
book may find it advisable to write in the margin such cross-refere 
ences as they may desire. 

The Index has been thoroughly revised and greatly enlarged. 

The author is under continued obligation to many manufacturers 
who have furnished new tables and data, and to many individual 
engineers who have furnished new matter, pointed out errors in 
the earlier editions, and offered helpful suggestions. He will be 
glad to receive similar aid, which will assist in the further 


improvement of the buok in future editions, 


WILLIAM KENT. 
Passaic, N. J., September, 1898. 


SIXTH EDITION. DECEMBER, 1902. 


THE chapter on Electrical Engineering has been thoroughly 
revised, much of the old matter cut out and new matter sub- 
stituted. Fourteen new pages have been devoted to the sub- 
ject of Alternating Currents. The chapter on Locomotives hag 
been revised. Some new matter has been added under Cast 
Iron, Specifications for Steel, Springs, Steam-engines, and 
Friction and Lubrication. Slight changes and corrections in 
the text have been made in nearly a hundred pages. 


vd PREFACE. 


SEVENTH EDITION, OCTOBER 1904. 


AN entirely new index has been made, with about twice as 
many titles as the former index. The electrical engineering 
chapter has been further revised and some new matter added. 
Four pages on Coal Handling Machinery have been inserted 
at page gII, and numerous minor changes have been made. 

W. K. 


Syracuse, N. Y. 


CONTENTS 


(For Alphabetical Index see page 1093.) 


MATHEMATICS, 
Arithmetic, ; 


PAGE 


Arithmetical and Algebraical SIONS, cuctesweis sisson cee teetens @eseeoveroeve 
Greatest Common Divisor,........... SP ar se Dd ee ees sans eae eetlevicue dae ale 
Least Lomnee Miupltipla nia, Ase ace ss scine per cicinsp es desaabiabtee ede os aeeiied 
Fractions.. wee ce ree reese reer ee ee eh es: SHOES COPS EES HES 9H SF 09882008 88 SH00 
PESCIIAIS, ee ocains c CTE elke Ge Zola cates lie eleniehe Deiseto de cleele siniea it elele blow ale ein 
Table. Decimal Equivalents of Fractions of One Inch. . ....... me pornsh 
Table. Products of Fractions expressed in Decimals...... elas Satorsiia sates 
Compound or Denominate Numbers......... AS SAR MPRION be DOU a AAGaSonc. 
Reduction Descending and Ascending...... Sia wiatp state oFo¥elei Be NOL RAE Raiders 
HaAtio and PropoOrcioned. or cis s«.01c8 bie Rand. lata ate See Soon oe "G sidleie’awing 
Involution, or Powers of Numbers ....... ....... .+-08 wetee elector abable'stetee'e 
Table. First Nine Powers of the First Nine Numbers........ Salsals senieiclale 
Pavies Hirst MOLccy, LOWE'S, OF Oe c tic ecw aves s cane pee eveb ess om bac cee nics 
Evolution. Square Root...........-+6- splesm subi s pienieeaicieepictte semen otc 
Cube Root ee ee e@ eer 2088 "se e808 @rcereeoeseeves eeneacee @e@eeeesee See eaeeeeeeseveose 
Alligation .. ewe ee ereerseereee reese e ves e@eeseesere0 @O0 SF -88 FH 1 SOSH SHOR DE OB ESSER EZE8 
Permutations ...e2.<sie0 96 sislp v'acisie'n ip eip come vip sin maine /uleeiaiais olonieramiteiiat gereaters 
Combination esses. 0/2 oes s shies wdipiniainlsisibaie(s/sle sieaisipow'e's.e sicielstete ree pie ee ein ae 
Asichinetical Progression ss.ccnsccs'ssceleevonaeseee vais secwsiscien asm eee cetes 
Geometrical Progression =. ...s'sssiales dewsNalsinews slots tle slenitiee cles evict ewe bagace. 
Interest eeeeeereeoeeeeeaee ee ese teee e@errveeeed ° COS SH SSS SFSSSHSSSSSSS SESS SSSSEees 
Discount. . eeoeweeeeor + @6e @re@eoeeeee- @0e 88 OOF. Ses eeeeeeseeens 
Compound WUCALOS Cais cee Boe aA ds e's hee nos Sons Siasiniele sicleieniele 
Compound Interest Table, 3, 4, By and 6 per cent..... Melsleinceh oticieisetee ene 
Equation of Payments ...... Bebeasg pelana ees deeecssici as 
Partial Payments sc aetees sence tale ee ceb cco wea sss Snepodacoochoccos act 
EA PATAUTIGICS S oticsciavc che oes ca ve sine tie aa ss eLdiwie dtais Oe Ebene ASB A pes tee eocccrevcccccios 
Tables of Amount, Present Values, etc., of Annuities....... ees esintis ten 


Weights and Measures. 


WON? -MGASUIC sesenacdet oss ocaee coal Secs Slee eases toes ceca beeopessworecne 
Old iiands Measure atest oc dosecicsgacsectecee eee SO ISSROGRNE = Che OnnGosst 
Nautical Measure ........ Astle bach 06 Ssisiistetsaras Sis/a/cete s5 cio oersc sis'e o'n lca Apo 
Square Measure. ..2..6.....086 sis sin aislelsia tclatcicleis slows ci¢.v'9'0 0'9,0 ss\o ome o.a.e ¢9\a sins 
Solid or Cubie Measure.. eeeeeee ee ee eeee OSS eeeeSeeesoeeeeeoeseeeoeeeveeene ee 
Liquid Measure ...6 .....+-sccceccccccccocces coscccccccs cece seccvccececs 
The Miners’ Inch eee ee ee Fe ee eee @reeeeeeSeOSr +s SOS SeeFeeseseeeSee sees SOeeesee 
PVObMeECALICS PHUUIC MM CASULC jnscetineeconest et see Seetes cc ca ae cece ce kereeee 
Dry Measure eerereee ses ee ee eeee @eroceseeee SSeS SGeeSs. See eeeseeee 2282888 +808 
Shipping Measure.. cemolpediclsisis aise esses vesegeccccrccecosscecccucctce 
Avoirdupois Weight. si Mofalalebeiataliia sive (a: st sib yctctelgtibis ie elsieip\t's s's's e/a bieic'eicte’e sisi ciateie 
Troy Weight eseeceereos eee sesese COOH SH SO HS EH SOHESOSESESHEEHHSSSHESEHTOH LESS C888 
Hpothecaries”, Weight... asapeste cc cee cise oe blast 0.0 [tc1e siewiee.d oo eave 
To Weigh Correctly on an Incorrect Balance, .........:cecsesccccccececes 
IF CUMIAT NICASIIT Oss sca « ainc'elaicisic chee sic ss Meme ruisbel\ss0 v/s 00eceete beens 
Measure Of time...c.cccccccccccccce POC OHSO ROT EHH OHHH OHO EET OEE OSES DeE% 


Vv 






OD 3ST AT So OF OF Ot i G9 69 09 BD TY es 


v3 CONTENTS. 


PAGE 


Board and Timber Measure..... fee cwietstautseae 


Table. Contents in Feet of Joists, “Scantlings, and Timber.. seein ai etsre’s 
HKrench-omMetric Measuresicua: :: ss tecice eee eee enema <wUelestaeee ts 
British:and) Wrench) Hquivalents,. 2.» cjaicise sits eicla’s eereinpcinieeie saiareisleayee enone 
Metric Conversion Tables... ...........00. ev ceicsesiescicccciccceviesee ers wens 
Compound Units. 

of Pressure and Weight...........cce0. Hoenn sia)s's\s\e\eie cv eislelaicinisia sie sienee 


of Water, Weight, and Bulk............... serterers eG ee ove siesielsioaule alen mara 
of Work Power, and Dutyeceenses conse cer Nout celeste Gp dose enUSadS int accie 
Of Velocity ie eure ciaetia » aieteeterere seeies Reaecnn Heer wesw seit amieeraisieis eises 


Of Pressure per UMIt Aredia. acc. se celecceoee cies oie ele/ele ele\eielel sia walsteee eats 
Wire and Sheet: Metall Gaurwesiis ic Sees loielitelcicisttaloleine Sale sicices ove eliceeaeie 
Twist-drill and Steel-wire Gauges..._...... HOGIBOOL Mewtioine.e aise sieeiniotmiot lesion 
Music-wire Gauge. ASC OUUIOO UCHCOOHOOO SO GOGNOOGO GORD Ie Conbaceobswns se 
Circular-mil Wie tuaeel Bis eieieteleaiesnte ne afeehictes weeeisicoilicics'e cea cine emeee 
New U.S. Standard Wire and Sheet Gauge, ASS Rie cee AO Ase ADO OUD OOO sc 
DEcimalGaugen ar: sce sce so eis oe slats ier reme nels sis ANee aathuns ohne settee Aor on 


SE | Algebra. 
Addition, Multiplication, etc.:.......0..ee+- An LE ee eae 


Powers of Numbers.cicersseses 16s sees be csiseae teicizre clasts eaice uislete sissielcie siete 
_ Parentheses, Division.................. Sucuisiees a's 65,68 wleleln e's biv'o'e suis sides wo sls 
Simple Equations and ProblemS..............6.+-++ eye: acc cececccccecccce 
Equations containing two or more Unknown Quantities. ......c.scsseeee 
Hlimination....-.......6 Soe BUTS Sees latte ciate late Set oerelaare ate as civie we sivvsiasieniae 
Quadratic Equations .........-... cece cece sees cee else whleiceecinienslsivicles eat 
Theory of Exponents... dca suid Selwe sistaco eRe aie leo Slale le ole ele wletow eet alela eer 
BinomialiTheorem . <5 acs aa aehen at en ners o fole. egldale elciclel clove gre eietenre 
Geometrical Problems of Construction.......... so aw cajeiee cal relates 


Of Straighe WOM CSra ke ee ecrs crete sem sala cl elculer temas cette cvs efo ort e'cla eie'n elafgiata eraieme 


OLFANPILES i ei% coc vole we 2 vi hel wleteialeislelalale ele ie ielniel-Nale eislelcleic ele Os veer ccercccccces 
Of CITGles ced lee es sioeis mos omeanyas eo isw be wee oreina eter ot lee tae era ne cralratclarets 


OLELPIANZleS «ioe Ce kien chile ose ate diesels 210 cre'0/tle/6/elialere etal ate eels wishele rele) eiatereimerete 
of Squares and se bani Soe rae iuie Sloe le oe is Sieestes bab vat Gicsase sjeelerererstalele : 
Of Che) HIIpSe.. woe ces ee sate sissies Salesian ewicreihe sales pf lecswepe aoeel sel elects 
OL the; Para DOlAr aiscwecei sere ctenscmiscs dr ae msds a ve vseeesece eel sianciowite 


Of thes yperbolaimiisas cow cca dass sostancec cts BOHUSLOOC Ceececsc sce eocese 
Of (HOI Cy.Cloid viasscwdaias carbo eee cream O45 «5s «Ne earheetes sie sletelsleielaleoetstcteetete 
of the Tractrix or Schiele Anti-friction Curve........ccccccesccccccccccs 


POLE SPITAL waciameskm oven ch ee she eee tes Sin ele e's'd a6 858 10 Cete Suis ele aIetne 
OfChe [CATCH ALY, yy-mcs cceircwai ewe ieee ole at sinbigiooe't nie ooo ele clelavaisteleiaitae mere 
OL CHEN VOLE. cede Catouieibe sass oor esiomeis oe ese shen o sinie) “snicleeiele sate stveieivette 
Geometrical Propositions ............ ccc cece cece ecee cece cect enc once 


Mensuration, Plane Surfaces. 


Quadrilateral, Parallelogram, etc. .........ec-cecceseseces cere eeneysasisys 
Trapezium and Trapezoid. ...... Pa eae prateroretehe orate cial relareinvetete sisi se a one rntetalett 
Triangles... BR COM OO RCL or COSUS OC aon NCO SdoL addadiobo 
Polygons. Table of Polygons. viele ser cejeisie ae piaverela’sle.eie o(e sin etaiereine Steteraertt 
Irregular Figures. . mielsic (alee #in'slie «018 /a.0)5\0 Sie)s'e) ele .ois,6.s\0\s/siesieivisis cp eleitsie sian 
Properties of. the Cipelo neh cnn rae Wine: SOONERS boo < viele hoistg'e bole Siort 
Values of w and its Multiples, etc..... 3 osieleieie seid) sos 9; ¢ bpelaj5/tjelageleteeestne sree ae 
Relations of are, chord, etc... . Sie e)e a's oie) siete's ole, afe oir ea MnteE Nene eve 
Relations of circle to inscribed square, ete.. wie b06, 6:0, cvaresvenelota oie erbeterele ee, 
SSCtOrS| ANG SOLIMEDUB aa. cc oe bane «sm alive wisiea es cleiee ais, ol avejelerersiheate alatajeiele spt: 
Circular Ring....... . Bealeielnarers ysis oishe winjojnle/aieie,sisisisisicls) sivieis\sire «lie abeeaiatetaiets sé slate 
The Ellipse ... .. Sieisle( twits Cuvier eases cies The Sic myatvelnare ste oie aye cists siaiaisle aa 
HSN @CELELUX ccc ere chars selene dicuicis o ssa oie wets oiCie's.elcioiee arate Giare elie erst stots acres mime 


The SDITAl ees ececeesle se Sere ersi cess eeseeO- coeeereseseee see se8e e@eeereere 20 
Mensuration, Solid Bodies, 


Prism... .ee eeeeseeeoevsessere SPSS SEOCHE HHS Seer eseseoeeseseseesoeeDTSEeEESER- 808 
Pyrami e@eeeeeos Goer averse ee @eres 2ee88 eote See Seeeeoeose SeFeeest ere ee eee. eee 
Wedg (2354 Se eSSe CFSHHSEH  CHSFTSHSHS SESS LESSEE HHH SHEESH DOSS HESHL See 


The Pdistuoidal Racal Daven 's 6 &.0'00.6 welt lela ere a e's 6,0 0.0/0 6ie tiattReeeneeitstare atetetee 
Rectangular Prismoid......cecssccscscccccccecccereces cscsscaccsccscee ves 
ylinder... S@eeseSGesoes oes eS eeSe FOSS SS. SSH SHHSHKSSSTHSSSCHP REST SESS + SESS ESHS HRS 


IB .202900009300008000 96080622 OHS O80 2900 O0FS 695800 HS OHHH GSCTHROLHOBHHHOSOO 


CONTENTS, Vil 


PAGE 
PHOTO do olos Ru C Cache Alb LS a cise eer renee ths BETES Coa vere erer 61 
Spherical Triangler... sf .c.dt. cee. oes g Patty Wit irh isthe Semele tt in Ge Ie ie ok Fs Ea a8 
Spherical Polygon............. BEES arco bind dupe se eee Cease ee oath eo eee Oo! 
Spherical Zone ...:......:.. wid eneeuter thes Ap Botacdieln Oe SPE eat teak 62 
Spherical Segment........ wetaticg hen eens Be ACAI ae MEER Cie Cacti AUS Seas 63 
PDMELOIA OF LA DSOIdRi rac atereos tac attons st ce tates Tone e Teer aad 63 
oly édromecge.foecee: “Es Rate ae Sens ree cease: AGIA tery RI nF RO ice Mees 
Cylindrical Ring ......... Fie ate Sai Retort Paras tei ithey br Kops ek Rida ols Ned 
POLIS OL REVOLULION ce ac. sete ccciares Haseena een ele se atn nee s dordaaatd em ater Oe 
DPINGIGS Pass ote cele ees eos setae eine eras on thigces SFL Onee ae eee se ee meOL 
Wrustrumy Of a SpHeroid: tas. css te tees Seo ees esse eee Te eee ee ae 408 
Parabolic Conoid.......... Banas ddaaige niger SUPICIAR ven wacl tI SaHARE A tse eu 64 
Wolunierof a Casktccenacedntcutecse tee eee Beet eat nae ane OF 
Irregular Solids.............-. Sieay Betas eeiaeee ieee sare Sacer esOnemancpn (0H! 
Plane Trigonometry. 
Solution of Plane Triangles..... PAR ARNEL) Fe cae dA LATS GARD ct mtics co necnon aul 
Sine, Tangent. SeCant, ,Cve oun apecciess bee cos ee eed eacts os Rape SEMA seers eee 65 
Sigus of the Tr igonometric Functions. sistansteieceie Boaer ope Bobbins pObindosc ober 66 
Trigonometrical Formule................. SOUS ATES TN NeON Be ceseo Oa dorr: 66 
Solution of Plane Right-angled Triangles............. Bip, Eepbbeobacons 68 
Solution of Oblique-angled Triangles...... .........-..0000- RARpARdaG oon” 68 
Analytical Geometry. 
GrdinatesiandsADSCISSAS sass casadecelne salon dee aa eines dn eee ce see ce nGeonena que, 
Equations of a Straight Line, Intersections, ete.......... nie gia gallate w ecetterd 69 
Equations of the Circle........ a Mtareicere ts tehebeelisseie Gi otsisieas’ote's asersys ada sraies Sarees o% 
POUAHONSOLINes HINNSCi6 x.9u couse ss .eacisragen es asrnes ohaberesegeeea es Tame 
Equations of the Parabola............ svatarotae diel tie Selene a Sain w-eininioug aie agate ieteets q 
Hquations of the Hyperbola........... 0.0.02. seecsees Aro SR onses Neatesyeiee 70 
WO PAT LO MICLCULVES: gags o's a)eeae cebu anise Heinen dete ieee eee: Poros 
Differential Calculus. 
WSO ILIONS 22 ton Mroxror-calemivetcren dercreceystcvoioisiors sriciauie eres eastteielnaeae pio amoraceerr: eile 
Differentials vf Algebraic WUNCtLONS cers eae ahi oiavsserdine cts cece einige aiaem «o's Suen d Le 
Formule for Differentiating......... svete, Sioisvese wieizia/Wieve «i slelniste. cite ip aie autia ernie ale ean! 
Pearbia le Dil erential s. oan a sc ccins civics onis scicc,y oS sm siento recie eeeiasswiaisinen cheat 
intemal Sr tigigsetaccuw cose mecleeere c Shnagetinariorib SAC nOe ECS AERO Baten utc 
Hormule Lora Intesration ..ciciersscimerssietee sereeen oe eee ecieele ote DSondeeien 74 
Integration between Limits......... eas otislelaeets EM Bat bbe Ey Boot acnereitc 
Quadrature of a Plane Surface..............ceeescccsees aie oR Fike stedsia deters 74 
Quadrature of Surfaces of Revolution.................0:: aipiaeiaie) a yahetow senate ys 15 
Cubature of Volumes of Revolution...... sisisp sspadyecescisisieiiraie ae eide Terie era LED 
Second, Third, etc., Differentials ...... siete eieie ae cissaisinn ds eles as rae sia RAMOR 7 
Maclaurin’s and Taylor’ s Theorems....... Bromus neve tictabercte sbeyalsiete sfaxblale seat! ” 
Nada ATICy Mi dM Ane weractueteeeu eee alice Sans SEU aTORO Aer, » Heweieeslgeae v 
Differential of an Exponential Function. ................cecesccccecceve: De raeeY 
Logarithms...... caislohavgiowla oleta ois Sareip het Bae OO 
Differential Forms which have Known TIntegrals.. eeieale Bee sth Siarsiai etd a Ghats aie 78 
Exponential Functions............-.-.6..202, Riss motets cis See io Ores eele een fh 
Circular Functions,......... ..... sisteendertea es, « Binder spares apePoe woe Penietee Vi 
The Cycloid......... B (areteesiar eaters BAP UIE Ss verre nents oe DORE A So EERIE ae ED 
Difeoral Calcwlusic.ancedescticedwcrestsr arte serene eerie teed brass «See aekees Renee ’9 
Mathematical Tables. 
eciprocals.o£ Numbers,l 10, 200054 eae atts ns oc Bisse cececee 80 
Squares, Cubes, Square Roots, and Cube Roots from 0.1 to 1600...... Reo. wel") 
Squares and Cubes:of DecimalSarm.rintieceleereee tide es © s< sts sae ce ene 101 
BitthuRoots and tithe Powers, ces asada bates eis os 2 ss atthe einen 102 
Circumferences and Areas of Circles, Diameters 1 to 1000................ 1038 
Circumferences and Areas of Circles, Advancing by Bighths from x to 
Decimals of a Foot Equivalent to Inches and Fractions of an Inch....... 112 
Circumferences of Circles in Feet and Inches, from 1 inch to 82 feet 11 
ER CMES 10: C 1111 CLOT: teretna eta en's Ac MMPI EMP a cS chy oc Bs ici giants BA 113 
Lengths of Circular Arcs, Degrees Given............... Ste ieee a 114 
Lengths of Circular Arcs, Height of Are Given ....... Siisid Sexier Se, 115 


Areas of the Segments of a Circle. .......... 1.2. cece eee eee oe Neate s aid eis 116 


Vill CONTENTS. 





PAGE 
Spheres nae hei tees io einssinens lacie oh s'eslente s sieieiternstaerste tet eats cleceeet Ce Spee tale! 
Contents of Pipes and Cylinders, Cubic Feet and Gallons. aren oa sverie tice dalely LER 
Cylindrical Vessels, Tanks, Cisterns, etc...... ........s0+02+0% emeleetediace , 121 
Gallons in a Number of Cubic Feet . 
Cubic Feet in a Number of Gallons 
Square Feet in Plates 3 to 82 feet long and 1 inch wide..,................ 123 
Capacities of Rectangular Tanks in Gallons.... 12... .cseeeee ceceeserees 125 
Number of Barrels in Cylindrical Cisterns and Tanks.......... ae a cist neticle 126 
BOP OPIS Hs warcein's osilsesisisiie sss cvsa sia cates ateloies Weeds | sumpis Coit tcesieGisealtee 127 
Table of Logarithms........ PU ADS Ni ie BAN irc a BES i So shad Dales = sie sie terete 129 
Phy PETOOMCHOSALILDIMS icc sons cis on nicciss «vciesiee no's eltvin gasieiseris ee aiEee 156 
Natural Trigonometrical Functions......................--- SABRC AEG Hr 159 
Logarithmic Trigonometrical Functions...............0..cceecrecsces wee 162 
MATERIALS. 
Ghemical ‘Elements. \o.cc2e.cosccee ste tee tienes Noo jeaotonnotenseccoeno LM 
Specific Gravity and Weight of Materials.. ...... ot beparaclathts epetanlet clas draets 163 
Metals; Properties:Of ss <6. .os.s cones spe deja nieie «01 Shilo pe BO LAGOR. atSiaibiels Gay 164 
The: MydromMeters : oeics co sccwscicic oc basy deletes sidels cg olalse biatdnrqietshets Selah oat eet 165 
Aluminum............. aun dod Soesaaonu AGUA Ese dennoc ste isl alate eal Alea ibiviele slaeter 166 
ATUGLINOI Ye erireicreieisislewie eierateie sich ons cus oleios alalch dmaate siaistaininals Jeivsigale a’ leh dectetds 166 
Bisa bh sis, sie ialaie's ede, 6 sins 0.0 0:6(h.c 0.5s.c'oiainr0,0\ see stahgie Sie,6'dho.o s steighanteimnlaineta tere oe detaleld 166 
Cadmium sescceeclentccess see e208 20808 @eeeeneeoere e@eererrecs e@eeereeeeeeeeeees eee. 167 
COPPER nk chcssetectiListisslercincte weietesics sted s seretstermterteac iste stercisis op imciats seta eis ehalelere 167 
Goldalesidsseddatined coe gts ce ecle's J olcisas be ascent ean ces 4 MARR eine bhéafdioho RIS 167 
THIGIUIA Sc3 cease cee eeeceee @eer-seervea2eees @-e@ @ te toot eeeoeeoeeeeeeeseeee eer eens 167 
FE OMK voidic fed aldaewea oi den's a 0 sie in'e tleivicieials «s/n q'eeicleio esis eGhisennstenescreseh gee dia siahte 167 
MCA sale, t sia visic Hoce 6vc'c.06s ose teiss.s sic cia ROR ODeD oj 0.0 dwelaeeate emebied eioaiche wichita 167 
Ma oNGRIUTR iis oes biw on ice sicte « o't oie cewerssimelsieleiclieie.ccies sisidie bole, dbs, Celestia abate 168 
Manganese..... Ldteltis pnis:s ieiécieaie so cioiesiowsio cn a.sie Ainverdeht ORES aTeN A efalels, early sides) LOS 
IM GNGURY js tis to cites e'etsleicjeials ts s(cleiuic.s /eiste nels si0)9)0, $,0/6 fh s\elabrela\niesieus @ shin delete sleneidate 168 
INOS) GonooaKeaddodcoante pike nis-sropils ad ooe rela asl VRS a Reabeielecn arerereneie ere ee BaatiGas - 168 
P]Atin UI eivecrelsicieis'e coio'sie's cee s weicieve Mave as etepe severeiarcus’e sistiile vc ejajatercteter etet etter tens 168 
PSELVEI ar a crecwlnrereeclee wclejes ave efefaroie/avaxesers je veveretanapetaiatsiersiace AS AIST sounieeleatoeeatd tania 168 
Tin OEE o'0' bide 6-4 O18, 0)5,0 ac6 68 oye) ocala ohcke: slip pip sie A SU APAOND Oh e asl eR eI ole ane io iultcichayhoate 168 
Gin@ .dascnes : Eb eidiscidle satu balsa ofa lipvagita, oa sore gow! io agora oynietttar ia cata eae ee dvisisiasieg phOS 
Miscellaneous Materials. 
Order of Malleability, etc., of Metals . 1.0... 2.0. csee cece eens cascececees 169 
Formulee and Table for Calculating Weight of Rods, Plates, ete......... 169 . 
Measures and Weights of Various Materials..... ........0. cece cece aces 169 
Commercial Sizes. Of Lron ;Barsy oo. .00:ciistis ble cinw olere, platoit vel sisisldia'n «Wie dee blames) am 176 
Weights. of Tron i Barsiiccddiciednin ciecsne saroniait shaletdisle tai ie ctevs wate old dials irs alateleaeheata 171 
Of Flat. Rolled Tron sed. ois aisic:s ie otemtien reese ahs Rip biodeloald Ells pdlalen pele lt a eae 172 
Of Tron and Steel: Sheets. oc. sic sista Saitelslale etal che Ge aeleld dies old tale aie ake Sites 174 
OF Plate: TOM ik iayere Sie eiwte o sie00 6 jove sare saa wre <aovs)o aavaraselalloveyeisinesicle MlSiad Ghayaiaakd aoaetee 175 
OF Steel BIGOMISE i). wis creme wie-ctem wae sollichs Aaeee le we eialale ental pep deat: eaichetae tee 176 
Of StructarallsS hapeseats cass = «ccs tees la shee oo aise aa ale reise eiioes aaichitiae 177 
Sizes and Weights of Carnegie Deck Beamsi asi Tle wae nece Pers) 177 
Steel Channels... ..5,...ctsict awe stot atte soir 178 
CO A = Zi DAVES cotaepccdaete ee oe-she elen sista aid Sigla Ws a@iolde 178 
-s es Pencoyd Steel Angles... satiaton Siousgee wie ne aise Bera ety ene 179 
GB as DOES) ey aictaraleieteneix Sebsietabaaselaeae Ssishisiae peas LOD 
s¢ We te Channels...... mote agin @ o'sis e's\'siecspelaiete avetete eee 180 
ee Je Roofing Materials.............. Seeeers toe aceuine 181 
Gy HC TPErra—CObtar...cocisiss.ceipviee ab ke waaioniate 156 dee ne metnokeen 181 
Ge fe UT LOS EF occa, Seba wate esata Hide siciplatigtac phetate nied eee 181 
SG se SPINS PIALES .....:c:e;sicerojoceqgrasth Og eha rics wiSi sia Bley dale 2 ache 
BS of DIALOS so -tac cccpaeretete oa 9-aieits Gadd oplods ds ible ect ae 183 
OL ce Pine Shinglesi. WGlei) dasscert ae coteale widen we Ble sisal 183 
a * Sky-light Glass...........e0. eT bide awh ido lasses CURE 184 
Weights Of: Various ROOECOVEriNg Ss... 5. seauie siecle deisiositias cae eee eee 184 
Cast- ‘iron Pipes OR ColumNnseh Frid ic iletihigee eave eeeaeGRee 185 
Oe Welte len gt ses he dis ssinlcis 2d". besiotetateteibers Sees 186 
os So Jaecus) PIRSsMOLIN ES... seein. 4.« osalaa Poa aeeeeebletelraliats 187 
«$ “Water and Gas-pipe....... a: she ldale cbt btaleiAe lal: alatols hie Sey MELeeE 
‘* and thickness of Cast-iron Pipes.......... o odictal ale clphelteeeeisn eta al lace .- 189 


Safe Pressures on Cast Iron Pipe......... Sisicleib alo le bier ofa Stele poate eiaLa stele oie SURES 


CONTENTS. 1x 


PAGE 

Sneet-iron Hydraulic Pipari niet f5t MEINE, ova cccvcescascsexeses Lol 
Standard Pipe Flanges.. shaclardrein siete athe ode, 018) @ sei sisleciee om mai @ tanec alee 
Pipe Flanges and Cast-i -iron Pipe. Wa se cealee ce ceueueeebereade sae) Vi De pedqe 193 
Standard Sizes of Wrought-iron Pipe. ......eseeecceesecee eens wie cheats eave 194 
WEFOUE NE ITA. Welded yVUbeSiwcnscncstentastrmsara nto adadiess coadde cio keoe rete 196 
BNO LEI UTD Ts b 1PlOS ap yctsy ater sd atercnstesaterecatatorer sreveney erothian eetn epatoret REARS Gein wet meses 197 
Weight of Iron for Riveted Pipe...... ssaretotand bo%s eS RSs AE te sip tales Mester see 197 
Spiral RLV CLOOREIDG Met car cee net ate heah eee eee MOLE A SA ae 198 
BEAMICSSIBFASS UUDINGsccadtcc ceed tasenarccoodsouratdhteshe eerste 198, 199 
Coiled Pipes.. se plaretevot orayin slsialviwvelotes oh dat he Ae.sig a argvelale Miatisreetals ake 
Brass, Copper, and Zine Tubing. Wig -Asisrelehina ie ¥ uratiot Halelelalcetdere came tacne se 200 
head and. Tin-lined Lead Pipeie: 6 i.2s. Ci. Mh wese a sen PECL eis eocla piesa’ 201 
Weight of Copper and Brass Wire and Plates..... ........ecsceese reece 7 202 
ca) LROUNG: DOLL. COP POLinwnuconctna ined dalek ssa she abet hide dele eee 203 

Sees ONCE ANG. BAL BLASS roaancadoeonenesahe os PISS NIT. totes ee a RUS 
Composition of Rolled Brass............. AEsde deus sed shireved dave ereme rate 203 
BEEES OL SU Obra .enacgre mt uiateve ack notaters ero se esteem aren tets katte ¢ Sista. toh eon te eee ne 204 
Screw-thread, U.S. Standard............-.0.. Sos do cee ee setae es see, 204 
Limit-gauges for Screw-threads...........cc.008 coos wietas'Galenas oy pe eee, 205 
size o£ Iron. for Standard Boltsi.-cctecacietetersletarerers otetele'eteteretereree ye Seiten crruGpin 206 
Sizes of Screw-threads for Bolts and Taps......-...0ssesesecsccescorscss 207 
Set Screws and Tap Screws... ....ccec sees ceees eesesees SP a aN shag 208 
Standard Machine Screws.........ce.seeseeee OS token ee diete ate rates ios 209 
Sizes and Weights of Nuts... Deeb esse ce ce decseeaess FOB se SEFTIFS 209 
Weight of Bolts with Heads..........0. sssscercccccss: setite aise ened SPR: 210 
MICE Ces BOGS) 5. eratarter alee arene ire ee cat rd Ga wae Oey Vibe ae Bed a Baa dee heat: 210 
Weights of Nuts and Bolt-heads....... Tele te E hre bie Hee wee Oe ee eelee 211 
RIVGUS wits cede cede cect see be bs Fete Soe bETIET SOA Ose eee 211 

Sizes of Turnbuckles............ Seance Aes danakeageivsdtacedés CERES PD QEE 
Washers.......,. Sascisatces ness ste eeeheeae see 08d ee bde cag istered. Sone 212 
Track Spikes........ 5 Ba caucnoneuoor PK 6S TE LS Tec aged ons ceed oe et mees poets 212 
Railway Spikes......... Seaceas 55 dad tana nae aldo datess sees se LESS 212 
OBL SWIKOS i. 042.5 2% wie soe so e% 0 Alereere F tiee Coe eae ies Gee alate Sua eae cate ede 
Wrought Spikes...5....cscecccccee: bbb b:5 cd V5.5 cole iits be EI eee eee E218 
Wire Spikes...... atatorsie atatelele!s(stn'« ce oes Raga tee. er  atleduetes Sees ele 
Oat Nails? pcecccc ce hice tislenctslch telco Motlaeies eda aie ste en ae crore vere Sele peni ee: 213 
Wer GANAS ss Seah soak xa beet sts teweiulecoeeee WEE FD ralteoristirs PIE Fe 214, 215 
Iron Wire, Size, Strength, etc......... OCOD OOD DE REAPER OCDGAL Bb eA ete 216 
Galvanized Iron Telegraph Wire.. BERIT Cee ee ate oo er oes Jive ree 21% 
ests‘of Telegraph Wire sis. 023 traddec acta cote clases brome eee e oon Harngiot 217 
Copper Wire Table, Bs W. Gauge: ssc secnccce cc ig sdee odded ie ENS SEES A", ae 218 
‘¢ Edison or Cireulak Mil Gaqugse.c to. f2- Aho eee cee 219 

y is sf. B, SH aGauee secre SPM. Ca ee Oe POTS 220 
Ensulated Wire rs ss sss 6s tisteleres sonst’ ol iarerabtyte eeratetel eee sale Foe P a hay dp nie ney 221 
Copper eee Wiressesgs crerneabee yeh tise a eGitetg eho Aare Pace gee: 221 
Hlectrice Cables.cs., staces ad lbaae cutee eden ted oles ben ee Sst PPS ok OR 221, 222 
Galvanized Steel-wire Strand... 5.2.0.4. o100: cee ce eiee es toe Ore ses eb sacccsceas 223 
Steel-wire ‘Cables for Vesselsic.es. 122 hore catch atest hc cece s de chepeses cons 223 
Specifications for Galvanized Iron Wire..............¢0-- Ad felt Spore ee 224 
SEVEN Sth OL PIANO Wile sehr te etre fate Diet ca Coors fae hs eee ene ene 224 
PiOueh-steel Wired eee rena re Ne era ea ce cess Care tote feeeuiis 224 
Wires of different metals.............. 5b bce De RISER HE iC PSC SAR PINTER 225 
mpecitications: for Copper Wit@useneten dca se sacs ieleda as Ktacaess ee es 225 
@able-traction ROpest:.s:s2t.cscesceeeeie css Fe yo ouitiind Oe IFIAMEIOBIOC Ne Sais 226 
Wire Ropes......... .. Peder tonite) COO O RII OS ER ear ane 226, 227 
Pouch-steelwRopes. Stathers setae es te cnc cet dsm oteee rae es Arisa niet: 227, 228 
Galvanized: LronmwirethOperotaticte tes cece cows ee cess see guesses 228 
Steel Mawsers her... Soe ose catieeters bes res Berle ste ee tae ait os cei e pettican 223, 229 
lat? WiretROpDeSs..5 fa eerie BRGctdo Hoda de eRDPBHNCMe KRAGCEHS 6 229 
Galvanized Steel Cables................ WRN s tetiate Tekin: oC busin a * a eceps seal eR 230 
Strength of Chains and Ropes..................- SOREL eros Sica 230 
Wotes'onmseof Wire Ropeanecrs tess cccleuvcstess ces Re Vane terra eecne 281 
Mockedawire Open. bes eemeticcs ists tee neice cece aas tse Settevriteee feces) 231 
CEAVCIC MAINS te ot tecgeit ees fe ne intents suicssiec on) one wep asses Ha ae 232 
Weights of Logs, Lumber, etc................. SOO AE SEB OIGS C0) ee 232 
Sizes orrmive Brick! 232. secsere tes. ccce: Sdn BORO aie oe og pue eeasalaSoeatee Gelert | COON 
Fire Clay, Analysis....... MVE rece oc stursttittels cc Het ch. Secnseures a aialhaceiers oo 284 
Magnesia Bricks.............- Reiss oleisce'e a tee SHANE ROARODNO DD ONOTOARBE (oases 235 


ASDOSUOS Te see vececssccee eco vece 90906 OOOO HO CeBMn MH = ZF 2 oF CHF HHHTTHSHHRORO OH OG 235 


x CONTENTS. 


Strength of Materials. 


PAGR 
Stress and stein an a Siathidk nce lave eiehaie ae nae «eee isle gd eaves se Lna Seamer teeta 
Elastic Limit.. ensjs)0l6( 6m ave,aleleieieisisieidje,ainia's eve elojetoa cieeietel sic twaicteie ence Rin ee aoe 
Yield Point.. Spe dels sinvess)dione asebroian Kay cee Cee ey ee pad mee 237 
Modulus of Elasticity .. Ricpeiesakelsitioxores akeucicio\epacneey albioysiseaasinioieasve ste Sees AO oaaiios 237 
Resilience ... aiwiayajsjecxsie.ctate,a et sta eleis te ialeiors|elain le eietetcetetete eae Eee 
Elastic Limit and Ultimate Strosa, are eae ee Sadie a.s.cetdee as See Cates eeeae 
MODECALEC SULLESSeSiicy rie sein arene face ciate sare atch anions © ajc Sie tla eis. selele AR ACs 238 
IREDCALed POC S re Le eo te re wl, tie a bpesee deh eteamine nein amloe mete eine Py i 
Stresses due to Sudden Shocks....... 1.2... ...ccececcccscrees selntelete, we 241 
Increasing Tensile Strength of Bars by Twisting.................- OAS ce 241 
Tonsil Strene tye... 15 ce semeeenis tke nitiey eet ee ee S alcbi cloelatles ote bidet 242 
Measurement of Elongation..... Sisie|*haveis, c-areioeccie'e sce SAMAR het oretons eilebist ae eae: 
Shapes of Test Specimens..... Sa Sareis sliible.Sculesoiapetlgniclet Sheek. eh a eens Bee oh 248 
Compressive Strength..... ...... ahetrauehesaus Sie .0i 8 Voki sere ticle, tae Sete soe. 244 
Columns, Pillars* Or Struts; o9'. loko cass cacciess leltous cet aalciscice emote Cae 246 
Hodgkinson’s Wormiula in .2k ewok o nwleis ajo cuateteleleteradaeieleles apeitewiate eae 246 
Gordon? s Horm a Wye ckiiecieciseisicisiielceen nies Le alsicemiateeentee« nid mitinsiiae 247 
Moment of Inertia........... pleas bioreleyeioiebicvou maha etree edievaiclereve ele a bicees wae 247 
Radius of Gyration.......... Weisielsraatene Ws. Betis aieltarnd cele sale dievdentee/ rae ees 247 
Hlements of Usual Sections....... Alejausra loll! Joveiereueloieiene ePetaere keterehe ore laters ere ane 248 
Strength of Cast-iron Columns)... .n).<5<ce0l0<0 90 hides eweleetl tes Te Rieietee a cOU 
Transverse Strength of Cast- iron Water-pipe icon cela wferfe)oatetcte stein Gh eens 251 
Safe Load on Cast-iron Columns .. ................. o bie wih ted ote Ll ocelg Mateo 
Strength of Brackets on Cast-iron Columms ...... 0.2.20... esse seee ee eees 252 
Eccentric Loading of Columns..........6. ssscsee coe rpc ccieonaceyioacdod ey 
Wrought-iron Columnscies secs ss) os sisenceccs lee). sue nee deesilenieeeteir eat 255 
Built Columns...... eategaos eueaes seats cans pe idisis Alaiajetenarelealels Leroi eae 
hoent< Columns2i. ts sais Cab etes hse ceases eps pene aay Vuiapet elaierd eterajalermerae 257 
Workine Wormulss for Strutsy 2551 dc6 ssccbae cs gesecee ri epsioy sees este eee 
Merriman;s HNormula for Columns seid. eess os o..sdelteele's siieletele ster Liege 266 
Working Strains in Bridge Members................e0ee08- aie eplvebalostenteens 262 
Working Stresses for: Steel. .i.2wiss scence sree peel clanecereeie diate Sei Riotecd eke 263 
Resistance of Hollow Cylinders to Collapse............-..essccceses ieee mek 
Collapsing Pressure of Tubes or Flues........-.20.-s-008 sie! ain feiefecstavere ewe 00 
Formula for Corrugated Furnaces...... Gbuplalisi/eieleip\ stele tela ellatersielatalelelctake Rieieiaers 266 
Transverse Strene thy nicl. + arate, ccsjse.s.c.6) saeininvai is evel sieletalicietsieia eit «eieietater scant rte 266 
Formulee for Pine of Beams...... Spine Acer: aeihte ake ro(ayeveprictele el sVousyainys Sica Sl OOS 
Safe Loads omiiSteel Beams eu. oo 6 oe vis os ov o:e o.siey 0. ojclonsieieletele siersieystsiete asian 269 
HMlastic: Resilience rai: voc cen ses te.e vise oes 5 Cumeraractkee eye aor eleidefin's ware ole sere 270 | 
Beams of Uniform Strength ................ eSeieaenases ss caw Adie cists eereel 
Properties of Rolled Structural Shapes......«....0..0.5..%.+-3 iia ati gteltloastareyete 27% 
& Steel Beams vary vines Giiteupet ob spiel acaceae seat ee Sytaihdtente Ge 
Spacing of Steel! Beams v.55 i seyien Se siie bevels sae cis ss eel allele sate when 276 
Properties of Steel Channels... 2.2.0.2 .60se-0 unos ol Suevers srepejwn qareiSaaehoe mabe SVE . 207 
SST SYA DES 30.0) aise! dele. soe ors cis iecels = orle Daer aR aw sueroaencte bie Polen evans 278 
ty SOMA NOLES cs cies ola esp a ' 6m Ae AG) ls GIES «tsa tals Pe eee eee 2794 
Ms Sr ZAMOBLT Strela se lceanl cs sik os eres eR Mf sans Pedare We yah Lingis wah crea ea eens 280 
Size of Beams fori Wloors secs cc cc. sec cee ec cl « sicicle o\eieia/a'eteGh oie ajein\’ele Stalere Settee 
Flooring Material............. as ole.) s ereverster arate tits) linoversretwlel ciaxsssi nevees HY. Zia Sideienteas 281 
Tie Rods for Brick A TChes | 22. cs ccleis ce cscs cle acre eleie’s sielpy ib taife leverage selene nets Cec 
Torsional Strength............ Bb wave elaleiele. ott a einpere tape siecayatevsel alee ytr ae scikessis seem 
Elastic Resistance to Torsion.........cc.ccccce cece en cccnece oats 'ecoretetetajeterpiets 282 
Combined Stresses.......... sauaial Wa Falla Weipitia ele) oi ct gyal reve akeiete a) sisveneseiats Vets sleet 282 
Stress due to Temperature.............cccccccccccsecsees oa, 097A Foy Sappiecchaters 283 
Strength of Flat Plates... . ssi ie) o:6fotPayavetanrahe ef aisistotpie:oreyayeiaveta oragsteetemne ore 
Strength of Unstayed Flat Surfaces .. Us demad owmeme senreys ae wteta Sees aici eee 284 
Unbraced Heads of Boilers .......... boo ss ereleraleleieraVeletaleletevatelz latele/etialecs ape eeemmn tice 
Thickness of Flat Cast-iron Plates........cccscecssces ool a iojistSis ayaze Kl Nearer dots 286 
Strength of Stayed Surfaces ............... secccccceces aye' sza-dhanevevelee ai oketerels 286 
Spherical Shells and Domed Heads.... _........... aieia) alts & suet oaye eeatetaaie wm clchslate 286 
Stresses in Steel Plating under Water Pressure............... Poeitse docs 287 
Thick Hollow Cylinders under Tension... ..........2. ccc ceeceeccecs ae elt 
Thin’ Cylinders under Tensloniyy 27 Pig ao. cule wig elsem a nosene Matis, eee 259 
Hollow. Copper Balls Vespa cits. «4 +e uisreiete iene n)seicscrcicucee ee eeaieetes pistele dara: 289 
Holding Power of Nails, Spikes, Bolts, and Screws ........0. ceveces eee 289 
Cutiversus Wire Nails’ Sete ss). 1 ueielontars Wes, osiclovs or sic eaters Wei tiereteietes OOo ieiactort 296 


Strength of Wrought-iron Bolts.... eoeocaenesesee -aeeeegee- ser pvetrerreones 292 


CONTENTS. Xl 


PAGE 
Initial Strain on Bolts............. Fs Sens vooavenemsetid eve en mesitelastekuscaere 
Stand Pipes and their Design.......... sareloieistscieere cca raises wiatsidaeistiatcin pees thee 
Riveted Steel Water-pipes........ Weis estates oft ties. APDOO OS COOL SeLBG: ATE CR aoe ee 
Mannesmann Tubes.........-..-se6- alee) e s/eicielsiis ste'siajsve ie siete tainted siletaala saahcol 
> Seber Meteo F of HAASAN SoGdoooe Hee Rate ereiaiced ols u chete s crete siete Nad shee 296 
Cast Iron.. ats eee SoRstiesocGeBi Sporidacandade Sane. pias sorsferseie aU 
Tron Castings.. ide Ne Sates oft len Sakae ole cicia'e/sielsinv slelvield’s seloiec ors 297 
Iron Bars, Forgings, GLO hk eas SoSS Aisttes ee dew Sapeveiete Reine S aise sfosiaes 297 
DLECL RAIS AIIGM LCS a ctctastites ces cst tess. cele siicieete ete Diletchted Geis aeiess 298 
Steel Axles, Shafts, APring Steel: : e ciatefeleleiehe sale mani Gather ele, se ate Coe E Ee ee 
Riveted JOlMMtsea se cacetsaetce ions catalase Bibs sid eta Sal cms tae ew arele SB BaLe CARY 
WGI geen eee Roe ire H ANAS aoe ac emy Ars « Brae a\ajd sianatd chart tcloe tals slotstovenia tes 300 
Copper. Brass, Bronze, OW ss reer Rood oddone ba aed slew sisiee meio sepiesaoCl 
Wire, Wire-rope.. nis 20's a eisieleie.e 0 cies Viele vis'eisie|ie ele oie eisivisialoes sel eeisia setOUL 
Ropes, Hemp, and Cotton.. nlajevejelelsisitie eiclelaisinaien c/s sive s cistelelsiaisiall clajeiea ac eee LOU L 
IBEIUING MOAN VAS nS emi cess cutis tise s ee eras lath «tale nad eeesesrs IETS SAE saneayouT 
Stones4 Brick MOement, 25% 5 csictvesc:ccte cis sis cle 6 us 0 cles o.cie-s ered claersato cuisveicie seis 
Tensile Strength of Wire 2 
Watertown Testing-machine estate ato ee aarere altsiete oreretore Hane GUE! 
Riveted Joints..........0. +--+. + eesseccerecceeeseceeees eles cvatstefereters sree see 803 
Wrought-iron Bars, Compression Tests......cccseos. coccscccscecces eee. 304 
Steel Bye-bars. ..- ws, cc cnecjieceses ciate iad Be crate Matt eiehe Sidieisials @ er ucieeise's< OOS 
WEOURHE-ITON COMMINS ok Vnccdans nian cee ss 5 cueibs bt ant olbaremsniane ised men aOUO 
Cold Drawn Steel........ aeBabS Sasiaidisie de solic cle clecciclece oleaeicieisicisisticcaar aaenUD 





American Woods.. wals)alfeieja(o's/4'e sie sieielele'a]s Stevels ofa vselaisie ciate sine OOO! 
Shearing Strength ‘of Iron and Steel.. Salk oe ahiwpre Tab aseelataiat's myoieiaielll «ae sack oie 306 
HollinosPOwer OF sDOler-LUDESi.:.cs sicisiels ccieis iets cre hola cual cleleteisicicjesicarae ha emo Ot 


Chains, Weight, Proof Test, etc.. a olapetttoseltie a/ine ccleveraeitete pitta cvelsicvarmee este thWre 
Wrought-iron Chain Cables......... ale Saas ast costed eis weiecslivesd seen OUS 
Strenoth of Glass. sacves<dsedsesvecvee Saige scion ease ctielseitestice bine de ateitte MOUS 
Copper at High: Temperatures .2 0. ....s sec uecss se siitereese dh ce selcsieslaceet ie demoUS 
Strength of Timber.............++.6 Sele rioeiy eve eisle cielo es solve clccisies clase cies OOS 
Expansion of Timber............. sivieiesieaiciesielsaavieeie! eles Cviese soeiieeed see) Ol1 
Shearing Strength iol W-OOdS: oo: cisicciceincienisiciesiceltece esis llstetel ae aielate 
Strength of Brick, Stone, etc. dd Keeistegeuececeoscndage asc ceedsioe 
se Flagging i Sera rereia ld) Wwieiaiaiesbisatche win ele wie cetere eta letie 
ss * Lime and Cement Mortar.........0.... Solelg ests slerset ects siete 
Moduli of Elasticity of Various Materials..... ea worden we eusee vase setae meIOle 
Factors of Safety... ..........5-. sierafi ale cle/sNicileie/cislelsieve sieisaiatelererl veiticte s acta peel 
Properties of Cork . a IeYohtoralerwel enlace tated Uelsiaie olds sto siaicieiteerts ob aciten olG 
Vulcanized India-rubber........ aiew se esis sienna sjeclitaiee sees elses ee siccisissisiee ss \OlO 
Xylolith or Woodstone............ Bicie ease Anemanae clelsinl Sieve sicisie's eles sis e's ofc eicre 316 
‘Aluminum, Properties and Uses... .-.<ccsscunediseacveseosiseecesoccacece O1F 


ca tle 


AllOVs OHCOpperandilin  DLONZOussescacecsies cscccccecceceseebacsietiscenicle 
Copper and Zine, Brass.. (SSCS SESE SOSHSEDEOSSHSEHSF SEBS SFSH OSES: ee 821 
Variation in Strength OE Bronzer eect rere oe tera cn ante cee EeT 
Copper-tin-zine Alloys... ........... bielesie| caice sicielt ew ceeceesosiais\ee sloiceniea aoe 
Liquation or Separation of Metals.......... $06.0 466,9E: Mrs le edie ay eanadeiesi Ged | 
Alloys used. ins Brags NOUNATICS N.\ccs.; «oe 94.1 cath elec sic.s’ 60, 6 cles eieicia Ave tren com DOD 
Copper-nickel Alloys........ HOWE Gti tidoe coe BOnUUdON U bociesdno UB Icbnee Ske 
Copper-zinc-iroit ANOYS | ,.ccisecccec ase senvensececces 









Tobin Bronze........ ; Peta eitie aioletiele’bl cco 
Phosphor Bronze acaeliarsiain ciseMictaasicis e isieicis/a)s:4.<\s'e\\ oe/eielere a eianeierats 
Aluminum Bronze...... Racine siea ce Sin eicintae ceria riislsiuivab cle. eiaoeactemtninertalrs 828 


PATTON SASS occ beanies a ice ch ces esets inal aletatetetiale: eaiels' sis, ~in.oie'els)atetalete’s coAcet 329 
Caution as So REreneth of Alloys....... siatels sarattels A Mlaciive edits af oisievclersiegisiheCheneree 
Aluminum hardened .....\..0scqssueesesees Beitateiienr secede crsiemsyeeis emia cence 330 
Alloys of Aluminum, Silicon, and Iron.......0....cccescesscccccccessoss-cs OU 
Tungsten-aluminum Alloys............ aelsinatels slems[sise <2 ao 9 ni sie oldie esleinaicisyep ool 
Aluminum-tin AJloys ..........,..0200- Priatst cata lcHe oi wth) cube, {6.06 ends wa oat eral 331 
Manganese Alloys............ aieleiss cit tukstalaa oisaPt sicioiate’e eieutiajeie d ojeisisieiele stele jeieies Oe 


Manpanese BronZe\.. si cssiediesaces s- 06 se. S e[dia ctala'chs.b:0,0 (0: sieisie ojein/ale e.eiatalpele ia OL 
German PEE cs ons hae aieisisia sais sicletelecele:sis'sitio'= olele/e sloin.a(t.sies ey s ofl e Memmatalelay emer 
GY Pm AIOTULD.. -.u auitteia sinc s.c0.40 0 ctitee wer hs cess coe as aware orapaadeed ste . 832 


Fusible Alloys. Sea BeSO sejcbccseeseesocncbecsoce C0is, enale cops Weis oie 5.5 . 333 
‘searing Metal Alloys.. #9 a+ OHH HAH F 4944 HOSS HORS AHHEHDRH F©RHTHASSH + HHH EASE Soae 333 


xii . CONTENTS. 


<a 
PAGE 
EASA a ac Meare hn ag be EERE EI SAND so oeeeess . 336 
White-metal Alloys.. LLL EST Sele aw ba tebe st Ts sees censor odee Cees bee fate 
TYPOS Otal Met ds tc ac asics: Zin bo tiae oh cules We belee'ularse veils COU Malds «eae vemen bad 
Babbitt metals. . eee eees eres SSesGeeeseeeeeseeeeeeeteeesee @erseeeeoeoeoeeuveveaee 336 
BGIGErs ete. cca AN ret NB Pa cctal hutate atta aloteterenere Seduce débsatosedesecese OOO 


Ropes and Chains. 
Strength of Hemp, Iron, and Steel RopeS......... sce cccccscsccccccvesesess O00 


BIB DeELO DON arte oe ee celeretts siis elels slates iste e'aletats 00 cecegsecceccesevetsscsvecs OOD 
Working Load of Ropes and Chains...........006- SPa ee vee WeNss aeeesiinceeeibod 
Strength of Ropes and Chain Cables.. ela(ale'dhole/elele etela’erc/e’s s bie oreleouia tai atatEM aS 340 
Rope for Hoisting or Transmission....... Preteen OU COO Koco okt 
Cordage, Technical terms'of:*.2- <<: .-.ts.0; bese ad eloeva d vuasetdos newer e- 341 
DMC PE OTSROPOSIE Cs ect tiletes! to sot.’ ols esetededdddeddes cage saenne a eikee hia antag 341 
(Oar satubeinefee 9 ot asasepraeem acer ceae Sb SOO OC Ss. wed Vaivesdtide: civgecacetnuerote 
Manila Cordage, Weight, etc........... a olss ct sen aa hie Dba? sled adh diete sisters en BAe 
Knots, how to make.. atotuletelsleie'e's sletu'she. o's v'eleloietels'c’s oft bets gett cig tid atta sled mer ROde 
Splicing Wire Ropes...... Settee dattet bets sojeislotstes' ee Welda dee bicewe de dienes trea 
Springs. : 
Laminated Steel Springs. ..........-..s.eeee BYNES otivlee b bleed os ole edhe tetas Oe t 
Helical Steel Springs .......... alceslete Salettaee svis’ers'ele oterciecietdeleis els a tv eee ais 
Carrying Capacity of Springs. aictah tele chet athe saleletele eleve del bed Valves. dhedee cues Wes miOae 
Hlliptical Springs tess nest ae eet eg Sd eS a Seid s Ceca eed uldel bie sc Ca aelemeDOe 
Phosphor-bronze Springs. ........ SeSSM Redes s cu cddscsccce nes sdesemeacetmome 
Springs to Resist Torsional Force. . pO thers ved old wielclelain este ta toe 
Helical Springs for Cars, ete... nn i. niwc cscs ete. [isis sda dees d Selects sesteehOUD 
Riveted Joints. 
Mair Dalry Ss) UX POLIMeNts)...joccs Vessunccucsaaea foeke canteen eneeies ches coremnrnOoe 
Woss.of Strength by. Punching ,..0. col s.4y. 0+ shlleidesinc ablaclee ee heme cen ne MnROE 
Strength of Perforated Plates .......... eesicieiaiers series o0disindaleeb s tsp sesmenOe 
Hand vs. Hydraulic Riveting........ ey ne ais AURA Ae pista 6a bos Sale pres os) OOO 
Pormulee oe-Piteh Of RIVELS,..). icici cilsisoissecjerowon teGeickic aes beiinie nic ooh teem U 
PHOPORLIONS. OL JOULES a /oi.ciccs) ce se gaps cuaiccasc ena cle kettle spielen « senued «hecpaaniesyaoe 
MICO CLEs Oli OllLS-ecpeu meres aes acter cast inrereess 26 saa Wate caste cecil 358 
MIamMevern OL wRLVels ice veces ccicse weedy insite eh TRG she biclese oh abs bw Blese oR OOL 
Streneth of Hiveted: Joints... ...idataedsce lets FN Pee Orn ota Gesot. ag ich: 361 
RIVelinp: ASSULCh, sie cietesacclssvey paccceaceccsice « ABS Gr Ancc Sob siseidipe ates oUle 
Shearing Resistance of Rivet Iron .........-..-..00 0 o0.0 005 Opis ba'pla ensign +) GOD 
Iron and Steel. 

Classification of Iron and Steel.................... eiies vibe VASE Bald aslaseiood 
Grading OfsPio Iron ira. - aces Speed Bile ol nse ore sis oie be, Hlelnatee ei ae eee 365 
Influence of Silicon Sulphur, Phos. and Mn on Cast Iron..... saucer hve ties 865 
Tests’ Of Cast) IrOmet tiie ts 24. de2 Fo SES Le Te eh eae AME we ba ale kee Re ieee - 369' 
Chenristry: of Moundry Tron’: +24. 754.2225 h2ses cor any eeriesiodte suede Vener Ove 
Analyses of Castings....... redeedtnddne cease! Ste Eh aoe bate UList. Calan ke 
Streneth of Cast'Iron....... 2.22.5 SUID OOO One asdabecavate oatennrd eels euAls 374 
Specifications for Cast Trom.).t.....cenew elec ve sevds cewnte bee Towhs anaes 374 
Mixture of Castaron with:Steel: sscicss cisco tabeliees souvabeus ceuemenes 375 
Bessemerized Cast Iron.............. sletetals abstelvbete Teetiies See tiles Areata Ooeeuelan 

BA OHATASt ENO mcs cle teics ele’ = stelatetcte efals|o'aatete’s t'vielorefe o cAkicshhtoattiroe lavaettod 

Malleable Cast Iron.............. oa 5305 cisco bt bUDSESN SUNS e cds econ Sodeet SRM eat 

WrO Uc htal ro ntemmermere at” Bit. seo bdeeie elelalatat ais celts iatates OR UUIEL oe ele bike 37 

Chemistry of Wrought Iron. See dR aad Chess dvgas SEI. VEteeanOnd 
Influence of Rolling on Wrought Iron os's*e'eletetel plate’ etp ove) o,a'efe! id atte Uire: d GRIER EMOTAE 
Specifications for Wrought Iron.............0.. diva Vellls ade a bb tela 3 IMGNI 378 
Stay= bolt [rom ee eee tee eR se alo os siste'e ld ornate do Vale Wels pa blab apne OS 
Formule fer Unit: Strains in Structwre@ss 27 ee a we ak dat biep cies oes 379 
Permissible Stresses in Structures «.... 10. .... cee eee eees el ES HS Oh . BS 
Proportioning Materials in Memphis Bridge. a:e'naie'oterel etal ath & Pa tstetenea heen sie saat 3x2 
Tenacity of Iron at High Se pbmmeabes slo" tet. /ale %/a'elaletatetetabere ene 5 IAA? AAT, 382 
Effect of Cold on Strength of Iron.... 2... ...00ccscccees Wesel pelos dacs 383 
EXPANSION GHMLEOMSD Ys TLE teres hoo! e'." steal atctatatidalotalaTats of<tutelohetetotereters Won tule ed lacie 885 
Durability of Cast Tro mW’. ’s's's\s!s etteteteta To's e's la a'o'e "eletouspoloel ene weela te avis ea amebcoa 
Corrosion of Iron and Steel.......... S'S 3800107: 224 See .. B86 


Preservative Coatings; Paints, etc............ FRY RAEN 6s = oct osetia Ms eee 387 


CONTENTS xili 


PAGH 
Non-oxidizing Process of Annealing.) :f2.<2 6222.0 7522 eee. 387 
Wanvarese ) latin rol Lone £ Sees 5 ule 5 ns te FREEADS Oe rere ee eee 389 
Steel. 
Relation between Chemicai and Physical Properties... ............... 389 
WATIALON ATP OULON SEIMEI Ura. + cca ds ou-nhal SUds oo oul te FRNA ae ne 391 
WHpen=NGAToh Wee Pens ae eee Pee NN Si AN aL gatos Ld, Goe Bie! Ae ee oe ee 392 
PS BSSOTIOT ay WE eee lo the eutpiie e beens Secdereae PELE Cake Bik SACI OER Ne 392 
Iardening Soft Stee lace oi. choo ee isenccan coy ae Rea css on a 393 
miATeet Ol COld Honing as kt be eee clate ai pcusulae® weg ahd deck REE ee 393 
Comparison of Full-sized and Small Pieces ...... 0.0). 05 Jabs. od oes 393 
fineatmentpomotrmevuralisteel yan. oer o eo eaa ote cre ono, ee Mada 394 
Influence of Annealing upon Magnetic Capacity. ..................-- 396 
Speciications foriotee!, we. Salas gpa ckee tc caudes We Ome ae nen 397 
Mhemicals ReEquirvyEMeENnts sis ec wuscheleica lee Doky fous PIMP. BE 397 
Kinds of Steel used for Different Purposes. .............0e0es00eceae 397 
Castings eA Xess MOrgsings seus wl Sl cows bbuncel dewuedds Gelage Balhoe Cae ae 397 
(Pires Hails, oplce-pars, structural Steel, 15... .c. a. wick 6 sousse's sions Seabee 398 
Moiler-piateandsRivet Steele. i024: Asda saunas fp SOM, OG ames 399 
May. Carbon besBburned out on steeln«.jcters spice, Geta vier oe aoe ee ae 402 
Recalescence of Steel.............. deg TNE GEMS FORT Te are Lae 402 
ECHCOLUNI CRIN DIo: Dal he eee ee Rete eae ennai ently eae neers 402 
HICCETIC CONC UCLLV IL yan tree terete te Eh tte oe techs cee os epee te ete 403 
OCCT A VIL eee SENT tks Weta Rs Se oie tote vindun ep eee 403 
Mccasions len aiMuress.t atin ae Cie cee Cree eee eee eee faa pale 403 
SecrepavlOnil LN kOe wee neetiions sore: weno eRe satin thus th. ci aoe 404 
HaATlICcts Wises £0n SURUICLUINCS 4 Gk mer aeons cate tee re ae A405 
ECR CSUIT ata a Phe ticets coe hiss uate eratin te meer tain Pie eet een 405 
LNA Wal gen a Cetereh te ots lee Raechee Aine aR ein pd nee aR Ere Sad acyl tae Pinal ar aamauty WR ie Selon ie 407 
INGICe la SLOG mere Nerina eccae oe core arene mir nice rhe ont are eee Aap: 1 
PATUITRTENULERT LOC Lee ra cons a) tate c echo eet oral oats, Sie an ERE. ee Bie 409 
IPATOIIE LOG ere elton © oie a eicle ts cas et ete ene TORE eet eee eats ents 409 
UN gi aNe ges eee a peat eX Me ots ie anh am AO he RR tig eRe a A a ta ny lib 409 
ROTM TESSCU LOC lene rets itchy ccace celeste on Rieter tt setae nr ea ad 410 
Coo yentl a (Eats ieee) ba aadin 4p Sige nan Re RIN Dae bir caieke: cin ay Mae ran) eas Bars See His 410 
eect Of ELeatlOnl Gulalitc ee based sy ee ee oer Oe) Sean Ses 412 
oe MEL a MMmering MetCes. t. ci, ee ee eta eee Cee © | ee ea 412 
Heating and Forging........... cis SRE Sein ea 5% nioet ee hare she SANSA 412 
Memrering Steels is sak psthyts eS Sete eGR Eee ae ee eee a 413 
MEECHIANICS., 
OT Cer U1 GOL LOT COs st ra aT NP CEMA, Me hte mate pe Tarr eon) ee eee J A15 
{saya aks Heels Re RE Seem. OAL. CRW conten OTE Meee ee ee P chal 415 
IN@Wtones awe OF wVlOblonye ss thot. os ete tt ee tee 415 
VEROLITOU OL ONCOd eon eatin te coe inte cee eS cies, me Wee et oe A15 
fenralle OPrai OL hOLCes Eira nl Oa Pete een SIS ee. dep kee 416 
MOMen bro a LL OLCe tetce re hiek Unee we UR nS rl et ne te Re anh Se 416 . 
Srahicali Moments OctaMllyy ss ce were ee et feet en tee a 417 
PO TADILILS Ob RD) A ee peeeneen Awe eee RE NEO Reece swe Tete ate cg aoe 417 
PATEL POLCeS Rete ere Chee st rt EA ee Le ee ice ib eee 417 
DUD LES ee ee Lae ee ieee ee ee rene cee ete aco ante Sze d 418 
UCI TIPLT OE LUT T TOLCES tins cya rte eh een eee, I. Nias 5 gue gains 418 
ETT TOCOLG LAN LEN erate rn ar ee alana) Sead ee 418 
NMomentrot Ler Glas tit mer heat ee ean e enn Set Boren TN re av ae 419 
On LTELOtCry TA tole eae ato ote emer tEr dime tetas”. 4 vie Oke gun dare 420 
iFevgio bib esi fo) Ghia mene have neh cs by Oremyeathcyceul ators oldvaes oe tet Bet curyrak Anam mpm RCm A) 420 
EET T EOL OO SCULAUIOIIn stem ie ieee eee nn Ca ME eos oo rus, yn e eemeane 421 
GENtTO OLE CrUUSSI ORT eae ny cre tiene iN ee er ss ale pan pee 422 
UN gVatd Seva CoheVhb usages QA ay saws cas Kee Gigi, SIN chs be Adee Oe cE eet 422 
Chaverbosw bi Rfexetehb UW Gi ese ae cowie ee elees cate. ne cece be DOR ow See ERE SE veh 423 
Rrentrirgpal ie OLGe nto sc hme Ae ne viele) sss s+ agmrenee .. 423 
ACCOLEL ALLO Meee Ride Pee Re Aa aR oc cies tee eae oe 423 
TERSM UD fp 8 Yoyo WG bee A erat eM uas, au cbs tac AUS tia SAC RR eee NP NS Qa 424 
er IICLOle eaten 0 cope ee RE ie Cece i es oe oe ie en 424 
ATO ATRVELOCILY oor: cents ce teste Te coca: ss! «6c; ai Wha a cal mee 425 
Heteniaue tov Clocity. snare. seer eiene ee RR CLG. | oe: 425 
iPareilelosnarl OL ViClOCINIEMEEESE . ---s faminin tc catl + +, sopeeacr andes ee 426 


WLAGS eee tec te tars Neo RRR o has 8 cd <0 Ct RUS A RS. SAE 427 


al 


XIV CONTENTS. 


PAGER 
Force of Acceleration,...........¢. sat eitehw ive bays hes tace radeon ive eta Ma Sen See 
Motion on Inclined Planes... . ............0.0000 Davee slain Putts isteraco 
DIOMENEGIN, Teo eee teen bee ie On ote ee ts tea oe ee sere aeo 
MISSVAVE Cette eee Cone cee nee Wrelansiaedic'eie ¢ Sielaleterale otatniain ee siete was chute 428 
Work, Foot-pound 5.05 ses See sei toe Te EPR asc See ee 
Power, Horse-power........cceccccscces.e ole hes eietes ere ees Nocees BR bond eet 429 
MONEY deeicnsice ws ciccs did Sreloeatare Ga Siotals aplovan Raieict ete Uelasieidie'eRsie ets's't o ‘so tentee seers -. 429 
Work of Acceleration. cess. ci retbeees swieobalastee bee iia'sie 310 eee MECC ae 430 
Moree Ol a DIOW Nisser cc merter tone eee Liielefe dia oie c oR vies CaM ORES aueese aoe 400 
impact Of Bodies o.3.:.../ lute cenesies vanes oes aS apa seas ol hee re whee 
Energy of Recoil of Guns.............. 6 TP eee aaa Sam renee een 431 
Conservation of Energy.......... wa eeie cles ae Second ae EUS. ESI 432 
Perpetual Motion ................. wisials c.aslets eum ele slepiate staleta states alae te steer enaae 
Efficiency of @ Machine............ceccssoccesesccceces siles se bts oblae rametaiene 432 


Animal-power, Man-POWEY.. cccccccocerccaccssssvascsveaberticines 
Work of. 8 FLOrs@ 6. ast vine oe lose nce decbelde detevetsebecte bole den ssn sues ann 


Man-wheel .......esceees Riese be Sasioe cclsicroules ciel dante cleo eeteetet cele coaeite 434 
Horse-gin.. ai elalsintelsiee ric Cate ccisiecctater eye PA er Oe ien d 
Resistance ‘of Vehicles....... Ae MeO R Ei Ribs 18 te Meds ce eee 485 
Elements of Machines, 
The Lever eee eevee ee ee @eeeoeseeeeroceeeeeeeeeeee @eo-e8e eee eves @eeeerveeeoe cease eeeees 435 
The Bent Lever. eee eeeeeesceeee eevee eee @rve@eeeeGeoeeeee eeoeeseeeGeeeee ee + eee. 8 436 
The Moving Strut. @ereeee eee eeee SGGeeseee+ eeoreeeee @ e@eee' eevevers eee 8@8 88988 436 
The Toggle-joint ..... eScie Sib.c.eieinie W oties © sipiesie saisielbiovese cies s/s baieiaicse)saieateneaten eee manse 
The Inclmeds Planes. sets ce. ce cnces Sisisie sisi AR AHAC piso ss ejel statue sia nlaisiate Stacaarerl 437 
The Wedge......... abst d Bled ole Wintd ois suninseistateia oleeiete hetersisisweieeicieiaben ae Saoticoocse. iy 
THE SCLOWieindes ves b cclstie apy Saas Alera: Selncnes bso neal pee wrestieidla’s aereietaeratee a cay 
LENO WaMitectenes see ec cce ees ates apieuclnce bas Matiaeec at eae unas ASHE: res tas 
hegPalle ysis. s seeste ae cs Pes ics aie aides tieiseglnstice cele 0 ro ete cicete siete oma ES 
Wifferential Pulley sis Sok hwcce cco cts esee sent eee ee eee BR sities Seseeaao 
Differential “Windlass Hoe. see were isa les o's ce Micle cise at abe O cielelcte eistaleta solehteeee esac ooo 
Differential Screw..... Sees he eas SIRS PT A See ae ee Selec cecince mete mee 
Wheel and "Axles. ..52. Nieccses cece cnet ee A ee a irtinc! BAO CHG ONC occas 439 
Toothed-wheel Gearing. : ihc 6 sled. s'ssib's clelcciae sie seleteaatee tisate Facaponoosdondy eh 
LNALESS SCLOW . 05.0500 vce edec dace cces cee cccecsccessessecn eilcsécsvedacs oe 440 
tnauses in Kramed Structures, 

Cranes and Derricks ..........«.. a! Sratarls-o dhe ide re a Bi eceie vereincs te Stet ORNT RAEIES eas 5 atguhy ee 440 
Shear Poles and Guys......... niavelaratetetel sie S io.0 o sth.0 os-cie 8 ei0ie a, 5a 3, Slalom aera 442 
King Post Truss or Bridge........ abel ole eaisvoistaleisielee'si¢,< encieie s.nie= Sit ele ate tore eee 442 
ete POStULMiss aap smece cts aes Seuetests eae See aie 6 a'acle-cie tale Siete ee ehainne eEiteaian «- 442 

urr Truss .... asYeleiblsTeleie ehoteietete’e e sieteiavs 4 ie 085% Hote Beles Wrotaral ates eterna 443 
Pratt or Whipple PrUSS. oc. ce ee aiaslole biislaieiovsie eisielss.e/siatua isla tele eetetetetets a diieeed ge 
Howe TTuSS:te1s acne ee alates Ravereters Saiccce's ceed sae Tees ecieeaetels she cet overs cemeteries 
Warren’ GIT GeIic cs jose: cscs 0 scslciriscinclsci sive seis cpenssisencices cle e visita eam 
PROOL, TLUSS ioc sicice sleccine c ccs cecie si co Solve sie'eeis'e\6 sie sislt cc's ecia’s o'elctatre aietctniet - 416 

HEAT. 

Thermometers and Pyrometers ..............c.ccccccceee wen olen 448 
Centigrade and Fahrenheit degrees compared. . sell cissisieaislea mete -. 449 
Copper-ball Pyrometer. ........ o000 oie aisin'se cen sep abieninisle steel sie niainne iene 451 
Thermo- electric Pyrometer. cs: ..0d..cc00 siateleleupleGe ain © 6 6:6, 0,00 0/oyn ojeisjereieetatemrel 
Temperatures in Furnaces..... eveisnaebieccistestitaiem tere «.le-0,0.310,0 Sa\sjajael ae iateieee 451 
Wiboreh Air Pyrometer: 2. ).iceccs+.cessicee on aia.e)s eiaiale'e e\ss.e7s pit iancola so Raerentos 2 453 
Seeger’s Fire-clay Pyrometer...........scccceccccce- cose © sais blb sein evans acaiee 453 
Mesuré and Nouel’s Pyrometer ............ Sela iot shan ieee atetene aie haxjece Ieetete 453 
Uehling and Steinbart’s Pyrometer.... . ...........- Sle aie feicemiets ea sis:stauarate 453 
Air-thermometernin cae tee ce oils is alc 6 elo aeles ole o,0,4.2 16.0.8 lee eiaieisieis aie acento ‘eee: 
High Temperatures judged by Color.....s+« SOAR IOS Aaa S ca sleaie ss Ora eee 454 
Boiling-points of Substances.......-...0..2. ees sees ceeeeeeee ole oie olan] seis sie 455 
Melting-points: stance moat selovic.c's t's oc, ccce ces ccnas aiciaoaleiaelajcieters wes smc SOD 
Unit of Heateic.c8.. ames aretenier Bete ielsieleteletoicas ae velnoas euitins AACBOnEeAI os tS 
Mechanical Equivalent of Heat...... eile colece cca cements va /nlemicerewkg lace 456 
Heat of Combustion.............2. wiv ai wleleia‘o s ele {svetatctniens a aicie else eatee tenets eee 456 
Specific Heat.. Se OOS BOD SEED OTe tileis'e see Seth ie via ecteletite crate die-7.21 tee 457 
Latent Heat of Fusion........+++++«- Rete. 002 SneG slash aiaiaiere a:6.0 se (COU IMEE 
Expansion by Heat........ Biatalelt's «\« 1c cleheemiale sccelsien  cleetestaaeeistsieicce «ss Caste 460 
Absolute Temperature. . oe eseeeeesed Sees eeee eee Sees eee SSS. eeeneeseee 461 


Absolute Zero ©2826 000 F288 87 F OOH OS HOSS S8 2 HH S242 G5HHOSOSO84L SHH HHH 22°46 463 


CONTENTS. xP 


PAGE 

Latent Heat euee @eeeeeeegnseae eee Cee SSS Ses FeseGeeSs + Get eer HH Sede See Geesees 461 
Latent Heat of Evaporation Be i stetrarae cate Sdbnbdo soso cbipihbAviccubose dl corn ft, 
Total Heat of Evaporation.............0- wees vers cote ese soncesesuueveces 462 
Evaporation and Drying. . SPE OR ACISOCO CODA AOS OO TO b SpA B bok tinea! elas 
Evaporation from Reservoirs. . . DicC OOOOE Be Sotto jaldseeis aces att 400: 
Evaporation by the ee Sas, tena riecisedcetyssisedayseon lore SB Wabec 463 
Resistance to Boiling.. HERORIUCUS TOU N DOU En OU COA ULIBO USE. thre) 
MEST AC LITO O Cea Gin ree crate ee eects he ee ele iotaars Sietiere eAc eats eeraneetia els atoms 464 
Solubility of Salt and Sulphate of Lime................ 0.0. .000~02 SOOO: 464 
Salt Contents of Brines.. Brute, Beat trufee UheeeG. Mare Rem aicaterers Misangteltie. a 464 
Concentration of Sugar Solutionssc2e75.dsece0 Ee wrapteiote sialelo om a0 
Evaporating by Exhaust Steam..... . ..... ee eek at me eae itt he aye teen 400 
Wye eT VLC arte es ee neti beisered Meda le etc e Pant ces eater 466 
achiAGlOMOLtEGAb nsety css ore ote os nora et tieetelte ders Bett ELSA AMIR etc 467 
Conduction and’ Convection of Heatz:.:>..cccc. bessccvesscccee Jessa le 408 
inate or externa) Conduction iit 2 ttas cee oie meee en Sear eehy One Seige 469 
Steam-pipe Coverings ........ Sone ete cena ates aS Sto dees tee eee 47 
Transmission through Plates......... Pe eee PAT a ereieeie actus have npraleiolere 471 
se IN Condensers Tubes oe sl isisici sie o a,0is aie ojeicisita.c'e ec cleisiicinnte tests 47 

~ s Gast-inom Platestc.s..soes.s 3 dioeuesince Bale hepa eee 474 
es fromyAirs Or Gases. FOL WatOlcicciecaies oleh Sieo:cids sable hie seen ATS 
&§ from Steam or Hot, WatermtovAir... .caeeteases tonite mcetae 475 
§§ through) Wallsvof, Buildings... ... . We aitss elke eels atelalslesle ets 478 
ENETIM OGY HAMMUCS ee eck riick creek weer Malrivcriemesne hieey UES Ei tiretee ote . 47 

PHYSICAL PROPERTIES OF GASES. 
Expansion of Gases..2.:. .e.csseecdreee awe, Bay! poe a \stel Me aisle sar ceesserolaca ciel 4" 
Boyle and Marriotte’s: LAW, <2. 2s sic. ss is cisteseatay Stain dele cinta cl sicieelslessie sereicie 479 
Law of Charles, Avogadro’s LAW........sscccccccccccves ce iSujajerats Bore epeleisiene 47 
Saturation Point of Vapors............ etarietoce sic crore miclaletcteaiavareietatiers Wacicbiene 480 
Law of Gaseous Pressure ...ccecessees eae We sayen gaieaietew cicued cisjeien ies eou 
PO Wr OLE GASCS okies hs he vce cay ase o sth -arsieinihelaieives oacisuble pv ataler/sevisieistasteiaié/a - 480 
EASON CLOM DY 1u1O WIGS sere) ifei0 ercvetaraicfelstsinlcicisa] siete voce ccecaccs ccccscoscccceses 400 
AIR. 
MLOPELiICS\OLAIP. cescccclencccdes coadts wa ceccietemeececen sl lence chee ten cee iol 
PAIT-IMANOMECH ac Jets cc bees Sacco cnatoncecceidnaasdads Mrne ents ddenovodond. Chl 
Pressure at Different Altitudes......... Aen iainase pSeabhihse sepsis cede eal 
ISALOMELEIC: PrESSUTES feeb Sine cc leet ot cua nece ee: donbdtodaseby.acn - 482 
Levelling by the Barometer and by Boiling Water....... SECS Ae Hoke 482 
PEGuING Ditkerence invA fit dG repcpiciceteteer scess ees c teas vse teem SeAcopnibe: Ue 
Moisturesin AtMOSphere:| ¢.e oe cece oieccees se Ne swlcalse sic ci cetesleeinttaemaco 
Weight of Air and Mixtures of Air and Vapor............ see GRaCHGoR Gace 484 
Bpecitichheat, of, Aina on oat ose legisla ees ssinisis eve viaiels.clela ole ul stele cere ta siete AC 
Flow of Air, 
Flow of Air through Orifices .. ....... reemsgee eee sialgin oe aieletetetarntolels opcia sioreeh sce 
Flow of Air in Pipes...... aeesS ten Gales wale sess reas S sighelsia'siaierera ae ale ence 485 
Mirect/of Bends in Pipes: <3. ie sesese Sievalar do's ciate ao Wale slae wisictee’s aloisisiais ciate aace 
Flow of Compressed Air........ce.ccccccsece aii sigtiowse s eis § sre Site me savatereaers 488 
MWables.of. Plow, Of AiD,..o.j,c.0,c. a0.s.0,00: ig reielateisteiaiaie satis nic! slalefaleis’«'n7aig; éielsin aie APP: to}!) 
Anemometer, Measurements.4 i 5 scccrs'te seis. sisiacre ees sye'st d's, sis/soed}eiesleli a cieere 491 
Mqualization wWly Pipes. 2... secs s As see sinters s eretsla Cistete ie oie/e.b, 5 oo siais\oslateasieions eae al 
HOSSiOL, Pressurepin) Pipes. .cisals = siesielele seieaeiees siivieic et ofe «e'0.0s. co Osis is cicion een aGe 
Wind. 

Force of the Wind........... ate cisieietie serene sig Sa MTNO RIO'S c's eis ke !ors slopes feeisinehi= mG 
WiIDd Pressure in; SLOLMs jac ste aetialettstesied o sia ei7t otal2 4 o's 0-001) dieseisieleleseieiele uA O) 
DWV 110 GIA Sieg cis ecclloe's eins carelare aie Relea Tara oesals,0 «dials wleisie lt lo clare snsi0js o,} aise eeele Sac aeO 
Capacity of Windmills............ h Simo recc.elt sl sterele SPS ay ols 6,515.0 oi scolstste a scnjesiecna’ 
Economy of Windmills ............... MRE Ue srelo Ee ete sie ease eid slolaisisiote icine sled 
Electric Power from Windmills...... Bete tieislso tctctaicic\sisisi aces Peycbdem adsense CU) 


Compressed Air. 


MesatingoL Air: by COMPLPesslOn...\.., «sso ditslace avis = « sic.s ela sttin vie o,0 oe Newlelseeiea cae 
ILOSS .OLsemeroy, in, COMPTeESseG AIL «saws .c.s0'a) ss 510 0.0jaisleers clelave'a;e satitietae’ sims 499 
Volumes and PressuresS...e.- Pecos ee PP PP OS eeoe eae /Poreeer2ees 1909 000% 000 500 


“V1 CONTENTS, 








PAGR 
Loss due to Excess of Pressure............ co 0c spec sdssdbodsobscocspacgieciae GOL 
Horse-power Required for an shasenganeameamedacc Sean Te 7 501 
Table for Adiabatic Compression........... slsiniecielenieinertiviyag teide caitetaniamae 502 
Mean Effective Pressures..........e0.--se00 oie ole eo ve. paidiige sle/eielp ginlgiemminnirir al De 
Mean and Terminal Pressures...,....... c\s.0. 50 ov eet palimaee we clea sigglepteeiges cue 
Air-compressors se eo rete ees e ee ws a eeeeeee®e CSCC H COLO THEHE SOSH HRHSCOS COE OESt OE 503 
IBERCLIiCal Results tetas ceca tec en cnet: scceccuvens cost «peste deaeransrnemoe. 
Efficiency of Compressed-air Engines. .....cccccccccccccsccccccce vocsece DUG 
Requirements of Rock-drills..........., sop decsisivaenspide ¢cae «sine a cima emglapOl 
Popp Compressed-air System. ........... © cielele celcomie sie g nb sleie stay cere aren eemtE 
Small Compressed-air Motors....... .. Diele's gare vista versie sysie-oicudls olpis siti s alaleratete 
Efficiency of Air-heating Stoves.. sig binae be Selene ale ciwie’naisia plete 
Efficiency of Compressed-air Transmission....... BGHOODIa) Cam ondCnhGnnan é- 

, Shops Operated by Compressed Air ........... sis’b closes scls cas a clsisiG pice aetiameunt 
Pneumatic Postal Transmission ee ee aT eee eseeeeee-Ceeeereeeeeseesesi C888 509 
Mekarski Compressed-air Tramways...... ABA ICORR Emma ORM AGtAGHoncn GIY 
Compressed Air Working Pumps in Mines........ ose cc erdnpnacepeereseass Ole 

Fans and Blowers. 
Centrifugal Fans.............+++.0ee-- els seelecias Sils glow 600s baleaneceeateiceeeel 
Best Proportions of Fans......... sialwislcis's c'cw oie clsiclaigic «ele e nel eipiaiglelelsise eicralv aterm chie 
Pressure due.to. Velocity. 22 3.5 Sei. tid so cicl'c al slaiele eluiele aleialale-dielawats selene saben ols 
Experiments with Blowers........+ Metiecicles cee ee ale Sa old Gin citte wcls c.clce euiets SemeEe 
Quantity of Air Delivered...............c0e0- wiclss b0ec pees on cdisiisciavicidgiesee Ore 
Efficiency of Fans and Positive Blowers.........scceccccccesee> veoleecusioe ole 
Capacity of Fans and Blowers........... Foaee wisn S tnee pipes Uk atie celclee saci 
TNablewt Centrifugal'Wans e252 205.06 Woe hse Leen ce ae 518 
Engines, Fans, and Steam-coils for the Blower System of ae veusey S19 
Sturtevant Steel Pressure-bDlOWeF ......s.cceccseceeecseeeceesevscerccccee, 519 
Diameter of Blast-pipes......... apcenpis aback: PAA iy: setts See eglestat peeeroLe 
Efficiency of Fans eeecre Svoeereeeerseee eeeeee ees eee es eSreeeSseeseeseeSeseessesd 520 
@Wentrifugal Ventilators for Mines 27 2222 cece sa voc clev elec e ccluicisiviclslelcte ses iell 
Hxperimients'on Mine Ventilators. .5..ccccccsccciscodscseccccsccens scawiscnidee 
Disk Fans ewer.eeeoeeese -@ererer eo ee ee Seo SeeeeeeSeSSe sees eeesqeoseesesegseseneer 524 
Air Removed by Exhaust Wheel......c,ccccccccccssccccecccccses ccwelesoetenood 
Efficiency of Disk Fans.............. ie ip clale lois elie sleisle © wicieiors eieiaiaisisicic elcieeeraisa mice 
Positive Rotary Blowers..........e.- bias @ sclegiebio'e e's sioes:sleisis e16n enti tan aeemOaG 
Blowing Engines......... Sislele siaisie sleisicts siareleioieier ateioc Se PE iis ody oo 
Steam-jet Blowers..... eeeereevece @eeeeeees SESE STCOFSFSSSeeerseseeeeeseeene 527 
PEDAIN- IGE LOK, VORLUGLION. » 2 droccarcacrteeasctcsseeta eine snap caeped st acces 
HEATING AND VENTILATION. 
MOIITLALION soe ete chee ee awe k Shio do egal sie sti cciom 6 Re a eee Sid. dw sige ewe 
Quantity of Air Discharged through a Ventilating Duct..... cel dis ctdlcig sate DOO 
Artificial Cooling OLVAIrR: otek idsien*s olelteloie wite'e wiole o eicrstale <a velbld talberditsis 531. 
Mine-ventilation. 00.3 ..0006.s +690 tegsapaeeee Nel siete, « o1b aieieisieia sisre ofeleleielsian Geena 
Friction of Air in Underground Passages E emesteeiisale ele\dieieisieinio ere see me eioieioe 531 
Equivalent Orifices............-..6 60. sees cece eee eee 208 hula olde alee. blatale wie OUI 
Relative Efficiency of Fans and Heated Chimneys..... oslo! Rate d tle ctecoe nee eee 
Heating and Ventilating of Large Buildings...... serd edie bolks Cod daisaicaeuae 
Rules for Computing Radiating Surfaces.........ssecessecccocececceserees OBO 
Overhead Steam-pipes.... ....... ces eceseces dewelisisiiette PPro rraier hace te T| 
Indirect Heating surface 00) ook cc ccotereeirndcin Se secede ededeee Mee eee SOA 
Boiler Heating-surface Required.. ist neeeehaeessetiene PeGcosue aa bikeie stoletarciele 538 
Proportion of Grate-surface to Radiator-surface........ othtaicie stand s'e Ses see OOd 
Steam-consumption in Car-heating,.........0..ceece cece Sornislcesis euaererene . 538 
Diameters of Steam Supply Mains................0- Sid wie eps" e1ele stereo hakete eee 539 
Registers and Cold-air Ducts........ 0... .....sesseeeceeeeees ee sy, 539 
Physical Properties of Steam and Condensed Water. .........-..0++++00- 540 
Size of Steam-pipes for Heating................ avtedandeae oe sitomoe@aldalaslslOae 
Heating a Greenhouse by Steam........... feta letate awe rertote ateraldectaltaree’s eet dete 541 
Heating a Greenhouse by Hot Water....... bieievere rere Siglers Stats Pies Bo ome leery aS 
Hot-water Heating: Gott tielcln v's se ire bloe euteln abe Hoe Pee scr LAMM 542 
Lawrof Velocity of HW loweewsie-s). «!s-+:nistisoaie sn <s) 0ls'soletelule neers ceyareleteia.siovecasatele 542 
Proportions of Radiating Surfaces to Cubic Capacities.....-..0.¢s+..ee-. O40 
Diameter of Main and Branch Pipes................cecccccsccccsccecerees 543 
Rules for Hot-water Heating........ ewida'eee Sin bie a0ts ako See stem eielolale scl» olelelemivaee 


Arrangements of Mains. ..e..- COCR TCE LO HCO ROH LHe PAOR OG SOHL OHH DS FEF BE08 544 


CONTENTS. | Xvil 


Blower System of Heating ana Konglatings. Piao) sivuemiwead vans toaxcedss whee 
fixperiments with Radiators... .. 2.0.2.6: eseciee reins e'-sies oc ovis ict Odaseelv ene OU 


Heating a Building to on E @er.e SPS O SESS SSH EHRHAEOTC SE HOETOHOSHRSHHOHSHESHE OOO YESS 545 
Heating by Electricity. Seciow ne, sesso sespeotes S¥eee ht Juma tae s odtiake Aen ahOte 
WATER. 

PES PANsSiOMOL WALED meats cco e teenth nee res hi are tvetre dev ccetaceuie egien 
Weight of Water at different temperatures.........00. a ticincie cevsieisie Steles ees Ch OG 
pressure OL Waterdiue CO IES. CIZ NL... .tecce sees © eee daisee ces Oren AS Pele t 
Head Corresponding to Pressures..... ...... Peete ccsictesiecinicie'sis cise gieiees eee 040 
PUD VAUCY tenets veteieees eee SOnCr chic tidtmaonmoricemhttn cite Neananeas exci ODO) 
Leva HE BRO Ng nloncdinscponotdnoadacnidodes Peeer ee ee es eoossen e@ecese eeeanee e@eeeee 550 
IBCECTZANE- DOING mente tie tise veltenicloclesicisc neccins: apincet tise mors ee aisitig Tet Ga 550 
Sea-water.... ... DORON SaCOdoconhoodr Rise ersle se AMBOCEAAGAEAe D sieetereaas 549, 550 
Wee andr snows tee: 2. sce. RRIBIDOISERODSn COREE SDISOOE OGRE OG Meee SAA oF 550 
Specific Heat of Water...... slotolelotetere eieejatstereiee hikers ne age ates cay jaaaieg ar 19\0) 
Compressibility of Water...... TRO ee Fe ORC Cee he a Lo aire er aneteld ising Galtate 551 
PmMiptirities Of Water es tsetec es cece ces SCHAPOCOT SORES DO OIUAD ie cee cian 551 
Causes of Incrustation. . mult ata nieraiaurcieasie cis werccote state ot SSA SR ASE ae 551 
Means for Preventing Inerustation SS SDOMADESE RCO SORE einoiaislelereie po sinre ee este 552 
Analyses of Boiler-scale.. wdnslaoia mH Ae ne ela a ater eee aletelatAatacute dp ae acta een 552 
Hardness of Water....... Cisic ctclal ne oluioh hela eraiete: tie! natal barat o Se erere TOMI Cea Pod OOS 
MuUniLyINeg, MCCA; WALL. a sivssccees sce vesncece enw ws be ees diletde tect weteatarn 00% 
HBOCCSNIN SALA WALT Ack che setae cies ane sk uke weee US oe einae et Role ds oewtacter 555 
Hydraulics. Flow of Water. 

Fomule for Discharge through Orifices.............. oo eee HetseRt ie SAEY 555 
Flow of Water from Orifices. AB OCDE DADOE HEDIOE COCO E DOD HORE RED cai Peles 
Flow in Open and Closed Channelee, ook AB SIERIOK AR CoRR DHEA CInE Son 
General Rormule for WlOwW 6. 0). ob vec cece oesc cee aes cess: ae ett recite OO 
ran lethall ior Meet Per Mil1G, ClCa: souls vecsecice se seer cence epee vere caer ce, O00 
Values of Vr for Circular Pipes ...... lace Gis Baie, aka ae ae cetes dpainan ened 559 
Feutter’s, HOrmulais.. . «secs ss .00,0 a. sieenvets gasinete asia slewalesinisias Adaiarpies thes ketinierst DOS 
Molesworth’s Formula....... Shei’ otef'o,at sileie'e/euste smeTTe Na vercMiemiorelr er a gais eyeiems a4 562 
aA ria SMOLIN WIG, 25.02 oe cishi sles sieie c8eis's'n-eieioinie ole sists oe eidlotefersis's aie 6 d:0 Sel ele G ders sels LODE 
PCY S DOP Wal. cca ces ccusc sss cae cecth ss nace gasplne e's por prowl > melee eb Slee ts 563 
Olde reH OTM ee sae ce seen g as hac ace t eeaeas wee aise nisie.esleie.e jess teehee rem nOs 
Velocity of Water in Open Channels... 2.2... cisco. cocsccsioe s eccpisies siocids O04 
Mean, Surface and Bottom Velocities. ....-.- eeeeoeae aisicvayeiquateara deta sera aioe 564 
Safe Bottom and Mean Velocities.............06+ piety eseid cious pyeid es hiapala'y aitipiaeke 565 
Resistance of Soil to Erosion... .  sfeisiarg: scolarptsiaivalee a(S) ciety slata(ncignOUld 
Abrading and Transporting Power of Water. Peer ra aiatarotorwia opitate at Ae ee 565 
Ginn de, Ol: SOW ERS ra ranean ake Palleid Bose oretes coed peter eka kets phslsh de cinseed een 566 
Relations of Diameter of Pipe to Quantity discharged... .... Saas wrote SOLIS 566 
Flow of Water in a 20-inch FEUD wes cect esac aiee ca ssegnepeaet dy Passi xaos 566 
Velocities in Smooth Cast-iron Water-pipeS........e.cee oars atest capastds are bis 567 
Table of Flow of Water in Circular Pipes............ceeecees eres ehdta}ctateians 568-57 
NROS SOL OAC ain perc mee tet a Nee er ore/ cones ays erareteysteni she Rips ie & reer terial 4 573 
Flow of Water in Riveted EXD OSstrsranes irate cite Goetinets aa oi es,se aioe 6 atest pee 
Frictional Heads at given rates hs CUSCHAT LO awentssleisies c's iclss's/e BoA CITT, Abe Way 
Effect of Bend and Curves.. rece ete sicee hoes aise tieesd cesuivenenl 
Hydraulic Grade-line.........-...-++05 --- Seaeeiah Seas einery eeirle w diciala Gus alae ea tepaan he, 
HMlow,of Water In HOUSC-SErVICS ElPCS.cusccesccsscssccesoctecctesscccst ue OF 
AGT“ DOUNGLETPOS: «rtetta a clonntalcfetatole asta ole Apacs Set OC OH AOS On EEE Apne otioot ( 
WMorticalebeteuegemts tec, ta ccc cielsle sienle-s bale swig APA ND shave 1a «alae ene eomn 
Water Delivered through Meters.. Dee rate eaioe a Gineleinie asie 9 po diary ekg lena 
WIPO SULCATIS cece ate anaes ice areca eretetelstoran naicioin(e ha oaie's Salcalire ooisiauceteek Pear 79 
Friction Losses in Hose .........-...++- Mieicrciaisterstdeiscisiae at 14 «*p's siacaloleisiaetnars 580 
Head and Pressure Losses by Friction.. Pe Maileint taiacids s- 109:3'99G aoe eae 
Loss of Pressure in smooth 214-inch ecoe..... esilacuetetls aia i 580 
Rated capacity of Steam Fire-engines. .... 12.1... 60. sees eee eee teen en es 580 
Pressures required to throw water through Nozzles.. o.aisiateraisie st gale OSL 
SET RSs TOM ett -she dsse oe tenets Aue ieetiiasis oi sialn'sie, = 00 cee ee KADIR o0 AGE 581 
Measurement of Flowing Water... . 00.005. ..0-ccccscscees Nee apoe coGOnG 582 
Piezometer.... ..... Be Scere Oe Bess ctererete <.0.o\s 0: s:b.ciesiete avin oaeeinevele 582 
BigotUheiGance.) | i. smeucwe mielmine sie Sey ule cial .0.0 o oleldtherbeldiele Sts steiatts  wDBa 
re Went Nl CLOT. <is ce GEMM eins wis beyrne tabyeie lainpieis os olele deta Sie'vle,s olsieiabepe hate acho 


Measurement of Discharge by means Of Nozzles... sesceccsoccevevcvcees 


boe 


XV111 - CONTENTS. 


Flow through Rectangular Orifices Pee dedicdean etecadedce ater @erc@eetee 584 
Measurement of an Open Stream..... Sak cwehseseve eaves cs snogaamuen sam wloe 
Miners’ Inch Measurements........ corse css ecctecccsevccccesocesseesess Dod 
KFlow of Water Over WeiILrs: .2'..020008 ch weeks sce seeteceseecccce encase HOU 
Hrancis’s Formula for WeiIrs:....ssccccccwcccierduscieces cevececionso. soceessenou 
Weir Table eee reee- 2 Os Oe ee CSC eGe See SPC eS eSet Se sF eset eeeeSSSSoe eee eseese ets one 587 
Bazin’s Experiments......... aisclenne os pat ess anissive'swals es oniesien et oe manatee 


Water-power. 


Power of a Fall of Water................> +s at ghisaiein a ataie tans ina aie 0 ete 
Horse-power fa Running Stream . 2. .cdoccesccsescsccsvesesicesensinniam sone 
Current Motors. .. d d0o Uemoooees neSegnn Suossoo dnc Said 589 
Horse-power of Water Flowing in a Tube. ae Lb vei sine odie-e oie ae'els esleieiottnareleee eee 
Maximum Efficiency of a Long Conduil......,ccce soccscorccccccccssces. OOD 
MAT -POWOr Wades Ho Css seein es initieisiycw. eine sieeen © aelcisin eis sisieieieiare Aprpeacge iat) 
Walune sot Water-pOwerss.. tcp cele siac cece css cin eee cisc.cce.s vielesuiele= ss sins e eintemee 
The Power of Ocean WaveS....+.+ss0sece ee sls s sretwaneje ea Sie Salva sisters Rerneme 
Utilization of Tidal Power...... plereieieisVensisieienelcisiete Giisie'e cis slejsiouteis Sere saislaeeemULD 


Turbine Wheels. 


Proportions of Turbines s. s/s vec ¢/<<jsiecnc.esi0<ics eise.e/eie visie selec siecle ele ereiins eee mney 
Tests of Turbines.......... Wiarephslueio/< akin bueahe-ai oinemeia-oleasve nego tates Co aetente oD 
Dimensions of Turbines...... See pauecrinte eevee winielg @ wee wis eae cinlnctis oolale a inet Cement 
The Peltom Water-wheel’.... sc scccccwe ccecw elec eoleccclsc over le eset eeee 597 


cane 


Theoretical capacity of a pump.. wnieie bulla etre essen atainadee sce sleglemel pen 
Depth of Suction sh Ae wan ons ss Se ve sak cece wets eRe tete sspetsicess Broce see 
Amount oi Water raised by a Single- acting Lift-pump...... Gacseaesores, ¢ Oe 
Proportioning the Steam-cylinder of a Direct-acting Pump.............. 602 
Speed of Water through Pipes and Pury, DASSALES | cena ec wlewele ciel ties MeemmOlle 
Sizes of Direct-acting Pumps.......... eieliclaie saleialeitieielers siete lola iter Boeoos alle: 
The Deane Pump ... Paes Sewiahe cots cea tiasiiete cece s cio sctnsetccslies ent cee rOue 
Efficiency of Small Pumps. SAA Bo  amibe ba aeons: sUmGC obbee ee beer eementitOUO: 
The Worthington Duplex Pump............. pie Sestitis ole elsleisercln (case ciemin ceeEOUe 
Speed of Piston... stjsn.2208.82 166 Hp ductdo ooo. sicce sotiocsnccescswbosaded sac (ll: 
Speed of Water viroped VALVES Ai Jiiel we ecvestlewiesceaw try eewee ees ers ses cries) OUD 
oiler feed Pinas eatin eis cleiesta attteie’ sale sie sets ocier cleclelsineleseiicinciaasetee eeermus! 
Pump) Valvesrs sss see lcee ba oo ele cde es assaeee geiee eeareteesienceiesnesee er OUL 
Centrifugal Pumps............ .. Gndao ods sh cosonenbas, PbodeHsdoncoubonose 606 
Lawrence Centrifugal Pumps.... ............. SG tioscineatuiccutece ctr mOUiMEE 
Efficiency of Centrifugal and Reciprocating Pumps. Lae ceecp anes emee seers OU 
Vanes of CentrifugalsPumpse since ss. ase cee cute ees Bacmanboncaonn. dace GUE 
The Centrifugal Pump used as a Suction Dredge... ........scccess:-see- 609 
Duty Trials'of Pumpinge Hngin€S. 2.) secc-cceccasneccccss Ad fodorr. nebo delll) 
Leakage! [Tests OF PUM pss: tess case ce cccicccieacecescesseteseve a smee enol 
Vacuum minpsemes mee ceniccss ssctics ec ss cles eeies estas eats ce Sees saierenemile 
He MP UISOMIeLC heer mies civeisle e's clesies ce cc's e's e ie sic c\sisie sie ciesie ct siniata.s oleaus eleleisin ie smc! 
The Jet PUNIP ese ieee eeeeeean S72 +, 2808: SCB8SSSCHGSFSSFHSHeHeeeeee2eons eee e@eeeooeeon 614 
The Injector...... stele ciacisre clas ced Cen a csieisiciars ccelne «eile celeslccnicler sieeiaerieen termi 
Air- lift Pump eee reeee COO COCO OOH POOH SOOO OOOO LC OO ESOL OEES POOL CESE SOOO LE 614 
MAGTH VATAUINCHRAinete cs stelels oe oa clete ao olelete s tnoe eirteee Sait a par atetereree'e selec omciied 
Quantity of Water Delivered by the Hydraulic Ram. SE NORDOD DOS cesses Uhr arora 


Hydraulic Pressure Transmission, 


Hnerey of; Water under Pressure .::... 2. 222) os ose ceadcee cet etseecres onemOle 
Efficiency of ApparatuS.......... Aeiuielelsle ele be cos tees celles cueeceie cee tite senate 
Hydraulic Presses y2tnver soe ees sc FREE Oe rC CCCI CU pnnpticgcc: (Ukr 
Hy dramlicsPowerineond Oita te le csiccleccc asst elatlacca ses cece casceccite 617 
Hydraulic Riveting Machines...... Seer ee Cees agoneny SBE ronomrerteso Bilis: 
Hydraulic Forging..... eietelen’s's Male'e sce 7 is ses sss see oitic a elon eave opesinilearee # siete 618 
The Aiken INtensifieriven sacle casscsscvcscess ccceceeersoe sceccetactce: ccm 
Hydraulic HONING Seve acieene veces ss <ocs eeoee ecoeeeeveee+s'aeeOe +. 008+6 e@eee eft 613 


\ FUEL. 


Theory, of Combustion seme ren cess sc suweedcinccres cov cevin caliclmeeees cies vis cmUROce 
Total Heat of Combustion..cece COO OO SOOEEEEEEOTDHPODOO OP COOOL ESOOOSS 4¥ 


CONTENTS. xX1X 


PAGE 


Analyses of Gases of Combustion... .......ccs scceccccecccccercccsessccccss 
Temperature of the Fire..... aiVel Nolalareldiovelaielaiwisieieloieisie cle eielelere sive saleinlsic ohgieleistste 
Classification LL OLIGEH UCL sine cues cocci eee tec onisientiae bot eee anes ee 
OVASSIMeatlon OF COBISE |. nccasisiss sete aneeebecccsecesecsiee rece seecetces cece 
Analyses of Coals......... Diels cltitleras slelelecierainc crests sie cece ci since ee eee sicielsve ces 
Western Lignites ee oe e@re@eeeeeeceeee tees Seoeeeoee+- eo OePFeoeeeeeeeoeear 2eeeeo 
Analyses of Foreign Coals. . SAAC AI Aatalalele oie alatole’evetae ors ere creleiercie, 
Nixon’s Navigation Coal....... PER SARECLE NSS clad ee e's au Rfestcleccee veeeetect ste 
Sampling Coal for Analyses...... AEs Seba coche ee bee e setts e ae 
Relative Value of Fine Sizes.'.......cccccee: coccnccceces Seitsistectecee 
Pressed: Puel s2 26.8424 ee eee SER TRND Seats Che Bice 6 Maldcewielcdievsllomec sees 
Relative Value of Steam Coals............003: ae traecleceete cles seleaitine 
Approximate Heating Value of Coals......... sedpecceteveses sve sities eieleravers 
Kind of Furnace Adapted for Different by eect matted iki sh aierefoleohietsie oft 
Downward-draught Furnaces... bic etafelate'e Rie'e dlo's ater’ elas) scomiateloteverers 
Salorimetrie Tests of American Coals... Ursaisiee desc cas'e sweats eave ticle 
Evaporative Power of Bituminous Coals. SOOO DR ONOBO CUO EEO IaGobboc 
wWeatherins-Of Coal siveae tines wees vie See ei ees dees ee cess 


Coke . COS eS SH OASSEH HOO EH HAE SHSHH HEE BHOTHSHSSSCHT SH TE SEHTHHEOH OE OS 


Experiments in Coking. . SEIS ALISO 0 DIDO TO Cx GOCOOOCO ODOT IOROUGCOUERHOGhe De 


COal Washing rer es ote ss see Eee ue Ree ce kesswe onan Blea Sitoeiieleecetters 
Recovery of By-products in Coke manufacture. . aetce este eee ects oes iS 


MAKIN OPAL OC COKE toe ite cele ae ee ges s EEE acetic oleic ailerons gl a in ialaieleleeaeine 6 


Generation of Steam from the Waste Heat and Gases from Coke-ovens. 


Products of the wee years ofiCoales trae Raves Sere WoL herhicsescee anO 


WoO0d. as Pueliccscccdncs ce Neididiodelatsss ya slovetarciatsre wet tte Slate sterectontrorene sie Sale aiateleianne 
Heating Value of Wood.. -e@eeee @eeereeceeeeeeeeeeee oO eee 228 2088 SO8SR4e 
Somposision OL WOO 116% sess Sele svece's counsels ce ene ealcses obs Weel RWEED oat 
ACHATEOAL pelea tiie siaeie es shiv eu lviswicicic Re coieeae mek einseystatatate sxe picisiclale eichiiele sre sleeve te 
Yield of Charcoal from a Cord Of W000 ........ccesce cocccceccccecccsces 
Consumption of Charcoal in Blast Fur NPY SST OPEN Septanners ite WaT LN. 
Absorption of Water and ae ee Mya CUAL CORD Ze ccicsielseleies cltielesterctntiecle- 
Composition of Charcoals.. ecaid a laysieie tens Oho eistoeitlale cise clamia odisteretletcicle 3 
Miscellaneous Solid Fuels ........... Melle gece sic cistnie 6 else sielsisie cla/eiote wistats ole 
Dust-fuel—Dust Explosions.........+. 
Peat or Turf *eeeee @eeeeee e@eeonreeee-+-@ @eseeGeveceeeeeeeeseeSeeeresegeeaeeeeeeve 
Sawdust as Fuel eeooeae+ee SPOSOSHSSSSTEHSSESOSSSCSHSESSESSHSSESEHS- FSS FES SCHHSFSS SSeS Hoos oe 


eeeceseoee Pee eeees ese eS eeFeRF ener ene0 






Horse-manure as har eee GTO TE tgn caer eeoveeeseseceseoesese j 


et Tamar as Duel av tvc.cssen seer tsrecseateccees treckie caebieateecee 
BPA WASP OL oct sts oe els es codec yeas atareleratclelente cial lclelslsaeiclole sasisiccetaciets 
Bagasse as Fuel in Sugar Manufacture... RaiR rast og nd vate tss Cees ene slot 


Petroleum, 


Products of Distillation testes ch cic cebastbcs cecstsccs eC oF eeeeee2esesee4e0 80 
Lima Petroleum.... see COSHH SHOTBTESSELOOH ESR 88 ifs iste alejsidle 06 eayeinie ce ncaa 
Value of Petroleum OS WUC sev scc cc ccincaws cae ccs Ocecawsicaccaccsssaces ee 
Gil US. Coal as UCL ccc ccc cons tesco eto SOOOCOOOL OOH+ SOROS ZOO TOTSESR D+ O08 


Fuel Gas. 


Carbon Gas..... SCO SCOHHHHEHTHLCHH+SHHGHST+- SH HTSOHHTSHHRSCHOHSE SEES SHEHSSESHESEH FOF 08 


Pan LIRA CHILO; O AS ate eeleesas ce ace ccoena eevee eeeereee 88006 eeeveeeeeo 
PILUIMINOUS GASre es cole c ce sie.cc silecouvs cy. 
WiaterGasstictcasaconcetrcete ce Deeivaiectaeikeaticre sles tise ceases celeuoitee 
Producer-gas from OnelVon of @oal coca, ene elss so. 
NaturaliGas inOhioiand Indiana: cic ices scces ns cidece cece coos 
Combustion ol. Produccr-gad 0 uc soeers Peels Ca ancccatdeean wed 
Use of Steam in Producers...........- Dalaclaiswiaterdtiela ciseibish: © eleiclaic.eleissiaumne aren 
SHS Muel Ol SMALE UIMACCS sc crc ciis fear ec cicee bcc sc ces cece csr eirons ae 


eeee sess seseeesa sees es 2£90:5080+ 800s o8 


% Illuminating Gas, 


Coal- -f7as. COC OCSEHS SHOT HESH HH SHSEHESSSSHOSSEEE SESE SESE ES @eevesses @eseosoreor C088 oe 


Water-gas eee eo re oes e verses seven ses+ Hoes eev3sese eeeeecesereeeseOoveevee8 eece 
Analyses of Water-gas and Coal PAGS. ocsleuss eiceierdiniteeicels sielisentalere 
Calorific Equivalents of Constituents... . ....cce ssccces cove 
Eiicioney.of a Water- Casi Piantys\ vo ceebbees Glee co cs velsdiadec calécdegeeeuias 
Space Required for a Water-gas Plant.. Bale ceweccoccunsbbscseceveuaweteen 
Wuel-value of Tluminating-gas......c. cnn ccacaaacscccsceaceancangsanqeace 


ees ee 6% se 008 


22 
623 
624 
624 
631 


. 631 


632 
632 


. 632 


632 
633 
634 


xx i CONTENTS. Ses 


PAGE 
Flow of Gas in Pipes. eoeesr~seeeeseeee ee SCOCSSHEOSHOKRHEKGSSSH THES SEHHSSHS SESE ES 657 
Service for Lamps............ tie aiawscsivvaueiaie waste cieus ale wie's.eeiele s wield sislen,s silo acesipa Oa 


STEAM. 


co ae and Pressure.... 8202 OSCOLOES FOSS SHEHHSHSHBTSHOHHHOCHHS SHOKSHOZLO8 659 


Totalsbeabienniccenc ua sesso. C00 ee 00S OF OCEOOPOOOe COCO TEER SL OO CEOE TOE S508 659 
Latent Heat of Steam. COSCO SOTSFSSHSSSSOCSESSSSEESESERBE SOR SHOSES FSH eOs es eeeees 659 
Latent Heat of Volume............ boc nbee cles cemescesice se cnineuuen se cteEtOU 
Specific Heat of marurased SHOAIN co en ok once sdckan toned t,t ee 660 
Density and Volume.. eeeeee SCSH]OSSSOSSSSSHSSEOSSHSSSOSCHSSEe COSC FSESSSSSetseas 660 
Superheated Steam........ pis 6'p pee picocecebecenespes seuaeeec hese aa en eeeEmCaT 
Regnault’s Experiments........ sicle ous aeibins' soe s Se 'sisiasios cidlescicie sn yie cua yeneeile 


Table of the Properties of Steam. .........0. -cccccccvccccecceccccesscevess Ole 
Flow of Steam. 


Napier’s ‘rmestararle® Rule Oe. 0000808 OOS 0002 Oe OFS oe OOF OSCOO OOO LOCO CS 669 
Flow of Steam in Pipes.. eevee seSFeSSF SSO SH8SSES SY SSS FHSS FSS GOSeCeracoear 669 
Loss of Pressure Due to Radiation...... wre sid/a siento sisie'bpiaic ais bedi. ele tetaiel amteemMaat 
Resistance to Flow by Bends............ 2.06 Sieje'e! « cialainm ald Sc/eials eic's slempeiaeele 
Sizes of Steam-pipes for Stationary Hngines.....scc.ccscco-ccccccccvece O19 
Sizes of Steam-pipes for Marine Engines..... sececcescvecccccccccsecccce: OFF 


Steam Pipes, 


Bursting-tests of Copper Steam-pipes........ soccesocicseececcvesccscees 5-1 DIS 
Thickness of Copper Steam-pipes.... .....ceccccecscce sovcccsccscesese. OVD 
Reinforcing Steam-pipes. iol ioeisleo wieineis'einee 6.0.0 suiae ee skleics tie sie niaee ple erase eReaD 





Wire-wound Steam -plpes....ccccccccccccccseccccceccsecseccscsesesese-ee OUD 
Riveted Steel Steam -pipeS...ecccrccccccssecrccessccccersssccccccseccccsess OLD 
Valves in Steam-pipes.......... wees th ee oniaeo bes ah eats 

Failure of a Copper Steam-pipe Basten ss Ae 

The Steam Loop.. Se Se SCS He SS SseeSee SSSCSee SCESCOSOSSHSSHHSSSESESEs? 


Loss from an Uncovered Steam-pipe.....- swine nee situ'veedde ve he ole ele hw eae OIE 


THE STEAM BOILER. 


The Horse-power of a Steam-boiler.......... ... cee ccecce es sin bias necema tren 
Measures for Comparing the Duty of ec SERRE Wace Ae ay icon seahOCS 





Steam-boiler Proportions..... SoboaEd bc ceee bcos over6sine cies cae uopieas sisi onOie 
Heating-surface. eee oee cone er oee ee SSOCSOCHSCHE SHEESH TSOHSTES*LSHHOHOHOSS SCHOSESSOLE SO? 678 
Horse-power, Builders’ Rating..... seeseeeeeanees @S SOF Cee EOE E OCHO LOEEEEAS2: 67 

Grate-SUurface ceases cctsss sess ue calssiacciege Sissi cisieeis Sees secee rece t eee e Com COE 
Areas of Flues.. ee r® SeeeeeseeS es Se ses SSeeeseenser> OOS eOOvue ete oe 680 
Air-passages Through Grate-bars.. eee ecises ees wits este nise aa eee eee emO EE 
Performance of Boilers.... .... .-....,sces-ee eT CEP et Ea oee hes | 
Conditions which Secure ata De Arica YOSSI SONORA CIS Hie eGaiitn (teks 
Mificiency: Of a Bolen ease le se cose cele s sislee sue see cebeartce eae ee cnniC’ 
Tests of Steam-boilers.. OSHC. CESESSCHHESESTESHOS HFSS OEHEHOEEEE HS 685 
Boilers at the Centennial Exhibition. . apie Cs sisaee els cm sects clo vidieieeieelst ce MUG 
Tests of Tubulous Boilers.............. ee ae 6k visite est ieee a ue ue ee eee et OOU 
High Rates of Evaporation............... 0,0'i5/0.5j sin apesin espe nisisiels eee ee He emo 


Economy Effected by Heating the Air............ ae c¥ ons, eech ese dclewseler GOs 
Results of Tests with Different Coals.. sb iweosSdinticesesicseeMOns 
Maximum Boiler Efficiency with Cumberland Goal <#ios5e te .oeineteebice ra OGo 
Boilers Using Waste, Gasesiic.. oc. seve else do sidbaal delta bubitbo eda. peers lGeD 
Boilers for Blast Furnaces......... Sh CCerdssienise ne bens c ecisic pcesisbbetisemmOnD 
Rules for Conducting Boiler TestS......cccsessccscsessocrsacs ssenescessee 090 
Table of Factors of Evaporation..........0..ceccccecces See ceniceeceisor, (NLS 









Strength of Steam-boilers, 


Rules for:Construction sssi-ectele «sec ese cc: test beecece suseeecencates een TO 
Shell-plate Formule. eeeecoereeoeere EES ERNE kc a 
Rules for Flat Plates. SCHSSSCHOSOSOHS SEES SH - SOF SHS HFESHT LOFTS BESHHL OEE HESESHHH EOE 701 
Purnace. OFM j..))...cmjajeicsieisowie-+.010.0:0e Se Haine wo oo sblele Sahu tin eet s thse SOUS 


Material for Stays vicc.comeeisesiciec.s:s10 eidleaiteijee «aie e'ele’ sap ome bate piépoecness sos 
Loads allowed on Stays... aia see's Ace cnencarsciines oem ebieiemecb osce'sssle ne itUe 
Girders 3... Sapien) ne ae eae «= «2 RRO beter id ee Pee covccvecsee 600 





Rules for Constructinn | of Boilers in Merchant Vessels in U. 8. eee 


CONTENTS, XX1 


PAGE 


U. s. Rule for Allowable Pressures. ..esece- COS CA8H-S_ S8IOSSHSAHSHSSSOHLOHAE 
Safe-working Pressures... 0... .....ceccectsecsecseees or eccccesesecscesices 
Rules Governing Inspection of Boilers in Philadelphia. eee iccccvcsesecces 


Mlues.and: Tubes for. Steam. Boilers 2. cogs se iseed Hos accadduitueecccacacsen’ 


Flat-stayed Surfaces. eeeesere POSSHHOHO SEAS HOSLEHSEHHHSOHES SFEREHEH B80 20H2 87086 


Diameter of Sth yaboltStucocecececne ce SOSH HOSHOSSHSHOH SASF SHHSOHSHSH SHOES GASE F790 q 
Strength of SAY Bois .csscre. x coecccrecwe salasedeveeneeseedeveceeecge ci osel @eee vs 


Stay-bolts in Curved Surfaces... 200. :cce co neccscccesoccscsscocccccsces 


Boiler Attachments, Furnaces, etc. 


Fusible Plugs. POS SHES SHOH OHH COHHHHSHHSHTHSSHHHCHSSH SHES SOSH SHSFOSHCHHESOOOEHHH*O0E8 
Steam Domes eee ree Sooee Oe GeGG 2272888882000 
Height of Furnace. eoeeoeesserrees e+: 08200808 ©6000 22H CSOT HHTFOHHOOOO ZEEE 
Mechanical Stokers. ee, ©C0l 00S SOSS OHHH OOHHHTHHHHESH OHDOT OOOO 
The Hawley Down draught "Furnace. ssbb ses bhd docs ohio teeter : 
Under-feed Stokers. 000008 OOS 08S OHS OHO HTD OOF OHH2GH OHH TOSE HOOT TEOS 


422 SOSH OCOSHSHLHT HOOF GEHMEDHOFE8 






Smoke Breventiony.ccsccsscccccse resccce cas chenceeeccesecsean ces aneecctes v¢ 


Gas-fired Steam-boilers SCHHSSHSHESSSHSFSHSSHESHOHSSSSSSSSSSHOSSHSSESHSHOSSOF HOS HBOS Oe 
Forced Combustion... ..00 socccccscccessoeccoccces POSCO CLO SSH SEHK SOAR ERS 
Fuel Economizers. :eeeee Oo 20H CODE THLE LOOKS HH) BOHTSOOHHOCOHHOOS -BOGEHEST ESOS 


Incrustation and Scale cel dis ecre.dis cle 6 COPS SOHSSHSHSSSEHLHHHE SOSH GRO H OSHS OOO 7 


Boiler-scale Compounds.,....e..e COHK SHOTS. 6+ SCHHOHHSHLSOTEHGH OHHH SFOS OOO? 
Removal of Hard MCAIGN. cs cess FTSSHSSHOH SeSeSVC OSS SSSHLSHHHH*STHSHLERE SEBS ROBE 


Corrosion in Mariner DOr Sncccccese ccaceccrocoretecce cccstpesccenecnenecent 


Use of ine eaorser ee ee 8 8e CCOHRHCHSFOH> FHHGOSSCHHSHHS SHFHHSSHTSOESFHSEHHH2FESRSHSF® 


Effect of Deposit on Flues. SOG SCHOSSEHSTESHHSSHEALHS FHOHOG 8HFFSHSHFHHESHSH BEBE 


Dangerous Boilers..... COSTS SHE SESHSEOSEOTSE SOSLOHSH OBHH> SHH HHSHHEHE TODS HOBO % 


Safety Valves. 
Rules for Area ees seeee oe 000 200s 2000000009008 - C08 08008 00000 


Spring-loaded Safety-valves.........e-sccccscscccccsccccceccccs cocgcseccce: fb 


The Taleetor: 
Equation of the Injector.. SOS SOHHSHHHHSHLHLHSSHHHHSHHSSHSOHEGHHOHTOHS?1 SCHHBSHCE 


Performance Of Injectors. .....00-cecccosecccccccccscccccccececcecovccone 
Boiler-feeding Pumps. COSCO CHORDRLOSH FOSS OOHH+ FTF GHHHSHHHT OHO OSOSHSTHHFRSOE vf 


Feed-water Heaters. 
Strains Caused by Cold Peed-wOlerie. jcc cececuss sectesseesccacees soccee 


Steam Separators. wenn 
Efficiency Of Steam Separators.......-c.secseccececcccvcccccvecscsoccocess 


Determination of Moisture in Steam. 


Coil Calorimeter. +2208 TSOH HOSE SHHHHSHHHHOHOHHFOSTGS OF SH FHF FHHTHFGHSHOG OOOO 
Throttling Calorimeters. © SHCHSSHSSHOHSHSSHHS SSEHSHSSHHOHSHHSESSEFHFFHTSGOSSSES+ 099808 


Separating Calorimeters. COs HOS COOH SHH GOOT FOOL OHOHTLOHHETH SOEOHHOOSCHABR Oe q 
Identification of Dry Steam.. © 600+ 20S 0890088 HOST LHOS OF SOHE E859 H899 2000 q 
Usual Amount of Moisture in Steam LOAM. . 2... «> Oecioeccesgescvonseoossccessees % 


Chimneys. 


Chimney Draught Theory SS SOC HOCH LOSS O98OS 22H 6098 41H9S9HHHTTOEHSEHOOBIOOS 
Force or Intensity of Draught. By Si clade siete» 606.656 cecevin ons 


Rate of Combustion Due to Height ‘of Chimney. SPARS da 0) coe sestenadwel & 
High Chimneys not Necessary POP ee eT Cee gee ec eee ses ooo Seer e0er ve 
Heights of Chimneys Required for TORE FUCIRs oes ccc. ccrvocgecse..as 


Table of Size of Chimneys.. ciraisisl singles side's a1... 9.04 n10.90 0,0 6.6 om «nl 
Protection of Chimney from Lightning.. 000000 s+ 00s ecese, 000s 200- cesses 


Some Tall Brie Chimneys. §,0)/0,6j0) 8 |G iste 6/018 0 00Oe. © 0008s 600000050 2999 GR 7H 98008 % 


Stability of Chimneys.. POO COO OREO C OOO HOOE LOS 098: 0008000 COOP HSOHHEHOT OOF? 
Weak CUOINNEYS ses cons eceeeieceececclcctecunchsosce 20098 °°C8008-80°898680 


Steel Chimneys.. © 4 OCOOS + CCE OOEEES 0808980900 55F285 Ee 2O8S GOOG FHHS HOGS 0O99 00 % 


Sheet-iron Ohimneys:. eee ee e@ocecse ©200+6e88 589882608 28998888982 8808 
THE STEAM ENGINE, 
Expansion of Steam. .................. 045. nig eiuieicic coc Seeeaes cee ceases: 


Mean and Terminal Absolute Pressuresotes ssc. s<<cceudtdudes cued! 


728 


929 


XX11 CONTENTS. 


PAGE 
Calculation of Mean Effective Pressure., sme iemen aeltiee ee a. ere 744 
Work of oteam ina. Single: Gylindem. ofc rceen sents nee oe eee 746 
Measures of f Comparing thé Duty/ of, Engines? yi. dyiiewws il. babies 748 
Eificiency.a hermal Units per Mintte. s5. esate neni. eet) ee ee 749 
Real Ratio of EXPAN SOD sil: | s:u cases hoes euaaetdios Gas oa rent ok es 750 
EU ihect, of Compress] O14) <4 seo ck x sha aechals cashew ceueuovs) cece deine eee ee 751 
Clearance in Low- and High-speed Engines... ...........00c0e+eeees 751 
@ylinder-condensatiom.ss nase ses soe daaves kek hOU Oe eae an ne 752 
Water-consumption of Automatic Cut-off Engines. ...............66. 753 
Experiments)on Cylinder-condensation. «i itao.s ta. 25 eed. «oes eens 753 
ANCIAL ORMIIAOTAING 2. 7 obese leuko ine Onto obo ena sice oe aie cs ee oe ee 754 
diedicatedt Cl Orse-DOWEF a occ co ccs inte bias. wratmoel enrea ata ammo nie canes Oe 755 
Rules sor ustimating, Horse-pOwels. o ««i%a.eic aie: 7s eee ee GS 
Horse-pover Constants oc sina reac «© cereale Riese ac» eatin ee ae 756 
HUGPOLG OleL MN CICAUOLS sec ces a ce crete GT RR MERC RE TIT tacks od vel ets et oe 756 
fiableton Hmeino:Conptamtse cs .1. 5 4:k ses cnc ocs cnet neielah ie caus en sie Rarer eae 756 
ilo Draw, Clearance on-[ndicator-diagram. ... «. foe os ane ee 759 
To Draw Hyperbola Curve on Indicator-diagram.............-.--se- 759 
Theoretical Water Consumption... ... SEC as Fe: 760 
Meakage’ot Steamiyne 5 ce cseeuae 8 Lea eleie 0" ks ana eat eee 761 
Compound Engines, 
Advantages Of COMPOUDCIUE hes are weeds tone. cuss cea ei ee near 762 
Woolfand Receiver Types of Fingines.. ...... > -aideees sae ae eee 762 
Combined aigeram serra cee ee ee ee ee ce ee ee RS aes 764 
Proportions of Cylinders in Compound Engines: .....2...)....5¢4.-- 765 
HRECEIVET BDACE. core tree eee ere t a he mer Rees ea 766 
Hormula for Calculating. Work of steam... one ele ne ee eee 767 
Calculation of Diameters of Cylimders: thiaitt ..0c2 sakes eran eee 768 
(riple-expansion ngines*= 182s oo asec ueotae GL on eee aoe 769 
PROPOFUODE OL CYMMUETS, pee can co oe © son + tends gale ae 769 
Formule tor Proportionine Cylinderse. a2. ge. 2s tc eet ene ee 769 
Types of Three-stage Expansion Engines. ....................2000-- oe 
Sequence of Cranks.) asaya iow wise, che on cae Ee a ee ite 
Velocity Ofsteat phrouem Passages: over cet te] nar cee eee (GOs 
Quadruplesexpansion Hinrinds. Fo ce tee aie elena rare eee Eee Vi2 
Diameters of Cylinders of Marine Engines: 3... 1g ee -  eee tio 
Progress\in/Steam-encines Wee een .MeSbeseen ater ee 2 2 ails cle clea ime 
A Double-tandem Triple- -expansion ENING} 655; +65 oe Dee 773 
Principal Engines, World’s Columbian Exhibition, 1893 Ree AM yl eo 774 
Steam-engine Economy. 
Economie Performance of Steam-enginés:........ 2.02.) oe ee eee TO 
Feed-water Consumption of Different Types. .................00000- GUE 
Sizes and Calculated Performances of Vertical High-speed Engines..... 777 
Most conomicaliPointtor Gutcohiermere ene te en ne Mei te 
Type of Engine Used when E:xhaust-steam is used for Heating. ..:.... 780 
Comparison of Comnound and Single-cylinder Engines............... 780 
Two-cylinder and Three-cylinder Engines Lae Ieee Ps Sialic nnaiy: | 781 
HitectioL Waterin sveam-on ltincienGy. ss. ee ee ee 781 
Relative Commercial Economy of Compound and Triple-expansion 
A Daeg aCe A 4 5 Maurya alerts SUES Sli Se aR pre iE EMORY Oa) 781 
Hichest(/Hconomy of Pumping-engrines.’. <a) isk. os ae ee 782 
Steam Consumption of Engines with Superheated Steam............. 782 
Relative Economy of Engines under Vale Lokds #2 ee anne 784 
Ffficiency of Non-condensing Compound Engines................... 784 
Heonomy of Lngines under Varying Loads... 8... | behest eee 7&4 
Steam Consumption of WAIOUSI SIZES) ook cee ete en eee 785 
Steam Consumption imisSmall Engines: ...°).0.7,-5......- PRIA ay 786 
Steam Cansumptiomnt.Vanious speeds. 5.59) 62 ts ee ee 786 
Limitation or Encinesopeedre.. o. ts ck. fe ee ee ee (87 
Influence of tho Steamermckeue cleat vo Le 787 
Gounterbalancing Mintineste os. Cero. 0 nek ee en 788 
Preventing Vibrations of PRINCE amines ss tate) em 5 <a 789 
Hound ationgspMm beac Semen ti very... cnet. desea eee cae ee creche 78 
GCost.of Coal torSteam=powern:: .. ostinato... 22 ene Sone 789 
Storing Steambieat..) ewes... . ale to. , |, ec oe ae 789 


Cost of Steam=pOwer. . cee... « s « . <ceepErreNeeh «13.1 st Peers. lola 790 


CONTENTS. XX111 


Rotary Steam-engines, 


BURL LUC OIMOS baad valet twice ha 0e ties ene eke eres 4 eat ee ate walslaiein sated en COt 
Rotary Steam-engines.... oer e ese ee eee seeeere e@eeeseeseeceeeeeeoeeaee ae eoe 792 


Dimensions of Parts of Engines. 


Cylinder eveeee ee e@eeeoereer eG + SSSSSSSSSSSHSSHSSHSHHEHSSHOSF SHC HZOCESSHSSHEKBEHS 992 
Clearance of Piston Se a lais die’s "braid ieis(e bs slolale'6e Glelefecicis’eeihacla cle cateseeniaetidoe 
MinckResS Of CVIINGEIiiss ceslcos cise siscee secs tiscictvese fe oslo ces desler csdecntoe 
Cylinder Heads.. ee eee eee eee G+ SS eeSrs See eSseeeseeeoae eee eG+ Bev eese ee e#eeeeeae 994 
Cylinder-head Bolts eeece SCOe SOG Se2eSseeeeFeSeeeee SS SFCFSHESTSHSS SESS BESE EE 995 
TEHEVEISCON.. 06006: Salbiate aise sie/nle sl ele'e'e e'e vie'e\slsis clele'elnicia elke site a¥ iterslarere sie Mevelal deters 795 
Piston Packing-rings eeere Peter eseeetOCeoeeseeseees @eoeeeesee eee eeee Se ereree 796 
etrOte Ce IStOl-FOMgsclinsscisics Sia co's cael: wes oe cine setlawis cals santos tata sae eats 796 
Diameter of Piston-rodS.....s.+sse0seee: ced cecrcccecesetosecsccccseeces eet Gt 
Piston-rod Guides.... .... SARC BB BCIIC COCR DOC GC OOO DUCOOE SS Bap ceahe autotest 798 
The Connecting-rod...... Sols Sinccib.c Gia's bile Gese ae Sule siee eure Sattae Pee eT Ee CoD, 
Connecting-rod Ends........ aloe cctaistaidis via nlsuiok ciplacioinioe © he Co nals ace ole iain ot UO 
Tapered Connecting-rodS........ccscee.seee plata aieipialavotareys sla hia spsieisiers SB atone tell 
The Crank-pin.. sada cegutd soln siaisieis/aeiele eieisiaitele tekics oer elsiee Rivne 
Crosshead-pin or Wrist-pin... ADO OOCDOHUICS SHeCOONOONOGS OAS: IHOLGULOSODUG Doone Hele! 
he Crank-arm: ons 0.cc case a ck Rislsiefele's'<isie's o/s e's ale nie’s eicrelstdl e(elclsie Siicicie eel oie ciate 805 
The Shaft, Twisting Resistance. Ghigo ec edeae neces decalectos' sas clednve tole sth Go. RCS 
Resistance to BONING Yin ele ce camels ot se bicmee Oo lee cles scare tabides Me enTecea OOS 
Equivalent Twisting Moment... sine {ls aieiniclaree nte elaleelg cise se Pisleeisicied settle este OC 
Fly-wheel Shafts............. Mune dpisiets eagle vib piers giajele siete cased cuics senidess mous 
Length of Shaft-bearings...... Moeiacenit eislve daw. 
Crank-shafts with Centre- crank and Double- crank Arms’ siatelevelate lets eetsioe amOlics 
QOrank-shaft wlth two Cranks Coupled at 90°............sccceerco-cevceees O14 
Valve-stem or Valve-rod. Cece ee  eeeeerersrs  ovsesesenene e@rceeeoeetseee+e Seeee 815 
Size of Slot- link. SCR SSSCS SHOOT SEHSSHSSSSFHSSSSHSSeeSseeese See Fees geeee ©OG+ see 8S8ee 815 
SITES CEOCTILVIC. wes clcis tac e cigs o's aoc wie vie16 ceiele. ce ole is'« suilsleleiniecinie cisie steneletercersrs Age Kenic 
The Eccentric-rod. eee eee Soe SCHGOK FS SS ese CGEHH-~- SHSSSF HFSS SHOHSFZOCBSSHOCLBEEE 816 
Reversing-gear eee *#200¢ @+@ereee SOeeeors st See SeSeS OSGeo FeO seSGSeeeeGeeeeese +- ee e2a0 816 
foeine-frames Or- Ded-plates.. . 60 inns cavawtessssiecesesveces snane cers s'pce O1F 


Piyswheelss 


Weight of Fly-wheels.. eeevooee os SeeescseeseoSec eres OSes ees eeueseeoseeeees snes 817 
Centrifugal Force in Fly-wheels. ... Mavesecicor ces ese cebcalece rl ee ace eh eOU 
Arms of Fly-wheels and PulleyS........ccsccccccscccs cocccece + coeseces 820 
Diameters for VATlOUS Speeds eters sseess secs ceses sce tesesiece setcitees ces soo 
SErAins in thes RUNS sec csnecleklee coe ite helee cle Uae Sees neta ten De eeeue 
Thickness of RII PS Tae cae ee ee eee cre Oto ee Bote ree Seen atta ae @e@eeeoeeces 4 
A Wooden Rim Fly-wheel eee eee Seeder eeS+ SOs eeSeSoe*See ss 8898280680486 8808: 008 824 
Wire-wound Fly-wheels. (OOS SSHHSHOSSHSTCHSSSHHHSSCHRHCHHOHSST SEED H SESE SSHOC ESS TEES §24 


The Slide-valve. 


Definitions, Lap, Lead, CtC.. 0. @eeesetsaevet@uvoseere @erceee sees eeeeesee FOee S8ee 824 
Sweet’s Valve-diagram.... Maillsecenccet cadets te ences esse hacen ges eee OO 
Die ZCuNer ValVe=sGIALTAN sc. vibesececcocescaclidccinarpiccccesecocteeeeere roel 
Port Opening. See eeetC ee See OF GOSSSFTSF SS FSHSHSSES*HO SBSH SESH FEE HEB Hi Be oe 828 

ead saereeeveese Seeeee rs SSCS eeee sO sess teseeeeseeeeeeeeeseese @eeeoeeees eeereeeees 829 
ARIE Leads. coke Jos. oes sect ten en, cndocanoncidbe oasis ld 29 
Ratio of Lap and of Port- -opening to Valve-travel........ Noe vidas ene ere OOD 
Crank Angles for Connecting-rods of Different Lengths............-....- 830 
Relative Motions of Crosshead and Crank............... ..ssccccccees sennoal 
Periods of Admission or Cut-off for Various Laps and Travels........... 831 
Diagram for Port-opening, Cut-off, and Lap....... 1. cosceeosece seeews os 832 
Piston- valves eseeeeeorvreeee vere 828 eee COC eSeSCSeSeeeeseSSese es seeSeSeee sees Geseteoce 834 
Setting the Valves of an Engine. COS. SOESSSH SESS HSS SSSECSSSSSFGSseees FOr eo 834 
To put an Engine 0m its Centro... ssccssescee. coccscccccscoccoecccsceeces O34 
Link- MOlOUs occu, coecwaeeen @eee eeseeeseseoeee Seeeeeesee SOSeoOseeseesee eo. O880 834 


Governors, 


Pendulum or Fly-ball Governors....... eins Tale ais «0 < eje.e tajelaea 5.6 Seen OEE 
No Chanee the! Speed of an sbineine. en wae iclniinisiscc «+ « o2.cfreits o alele aie ns as OO 
Jiivewheelorioualt. GOVGROle mas. .c 2 stein ctvela’s » © -sunuseavouers aie enters) oi 838 
Calculation of Springs for Shaft-governors....,,....,.++ Soe CSE: 





XXIV CONTENTS. 


Condensers, Air=-pumps, Circulating-pumps, ete, 


PAGH 
Phe Jet) Comdenserngs be aoten dice WA wale oe Rie 8 hod ekg ee ee 839 
Tlector: Cond enReUs. tnc) 1b Hal F Muntechis ele Grand 4 Hh vee eS Le ee 840 
ihhe Surface Gondenser: yar Ml oak oo dec ee eee 840 
Condenser Dubess: Wate. Aa Pad © 0d Rae, 7 oc ee ae 840 
MMe Dlatesse sane ioe ete > cascals beeen teases ale Popa ey se Cae Rae ae 841 
ShacingiofeCUbes, cheb oe to. ysuceron diet tw io ge us sates > Cae eee rene 841 
Quantity or Cooling (Water... 2 oo le atlas es eee) ope cel a Mae eae 841 
PAST = IULTIA PS AS Sis li Hac oslt RB Blea GN gy Belge, ay Bhatti was sk casi Lava Se ct ee 841 
veathrougn V alVve-sea. Soe ccc we cutee uc pledeceais kis anna One ane 842 
Citcul aby e =p UM Dis: ca (fast tes bck fae EUS Catan DP eee 843 
Pred-pumpeton Marine Hnpines': 2 cco. a:b. ou esas clas Ae eee mn 843 
An Evaporative purtace: Condensers... a5. oc cae es cee 844. 
Continuous, Use.at Condensing Water!.. ........ 5... -eneey seis ee 844 
imereace of bower by Condensers, . 6). 0) tt to oe, eee 846 
Piyaporators and Wistilers, 2c.) visaa viv cs duns gl eaue re oR a eee 847 

GAS, PETROLEUM, AND HOT-AIR ENGINES. 
CHASZOMOINIOS. KH ey ECS Fa de hae ENCE OEE BG Ute Ge He tee tA 847 
ificiency. of the Gas-engines «Kane ainpssaves waecasecdsr we cosh enn is een eee 848 
Testsiok thewwimplex Ga@s-en@ines tvs acy aces a 6 seers AO EE. Oe ae eee 848 
(APS 9 02H 2 P> MQS-OR PINE yrs nes oe cot boar ee Us it one 4 3sch neck nik EE 848 
ash of an Otto: Gas-eneine.«rk ciao. y Hhkoe ve dina bateben reer boo) RRO 849 
‘Temperatures and. Pressures: Developeds wis. 1sne cscs beds th bh dadeks 849 
Test of the Clerk Gas-engine: sities ia pen eie REINO. BON OF, Oe 849 
Combustion of the Gas in the Otto Engine......... 00.00.00 0.0 0. eee 849 
Use of Carburetted Airin Gas-engines, .01.. foe DIN 849 
‘The Otto Gasoline-eneihne: Se Hi Pept, 2. Ree ee ee 850 
ihe Priestman, Petroleum-engince’:. 22 fie? Bye ek a 850 
Test'of a 5-H.P.. Priestman Petroletim-engine)..... 274071" ¢ oe ee 850 
Naphtha-engines: 6257971 h-crtah tse. tangents Penenne eee man dae 851 
Hottaicor Caloric ~Hing@ines: drag ones nese b.tad ohh. Ft ocwee Oke Ae Hee 851 
Test of a Hot-aireHnginel dhs we Pk thawed oa 4 ep ene ante Dele Pee 851 
LOCOMOTIVES. 
IRESIStANCCIOLE LRALEGH I pemet e eta ete Hee eee ar ne eLearn 851 
Inertia and Resistance at Increasing Speeds. ..................0-00. 853 
Efficiency of the Mechanism of a Locomotive. .........¢.00000stesee 854 
SIV esOL OCOMOUY Cr IL GELS. visvcs, 5m oe eaten I Geko eee 855 
Size.of, LOCOMOtIVE BOerS ce ace poi re ccc. opuisd Fast Poona ie aca cee 855 
Qualities Essential for a Free-steaming Locomotive. ......... Me ere ne fe 855 
WMG OELEN S iOCOMOR VG scales vk wpeties Mince sete, uius cue er en OR ee eee $55 
Grate-surface, Smokestacks, and Exhaust-nozzles for Locomotives .... 856 
xc hast. N OZ Zles iid ta oe Bee ie ors hie Ane da ho) Wie rea a BN ne as 856 
Pire-briekvA TCHS in. e.atw ko tok neil cel nets a as oe ls, <a OIG ER 857 
Size.sweleht.pbeactiveseOwerrehe: saa ane peat 7 ee eee aah ota. cee eee 857 
heading American. Dy pesst ee meet MOP ARPA APNE. 5c co. Gleee Se ane cae 858 
Steam Distribution for High) Speed. ...00. ise epee see Fs agent Oe 858 
SpeedotRailway cL rainss pra.y. spare case eee See ain eres ee ae 859 
MOTI ee tOn GuIVesSs oh eae Pee ae oe Hei crit eat enciirticngl ae, ee ae ee 859a 
Performance of a High-speed Locomotive. ...............--4. Henne, SO9G 
Wocomotiveuink-moOtions esta.) 5 Seo. 2 lick Lee ae 859a 
Dimensions of Some American Locomotives. ............-2eeeee 859-862 
indicated«WiaterConsump tloniediven hat, debated le sins cpa is, Diet eceemieee ae Soe 
locomotive Lestine A ppardtusins 2 aac eeiks pee mae alee 863 
Waaste:of uel in esocOMmotives sis. abe alee. bockaci einen dee eee in EE cade 863 
Advantages of Compotindings. oi), sa Ado eben 6 lowe ae py he Be Bs 863 
Gounterbalancing Wocomotives.¢a.: Giles bieiwsis > sare al sidpsid ae ape 864 
MaxamiuimioatevloaGeon Staci allais cumini .: «5. <ieimsstesccbacioie Ren erneee 865 
Wartow-rauce Riatlway.s..).,. ei ebues + al tle teh Meg. nreeiaath selene 865 
Petroleum -burning Tacomotivessdees. « <4 sel heel ganatecdneae 865 
irelessuOCO mM ObIVGSMmieiess.. «i cacuc Bese cw: celbua oe bedrus Sue Ree 866 
SHAEFTING. 

Diametersito Resist, Torsional Strain. eae... ... cs owispeieepie cles ej 867 
Metectionmrabattine wae a2. lets Aeimeeet. |; ocdcs ier fetereten mia eiaptes tee tenet 868 
Horse-jowerl ransinittedsuy Slattingwer...... sss sis snumete cin se pemee 869 


Table for Laying Out Shafting...... SAPs c yiisns ie tee HR TORE Te CAS TOe, ¢ atten AL 


CONTENTS. XXV 


PULLEYS. 
PAGE 
EMPOLONS Or Pulleyes eee Ves oe AUPE SS ORE Oe GEE Se oe 873 
Gonvexity of ulleyersa ioe se ore ee i eg See ek eens Pee 874 
Gone or Step Pulleysss's cag ee er re re PR EE rete ares 874 
BELTING, 
EMIT YO SSCL MALE SEN) Gog «os <0, 2 seinraspan ane, Seca sucks thsi ct ART whe ee toesn oe ee 876 
GTM cL CLSIOM epee Senses te cee care ort eee ee ere ete enate ene etna eee 876 
Relting s>ractice, ob ormuls lor Beltmgi ge. 6. aod. oe eat os cee eee 877 
Morse-po wer Ol a Deljconennen. widen. yee c.. che 6 cis cate eres ea ee 878 
MME ele Sen ObiiU lates) ose eal eee Ae ect an ete ee oe ie ee ene 878 
Width GL belt Lor Given it OLSe-DOWEL «6 .ccs so nue oo een eee 879 
aatlor Sei Ul eceL@ rem ClUING 4. sg a etn cies ec ai tat olccla,, SRO one Eti a eee 880 
EES TON ISELT IE Pat cet ty Ree PCa) SAARI ee eet rec an sae pce ee een ene 882 
ACI OLOLA CUS twtr re eae ce haere hie the cae ceil e or tee The ene 883 
Settine 1 belt on QUuarter-fwashnent ous Piyeberend Geyeh tac oe ee 883 
apincoplie Ween oLnuOl Gel Goss aceo. tev ete: ie osu eg oon a Emenee eis 884 
oe eincduuheaAmele Of the Are of Contucue nt. 50. ti ite oe ee 884 
Womindihe Veneta of Belt when Closely Rolled 2.710. oa ee 884 
o,sund the Approximate Weipht of, Belts!) o 3s... eu ee ee ee 884 
Relations of the Size and Speeds of Driving and Driven Pulleys...... 884 
TG Elec ahd Bathe ay el bs Yo) iicte iy ees ne pe ial ala a CTR See MER MEMBER Lr. oe gl 4 885 
Sioere foil aya Us: is see RS Gee eR ee eRMRT. Gre rem a SPMMeedo dae Aig cat 885 
Arrangements Olebelts ana. billets... taste ne sn cae eee te ee 885 
Care of Belts..... MS Ss oy OR, GALL RENE 2s aM aie tea Im Burm ak: ye 886 
Berne Leo imIrShulMOer wee tank oie wives 5 oo soak hoe he Ae nL ee ee Lee 886 
Burpsion, 1ugependent,o. Digmeéter... see. o0 hoes. Pie eee 886 
CRC GIS EES CLES ate na ty rue teekeainns Soe UO ee. Riis ee eee ae eee 886 
lees CB ENR ee CHR ee eee a PCE meee ne ieee Pelee aun, 886 
level hme Byw cilavee. SARE enka ae CAAT ® Rete cto One Es comeeeeMee cv skareae Pein Mis ce 887 
Comment Lol OloeneOly ViGaAUNera. i |: oc ches ekeuek. an Cee kaon teen ot pee 887 
TRY DID) at ey pid Brey Fb sca oh co os Ble ea a ee ee OEE han ae ANA ok rd ee . 887 
GEARING. 
iptéel ertch=circle:, CG s, 5-3. chase CRE Oe Oils ole cae cts Mn rt ees 887 
Migmettal anc Circular Pitch... 3. ante eiestel lice ink ear aoa rca 888 
B@hordal (Picci wes etc cs oo ss Gn SARELEE ST SRE DS ER Sei gain iea pede oie cde 889 
Diameter of Pitch-line of Wheels from 10 to 100 Teeth.............. 889 
Proportions of Teeth... a... <5». melee ealtigaes F stewere)} ai 1 hae ene es 8389 
IPLODOTMOm Of (Gearawheblacivy ack wet b ache conO TRIMS oben ee 891 
AR EB coy a RC St ol Be pe ee Om a PS Sa” i Sg a rE Tl ink a Pa A eta 891 
Rules for Calculating the Speed of Gears and Paberaemiyr str. cccae ste oe 891 
Milling Cutters for Interchangeable Gears. ............00.s ces euees 892 
Forms of the Teeth. 
PEI ClO al EL OOCH. cite Lan eet eee ROR nee Mat ae eC te cae iat 892 
NOELIA VOlUte cL OCU cia oe etn Ce PROC ES coe ee ates 894 
Mpprosimiation by, Circularganceizett. 2 eee Peon nse ool 896 
Stem Ded GGATSE swetan cet ace cies ae CGC ee Re SR MRE ES cee hone ene eee 897 
PE WISLOC: LL GGULioe at ee, Ht haart alee il Menten GRO Ue te, OS. aN eae mee 897 
Sora lV Gearg eran. ores et ere Le te AAP en E.'s gic tne a ane 897 
WyWerm Gearing: Ski Rice Whee enchant NED ERG) osc eke Pe, 897 
Meeth of Bewelowheelss. tx: : cent alae eee Aten ed blak eh es ... 898 
Annular and Differential Gearing. Jic.cw weet ae Apiiie fia es be be ae 898 
EANGLENCY, Of GEALiTi Gein wc ieee Ae AAT AED NG Rie a. Ok blo ota Te ea UIENE 899 
Strength of Gear Teeth. 
Warious, HOLIMULe TOL StLChe ull eee eee tee ee tk ee 900 
Wo Parison: OL Lona la, ape eeiti iGe whe eeshontic tsa eek clk & AC AER RRR 903 
W Chtecusbieyl ey care Wme WME rarcnyravery. 6.58 SANs Geet Se ROMO ELALA Ft eae 905 
A Heavy Machine-cut Spur-gear..... Lois BED Se RU Soe ais bik 905 
ig egekcpor dL Cretan ive we oe ae Ln. io: AGN Gt yh GL Ee haere: vc. = 905 
Pie tioMstiksTOOVEGd GOBLIN Gee aee ts c+s1cieheree nA tHE ee ii. da hiRO a tee 906 
HOISTING. 
Weirhtand strength of mud awe, <0. cee tently \.-. 1 1 ARERR) ePaper a 906 


Working morength of Blocks... oi). cs Mieie las’ » « ecdheidarpetlia aus WhRRes ane 906 


Xxvi CONTENTS. 


PAGE 
Piiciency, ots Chain=DlLOcks...temekciec lie a oe Scie kieran ener rch te 907 
Proportions of: Hooks! so °.4.085 0S are, mists, ies oe ne Ce ee 907 
POweroL ELOIsting) HMGINes wlin-6 yess eee ete eeek ne hs Gren ne eT en Petre ee 908 
itech olislacks ROpe On) Strain! in, Hoisting: :. 2 2 ee ee eee ee 908 
LimitrofiDepthtior Hoistinas.k ke cee ee on Sens Eee eee ee 908 
large Hoisting =Records sc 0). a eee at Oe Se ee ee eee 908 
PHeumatic! HOw tng a dle eee owes oA sep tela i eo, 0s tne pee ee eee 909 
Counterbalancing’ of Winding-enginesti. > 5 2.505... soe eee 909 

Cranes, 
Clagsificationvol Cranes oe oo oct as we nr ee cs ne ee eee 911 
Positioniot the Lnelined Brace im a ib Crane v1.) ob Leone eae eee 912 
ARO TOSUUrAVellIN-Granerme circ sak eocenitcn a iettievs ot ete bate eee 912 
Agl50=ton! Pillar Cramens asc. On, Joie cucee hens 4 lee eae eerie eho Nee ere 912 
Gompressed-air Travelling Cranés.ca.no. 4 chic Ree Ee 912 
Coal-handling Machinery. 
Weightiol Overhead Bing joc... oi: epee beh eek seh hea eee ae 912a 
Supply-pipes. from@Bins? 3: We yh ee: uu ccatras chelsea ah cna s ox eateen eee ene ae 912a 
‘Ryipes or Coaletilevatonsiectiestan oleae sab te thar ra Nec eee ne ere 912a 
Combinedthilevatorssand Conveyors © as ee aia ce oe ee eee 912a 
Coal: Convey onside js. acta elewsye oven get a tdtonc abi eisede econ rk ee eee ae eee 912a 
Werth tiGhsChain ee Br asak citi ietene etch erie eiciee she aie etait topo nae as 912b 
Wier: Of lili gh tai. 1e, cama ite cae wei e kee Soe cliee faeie ae Ae dan eee eer eee 912¢ 
lorse-power of ConveyOrssieus 5 Sati cite Seti aaees cals ener ste ae 912c 
Bucket (Con Vey Orseiaul ig. ee Chet Me GRMOR, Cea rine acai eo nee ae eae 912¢ 
DOLE w CONG yOLSasac eter suai ss at oc oie incl Sha aec teen eee 912d 
Belt Conveyors wise Baa cee tecehetes, srarotene ecoer yee ermine arene 912d 
Capacity, of belt COnVEYOTs spite cetecoseucmernlsyipectia aie suelo a iaete eee 912d 
Wire-rope Haulage. 
Self-actingsinclineds Plamen cen.s ck cts hcetare ay Tein e cheeeere eee eee 913 
SimplevEn gine; Plane 7.0 wes cto aite ctep eve reetee ke Nee eeliie ee uri ban, foe ee eee eee 913 
MP ail=rOpe SV StEIAs.cnces sed lec le eho SaeRer ed Se nea Ice elon votes ci neat Rises eae 913 
rid less ROP hS ySteU.t. versie ons ee 6 aiexe a) alist fe" (even: Oe sre alien aieaticey eee ee 914 
Wire-rope: Tram waves of eer eeNee seis eee bee eo ee Seotane he, Cnet eee 914 
Suspension Cableways and Cable Hoists: 214.203!) 050225). ue ae 915 
Stress in Hoisting-ropes on Inclined Planes..................-..020. 915 
Tension Required to Prevent Wire Slipping on Drums............... 916 
‘Paper Ropes OL Unitorm,Lensile! Strength. =. oe. <i een 916 
Effect of Various Sized Drums on the Life of Wire Ropes............ 917 
WIRE-ROPE TRANSMISSION, 
MIAStICnLaMit Of) Wile LLvODOSs. sisycreis.ewiare ors che cromenete ee tail vec eae ee 917 
Bending Stresses of Wire, Roped’. mi). fe. tee.) os ee ee eee 918 
PlOrse-DO Wer Le ransmatted> se secs c ils ein a Cork elec ier ities ee ee ee ee ee 919 
Diametersron WWaimMmMuUni Mea vessecens ome cect arecchemie cite ene an 919 
Dellechions Of the Rope 02% scans +=» o's kno oh> «lp 5 steer aurea oor 920 
one-distance.s Lransmissin cw. <p sate chean a ete ss eeee rote elena ORR te 921 
ROPE DRIVING. 
Formule for Rope Driving. o.5, ssicesseeuens + <> +r sbi eae 922 
Horse-power of Transmission at Various Speeds. .............seee-- 924 
Sac.of, the Rope, between Pulleys. ).) .cemene | / chen nie ee 925 
(hension: om the slack, Part’ of, the Riopen.e eee... ...ce ake Pann eee 925 
Miscellaneous Netesion .Ropesdriving seem... «ic oe ogueien iene eine 926 
FRICTION AND LUBRICATION. 

@oeihcrent Of HrictlOmey suc, «os aos dake le ko «cs 2 Oe ete aera 928 
OUI SL TICTIONas ibe toie = c.6%> « « oc atete eee on sass si EUR nied a: 928 
ESEIGUIODLOL SOLIGS., neletetel. bs + avaue ce ie eeeede leks vs SUS RS dale Le rea 928 
PUCTIONSOUUINESL. cn ce ERG wc  o OE REI noe's 6 0 Risdon aoe neve de 928 
awe ot wimiubricated smaetion® fs hieuseire s,s 5 cae ee eS ee 928 
BrictionsormelidineSteelalires. ..; s. eee ows <a leone eran <n 928 
@oefficienttorm Rolling’ Bretion: 32... teaere. . .. .. s, Ldbeabeuieieee cas ty crane 929 
Wawerot meh rictionpemtey sd. «07 coke eetaes | )ccckc ld Ateneo bss aaa 929 


Angles of Repose, . . aah gine-t vy: scapes fof eR Eos eae 


CONTENTS. xxvil 


PAGE 
rrevion oF Motion ys oy a v4 Go cs be ese nek eee ee 929 
@heticient of Hriction of. Journals... sess nee Ae eee ee 930 
Ex pornnentsson PricwOon Of a JOULNAlL «a8 oe ete re eee ee 931 
Coefficients of Friction of Journal with Oil Bath.................... 932 
Coehicients of. Hriction of Motionvand of WREStlL ...... 0k eee bee. 932 
Dette OLA t-iriction WMetalsaite. mel erie ek hee hee RD Ra 932 
ME Staron tOk Dearingse ce coi diet oe ee ae Nene ee a eae 933 
Mmction of Metal Under: Steam-pressure......../. . +d) eh thieine-clew seks 933 
Birnie S LAWS. OL ETICEIOMGS cvete: ce sack Gite ie Ree Seta eee 933 
Laws of Friction of well-lubricated Journals. ...............2020e0: 934 
Millowable Pressures on Bearing-surfaces ojo... oe ee os oe ow olin oe 935 
Mil Mressuresine ae Bearing wie es Ee Ot oe ene ete chee ee 937 
imrction of. Car-journalsBrassesa. fice sateme cicmnsi ean nclaacclc ce oa 937 
Peaperments onjOverheatine of Bearings. bis. .05. os. aeamee aie ee 938 
MOMment Of Mme tloneannd, WiOlkiOl Mrlctlol i mes ic tren caer eee 938 
BIOS SCATIN OSS «teenie ae kets ee ore Shire eee eee eT eh ten a eS 939 
ier scnicle: Curves. mas oer ete tie Lee oe ee ne 939 
Pretion Olay lat Pivots bearinies 0,21, tana ey tt ten ek eee ee 939 
Mereury-DathiretviOuspectsits cures eete sal clr ree, a en ee eats ere 940 
JB OIDL AIRY SS Woh a ea: Paka epee soning nr i pel shetty hye ak apiece Vowel MCN ly Wi IN MR eA pa 940 
CUO FLOUErS set ort cee RR ee aeaney eer tee OM aR HLTA RS oTY rae ne 940 
Bearings for Very High Rotative eve Be ea en sey ns ERNMENT ah oe i 941 
Friction of Steam-engines ERS ee RCPS alc RE Lara ee na tetas Cea ame ae a 941 
Misiriomiion On Lele ricton OL Minoimesm. ss) ise at eet eee 941 
Lubrication. 
PUPA DLityFOLMeUDTIC ATM bS: factors © 5.4 ea sen teehee eae che SEE 942 
Maliiica tons OfPLATDTICANGS. ween imes Mee tet tcitie aoeese ce eee a sae eo 943 
ATHOuUnt OLO1 COmrun all Lunpiniese sents ae ete eerie aeteton herent 943 
[Reeth CLOTH Ola) LIS) ror ek NE bie ae weiner Nuns br Geen act Ly hme eee 943 
Bernawhie bes SO MeChICA LIONS. re ct cs niet a tee cet te eke ee eee 944 
SoraeMixturestoreMachine: Loos. . jcscucedeneo sea eee Pe ee ete 945 
Solid Lubricants...... ava 9,cu) ARBs) ata a co Val eeeaanaeebsmenazaLsel ohpp ey aaa DP ae, ae Aa 945 
Graphite, Soapstone, Fibre-graphite, Metaline...................... 945 
THE FOUNDRY. 
GiipolayP ra ctiGe.nsienskus de tichetos as eee eke Mn ea aka ean bre si gedecee ei ees 946 
Charging a Cupola SoekG- RNG ES ath PREMADE SR POTN, RE eek Oe MUM On nee as 948 
Ghargestin Stove) Houndries. i444. sere kee han neta eet ani 949 
iesults-ol Increased: Drivin gion. oa. os fine hha hes hee es reece 949° 
Fariess Gee DO WEESsi sete. i crdns ea tstenencanie iestoae ar ee) sane eA EEN Ae Re 950 
ossr Ore Eron 11 MiGltimg: ve ae nner Aaa Aone Saag cteee eh tee pe Rae 950 
ENOL OOLLOMELS. Coase ace tia tire Ate elena ation sae torenet er cee Sodan e ss tana TREN Se 950 
Surimicage, Of Cagtings. «4st. kalales tess neha ie eeu PaLany 951 
Wereht of Castings irom Clehy Ole ater memantine pendence ox scien 952 
Mouldune Gandecn. «tecccede ce Oe one toe eR eeaaS SEEN ae hat 952 
Maundy, Uadlesis 8 sts ick are TA CeaC INCE. Se inicve nt Ae Sc cicipr ae ne 952 
THE MACHINE SHOP. 
Sneed of Cutting. Tools: .2/7.. 5. 0i0e a. eae RTOS Sree 953 
able of Cutting. Speedsy, 25 o> xanga nee TOs 6 IL WEE 954 
Speed ofan urret) Mathes! saat alice nie etseote oterer vances a ates e chi te, Pan ONE 954 
Ors: Oh Cube gel OGls i. 5.<, sect yes tae or hater oie hans Ste Lei.) . Sten ae 955 
inwe for.Gearing, Lathes. $41.) me Weateaes. eatin & cada of) bi.. Hl pe ee 955 
Change-cears: for Lathes. 2 e-iomnise kis eles fans ils ii? )41. Se nel 956 
iMotric Screws threads. ss v\.< aie eens <5 etek EY Wins oN. OD 956 
Netting hen Ranersneaplia tery eke metre euetete nai. ccs S<, 900) sho ate tenets 956 
Speed. of (Drilling vELoleass tyes eae tae ARCS A aes, et RAT 956 
Speed otelwist=crilistaoe «nn dees arom Eas oe. oo ik eee 957 
Malina: CriGt@ess. i sabe bet amet anne ey Mes ce uae a Suans. «/ < o's ap aiaaualalen eae 957 
Speedo; ut LETS... sua. bee rene Cr tei e Wetec area Sich asics tof -ni(e; ohietspenenegeD acme 958 
esultsewith Milling ome himeseme ses wien eo ae iniiele + >.> sex hound yahewabe 959 
Millingeyathsor Arainsteteecerrds son ccetaereilsctilae & ais = or gods tees ah eee 960 
Millingonmdehine vs: \Planeraeemee ts /0ceeeENers cela << + +o gas no he ieee 960 
Power Required for Machinewlools,:. cebu asbides cf) «oes eve coe eee 960 
HesviveViorki om 4. Pla ncimppeis. co 5 ewe ic...) - > sos augalcee 9.0 <ka nent 960 


Elorse-powersto. run) Lathesaerncet cae armenia: . . -'s viimche + «eae, 961 


RxXV111 CONTENTS. 


PAGE 

Power used by Machine Toolss; ccaach sda oa os oa tity ee tae 963 
Power Required.to Drive Machinery. .,, ja¢a1q0) de. noise deniers 964 
Power used in Machine-shops....-.... geernah ay ba fe De, Ga 965 

Abrasive Processes. 
The Cold Saw ests) vad. shleot ea ees 2 SOP ea ee 966 
Reese’ sii usinge-diskey iy Peewee ese eS ee se here ee ee ee eee 966 
Citting’ Stone with Wires fess Oa are Pees eo ne ee 966 
The: Sand-blastsa’s ss iis ses 3) Fed. war nex: ke eee ee ee eee 966 
Prmiery—wheelee etd ia see es can UE Meee ee Cae Ee ELLIE, a) ReOAS les 967-969 
Grindstone! s 6 nak vies ce oh ete ee BIS AO SOI aes 968-970 
Various Tools and Processes. 
‘aps tore Machine-screweit. cs. ous. lite gal ater SBCs oe ee as eee 970 
La MOTUS Se ween ous one ecehae aie chs Cotuann te tie None See acheT SEN pen oe ote nae ba 971 
‘Raper Bolts,.Ping,: Reammers},0bCsi.s mas sn aes cite ele tec cuciertacceta a 972 
Punches, Dies, PRESBOS. ie ous ke he ee. es henna EL eS Oe eee 972 
Clearance Between. unc and ‘Dien: ite. nee one eees, nee 972 
Size ot Blanks tor Drawittl-press.)..tc) 20 oe hc etc ce eens eee 973 
Bressure Of LT OD=PleSsac te euis aie eee oe eee PTA een eee 973 
BG Of IVE CEAIS. het carte oe Se rete sires ete Rare ib on ran teen in ee Ata 973 
PIIBCLIT IGANG SMT ITC SEL UGG ue tas ere te ocenets cn orca e tei aaa ane tae Re 973 
Efficiency Ol Sere wee ee ae cee ce eee tee rye pen 974 
POWELL SI OCLEWeUNLe ain: core. ci een RUT cus eit ee cna nee ee 975 
Proportioning. Parts OL wLaclinernds Me gaan ice. 3s. sie ae ee 975 
Konsitor Geary eters ne a ORE Rae een, Oe td cee eh pene 975 
Holding=power Gt Set-stre waren anc. ccsde dete aos ee ene ee eee 977 
ELOIGING= DOWEL OL IVEY Sc het Ree a ete cele nees A bat Ae 978 
DYNAMOMETERS. 
Traction Dynamometersh.) 245.000. ..)s.dna tt cena send Geen ee eee 978 
RHEL PrOM yp Blakes i. 12d teu iebine ovine Sotusuieuele eosalieurdutoe Siok ao eee 978 
ithe-Alden.-Dynamometer: @:c qamiiaee .cuiic ee kk ce DE oe 979 
Ganacity. of Hiaction=brakes tn © 5 eh teeny otk ee 980 
‘Lransmission dl) ynamometerss gatas Sook, eae ao coe Ce ean ees 980 
ICK MAKING OR REFRIGERATING MACHINES. 
“Operations of a) Refrigerator=machine:;:..... 0) see ate eee ecn ae 981 
“Pressures, etc:,/oF Available Liquids... /04-i000 02) 00 J tee eon. fan 982. 
Tce-melting Piffecteas Ser Ras Setar a, coe ee Cc a ae 983 
PL her=maehines.. 1) h.cl ener i, teeth | eta h ham GAciet hah ae Sela a eek ee Meee 983 
ATT MACHINES ares eo eke tee a a Mo ealntetohe ehcletahatal tbe latetetanenee ahi tee eaene eee 983 
Ammonia Oompression=machines; ‘a. </)... ...4 0 Fe eo de oe eee 983 
Ammonia A bsorption-machiness ..') 6 2. ae ae nf ae, mead ee eee 984 
Sulphur-dioxide: Machines. 20 5.\.fn. 00 os Stet var fal atta ol diate eaten ae 985 
Performance of Ammonia Compression-machines. .........eeeeeeeee 986 
Economy of Ammonia Compression-machines.. ..,....... save avettotaueteneee 987 
Machines: Usinge Vapor of Waters f¢ = Se tare. cake heen eee 988 
ficiency of, a Refrigerating-machine, .. s.c..5- ..-. alah. eae ae 988 
est Trialsof Refrizerating-machines; . 5.1. s,. « . vtineenien. Me area ae oe 990 
Mem perature Ra Ne «i aecyesa tus, dcotoss yeep svtbebenebarel eis os nc SESE ee tek ae 991 
Metering ther Ammonia. i. oo. cay wl or dese oa se ED a? See 992 
Properties of Sulphur Dioxide and Ammonia Gas...,.....0s000.% bubs 992 
Properties of Brine used to absorb Refrigerating Effect.............. 994 
Ghloride-of-calermmm Solutions cea aids si eas a << oe ee eee 994 
Actual Performances of Refrigerating Machines. 

Performance of a 75-ton Refrigerating-machine................- 994, 998 
Grlinder-heatingsioeses 1) oe eb ee oa. s soar bare tue peer wes aOOT 
Tests of Ammonia Absorption=machine, ..+....ids<e<ceen nts es mere a tHe 
Ammonia Compression-machine, Results of Tests..........+eeeeeee- 999 
Means toreA pplying therCold; :.4.% sewneen «3 2 Oe ee 999 


Artificial _ Icesmanufacture. 
Test of the New York Hygeia Ice-making Plant. .................. 1000 


CONTENTS, XXIE 


MARINE ENGINEERING. 


ae PAGE 
Rules for Measuring Dimensions and Obtaining Tonnage of Vesséls.. 1001 
ive Displacement ofaeVesselus) Jlitoih. dhe ttill Se.wdpepiosiiG Tae 1001 


RpeICLEIIG OF FUMIO OOSE 0), ie, aul chat pct: esearch circus aE AAG tal ROLE ER 1002 
feweritcient: of Water-linesiit loin sit OR ee Oh ae Bee a ee 1002 
RESET COOL AS TIS ey aie Mic cp Reed ah bs sel Soa RA any Pete eee sack eee 1002 
auticient-of Performance of ‘Vesselss. Wo 32 Gac). ted Sei. Sd ee 1003 
Defects of the Common Formula for Resistance. ..............:+<. 1003 
emkine Sb OrMmulas seme ne URN ae ote ee Be OR cic Sa aeee GO adie 1003 
SRP ee SENT Ct OCs epee Sede nots Uae 2 datas come io ee 1004 | 
ihownd-the |.H.P. from the Wetted Surface. tig. 0.4 blloeeG en: 1005 
ieee Mum LOrgise Method ie cn finer Steet eitrieat: see EReEChSebee Eviite)s bee Grea 1006 
Relative Horse-power required for different Speeds of Vessels........ 1006 
Resistance per Horse-power for different Speeds. .................. 1006 
Results of Trials of Steam-vessels of Various Sizes................. L007 
Ppecadkon Canale. Ati. faa nds 6 sce od ie oe A neocibaeee b 1008 
Results of Progressive Speed-trials in Typical Vessels............... 1008 
Estimated Displacement, Horse-power, etc., of Steam-vessels of Various 

SIZES aut sere POW RIO. CU Some te Nivedita rye ke oa igh cnn 1009 

The Screw-propeller, 
MEZO COLD CLOW cote fice oie) c hete cela ted Ee Ee te ee RE See 1010 
ieropeller Cocihcients.: psd Ith ahead OO eee ok 1011 
PeClenGy Ol bie ELODCH Orig. bn 5.) oly cusetes ete sieht,» cate EP Ree 1012 
Piteh-ratio and Slip for Screws of Standard Form.................. 1012 
OES ST Ole LVCCENt ELCSCAT CHES otc. ac scene Paice 0 ones See en ara aches 1013 
Whe Paddlie-wheel. 
addle-wheel with Radial Moats. seis aeons ee on ieeisel, lah cles 1013 
Heachering caddie-wheels. 2. . 4s fa .c.sce ee EEL cee een, See 1013 
meanciency of Paddle=wheels. ai: jeueesase as ee eee eek. ees oe 1014 
Jet-propulsion, 
HNeACULOly Ola LOt ww amie. sk ee arose sore Oe ee eee Rhee ee Re ee 1015 
Recent Practice in Marine Engines. 

STOO METAS temps ae ike aia a OA IR rece MeN ans cpt eh ge ea 1015 
SGT CTs ye Re has te, RN ee Re tens elt. 5 ain ce ay Be 1015 
Bea V IVES. © Sites cree Bis reg cities wiidy. | Poured oes «lee 1016 
RPESNECET HGS. ho ee ae nd me GOR eee pee da a ae epee AOL 
Auxiliary Supply of Fresh-water Evaporators. ..............3-+04- 1016 
Wieirs*biecd=water Shea tele wets on yeti enone s Neen Cele ie. hu dua Fe peas 
Passenger Steamers fitted with “I'win-serews..0.....00.05.5..2.5... 1017 
Comparative Results of Working of Marine-engine, 1872, 1881, and 

PROMS cece oie a wie esen ECO Ce eee eer oe REEL oe eA Coed ere: 38) Eig Fae AP th i 1017 
Weight of Three-stage Expansion-engines. . 00°). 6 0. ek ce ee ld 1017 
Particulars of Three-stage Expansion-engines...................5.:. 1018 

CONSTRUCTION OF BUILDINGS. 
Walls of Warehouses, Stores, Factories, and Stables ............... 1019 
Strength of Floors, Roofs, and Supports Serco lni cde, Se oe ay a 1019 
Wolumns) and) POSts: i + cuisuwus se a et | BE een La 1019, 1022 
Birenroal Billdingss oy eee ke eee ee ae cts 3 cA Be 1020 
i EP naQa lpr tines) on COT MUDOOURICE Cem Bah le SU ale CG 5 i Se eM Bo eh 1029 
fantels, Bearings, and, Supports. ...5.......0. es on? 1020 
DELAINS Ol GGAirGders ANC Mind VALS te eee Rat REEL Sush 0 Dock: A) ewe 1020 
WMaximum Load on Floors.........................-000 00) 1021 
Strenethiof FlOONs.) 2 Pee. fe ile sl ee 1021 
Safe Distributed Loads on Southern- TUG HMDS OANIG ters hhc <ids, .otbits cReneeauca 1023 
ELECTRICAL ENGINEERING. 

ions. S: weyetem of PhysicaliMeaspremente ee 1024 
Practical Units used in Electrical Calculations. .................... 1024 
Pica iOusnieyariOus  ODiMGen t.ho ee”. ota Se SUR Sita 1025 
Equivalent Electrical and Mechanical Units....................00- 1026 


Analogies between Flow of Water and Electricity. ................. 1027 


XXX CONTENTS. 


Electrical Resistanee. 


PAGE 
Laws: ofblectrical* Resistance! s'i0.70 1.2 Tem ot ea eee 1027 
Electrical Conductivity of Different Metals and Alloys.............. 1028 
Conductors and: Insulatorspe oases tices ee 1028 
Resistance Varies with Temperature... <2... ...... dues se ee ee eee 1028 
ATIC ATTNT A otal, vo ce ves Soni nce hte eller a heace cath ev cote e dee ce aa A ae a 1029 
Standard ot Kesistance of Copper Wirelsces. 92 ane ee eee 1029 

Direct Electric Currents, 
DN? SLE Weis uated Fe ea sae adhe ae Sat eMC Be ne Neos at Ae A 1029 
Series and-Parallel’or Multiple 'Circuits.<2+7 990", A Ge or ee, ee 1030 
Resistance of Conductors in Series and Parallel.................... 1030 
internal: Resistance? Am stan ee a te ed ee he ec 1031 
Electrical, Indicated, and Brake Horse-power.. ................... 1031 
Power of the Circuits ..+ eies Me. be Rene), eee ee 1031 
Heat: Generatedib yrakCurrentsy cn eotesce ca) oo ceeees aed eI ee ae 1031 
Heating of. Conductorsaeye se Aes 2. Se nyt Oi eee ee ee 1022 
EOUSIODNOL HWirese eee CE Ee) Sears OTE RPP eee eee eee 1032 
INWEP HA bateany ie Ofelia een eats Le card CRIA SMR soo DALE eae eet 1032 
Allowable Carrying Capacity of Copper. Wires. 30°07). -)2 jay ee 1033 
Underwriters?) Insulationtss shies Anemos ele ek ee te ene 1033 
Copperawires Pa bleree yseecna spo < wuneneee sean noha aes ecole sees ae 1034, 1038 
Electric Transmission, Direct Curcediat 
Section-of WiresRequired-tor a Givem Current...) 0 nee eee 1033 
Weight of Coppertor a'Given’ Power si... onus be eee qe: coe ee 1036 
SHOLESCIFCULIN ES See ey CR Ge che neo e ae ee cee 1036 
Hceonomy of Hlectric -lransmission css aa. fetes toe ie eee eee 1036 
Wire Table for 110, 220, 500, 1000, and 2900 vale Circuitss je oe eee 1037 
Efficiency of Long- distance. Transmission......................... 1038 
‘rablevot.Mleetrical: Horse-power8e, <0 ctu. cs 1... here ee ee 1039 
Cost of Copper for Long-distance Transmission. ..,........... a= L040 
Systems of Electrical Mistriputionss verse. et ee eae ee 1041 
Electric Lighting. 
PATOPLACHES. oS sate oem ee Nee smote Dal te Ree ee 1042 
Incandescent Warn Ps. pe Heyer a as Oe Ee. eee yee eee ee eee 1042 
Variation in'Candle-powerland, Lites ms). 14. hola Jeena e eee 1042 
Specifications for bampsesyih sy nacoe es Wack Slo eee ee 1043 
Speciale Lamps Aho ape eas aah dee he ectnlees Gesu eS OmeL rede Gee ee a 1043 
INemsti arin pis crete slat sealitete ose ca ae tilete oUt el eee ote Ln 1043 
Electric, Welding 05.56 ek ne oe tae oto eee ha eee es 1044 
Eileetric.,.Heaters):'e ee Oe cia Oak ee ee ae 1044 
Electric Accumulators or Storage-batteries. 
Mescriptionvel Storage-patteriesacua. 1.0 seioe ae ee. ee eee eee 1045 
Sizeyand Weights of Storage-batteries: (2... .-.0 -.. ules Jo eee 1048 
General ‘Rules for. Storage-cellss 77h are. eet See ee 1048 
Milectrolysis.. ois er ee Ee ea ea eee 1048 
Electro-chemical Equivaients..3. oc eee 1049 
Eificiency otras vorage-celle cea. ce cee ttn eee on eee 1048 
Electro-magnets. 

Units ot Blectro-marnetic Measurementse.). .. . .... )s).ve/eee ees 1050 
iines* of Hhoopszot Force... ou tstcesee tense see os Dine a easehae ene ee 1050 
PNET MAG NEebICR@ITCUIE, oie-. cutie cig Stele ee lerieh cle oe sh SRR RSE Ege 1051 
Permeabilupyc ae sc sis ss «cele a ease Meteo tees oS eA ean a cet en 1052 
Tractive.or Lifting Force ofa Marmeties... . .2.)5.)ac melee nea eee 1053 
Miagomnet. WiInGIngstlaims. s,s. cs ee tee os See TS Seen a ee 1053 
Determining the Polarity of Electro-magnets....................2% 1054 
Determining the’ Direction of -ayCurrente:.\) oo. sec ee eee 1054 


Dynamo-electric Machines. 
Kinds of Dynamo-electric Machines as regards Manner of Winding... 1055 


Moving Force of a Dynamo-electric Machine... .................... 1055 
Noraue.ou an Arma tUteseic, st... -. VaeRMeMMne re -+ ©, oo)s Rolie tart eRe ee 7 ete 1056 
Electro-motive Force of the Armature Circuit. .................... 1056 
Strength othe Magneticntield. 2) sieewre. >, . sl cence) ol oe 1057 


Wynamo (esteny; iecteenan.  . +s > cGMMpeece nite a) = > Lia Gamma Ps.) aes 1058 


CONTENTS. XXX1 


Alternating Currents, 


PAGE 
Maximum, Average, and Effective Values. ................0.00005. 1061 
EEO CULLEN Venti tick at tt ae cE. MeN ate BVP an, eae a | hae SO 1061 
inductance; Capacity, Power PH actors. saeac Jace Wee OL oe 1062 
fiveactance, Linpedance PA dimittances ot wi) ae eee aein le cit ee ets el 1063 
DP PLTLOC by HACbORS | Rate tan bee ph lito UE aE cen Nios Gmmhewe lic icc. Ae tiie emia ho 1063 
Mbhm’s Law Applied, to Alternating” @urtents::. 4... s.l. soe kee 1064. 
PEM DCAUAN CE MOLY PONS WN sete yore eee AN Te Ee Ko oe es rea recente 1066 
Cap Aclty. Ol CONGUCEOLS Mss. oC Heke eM ene ends ce ep en ee pa 1066 
Self-imductance of Lines and’ Circuits...) 29209, yee, 1066 
Eapacitycor CONGUCTOTS) ort cos tee OP ee et ee eet ea EEE 1067 
Singte-phase and Polyphase Currents. 4): 0.) 8. 2) 1068 
Measurement of Power in Polyphase Circuits.... .............00-. 1069 
Aiternating-curreny Generators. hase aeatn ee een saree Rt aun 1070 
(ELanerormersss Con ververs, "GGGr Meee RAI w ae RY ET ae 1070 
pyvenronous Motos. 0001.0) 62 ns a etl, AER Pease nidliaS ok iat) a 1071 
nguction Motors. ie Hey ae ain caine Faye a Ae Qe, Ca 1072 
Calculation of Alternating-current Circuits...) 2.202305). Oa 1072 
Weight of Copper Required in Different Systems.................. 1074 

Electrical Machinery. 
Direct-current Generators and Motors ...............e.0+00. 1074-1076 
Altemating-current, Generatorses)4 Jae Met ensue Aen EOE 1077 
EMU LIOMSNLOLOLS ets 1, feed fot EA. TRE RO ed eR PANE bar TR hee Ra 1077 
Symbols Used in Electrical Diagrams................. 1078 
APPENDIX. 
Strength of Timber. 
Sates tondvonaw hite-oak Beamss): spielen cee aire eee ore gene LORD 
Mathematics. 

Hommislaskore Interpol attoms es cents ince: tee cs cheba eRe oe is eee 1080 
Maxima and Minima without the Caleultisa.5) (2.5. 4. cut. cies eck. 1080 
Riveted Joints. 

Pressure Required to Drive Hot (Rivetssco se csicecls os oe wees cca 1080 


Heating and Ventilation, 
Capacities for Hot-blast or Plenum Heating with Fans and Blowers. . 1081 


Water-wheels. 

Water-power Plants Operating under High Pressure................ 1081 
Hornmale for Power of Jeu Water-wheels wi.ae vtec sea oe eee 1082 
Gas Fuel, 

Compositions Energy, ete.jpof: Various! ‘Gases, .cu. 06 oases. des ced. 4. 1082 
Steam-boilers, 

Rulesstormsteam-boler Constrictione coo sekeie eee. Ae osha ee 1083 
ovler +H COG a ast eg eee ole ee ene OL Te ERR ic a ees cee erate a ean 1983 
Heed=WaAter LEA LOLS. ie. ih eee tite eee a EE ol tx. cece ils 1033 
The Steam-engine. 

Current) Practicein Eneine Proportionse cua spies. ols. dsmudine ee 1084 
Work of Steam-turbines:: J. 5j)502)..., NE a ree eb sey ice nn) 2e hea SEEPS lots 1085 
RelativersCosp of Different. Sizes of Pmgines.. cnet. ee eee 1085 
Gearing. 

Hifficlency olny Ori Gealin main mae enna en eet! ce eae 1086 
Hydraulic Formule. 

Hiaw OuWaver trom Orilices meted... eee AL ieee ole rab neete ane 1087 
Tin and Terne Plate. 

Pennamheeiin Co.c8 SPeCIIGHHONS. +... 5 RENE our cals sso oh ee aealee eee 1088 


LIST OF AUTHORMTBIES |e terre rere 1089 


NAMES AND ABBREVIATIONS OF PERIODICALS 
AND TEXT-BOOKS FREQUENTLY REFERRED TO 
IN THIS WORK. 


Am. Mach. American Machinist. 

App. Cyl. Mech, Appleton’s Cyclopzedia of Mechanics, Vols. I and I. . 

Bull. I. & S, A. Bulletin of the American Iron and Steel Association 
(Philadelphia). 

Burr’s Elasticity and Resistance of Materials. ; 

Clark, R. T. D. D. K. Clark’s Rules, Tables, and Data for Mechanical En- 
gineers. : 

Clark, S. E. D.K. Clark’s Treatise on the Steam-engine. 

Gol. Coll, Qly. Columbia College Quarterly, 

Engg... Engineering (London). 

Eng. News. Engineering News, 

Engr. The Engineer (London). 

Fairbairn’s Useful Information for Engineers, 

Flynn’s Irrigation Canals and Flow of Water. sos 

Jour. A.C. 1. W. Journal of American Charcoal Iron Workers’ Association. 

Jour. F. I, Journal of the Franklin Institute. 

Kapp’s Electric Transmission of Energy. 

Lanza’s Applied Mechanics. 

Merriman’s Strength of Materials. 

tie bk Supplementary volume of Appleton’s Cyclopzedia of 

echanics. 
Proc. Inst. C. E. Proceedings Institution of Civil Engineers (London), 
Proc. Inst. M. E. Proceedings Institution of Mechanical Engineers CLon- 


don). 
Peabody’s Thermodynamics. 
Proceedings Engineers’ Club of Philadelphia. 
Rankine, 8. E. Rankine’s The Steam Engine and other Prime Movers. 
Rankine’s Machinery and Millwork. 
Rankine, R. T. D. Rankine’s Rules, Tables, and Data. 
Reports of U.S. Test Board. 
Reports of U. S. Testing Machine at Watertown, Massachusetts. 
Rontgen’s Thermodynamics. 
Seaton’s Manual of Marine Engineering. 
Hamilton Smith, Jr.’s Hydraulics. 
The Stevens Indicator. 
Thompson’s Dynamo-electric Machinery. 
Thurston’s Manual of the Steam Engine. 
Thurston’s Materials of Engineering. 
Trans, A. I. E.E. Transactions American Institute of Electrical Engineers. 
Trans. A.I. M. E. Transactions American Institute of Mining Engineers. 
Trans. A.S. C. E. Transactions American Society of Civil Engineers. 
Trans. A. S. M. E._ Transactions American Soc’ty of Mechanical Engineers. 
Trautwine’s Civil Engineer’s Pocket Book. 
The Locomotive (Hartford, Connecticut). 
Unwin’s Elements of Machine Design, 
Weisbach’s Mechanics of Engineering. 
Wood’s Resistance of Materials. 
Wood’s Thermodynamics, 


MATHEMATICS. 


Greek Letters, 


A ea Alpha My 7) Bita 

B B Beta (2) 3 @ Theta 

T yy Gamma |jI t Jota 

A 6 Delta K ck Kappa 

E e Epsilon | A A Lambda 
Z ¢ Zeta Vi See eee NU 


Arithmetical and Algebraical Signs oud 


plus (addition). 
positive, 

minus (subtraction). 
negative. 
plus or minus. 
minus or plus, 


xT HR 1 Seal 


equals. 
multiplied by. 
aborab=a xb. 


-- divided by 
/ divided by. 


a 15 
—=a/b=a-~-b, 15-16= — 
b if J 16 
ee" + 1000 


y square root. 
Vv cube root. 


WV 4th root. 
ris to, 4s so is, : to (proportion). 
2243 : 6, a8 2 is to 4 so is 3 to 6, 
. ratio; divided by. 
2 :4, ratio of 2to4= 2/4, 
.*. therefore. 
> greater than. 
< less than. 
oO square. 
© round. 
° degrees, are or thermometer. 
’ minutes or feet. 
” seconds or inches, 
417111 accents to cuneush letters, as 
a’, Cee a’ 
Qj, Ag, As, Ay, in read a sub1, asubb, 
ete, 


()0] { ; vincula, denoting 
that the numbers enclosed are 
to be taken together ; as, 


(a+bje=4+3 x5=35, 
a?, a’, a squared, @ cubed. 
an, a raised - the nth power. 


ai= Var, a = ake 











ant = a aers = = 
10° 1 ne the oth power = 1,000,000,- 
sin. a = the sine of a. 
sin.—1q= the are whose sine is a. 
sin, a-? = —— 
sin. a. 
log. = logarithm. 
log., Ae? yp. log. = hyperbolic loga- 
ri 3 


N v Nu de LG Tau 

B & Xi Y vu Upsilon 

O o Omicron |® @¢ hi 

ll 7 Bi xX x Chi 

P p Rho Lye Pal 

cous Sigma f ow» © Omega 
Abbre viations, 


: right angle, te 
do pert bendic ular to; 
Sif]. SINE, °,, Mert Midis vi 

cos.. cosine, 

tang., or tan., tangent. 
sec., Secait, 

versin., vorsed $1ne, 
cot., cotangent, 
cosec., cosecant. 
covers., co-versed sine: 

In Algebra, the first letters of the 
alphabet, a, 6, c,d, etc., are gener- 
ally used to denote known quantitiés,, 
and the last letters, w, x, y, Z, etc., 
unknown quantities. 


Abbreviations and Symbols com- 
monly used. 
d, differential (in calculus). 


Is integral (in calculus). 


fs rf integral between limits a and b. 


4, delta, difference. 

3. sigma, sign of summation. 

aw, pi, ratio of circumference of circle 
to diameter = 3.14159: 

g, acceleration due to gravity = $2.16 
ft. per sec. per sec. 


Abbreviations frequentiy used 
this Book. 


L., 1., length in feet and inches. 
be , breadth in feet and inches, 

D. d. ” depth or diameter. 
H.. oT, , height, feet and inches. 
Ales ge thickness or temperature, 
Vv. v. » velocity. 
bee force, or factor of safety. 
f., ’ coefficient of friction. 
E, coefficient of elasticity. 
R., r., radius. 
W., W. , weight, 
Pe D., pressure or load. 
eel -power, 
-, indicated horse-power, 
aS brake horse-power. 

., high pressure. 

intermediate pressure, 

low pressure. 

G., American Wire Gauge 

(Brown & Sharpe). 
.G., Birmingham Wire Gauge. 
.Mm., orrevs. per min., revolutions 
per minute, 


im 


ao 


bd meaSaE) 
oe sas 


« 
hoe 


s 


2 MATHEMATICS, 


ARITHMETIC. 


The user of this book is supposed to have had a training in arithmetic as 
well as in elementary algebra. Only those rules are given here which are 
apt to be easily forgotten. 


GREATEST COMMON MEASURE, OR GREATEST 
COMMON DEIEVISCR OF TWO NUMBERS. 


Rule.—-Divide the greater number by the less; then divide the divisor 
by the reniainder,‘and so on, dividing always the last divisor by the last 
remainder; until, there is no remainder, and the last divisor is the greatest 
common measure required. 


LEAST COMMON MULTIPLE OF TWO OR MORE 
é “NUMBERS, 


Bule.—Divide the given tiumbers by any number that will divide the 
greatest number of them without a remainder, and set the quotients with 
the undivided numbers in a line beneath. 

Divide the second line as before, and so on, until there are no two numbers 
that can be divided ; then the continued product of the divisors and last 
quotients will give the multiple required. 


6 


FRACTIONS, 


To reduce a common fraction to its lowest terms,—Divide - 


both terms by their greatest common divisor. 39/52 = 3/4, 

To change an improper fraction to a mixed number.— 
Divide the numerator by the denoininator; the quotient is the whole number, 
and the remainder placed over the denominator is the fraction: 39/4 = 934, 

To change a mixed number to an improper fraction.— 
Multiply the whole number by the denominator of the fraction; to the prods 
uct add the numerator; place the sum over the denominator: 1% = 15/8. 

To express a whole number in the form of a fraction 
with a given denominator.—Muttiply the whole number by the 
given denominator, and place the product over that denominator: 13 = 39/3. 

To reduce a compound to a simple fraction, also to 
multiply fractions,—Multiply the numerators together for a new 
numerator and the denominators together for a new denominator: 


25 4059 8 248 

gs 9 also 3X3 9° 

Wo reduce a complex to a simple fraction,—The numerator 

and denominator must each first be given the form of a simple fraction; 

then multiply the numerator of the upper fraction by the denominator of 

the lower for the new numerator, and the denominator of the upper by the 
numerator of the lower for the new denominator; 


= Ee —e 
. 


By A 56 


Vo divide fractions.—Reduce both to the form of simple fractions, 
invert the divisor, and proceed as in multication: 


3 Stes od 18S ¢ 
CS BW gap ed LR 5 empl ar F 
VAP Fig a SG e0L 


Cancellation of fractions.—In compound or multiplied fractions, 
divide any numerator and any denominator by any number which will 
divide them both without remainder, striking out the nuinbers thus divided 
and setting down the quotients in their stead. 

To reduce fractions to a common denominator,.—Reduce 
each fraction to the form of a simple fraction; then multiply each numera- 


DECIMALS. 3 


tor by all the denominators except its own for the new numerators, and all 
the denominators together for the common denominator: 


1 i 3 Re ue tap 
Oh Bi ik cdo eae ea: 

Wo add fractions.—Reduce them to a common denominator, then 
add the numerators and place their sum over the common denominator: 


io | 
os peagegaeuemeedaaa ep 


a ae ee = 111, 
oo 42 Dee 


To subtract fractions.—Reduce them to a common denominator, 


subtract the numerators and place the difference over the common denomi- 
nator: 





1e8utH 61 
Dic, ae thane, ta 
DECIMALS, 


To add decimals.—Set down the figures so that the decimal points 
are one above the other, then proceed as in simple addition: 18.75-+ .012 = 
18.762. 

To subtract decimals.—Set down the figures so that the decimal 
pens ere one above the other, then proceed as in simple subtraction: 18.75 
— .O12 = 18.738, ; 

To multiply decimals.—Multiply as in multiplication of whole 
numbers, then point off as many decimal places as there are in multiplier 
and multiplicand taken together: 1.5 x .02 = .030 = .03. 

To divide decimals.—Divide as in whole numbers, and point off in 
the quotient as many decimal places as those in the dividend exceed those 
in the divisor. Ciphers must be added to the dividend to make its decimal 
places at least equal those in the divisor, and as many more as it is desired 
to have in the quotient: 1.5 + .25=6. 0.1-+0.3 = 0.10000 + 0.3 = 0.3833 +- 


Decimal Equivalents of Fractions of One Inch, 





1-64 .015625 














17-64 .265625 33-64 -515625 49-64 «765625 
1-32 .03125 9-32 £28125 17-82 .53125 25-32 «78125 
3-64 .046875 19-64 .296875 35-64 54687 51-64 . 796875 
1=16 0625 5=16 8125 9=16 5625 138216 | .8125 
5-64 078125 21-64 .028125 37-64 .578125 53-64 828125 
3-32 .09375 11-32 843875 19-32 59875 27-32 84375 
7-64 109375 23-64 .809375 39-64 .609375 55-64 859375 
1=8 125 328 1) 528 625 7=8 875 
9-64 .140625 25-64 .890625 41-64 -640625 57-64 890625 
5-32 15625 13-382 -40625 21-32 65625 29-32 90625 
11-64 171875 27-64 421875 43-64 -671875 59-64 .921875 
3216 1875 7=16 -4375 11-16} .6875 15916] .9875 
13-64 203125 29-64 453125 45-64 703125 61-64 953125 
7-32 .21875 15-32 -46875 23-32 «71875 31-382 96875 
15-64 . 234375 31-64 484375 47~64 734375 63-64 984375 
1=4 .20 1le2 50 o=4 AG) 1 : 





To convert a common fraction into a decimal.—Divide the 
numerator by the denominator, adding to the numerator as many ciphers 
prefixed by a decimal point as are necessary to give the number of decimal 
places desired in the result: 14 = 1.0000 +3 = 0.2333 +. 

To convert a decimal into a common fraction.—Set down 
the decimal as a numerator, and place as the denominator 1 with as many 
ciphers annexed as there are decimal places in the numerator; erase the 


ARITHMETIC, 





6848" |€0e8" |2T9L° |TSOL° |SPP9" |6S8S" [ELcs" | 889F" | GOTH’ | OTS’ | O86" | FRE’ | SOLE” | SLIT’ | 98S0" | SLg6" 
999° |60TL° |€999° |9T09° |69F9° |GcGh" | SlEP” | BBE" | T8eB" | FES" | LTS" | THOT” | FEOT’ | 2hS0° | OSL8" 

1099" |F609° |98gq° |SL0g° joLch’ | e90r° | gace” | zhOe | Bese | Te0s’ | Sst" | OTOL’ | 80S0° | Sers 

G69" |9STS" |889h° |6lob" | OS4S" | F8ce" | SSS’ | PRES | S{BT° | BORE” | 8860" | 69FO" | OSL 

LoLb° |L6ch* |L98E" | SEFS" | 8008" | BLS" | SFIS’ | GILT’ | 683° | 6980" | O&FO° | S289 

9068" |9TSE" | Sls" | PELG" | PES" | ESET | GOCE’ | SLIT’ | 1820" | Té6sO° | Oecd" 

POTS" | SI8s" | TOG | GOTS” | BSLL° | 9OFE’ | SOE" | 8040" | eg80" | Sc9o° 
Q0SG" | S8TIG" | GL8T° | OST’ | OSZE’ | 8860" | $e90° | STO" | 0009" 

vIGE” | TROL’ | 298k’ | S60E° | O@80" | ZFSO" | E120" | SLEP 

90FT" | SZIE’ | 2860" | 040" | 69FO" | FEeO" | OSLE" 

2160° | T820° | 9890" | F680" | S610" | Sere’ 

g390°" | 69F0° | SIg0° | 9ST0° | 00Se 

. eceo” | FEGO" «| LTO” | S28E° 














i ~ 
@00°T |SL86° |OSL8" |SeT8" |00SL° |489° |OSe9" |Sc9S" | o0g° Gish” | OSE" «| GETS" «| OOGG" «=| SLBT" | OSeT” =| $290" 000° T 
| 














Tj/H £/Stt ete] & pe] & fe aS eek Sa Pa Sa Ge Sa 


el 


*s[VUILDOG UL possoidx@ sSUOPIIVIy Jo JONpoAg 


oie) 














COMPOUND NUMBERS. 5 


decimal point in the numerator, and reduce the fraction thus formed to its 
lowest terms: 


ile Where | Spe es aes 
ioe 47 T0800 8 


Vo reduce a rectrring decimal to a common fraction.— 
Subtract the decimal figures that do not recur from the whole decimal in- 
cluding one set of recurring figures; set down the remainder as the numer- 
ator of the fraction, and as many nines as there are recurring figures, fol- 
lowed by as many ciphers as there are non-recurring figures, in thé denom- 
inator. Thus: 


, nearly. 


; .79054054, the recurring figures being 054. 
Subtract 79 


See 


78975 f 17 
99900 = (reduced to its lowest terms) in 


COMPOUND OR DENOMINATE NUMBERS. 


Reduction descending.—To reduce a compound number to a lower 
denomination. Multiply the number by as many units of the lower denomi- 
nation as makes one of the higher. 


3 yards to inches: 3 X 36 = 108 inches. 
.04 square feet to square inches: .04 x 144 = 5.76 sq. in. 


If the given number is in more than one denomination proceed in steps 
from the highest denomination to the next lower, and so on to the lowest, 
adding in the units of each denomination as the operation proceeds. 


8 yds, 1ft. 7in. toinches: 8x 3= 9, +1=10, 1012 = 120, +-7 = 127 in. 


Reduction ascending.—To express a number of a lower denomi- 
nation in terms of a higher, divide the number by the number of units of 
the lower denomination contained in one of the next higher; the quotient is 
in the higher denomination, and the remainder, if any, in the lower. 

127 inches to higher denomination. 


127-12 = 10 feet + 7inches; 10 feet+ 3 = 3 yards + 1 foot. 
Ans. 3 yds. 1 ft. 7 in. 


To express the result in decimals of the higher denomination, divide the 
given number by the number of units of the given denomination contained 
ia one of the required denomination, carrying the result to as many places 
of decimals as may be desired. 


127 iuches to yards: 127 + 86 = 332 = 3.5277 + yards. 


RATIO AND PROPORTION, 


Ratio is the relation of one number to another, as obtained by dividing 
one by the other. 


Ratio of 2 to 4, or 2 : 4=2/4 = 1/2. 
Ratio of 4 to 2; or 4 : 2=2. 


Proportion is the equality of two ratios. Ratio of 2 to 4 equals ratio 
of 3 to 6, 2/4 = 3/6; expressed thus, 2 : 4: : 3:6; read, 2is to4 as 3 is to 6. 

The first and fourth terms are called the extremes or outer terms, the 
second and third the méans or inner terms. 

The product of the means equals the product of the extremes: 


2 Aso BONES Xi GSa129 15 4 = 12. 
Hence, given the first three terms to find the fourth, multiply the second 
and third terms together and divide by the first: 


2:4:: 38: what number? Ans. ———=6, 


6 ARITHMETIC. 


Algebraic expression of proportion.—a: b::c¢: d; =a ad 
: be be ad _ad 
= OCR from which a= 7;@=73 Sea Os 5” 


Mean proportional between two given numbers, Ist and 2d, is such 
a number that the ratio which the first bears to it equals the ratio which it 
bears to the second. Thus, 2: 4:: 4: 8; 4is a mean proportional between 
zand 8. To find the mean proportional between two numbers, extract the 
square root of their product. 


Mean proportional of 2and8 = V2 x 8 = 4, 


Single Rule of Three 3 or, finding the fourth term of a proportion 
when three terms are given.—Rule, as above, when the terms are stated in 
their proper order, multiply the second by the third and divide by the first. 
The difficulty is to state the terms in their proper order. The term which is 
of the same kind as the required or fourth term is made the third; the first 
and second must be like each other in kind and denomination. To deter- 
mine which is to be made second and which first requires a little reasoning. 
If an inspection of the problem shows that the answer should be greater 
than the third term, then the greater of the other two given terms should 
be made the second term—otherwise the first. Thus, 8 men remove 54 cubic 
feet of rock in a day; how many meu will remove in the same time 10 cubic 
yards ? The answer is to be men—make men third term; the answer is to 
be more than three men, therefore make the greater quantity, 10 cubic 
yards, the second term; but as it is not the same denomination as the other 
term it must be reduced, = 270 cubic feet. The proportion is then stated: 


3 X 270 
54 


The problem is more complicated if we increase the number of given 
terms. Thus, in the above question, substitute for the words ‘tin the same 
time ” the words ‘“‘in 3 days.” First solve it as above, as if the work were 
to be done in the same time; then make another proportion, stating it thus: 
If 15 men do it in the same time, it will take fewer men to do it in 3 days; 
make 1 day the 2d term and 3 days the first term. 3:1 :: 15 men: 5 men, 

Compound Proportion, or Double Rule of Three.—By this 
rule are solved questions like the one just given, in which two or more stat- 
ings are required by the single rule of three. In it as in the single rule, 
there is one third term, which is of the same kind and denomination as the 
fourth or required term, but there may be two or more first and second 
terms. Set down the third term, take each pair of terms of the same kind 
separately, and arrange them as first and second. by the same reasoning as 
is adopted in the single rule of three, making the greater of the pair the: 
second if this pair considered alone should require the answer to be 
greater. 

Set down all the first terms one under the other, and likewise all the 
second terms. Multiply all the first terms together and all the second terms 
together. Multiply the product of all the second terms by the third term, and 
divide this product by the product of all the first terms. Example: If 3 men 
remove 4 cubic yards in one day, working 12 hours a day, how many men 
working 10 hours a day will remove 20 cubic yards in 3 days ? 

Yards 43 20 

Days 3. 1[s%¢ 3 men. 

Hours LON eee 

Products 120 : 240 :: 3:6men. Ans. 


To abbreviate by cancellation, any one of the first terms may cancel 
either the third or any of the second terms; thus, 3 in first cancels 8 in third, 
making it 1, 10 cancels into 20 making the latter 2, which into 4 makes it 2, 
which into 12 makes it 6, and the figures remaining are only 1: 6:: 1: 6. 


INVOLUTION, OR POWERS OF NUMBERS. 


Involution is the continued multiplication of a number by itself a 
given number of times. 'The number is called the root, or first power, and 
the products are called powers, The second power is called the square and 


= 15 men, 





54: 270:: 3: ~ (the required number); # = 


POWERS OF NUMBERS. 3 7 


the third power the cube. The operation may be indicated without being 
performed by writing a small figure called the index or exponent to the 
right of and a little above the root; thus, 33 = cube of 3, = 27. 

To multiply two or more Aaeditee of the same number, add their exponents} 
this, 22) 023 == .25 por eS i= 382) ==) 25. 

To divide two powers of the same number, subtract their exponents; thus, 
Q3 = 22 = Q1 = 2; 22+ 24 = g—? Beye The exponent may thus be nega- 
tive. 23 + 23 = 20 = 1, whence the zero power of any number=1. The 
first power of a number is the number itself. The exponent may be frac- 


tional, as 23, 28, which means that the root is to be raised to a power whose 
exponent is the numerator of the fraction, and the root whose sign is the 
denominator is to be extracted (see Evolution). The exponent may be a 
decimal, as 29°5, 21°5; read, two to the five-tenths power, two to the one and 
five-tenths power. These powers are solved by means of Logarithms (which 
see). 


First Nine Powers of the First Nine Numbers, 








$$ 


2d 3d 4th 5th | 6th 7th Sth 9th 
Pow’r|Pow'r|] Power.| Power.| Power.| Power.| Power. | Power. Power. 


ef | 


1 1 1 il al 1 1 1 1 
2 4 8 16 82 64 128 256 512 
3 9 27 81 243 729 2187 6561 19683 
4 16 64 256 1024 4096 16384 655386 262144 
5 25 125 625 3125 15625 48125 390625 1953125 
6 36 216 1296 7776 46656 279936 | 1679616 | 10077696 
7 49 343 2401 | 16807 | 117649 823543 | 5764801 | 40353607 
8 64 512 4096 | 82768 | 262144 | 2097152 | 16777216 | 134217728 
9 81 729 6561 | 59049 | 531441 | 4782969 | 43046721 | 387420489 





The First Forty Powers of 2. 




















s| $ || 3 | gs || 8 g 5 g 5 g 
Slee ced Ml. erihers 5 a E 4 

oy es ay > a > ay - a > 
Olaiiat 9 B12|| 18 | 262144|| 27 | 134217728]| 36 68719476736 
1} 2/]| 10 | 1024)| 19 | 524288]| 28 | 268435456/| 237 || 137438953472 
2} 4/|| 11 | 2048]; 20 | 1048576|| 29 | 536870912|| 38 || 274877906944 
3} 8 {i 12 | 4096/] 21 | 2097152|| 30 | 1073741824]| 39 || 5497558138K8 
4, 16|| 13 | 8192|| 22 | 4194304]| 31 | 2147483648]| 40 ||109951162777 
5] 32 || 14 | 16384|| 23 | 8388608] 32 | 4294967296 

6| 64 || 15 | 32768/| 24 |16777216|| 33 | 8589934592 

Tl 128 |} 16 | 65536)| 25 |33554432|| 34 [17179869184 

8} 256 || 17 |131072|| 26 |67108864|| 35 |34350738368 




















EVOLUTION. 


Evolution is the finding of the root (or extracting the root) of any 
number the power of which is given. 


The sign 4 indicates that the square root is to be extracted: V V V3 the 
cube root, 4th root, nth root. 

A fractional exponent with 1 for the numerator of the fraction is also 
used to ao that the operation of extracting the root is to be performed; 


thus, 24,22 = 2, V2. 
When the } power of a number is indicated. the involution not being per- 
formed, the extraction of any root of that power may also be indicated by 


8 ARITHMETIO, 


dividing the index of the power by the index of the root, indicating the 
division by.a fraction. ‘Thus, extract the square root of the 6th power of 2: 


ee 6 3 8 
V 2% = 2 =W=2 ='8. 
The 6th power of 2, as in the table above, is 64; 4/64= 8. 


Difficult problems in evolution are performed by logarithms, but the 
square root and the cube root may be extracted directly according to the 
rules given below. The 4th root is the square root of the square root, The 
‘6th root is the cube root of the square root, or the square root of the cube 
root; the 9th root is the cube root of the cube root; ete. 

To Extract the Square Root.—Point off the given number into 
periods of two places each, beginning with units. If there are decimals, 
point these off likewise, beginning at the decimal point, and supplying 
as many ciphers as may be needed. Find the greatest number whose 
square is less than the first left-hand period, and place it as_the first 
figure in the quotient. Subtract its square from the left-hand period, 
and to the remainder annex the two figures of the second period for 
a dividend. Double the first figure of the quotient for a partial divisor; 
find how many times the latter is contained in the dividend exclusive 
of ‘the right-hand figure, and set the figure representing that number of 
times as the second figure in the quotient, and annex it to the right of 
the partial divisor, forming the complete divisor. Multiply this divisor by 
the second figure in the quotient and subtract the product from the divi- 
dend. To the remainder bring down the next period and proceed as before, 
in each case doubling the figures in the root already found to obtain the 
trial divisor. Should the product of the second figure in the root by the 
completed divisor be greater than the dividend, erase the second figure both 
from the quotient and from the divisor, and substitute the next smaller 
figure, or one small enough to make the product of the second figure by the 
divisor less than or equal. to the dividend. 


271214 
1189 


8347/2515 

2429 

3542/8692 
7084 


85444, 160865 
1141776 


854485] 1908936 


1772425 








To extract the square root of a fraction, extract the root of numerator 


and denominator separately. /3 = , or first convert the fraction into a 


decimal, vi = / HE+ = 6666+. 


Wo Extract the Cube Root.—Point off the number into periods of 
8 figures each, beginning at the right hand, or unit’s place. Point off deci- 
mals in periods of 3 figures from the decimal point. Find the greatest cube 
that does not exceed the left-hand period; write its root as the first figure 
in the required root. Subtract the cube from the left-hand period, and to 
the remainder bring down the next period for a dividend. 

Square the first figure of the root; multiply by 300, and divide the product 
into the dividend for a trial divisor ; write the quotient after the first figure 
of the root as a trial second figure. 

Complete the divisor by adding to 360 times the square of the first figure, 
30 times the product of the first by the second figure, and the square of the 
second figure. Multiply this divisor by the second figure; subtract the 
product from the remainder. (Should. the product be greater than the 
remainder, the last figure of the root and the complete divisor are too large ; 


CUBE ROOT. 9 


substitute for the iast figure the next smaller number, and correct the tria) 
divisor accordingly.) 

To the remainder bring down the next period, and proceed as before to 
find the third figure of the root—that is, square the two figures of the root 
already found; multiply by 300 for a trial divisor, ete. 

if at any time the trial divisor is greater than the dividend, bring down ane 
other period of 3 figures, and place 0 in the root and proceed. 

The cube root of a number will contain as many figures as there are 
periods of 3 in the number 

Shorter Methods of Extracting the Cube Root,--1, From 
Wentworth’s Algebra: 


1,881,365,963,625|12345 
i rigs? 











800 x 12 = 300) 881 
30 x 1 x 2 =| 60 
Q2 — fas 
364] 728 
64 | 153365 
800 x 122 = 43200 
80% 12 x13) = 1080 
37 = 9 
44289 } 132867 
1089) 20498963 
800 x 1232 = 4538700] 
30 x 123 x4 = 14760: 
42 = 16 | 


4553476 ¢ 18213904 
14776 | 2285050025 


800 x 12342 = 456826800 
380 x 1234 x5 = 185100 
5? = 25 


457011925 |2285059625 


After the first two figures of the root are found the next trial divisor is 
found by bringing down the sum of the 60 and 4 obtained in eompleting the 
preceding divisor, then adding the three lines connected by the braee, and 
annexing two ciphers. This method shortens the work in long examples, as 
is seen in the case of the last two trial divisors, saving the labor of squaring 
123 and 1234, A further shortening of the work is made by obtaining the 
last two figures of the root by division, the divisor employed being three 
times the square of the part of the root already found; thus, after finding 
the first three figures: 


8 x 1232 = 45387|20498963|45.1-- 
IBIS48 Ce 


“234416 
226935 
74813 


The error due to the remainder is not sufficient to change the fifth figure of 
the root, 

2. By Prof. H. A. Wood (Stevens Indicator, July, 1890): 

I. Having separated the number into periods of three figures each, count- 
ing from the right, divide by the square of the nearest root of the first 
period, or first swo periods ; the nearest root is the trial root. 

Il. To the quotient obtained add twice the trial root, and divide by 3. 
This gives the root, or first approximation. ‘ 

Ill. By using the first approximate root as a new trial root, and proceed- 
ing as before, a nearer approximation is obtained, which process may be 
repeated until the root has been extracted, or the approximation carried ag 
far as desired. pr 


10 ARITHMETIC, 


ExamMpPLe.—Required the cube root of 20. The nearest cubé to 20 is 38, 
32 = 9)20.0 
9.2 
6 
3)8.1 
> Fist 
2.72 = 7.29)20.000 
5.4 
3)8.143 
2.714, Ist ap. cube root. 
2.7142 = 7.365796)20.0000000 
"2. 7152534 
5.428 
8)8. 1432534 


2.7144178 2d ap. cube root. 


REMARK.—In the example it will be observed that the second term, or 
first two figures of the root, were obtained by using for trial root the root of 
the first period. Using, in like manner, these two terms for trial root, we 
obtained four terms of the root; and these four terms for trial root gave 
seven figures of the root correct. In that example the last figure should be 
7. Should we take these eight figures for trial root we should obtain at least 
fifteen figures of the root correct. 

To Extract a Higher Root than the Cube.—tThe fourth root is 
the square root of the square root; the sixth root is the cube root of tbe 
square root or the square root of the cube root. Other roots are most con- 
veniently found by the use of logarithms. 


ALLIGATION 


shows the value of a mixture of different ingredients when the quantity 
and value of each is known. 

Let the ingredients be a, b, c, d, etc., and their respective values per unit 
W, X,Y, Z, etc. 


A =the sum of the quantities =a+b-+c-+ d, ete. 
P=mean value or price per unit of A, 
AP=aw+bx+cy+dz, ete. 
aww + ba + ey + dz 
J : 





1a 


PERMUTATION 


shows in how many positions any number of things may be arranged in a 
row; thus, the letters a, 6, c may be arranged iu six positions, viz. abc, acb, 
cab, cba, bac, bea. 

Rule.—Multiply together all the numbers used in counting the things; thus, 
permutations of 1,2, and3=1x2xXx3=6. In how many positions can 9 
things in a row be placed ? 


1X2x3x4x5x6xX7X 8 X 9 = 362880. 
COMBINATION 


shows how many arrangements of a few things may be made out of a 
greater number. Rule: Set down that figure which indicates the greater 
number, and after it a series of figures diminishing by 1, until as many are 
set down as the number of the few things to be taken in each combination. 
Then beginning under the last one set down said number of few things ; 
then going backward set down a series diminishing by 1 until arriving under 
the first of the upper numbers. Multiply together all the upper numbers to 
form one product, and all the lower numbers to form another; divide the 
upper product by the lower one. 


GEOMETRICAL PROGRESSION. ug 


How many combinations of 9 things can be made, taking 3 in each com- 
bination ? 


9xX8X% _ 504 _ gy 
OE a ee Wi) ; 


ARITHMETICAL PROGRESSION, 


in a series of numbers, is a progressive increase or decrease in each succes- 
sive number by the addition or subtraction of the same amount at each step, 
as 1, 2, 3, 4, 5, ete., or 15, 12, 9, 6, etc. The numbers are called terms, and the 
equal increase or decrease the difference. Examples in arithmetical pro- 
gression may be solved by the following formule: 

Let a = first term, J = list term, d = common difference, » = number of ~ 
terms, s = sum of the terms: 





l=a+(n—1)d, =~ 3a a4/ eds + (a Fa), 
2s s (n—1)d 
= eerrees Gale ed 9 
1 lta, l?—a? 
si 5 Pa + (n — 1)d}, 12 Seog ant 
1 
= (l+a) 5) = g rll — (n — 1)d). 
3 s (n-1)d 
a =l1— (n —1)d, = hath, ae? 




















1 2s 
yay Warn) — 2ds, =—-1 
ipesesiee) 2(s — an) 
a eae ls nav — 1) 
12 — a2 2Anl — s) 
a) ee ew, 1 nr — 1) 
ae | d-204Qa— d+ 8ds 
x= —G -+1, 2d ; 
Qs _ +d tyV2l+ a? — 8ds 
We bed a as Ter oe od 


GEOMETRICAL PROGRESSION, 


in a series of numbers, is a progressive increase or decrease in each sue. 
cessive number by the same multiplier or divisor at each step, as 1, 2. 4, 8, 
16. ete., or 243, 81, 27, 9, ete. The common multiplier is called the ratio. 
Let a = first term, / = last term, r = ratio or constant multiplier, n = 
number of terms, nu = any term, as Ist, 2d, ete., s = sum of the terms: 











- Qisog oe yi cn eras 
1= ar” 1, = he ’ = ae ’ 
iog 1 = log a + (n — 1) log r, ue — yn" 71 ~- a(s—al"~1=9 
m = ar —1- log m = log a + (m ~ 1) log’, 
n—1,— n—T1 n 
a a(r” ~ 1) _rl—a jv % b® 1] 
Ao) v= Si) aii ee ae 


32. ARITHMETIG, 

















Y} (r — 1)s 
eeu anon log a = logt — (n— 1) log”, 
n-1/F s-a log 1—loga 
ee = yee log r= "Ty 
ar Bp SOs Myo waa! 2 be lg 
r bey = 0, ecole y 4, 7 aia Route 
sig stort | _. log [w + (* — 1)s] — loga 
ay log # ay, log r ’ 
kee Teme eae? _ log 1 — log [lr — (r ~ 1)s] 
=1a6 = dase Oe prt ; je log # +1. 


Population of the United States. 
(A problem in geometrical progression.) 


Increase in 10 Annual Increase, 


Year. Population. Years, per cent. per cent. 

1860 31,448,321 

1870 89,818,449* 26.63 2.39 
1880 50,155,783 25.96 2.33 
1890 62,622,250 24.86 2.20 
1900 76,295,220 21.834 1.994 
1905 Est. 83,577,000 ed Est. 1.840 
1910 ” 91'554,000 Est. 20.0 “1840 


Estimated Population in Hach Year from 1870 to 1909. 


(Based on the above rates of increase, in even thousands.) 

















1870....] 39,818 1880....| 50,156 18903-7162, 622 1900....| 76,295 
Siler 40,748 iBetel lesb eal tel 1891s 63,871 T9015 ce] ht, 099 
1872 =| = 41,699 1882. 27.1 525433 Mele os 65,145 1902....| 79,129 
1873....| 42,673 1883....{ 53,610 1893....) 66,444 1903....] 80,585 
1874... 43,670 1884....| 54,813 1894... 67,770 1904....| 82,067 
1875....| 44,690 1885....]| 56,043 1895....} 69,122 1905.2 83,077 
1876....) 45,373 1886....} 57,301 1896....] 70,500 1906..3.} 85,115 
AS Vien elie 46,800 1887.... 58, p88 TO O(erecil) a re O00 1907....| 86,681 
1878 .. | 47,893 1888... 59, 003 1898....| %73,2e41 1908.25.) 88,276 
1879....| 49,011 1889....) 61, 247 Use oosl)  Aeltlis! 1909....} 89,900 | 
The above table has been calculated by logarithms as follows : 
log r = log l — ee a + (n — 1), log nt = log a ay (m — 1) logr 
Pop. 1900... .76,295,220 log = 7.8824988 =logl 
+ 1890.. - 62,622,250 log = 7 alia = log a 
diff. = .08577' 
n = 1l,n —1= 10; diff. + 10 = ‘00867703 = logr, 
add log for 1890 = 7.7967285 = log @ 





log for 1891 = 7.80530553 No. = 63,871... 
add again 00857708 


log for 1892  %.81388256 No. = 65,145... 


Compound interest is a form of geometrical progression ; the ratio be- 
ing 1 plus the percentage. 








* Corrected by addition of 1,260,078, estimated error of the census of 1870, 
Census bulletin No, 16, Dec, 12, 1890, 


DISCOUNT. 13 


- 


INTEREST AND DISCOUNT. 


Interest is money paid for the use of money for a given time; the face 
tors are: 
p, the sum loaned, or the principal: 
t, the time in years; 
7, the rate of interest; 
i, the amount of interest for the given rate and time}; 
a=p+i= the amount of the principal with interest 
at the end of the time. 


Formule : ’ 

7 = interest = principal < time x rate per cent = i= Sait 
a= amount = principal + interest = p + a 

ie DES 1007. 
r= = iphe 
p = principal = 1001 os qn Bits 
Pe Ee rant) GER E AEPEIOD: 

1007 : 


¢ = time = —. 
pr 


Tf the rate is expressed decimally as a per cent,—thus, 6 per cent = .06,— 
the formule become ‘ ‘ : 
i= prt: a= (+ rt); preeas seen gsi Ge 
~= pits =p ’ ~ pe’ pr’ ; tr 1+ rt 
Rules for finding Interest,—Multiply the principal by the rate 
per aunum divided by 100, and by the time in y and fractions of a year. 
principal < rate X no. of days , 
365 x 100 ‘ 
In banks interest is sometimes calculated on the basis of 360 days to @ 
year, or 12 montis of 30 days each. 
Short rules for interest at 6 per cent, when 360 days are taken as 1 year: 
‘Multiply the principal by number of days and divide by 6000, 
Multiply the principal by number of months and divide by 200. 
The interest of 1 dollar for one month is % cent. 





If the time is given in days, interest = 


Interest of 100 Dollars for Different Times and Rates, 


Time. 2% 3% 4% 5% 6% 8% . 10% 
I year 2.00 $3.00 $4.00 $5.00, $6.00 $8.00 $10.00 
1 month 162, BS Or ae VF canal "662 83h 
{ day = sty year .00S5§ 00834 .01113 01388 01662 02282 02774 


1 day = siz year .005479 008219 010959 .013699 016438 10219178 0273973 


Discount is interest deducted for payment of money before it is due. 

Wrue discount is the difference between the amount of a debt pay- 
able at a future date without interest and its present worth. The present 
worth is that sum which put at interest at the legal rate wiil amount to the 
debt when it is due. 
_ To find the present worth of an amount due at future date, divide the 
amount by the amount of $1 placed at interest for the given time. The dis- 
pount equals the amount minus the present worth. 

What discount should be allowed on $103 paid six months before it is due, 
interest being 6 per cent per annum ? 


103 
141x 06 x = 


Bank discount is the amount deducted by a bank as interest on 
money loaned on promissory notes. It is interest calculated not on the act- 
ual sum loaned, but onthe gross amount of the note, from whith the dis- 
count is deducted in advance. It is also calculated on the basis of 360 days 
in the year, and for 3 (in some banks 4) days more than the time specified i 
the note. These are called days of grace, and the note is not payabie ti 


the last of thesedays. In some States days of gracé have beeu abolished. 


= $100 present worth, discount = 3.00. 


‘14 ARITHMETIC. 


What discount will be deducted by a bank in discounting a note for $108 
payable 6 months hence? Six months = 182 days, add 3 days grace = 185 


103 X 185 
days’ = $3.176. ! 


Compound Interest,—In compound interest the interest is added to 
the principal at the end of each year, (or shorter period if agreed upon). 
_ Let p = the principal, 7 = the rate expressed decimally, 1 = no of years, 
and a the amount: 





n 
a 
a= amount = p(i+ 7)”; r=rate= 2 —1, 





Eel a log a — log p 
= principal = ———— ; ; =n= i, 
p=p it aan no. of years=n log @ 1) 
Compound Interest Table. 


(Value of one dollar at compound interest, compounded yearly, at 
38, 4, 5, and 6 per cent, from 1 to 50 years.) 





ms a af es 


1.03 3.04 1.05 1.06 16 | 1.6047 | 1.8730 | 2.1829 | 2.5403 
1,0609 | 1.0816 | 1.1025 | 1.1286 | 17 | 1.6528 | 1.9479 | 2.2920 | 2.6928 
1.0927 | 1.1249 | 1.1576 | 1.1910 | 18 | 1.7024 | 2.0258 | 2.4066 | 2.8543 
1.1255 | 1.1699 | 1.2155 | 1.2625 | 19 | 1.7535 | 2.1068 | 2.5269 | 3.0256 
1.1598 | 1.2166 | 1.2763 | 1.8382 | 20 | 1.8061 | 2.1911 | 2.6583 | 3.2071 


1 
2 
3 
4 
5 
6 | 1.1941 | 1.2653 | 1.8401 | 1.4185 | 21 | 1.8603 | 2.2787 | 2.7859 | 3.3995 
7 | 1.2299 | 1.3159 | 1.4071 | 1.5036 | 22 | 1.9161 | 2.3699 | 2.9252 | 3.6035 
8 | 1.2668 | 1.3686 | 1.4774 | 1.5938 | 23 | 1.9736 | 2.4647 | 3.0715 | 3.8197 
9 | 1.3048 | 1.4233 | 1.5513 | 1.6895 | 24 | 2.0328 | 2.5633 | 3.2251 | 4.0487 
10 | 1.3439 | 1.4802 | 1.6289 | 1.7908 | 25 | 2.0937 | 2.6658 | 38.3863 | 4.2919 


1.7103 | 1.8983 | 30 | 2.4272 | 3.2483 | 4.3219 | 5.7435 

: 1.7958 | 2.0122 | 35 | 2.8138 | 3.9460 | 5.5159 | 7.6862 

13 | 1.4685 ; 1.6651 | 1.8856 | 2.1329 | 40 | 3.2620 | 4.8009 | 7.0398 | 10.2858 
1.9799 | 2.2609 | 45 | 8.7815 | 5.8410 | 8.9847'| 13.7648 

2.0789 | 2.8965 | 50 | 4.383 7.1064 | 11.4670 |18.4204 


At compound interest at 3 per cent money will double itself in 23144 years, 


at 4 per cent in 1724 years, at 5 per cent in 14.2 years, and at 6 per cent in 
11,9 years. % 


EQUATION OF PAYMENTS. 


By equation of payments we find the equivalent or average time in which 
one payment should be made to cancel a number of obligations due at dif- 
ferent dates; also the number of days upon which to calculate interest or 
discount upon a gross sum which is composed of several smaller sums pay- 
able at different dates. 

Rule.—Multiply each item by the time of its maturity in days from a 
fixed date, taken as a standard, and divide the sum of the products by the 
Pye of the items: the result is the average time in days from the standard 

ate, 

A owes B $100 due in 80 days, $200 due in 60 days, and $300 due in 90 days. 
In how many days may the whole be paid in one sum of $600 ? 


100 x 80 + 200 x 60 + 300 x 90 = 42,000; 42,000 +- 600 = 70 days, ans, 


A owes B $100, $200, and $300, which amounts are overdue eee 80, 
60, and 90 days, If he now pays the whole amount, $600, how many day@ 
interest should he pay on thatsum? dns. 70days, = 


ANNUITIRES. 1%) 


PARTIAL PAYMENTS, 


‘I'o compute interest on notes and bonds when partial payments have been 
made: 

United States Rule.—Find the amount of the principal to the time 
of the first payment, and, subtracting the payment from it, find the amount 
of the remainder as a new principal to the time of the next payment. 

If the payment is less than the interest, find the amount of the principal 
to the time when the sum of the payments equals or exceeds the interest 
due, and subtract the sum of the payments from this amount. 

Proceed in this manner till the time of settlement, 

Note.—The principles upon which the preceding rule is founded are: 

1st. That payments must be applied first to discharge accrued interest, 
and then the remainder, if any, toward the discharge of the principal. 

2d. That only unpaid principal can draw interest. 

Mereantile Method.—When partial payments are made on short 
es ep interest accounts, business men commonly employ the following 
method: 

Find the amount of the whole debt to the time of settlement; also find 
the amount of each payment from the time it was made to the time of set- 
tlement. Subtract the amount of payments from the amount of the debt; 
the remainder will be the balance due. 


ANNUITIES. 


An Annuity is a fixed sum of money paid yearly, or at other equal times 
agreed upon. The values of annuities are calculated by the principles of 
compound interest. 

1, Let i denote interest on $1 for a year, then at the end of a year the 
amount willbe 1-+7. At the end of n years it will be (1+ 7)”, 


2, The sum which in n years will amount to 1 is or (1+7)- ”, or the 





(1+ 2)™ 
present value of 1 due in » years. 
(1+7)"-1 
1 e 


4. The present value of an annuity of 1 for any number of years n is 
1—(1-+%)-” 


3. The amount of an annuity of 1 in any number of years n is 


u 
5. The annuity which 1 will purchase for any number of years n is 
tu 
roa) ; 
t 
6. The annuity which would amount to 1 in n years is —————., 
z A G+i"—1 
Amounts, Present Values, ete., at 5% Interest, 








Years| (LD) (2) (8) (4) (5) (6) 

ee aye (Peay ke Ot a eerie me FL EI 

a a 1—(1+-2)-"aA +2)" -1 

Vercors 1.95 . 952381 1. 952381 | 1.05 The 

2 1.1025 907029 2.05 1.859410 .537805 .487805 
at te 1.157625 | .863838 8.1525 2.723248 3867209 .817209 
45, 1.215506 | .822702 4.310125 3.545951 . 282012 2382012 
D5 eek 1.276282 | .783526 5.525631 4.829477 . 230975 .180975 
62x 1.340096 | .746215 6.801913 5 075692 .197017 .147018 
(aa. 1.407100 | .710681 °8. 142008 5.786373 . 172820 . 122820 
Ba eax 1.477455 | .676839 9.549109 6.463213 .154722 . 104722 
eed acic 1.551328 .644609 11.026564 7.107822 . 140690 .090690 
10:25: 1.628895 | .6138913 12.577893 7.921785 . 129505 079505 


ARITHMETIC. 


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WEIGHTS AND MEASURES. 17 


TABLES FOR CALCULATING SINKING-FUNDS AND 
PRESENT VALUES. 


Engineers and others connected with municipal work and industrial enter- 
prises often find it necessary to calculate payments to sinking-funds which 
will provide a sum of money sufficient to pay off a bond issue or other debt 
at the end of a given period, or to determine the present value of certain 
annual charges. The accompanying tables were computed by Mr. John W. 
Hill, of Cincinnati, Eng’g News, Jan. 25, 1894. 

Table I (opposite page) shows the annual sum at various rates of interest 
required to net $1000 in from 2 to 50 years, and Table II shows the present 
value at various rates of interest of an annual charge of $1000 for from 5 to 
50 years, at five-year intervals and for 100 years. 


Table II.—Capitalization of Annuity of $1000 for 
from 5 to 100 Wears, 











Rate of Interest, per cent. 


[ Years. 





214 3 314 4 4\6 5 516 6 


5] 4,645 88 | 4,579.60! 4,514.92] 4,451.68] 4,889.91] 4,329.45] 4,268.09] 4,212.40 
10] 8,752.17 | 8,530.13] 8,316.45] 8,110.74] 7,912.67] 7,721.73] 7,537.54) 7,860.19 
15/12.381.41 |11,937.80|11,517.23/11,118.06|10,739. 42/10,379.53| 10,037.48] 9,712.30 
20] 15,589. 215/14,877.27| 14,212. 12/ 13,590. 21/ 13,007. 88/12, 462. 13|11,950.26/11,469.96 
25/18,424.67 |17,413.01| 16,481.28 15,621 .93|14,828. 12]14,093. 86|13,413.82| 12,788.38 


30/20,930.59 | 19,600. 21/ 18,391 .85)17,291. 86/16, 288. 77/15, 372.36] 14,533.63) 13,764.85 
85) 23,145.31 |21,487.04/20,000.43) 18,664.37|17,460. 89) 16,374.36) 15,390.48) 14,488 .65 
40/25,103.53 |23,114.36/ 21,354.83, 19,792.65}18,401 .49)17,159 01) 16,044 .92}15,046.31 
45/26,833.15 |24,518.49/22,495.23 20,719. 89/19, 156 .24|17,773. 99) 16,547 .65) 15,455.85 
50/28,362.48 |25,729 58) 23,455 .21/21,482.08/ 19,761 .93)18,255 .86)16,931.97)15,761.87 
100/36,614.21 31,598 .81/ 27,655.36 24,504. 96/21 ,949 .21/19,847.90}18,095 83] 16,612.64 | 




















WEIGHTS AND MEASURES. 


Long Measure.—Measures of Length, 
12 inches = 1 foot. 

3 feet = leyard; 

760 yards, or 5280 feet = 1 miie, 

Additional measures of length in occasional use: 1000. mils = 1 inch; 
4 inches = 1 hand; 9 inches = 1] span; 24 feet = 1 military pace; 2 yards = 
1 fathom; 5% vards. or 164% feet = 1 rod (formerly also.called. pole or perch). 

Old Land MWeasure.—’.92 inches = 1 link; 100 links,.or 66 feet, or 4 
rods = 1 chain; 10 chains, or 220 yards = 1 furlong; 8 furlongs = 1 mile; 
10 square chains = 1 acre. 


Nautical Measure, 


set ace a ee 115156 Star t = 1 nautical mile, or knot.* 


3 nautical miles ae = 1 league. 
60 nautical miles, or 69. e wee 
St ahiaanilet = 1 degree (at the equator). 
360 degrees = circumference of the earth at the equator. 


*The British Admiralty takes the round figure of 6080 ft. which is the 
length of the ‘‘ measured mile’ used in trials of vessels. The value varie$ 
from 6080.26 to 6088.44 ft. according to different measures of the earth’s di- 
ameter. There is a difference of opinion among writers as to the use of the 
word * knot” to mean length or a distance—some holding that it should’ be 
used only to denote a rate of speed. The length between knots on the log 
line is 1/120 of a nautical mile, or 50.7 ft., when a half-minute glass is used; 
so that a speed of 10 knots is equal to 10 nautical miles per hour, 


18 ARITHMETIC. 


Square Measure.—Measures of Surfacé. 


144 square inches, or 183.35 circular = 1 square foot. 


inches 
9 square feet = 1 square yard. 
3014 square yards, or 27214 square feet = 1 square rod. 


10 sq. chains, or 160 sq. rods, or 4840 sq. { 
yards, or 43560 sq. feet, 
640 acres " = 1 square mile. 


An acre equals a square whose side is 208.71 feet. 

Circular Inchs; Circular Mlil.—<A circular inch is the area of a 
circle 1 inch in diameter = 0.7854 square inch. 

1 square inch = 1.2782 circular inches. 

A circular mil is the area of a circle 1 mil, or .001 inch in diameter- 
10002 or 1,000,000 circular mils = 1 circular inch. 

1 square inch = 1,273,289 circular mils. 

The mil and circular mil are used in electrical calculations involving 
the diameter and area of wires. 


= |] acre. 


Solid or Cubic WMeasure.—Measures of Volume, 


1728 cubic inches = 1 cubic foot. 
27 cubic feet = 1 cubic yard. 
1 cord of wood = a pile, 4 « 4 x & feet = 128 cubic feet. 
1 perch of masonry = 1614x114 X1 foot =2434 cubic feet. 


Liquid Measure. 


4 gills = 1 pint, 
2 pints = 1 quart. maT eM 
. S. 231 cubic inches. 

4 quarts = 1 gallon} jing. 977.914 cuble inches, 
311% gallens = 1 barrel. 
42 galluns = 1 tierce. 

2 barrels, or 63 gallons = 1 hogshead. 
84 gallons, or 2 tierces = 1 puncheon. 


2 hogsheads, or 126 gallons = 1 pipe or butt. 
2 pipes, or 3 puncheons = 1 tun. 


A gallon of water at 62° F. weighs 8.3356 lbs. 

The U.S. gallon contains 281 cubic inches; 7.4805 gallons = 1 cubic foot. 
A cylinder 7 in. diam. and 6 in. high contains 1 gallon, very nearly, or 230.9 
cubic inches. The British Imperial gallon contains 277.274 cubic inches 
= 1.20032 U. S. gallon, or Iv Ibs. of water at 62° F. 

The Miner’s Inch,.—(\\estern U.S. for measuring flow of a stream 
of water). 

The term Miner’s Inch is moro or less indefinite, for the reason that Cali- 
fornia water companies do not all use the same head above the centre of 
the aperture, and the inch varies from 1.386 to 1.78 cubic feet per minute 
each; but the most common measurement is through an aperture 2 inches 
high and whatever length is required, and through a plank 1} inches thick. 
The lower edge of the aperture should be 2 inches above the bottom of the 
measuring-box, and the plank 5 inches high above the aperture, thus mak- 
ing a 6-inch head above the centre of the stream. Each square inch of this 
opening represents a miner’s inch, which is equal to a flow of 14 cubic feet 
per minute. 

Apothecarics’ Fluid Measure. 
60 minims = 1 fluid drachm. 8 drachms = 1 fluid ounce. 

In the U. S. a fluid ounce is the 128th part of a U.S. gallon, or 1.805 cu. ins. 
It contains 456.3 grains of water at 49° F, In Great Britain the fluid ounce 
is 1.732 cu. ins. and contains 1 ounce avoirdupois, or 437.5 grains of water at 
62° F. 

Dry Measure, U. S. 
2 pints = 1 quart. 8 quarts = 1 peck. 4 pecks = 1 bushel. 
The standard U.S. bushelis the Winchester bushel, which is in cylinder 


WEIGHTS AND MEASURES. 19 


form, 1814 inches diameter and 8 inches deep, and contains 2150.42 cubic 


inches. 

A struck bushel contains 2150.42 cubic inches = 1.2445 cu. ft.; 1 cubic foot 
= 0.80356 struck bushel. A heaped bushel is a cylinder 1814 inches diam- 
eter and 8 inches deep, with a heaped cone not less than 6 inches high. 
It is equal to 114 struck bushels. 

The British Imperial bushel is based on the Imperial gallon, and contains 
8 such gallons, or 2218.192 cubic inches = 1.2837 cubic feet. The English 
quarter = 8 Imperial bushels. 

Capacity of a cylinder in U.S. gallons = square of diameter, in inches x 
height in inches X .0034. (Accurate within 1 part in 100,000.) 

Capacity of a cylinder in U.S. bushels = square of diameter in inches x 


height in inches X .0003652. 


Shipping Measure. 


Register Ton.—For register tonnage or for measurement of the entire 
internal capacity of a vessel : 


100 cubic feet = 1 register ton. 


This number is arbitrarily assumed to facilitate computation. 
Shipping Ton.—For the measurement of cargo: 
1 U.S. shipping ton. 
40 cubic feet = ~ 31.16 Imp. bushels. 
32,143.00. Sans 
i 1 British shipping ton. 
42 cubic feet = < 32.719 Imp. bushels. . 
(35.75 U. S. 4s 


Carpenter’s Rule.—Weight a vessel will carry = length of keel X breadth 
at main beam xX depth of hold in feet + 95 (the cubic feet allowed for a ton), 
The result will be the tonnage. For a double-decker instead of the depth 
of the hold take haif the breadth of the beam. 


Measures of Weight.—Avoirdupolis, or Commercial 
Weight, 


16 drachms, or 437.5 grains = 1 ounce, oz. 


16 ounces, or 7000 grains = 1 pound, lb. 
28 pounds = 1 quarter, qr. 
4 quarters = 1 hundredweight, ewt. = 112 Ibs. 
20 hundred weight = 1 ton of 2240 pounds, or long ton. 
2000 pounds = 1 net, or short ton. 
2204.6 pounds = 1 metric ton. 


1 stone = 14 pounds ; 1 quintal = 100 pounds. 
The drachm, quarter, hundredweight, stone, and quintal are now seldom 


used in the United States. 
Trey Weight. 


24 grains = 1 pennyweight, dwt. 
20 pennyweights = 1 ounce, oz. = 480 grains. 
12 ounces = 1 pound, lb. = 5760 grains. 


Troy weight is used for weighing gold and silver. The grain is the same 
in Avoirdupois, Troy, and Apothecaries’ weights. A carat, used in weighing: 
diamonds = 3.168 grains = .205 gramme. 


Apothecaries? Weight. 


20 grains =1scruple, D 
8 scruples =1drachm, 3 = _ 60 grains. 
S8drachms=1ounce, 3 <= 480 grains. 
#2 ounces =1pound,lb. <z= 5760 grains. 


To determine whether a balance has unequal arms,— 
After weighing an article and obtaining equilibrium, transpose the article 
and the weights. If the balance is true. it will remain in equilibrium ; if 
untrue, the pan suspended from the longer arm will descend. 

To weigh correctly on an incorrect balance,—First, by 
eubstitution, Put the article to he weighed in one pan of the halance and 


20 ARITHMETIC. 


counterpoise it by any convenient heavy articles placed on the other pan. 
Remove the article to be weighed and substitute for it standard weights 
until .equipoise is again established. The amount of these weights is the 
weight of the article. 

Second, by transposition. Determine the apparent weight of the article 
as usual, then its apparent weight after transposing the article and the 
weights, If the difference is small, add half the difference to the smaller 
of the apparent weights to obtain the true weight. If the difference is 2 
per cent the error of this method is 1 partin 10,000. For larger differences, 
or to obtain a perfectly accurate result, multiply the two apparent weights 
together and extract the square root of the product. 


Circular Measure. 


60 seconds, ’’ = 1 minute, ’. 
60 minutes, ’ = 1 degree, °. 
90 degrees = 1 quadrant. 
360 ¥ = circumference, 
Time, 
60 seconds = 1 minute. 
60 minutes = 1 hour. 
24hours = 1 day. 


@ days = 1 week. 
365 days, 5 hours, 48 minutes, 48 seconds = 1 year. 


By the Gregorian Calendar every year whose number is divisible by 4 is a 
leap year, and contains 366 days, the other years containing 365 days, ex- 
cept that the centesimal years are leap years only when the number of the 
year is divisible by 400. 

The comparative values of mean solar and sidereal time are shown by the 
following relations according to Bessel : 


365.24222 mean solar days = 366.24222 sidereal days, whence 
1 mean solar day = 1.00273791 sidereal days; 
1 sidereal day = 0 99726957 mean solar day; 
24 hours mean solar time = 24» 3™ 568.555 sidereal time; 
24 hours sidereal time = 23 56™ 4.091 mean solar time, 


whence 1,mean solar day is 8™ 558.91 longer than a sidereal day, reckoned in 
mean solar time. 


BOARD AND TIMBER MEASURE, 
Board Measure, 


In board measure boards are assumed to be one inch in thickness. To: 
obtain the number of feet board measure (B. M.) of a board or stick of 
square timber, multiply together the length in feet, the breadth in feet, and 
the thickness in inches., : 

To compute the measure or surface in square feet.—Wher. 
all dimensions are in feet, multiply the length by the breadth, and the pro- 
duct will give the surface required. 

When either of thé dimensions are in inches, multiply as above and divide 
the product by 12. 

. When all dimensions are in inches, multiply as before and divide product 

y 144. 


Timber Mieasure. 


To compute the volume of round timber.—When all dimen- 
sions are in feet, multiply the length by one quarter of the product of the 
mean girth and diameter, and the product will give the measurement in 
cubic feet. When length is given in feet and girth and diameter in inches, 
ol ue the product by 144; when all the dimensions are in inches, divide by 
1728. : 

To compute the volume of square timber.—When all dimen- 
sions are in feet, multiply together the length, breadth, and depth; the 
product will be the volume in cubic feet. When one dimension is given in 
inches, divide by 12; when two dimensions are in inches, divide by 144; when 
all three dimensions are in inches, divide by 1728. __. 


WHIGHTS AND MEASURES. ai 
Contents in Feet of Joists, Scantling, and Timber, 
Length in Feet. 























Size. | 13 14 | 16 18 | 20 22 | 24 | 26 | 28 | 80 
Feet Board Measure. 
2x 4 8 9 11 12 13 Le 16 | 5H paitumpemb!)e 20 
2) <6 12 14 16 18 20 22 24 26 28 | 80 
OLS aetes 16 19 21 24 ae 29 82 35 ij 40 
2x 10 20 23 27 30 83 ot 40 43 47 50 
264 12 24 28 32 36 40 44 48 52 56) 60 
2x 14 28 33 37 42 47 51 56 61 65 70 
Became) 24 28 32 36 40 44 48 52 56 60 
ny ed) 30 35 40 45 50 55 60 65 70 5 
3x 12 36 42 48 54 60 66 %2 78 84 90 
3 xX 14 42 49 56 63 70 U7 84 91 98 105 
Cee a! 16 19 21 24 27 29 32 35 37 40 
BUS 19} 24 28 82 36 40 44 48 52 56 60 
4x8 32 37 43 48 53 59 64 69 rt: 80 
4x 10 40 47 53 60 7 73 80 87 93 100 
4x 12 48 56 64 72 80 88 96 104 | 112 120 
4x 14 56 65 5 84 93 103 gues i ale al 131 140 
6G 36 42 48 Evia (ale 66 %2 78 84 90 
ox" '8 48 56 64 us 80 88 96 104 112 120 
6 xX 10 60 70 80 90 100 110 120 1380 140 150 
6>< 12 72 84 96 108 120 132 144 156 168 180 
6x 14 84 98 112 126 140 154 168 182 196 210 
8x 8 64 i) 85 96 107 va by 128 139 149 160 
8 x 10 80 93 107 120 1383 147 160 173 187 200 
ee ay 96 112 128 144 160 176 192 | 208 224 240 
8x 14 112 131 149 168 187 205 || 224) 248 | 261 280 
iO) Se 100 117 133 150 167 183 | 200] 217 | 233 | 250 
10 x 12 120 140 | 160 180 | 200 | 220 | 240] 260}; 280 300 
10 x 14 140 163 187 210 Ppl bye) P40) 303 | 327 350 
Neg Se nies 144 168 192 | S1G4* B40m 264 | 288) 312 | 3836 360 
12 < 14 168 196 224 | 252 | 280 | 308 326 364 392 20 
14 x 14 196 |} 229 261 294 yy al) 392 | 425 | 457 490 





FRENCH OR METRIC MEASURES, 


The metric unit of length is the metre = 39.37 inches. 

The metric unit of w eight i is the gram = 15.432 grains. 

The following pr efixes are used for subdivisions and multiples; Milli = zy, 
Centi = ;35, Deci = 75, Deca = 10, Hecto = 100, Kilo = 1000, Myria = 10,000. 


FRENCH AND BRITISH (AND AMERICAN) 
EQUIVALENT MEASURES. 


Measures of Length. 


FRENCH. BRITISH and U.S 
1 metre == 39.37 inches, or 3.28083 rece or 1.09361 yards. 
.0048 metre = 1 foot. 


1 centimetre = .3937 inch, 
254 centimetres = 1 inch. 

1 milimetre = .03937 inch, or 1/25 inch, nearly. 
25.4 millimetres = 1 inch. 

1 kilometre = 1093.61 yards, or 0.62137 mile, 


22 


ARITHMETIC. 


Measures of Surface, 


FRENCH. 
1 square metre 


.836 square metre 

.0929 square metre 
1 square centimetre 
6.452 square centimetres 


BritisH and U.S. 
{ 10.764 square feet, 
) 1.196 square yards. 
1 square yard. 
1 square foot. 
.155 square inch. 
1 square inch. 


ll W It tl 


1 square millimetre .00155 sq. in. = 1973.5 circ. mils. 
645.2 square millimetres = 1 ‘Square inch, 
1 centiare = 1 sq. metre = 10.764 square feet. 


1 are = 1 sq. decametre = 100.4 eae 
1 hectare = 100 ares = A064 aes Soa Aall acres. 
1 sq. kilometre = .386109 sq. miles = 247.11 

= = 88. 6109 ** 


1 sq. myriametre 
Of Volume. 
BritTisH and U.S. 
oS i 35.314 cubic feet. 
y 1.808 cubic yards, 
= 1 cubic yard. 
.02832 cubic metre = 1 cubic foot. “] 
: : 61.023 cubic inches, 
1 cubic decimetre =14 ‘0353 cubie foot. 


28.32 cubic decimetres = 1 cubic foot. 
1 cubic centimetre = .061 cubic inch. 
16.387 cubic centimetres = 1 cubic inch. 
1 cubic centimetre = 1 millilitre .061 cubie inch. 


FRENCH. 
1 cubic metre 
.7645 cubic metre 


oe 


1 céntilitre = = 610 * 
1 decilitre = : =e Oe Ocimuiee a 
1 litre = 1 cubic decimetre = 61.023“ ‘* = 1.05671 quarts, U.S. 


2.8375 bushels, 


1 hectolitre or decistere. 3.5314 cubic feet 
28.37 bushels, 


1 stere, kilolitre, or cubic metre = 1.308 cubic yards 


Of Capacity. 
BritisH and U. S. 
61 023 cubic inches, 
4 .03531 cubic foot, 
| .2642 gallon (American), 
(2.202 pounds of water at 62° F. 
= 1 cubic foot. 
= 1 gallon (British). 
= 1 gallon eae sek 


Of Weight. 


66 


FRENCH. 
1 litre (= 1 cubic decimetre) = 


28.317 litres 
4.543 litres 
3.785 litres 


FRENCH. BRITISH and U. S. 
1 gramme = 15.432 grains. 

.0648 gramme = 1 grain. 

28.35 gramme = 1 ounce avoirdupois. 


= 2.20416 pounds. 


1 kilogramme 
1 pound. 


.45386 kilogramme 


1 tonne or metric ton 


.9842 ton of 2240 pounds, 
1000 kilogrammes 
1.016 metric tons 


19.68 cwts., 
1016 kilogrammes ; 1 ton of 2240 pounds. 


2204.6 pounds. 

Mr. O. H. Titmann, in Bulletin No. 9 of the U. S. Coast and Geodetic Sur- 
vey, discusses the work of various authorities who have compared the yard 
and the metre, and by referring all the observations to a common standard 
has succeeded in reconciling the discrepancies within very narrow limits. 
The following are his results fo: the number of inches in a metre according 
to the comparisons of the authorities named: 


Il 


Ul I 


18i fen HH assletien.: ¢.s..cscedee eee 39.36994 inches. 

18182. Katerspereins. .:.. 2b seers. 39.36990 

1835s), Bailivaseeeticcs.  . <:.)s lotcemeereetosts 39.36973 es 

1866...-Clarkewrie ws... ... 0 eae. © 39.3697 Ay 

{SS5eqcCo mist Oekween.%.. . ic See eeIeee 39.36984 
The mean of these is............. 39.36982 


METRIC WEIGHTS AND MEASURES. 23 


METRIC CONVERSION TABLES. 


The following tables, with the subjoined memoranda, were published in 
1890 by the United States Coast and Geodetic Survey, office of standard 
weights and measures, T. C. Mendenhall, Superintendent. 


Tables for Converting U. 8S. Weights and Measures= 
Customary to Metric. 


LINEAR. 





Inches to Milli- Miles to Kilo- 


Feet to Mecres. | Yards to Metres. 








metres. metres. 
= 25.4001 0.304801 0.914402 1.60935 
eS 50.8001 0.609601 1.828804 3.21869 
3= 76. 2002 0.914402 2.743205 4.82804 
i 101.6002 1.219202 3.657607 6.43739 
5= 127.0903 1.524003 4.572009 8.04674 
6 = 1E2.4003 1.828804 5.486411 9.65608 
vies 177.8004 2.133604 6.400813 11.26543 
Ss = 203.2004 2.438405 7.815215 12.8747 
9 = 228 .6005 2.743205 8.229616 14.48412 

y SQUARE. 
Square Inches to] Square Feet to Ss : 
: alt cea cterat a quare Yards to Acres to 
oe ee vy asec a Square Metres. Hectares. 
t= 6.452 9.290 0.836 0.4047 
2 12.903 18.581 1.672 0.8094 
oes 19.355 27.871 2.508 1.2141 
tes 25.807 37.161 3.344 1.6187 
5= 32.258 46.452 4.181 2.0234 
= 38.710 55.742 5.017 2.4281 
ea 45.161 65.032 5.853 2.8328 
8 = 51.613 74.323 6.689 3 2375 
oe 58.065 83.613 7.525 8.6422 
CUBIC. 





Se iecenSe Cubic Feet to Cubic Yards to Bushels to 


Oe EEL Cubic Metres. Cubic Metres. Hectolitres. 
1= 16.387 0.02832 ‘0.765 0.35242 
2= 32.774 0.05663 1.529 0.70485 © 
3o= 49.161 0.08495 2.294 1.05727 
4 65.549 0.11327 3.058 1.40969 
5= 81.936 0.14158 3.823 1.76211 
6= 98.323 0 16990 4.587 2.11454 
c= 114.710 0.19822 5.352 2.46696 
8 = 131.097 0.22654 6.116 2.81938 
9= 147.484 0.25485 6.881 3.17181 





t 
, 





Fluid Drachms 


ARITHMETIC. 


CAPACITY. 
































to Millilitres or | Fluid Ounces to | Quarts to Litres./Gallons to Litres. 
Cubic Centi- Millilitres. 
metres. 
1= So fl 29.57 0 94636 3.78544 
ye 7.39 59.15 1.89272 7 57088 
5 = 11.09 88.72 2.83908 1135632 
4= 14.79 118 30 8.78544 15.14176 
3) = 18.48 147.87 4.73180 18.92720 
6= 22.18 177.44 5.67816 22.71264 
df == 25.88 207.02 6.62452 26.49808 
8 = 29.57 236.59 7.57088 30. 28252 
oi 33.25 266.16 8.51724 34.06896 
WEIGHT 
r 
ea ee ae Avoirdupois Avoirdupois oe 
Grains to Milli- Ounces to Pounds to Kilo- op Na to 
Sreinnie>. Gramimnes. grammes. 3 
1= 64.7989 28.3495 0.45359 31.10348 
a 129.5978 56.6991 0.90719 62 .20696 
ap Ses 194. 3968 85.0486 1.36078 93 .381044 
CW 259.1957 118.3981 1.81437 124.41392 
5= 823.9946 141.747 2.26796 155.51740 
6= 888 . 7935 170.0972 2.72156 186 . 62089 
"= 453.5924 198.4467 8.17515 217..72437 
s= 518.3914 226.7962 3.62874 248. 82785 
9= 583.1903 255.1457 4.08233 27993183 
1 chain = 20.1169 metres. 
1 square mile = 259 hectares. 
1 fathom = 1.829 metres. 
1 nautical mile = 1853.27 metres. 
1 foot = 0.304801 metre. 
1 avoir. pound = 453.5924277 gram. 
15432.35639 grains = 1 kilogramme. 
Tables for Converting U. 8S. Weights and Measures= 
Metric to Customary. 
LINEAR. 
Metres to Metres to Metres to Kilometres to 
Inches. Feet. Yards.* Miles. 
1= 39.3700 3.28088 1.093611 0.62137 
2= 78.7400 6.56167 2.187222 1.24274 
3= 118.1100 9, 84250 3.280833 1 8641) 
4= 157.4800 13. 12333 4.374444 2.48548 
5= 196.8500 16.40417 5.468056 3.10685 
6 = 236 . 2200 1968500 6.561667 8.72822 
(= 75.5900 22 96583 7.655278 4.34959 
s= 314.9600 26.24667 8.748889 4 97096 
9= 854.3300 29 52750 9.842500 5.59233 





























METRIC CONVERSION TABLES. 25 
SQUARE. 
Square Centi- : : : na 
metres th Square Metres Square Metres Hectares to 
Square Inches. to Square Feet. |to Square Yards. Acres. 
1= 0.1550 10.764 1.196 2.471 
2= 0.3100 21.528 2.392 4.942 
= 0.4650 82, 292 3.588 7.413 
4= 0.6200 43.055 4.784 9.884 
5= 0.7750 53.819 5.980 12.355 
6= 0.9300 64.583 7.176 14.826 
T= 1.0850 75.347 8.372 17.297 
s§= 1.2400 86.111 9.568 19.768 
oe 1.8950 96.874 10.764 22.239 
CUBIC: 
Cubie Centi- Cubie Deci- : ‘ 
: -_ | Cubic Metres to | Cubic Metres to 

Ings no Cubie | metres to Cubic (°Cuble Feet, °¥ |!" Cubic Yards. 
1= 0.0610 61.023 35.314 1.308 
2= 0.1220 122.047 70.629 2.616 
3= 0.1831 . 188.070 105.943 5.924 
4= 0.2441 244.093 141.258 5.232 
5= 0.8051 805.117 176.572 6.540 
6= 0.3661 366.140 211.887 7.848 
j= 0.4272 427.163 _ 247.201 9.156 
8 = 0.4882 488.187 282.516 10.464 
5=— 0.5492 549.210 817.8380 11.771 

CAPACITY. 

Millilitres or | Qentilitres Dekalitrés | Hektolitres 

Cubic Centi- aes Litres to 

litres to Fata} #9, Fluid Quarts £0 sa A 

: Dréctime: Ounces. : Gallons. Bushels. 
1= 0.27 0.338 1.0567 2.6417 2.8375 
2= 0.54 0.676 2.1184 5.2834 5.6750 
3= 0.81 1.014 3.1700 7.9251 5125 
4= 1.08 1.352 4.2267 10.5668 11.3500 
5= 1.35 1,691 5.28384 13.2085 14.1875 
6 = 1.62 2.029 6.3401 15.8502 17.0250 
T= 1.89 2.368 7.8968 18.4919 19.8625 
8= 2.16 2.706 8.4534 21.1386 22.7000 
I= 2.43 8.043 9.5101 23.7753) 25.5375 








26 ARITHMETIC. 








WEIGHT. 
Milligrammes Kilogrammes Hectogrammes | Kilogrammes 
ee Grand 3 to Graing (100 grammes) to Pounds 
‘ ; to Ounces Av. Avoirdupois. 

ses 0.01543 15432.36 3.5274 2.20462 
or 0.03086 30864 .71 7.0548 4.40924 
a 0.04630 46297 .07 10.5822 6.61386 
4= 0.06173 61729 .43 14.1096 8.81849 
5= 0.07716 77161.78 17.637 11.02311 
6= 0.09259 92594 .14 21.1644 13.22777 

7 = 0.10803 108026 .49 24.6918 15.43235 
ee 0.12346 - 1238458 .85 28.2192 17.63697 
9= 0.13889 138891 .21 31.7466 19.84159 

WEHEIGHT—(Contineed). 
Quintals to Milliers or Tonnes to | Grammes to Ounces, 
Pounds Av. Pounds Av. Troy. 

eS 220.46 22046 0 02215 

ee 440.92 4409.2 0.06430 

3) 661.38 6613 8 0.09645 

a= 881.84 8818.4 0.12860 

Ks 1102.30 11023.0 0.16075 

6=— 1322.76 13227.6 0.19290 

a 1543.22 15482 .2 , 0.22505 

fo} 1763 68 17636.8 0.25721 

9= 


1984.14 19841 .4 ; 0.28936 


The only authorized material staridard of customary length is the | 
Troughton scale belonging to this office, whose length at 59°.62 Fahr. con- 
forms to the British standard. The yard in use in the United States is there- 
fore equal to the British yard- 

The only authorized material standard of customary weight is the Troy 
pound of the mint. It is of brass of unknown density, and therefore nut 
suitable for a standard of mass. It was derived from the British standard 
Troy pound of 1758 by direct comparison. The British Avoirdupois pound 
was also derived from the latter, and contains 7000 grains Troy. 

The grain Troy is therefore the same as the grain Avoirdupois, and the 
pound Avoirdupois in use in the United States is equal to the British pound 
Avoirdupois. 

The metric system was legalized in the United States in 1866. 

By the concurrent action of the principal governments of the world an 
las WE pai Bureau of Weights and Measures has. been established near 

aris, 

The International Standard Metre is derived from the Métre des Archives, 
and its length is defined by the distance between two lines at 0° Centigrade, 
on a platinum-iridium bar deposited at the International Bureau. 

The International Standard Kilogramme is a mass of platinum-iridium 
deposited at the same place, and its weight zn vacuo is the same as that of 
the Kilogramme des Archives. 

Copies of these international standards are deposited in the office of 
standard weights and measures of the U. S. Coast and Geodetic Survey. 

The litre is equal to a cubic decimetre of water, and it is measured by the 

uantity of distilled water which, at its maximum density, will counterpoise 
the standard kilogramme in a vacuum; the volume of such a quantity of 
water being, as nearly as has been ascertained, equal to a cubic decimetre, 


WEIGHTS AND MEASURES—COMPOUND UNITS, 27 


COMPOUND UNITS. 
Measures of Pressure and Weight, 


( 144 lbs. per square foot. 
2.0355 ims. of mercury at 32° F, 


1 lb. per square inch. mae ene 1G hee ppoes He 
2. 309 ft. of water at 62° F. 
2c Lis; oe cere, OSL, 


.1276 in. of mereury at. 62° F. 
1.732 ins. of water at 62° F. 
2116.3 lbs. per square foot. 
33.947 ft. of water at 62° F. 
30 ins. of mercury at 62° F 
29,922 ins. of mercury at 32° F, 
760 millimetres of mercury at 32° F, 


1 ounce per sq. in. | 
| 
.03609 lb. or .5774 oz. per sq. in. 
{ 
! 


1 atmosphere (14.7 Ibs. per sq. in.) = 


5.196 lbs. per square foot. 
.0736 in. of mercury at 62° F. 
5.2021 Ibs. per square foot. 
-036125 Ib. son neh: 
.433 Ib. per square inch, 

62.355 Ibs. ‘* foot. 

.491 Ib. or 7.86 oz. per sq. in. 

1.182 ft. of water at 62° F. 

13.58 ins. oye uOgorH. 


Weight of One Cubic Foot of Pure Water. 
62.418 lbs. 


1 inch of water at 62° F. = 


1 inch of water at 32° F. 


1 foot of water at 62° F, 


1 inch of mercury at 62° F. 


Abiecor thr COZIN 22 —) Ol) > cies ye cterchayetere tee onerstora ici aie eera tery 

eS Se He! (MAXUM en SIbY) iat otce tee eae eee See 62:425 “* 

‘UIG2- WM (Standard temMpevature) seers jel xckepic eee ae 62.355 3 
59.7 


*¢ 21° F. (boiling point, under 1 atmosphere)........ 


Amer ican gall Ola eubi c ins. of water at 62° F. = 8.3356 Ibs. 
Vigan o' * = 10 lbs. 


Bsa : =) ty ae 
Measures of Woxk, Power, and Duty. 

Work.—The sustained exertion of pressure through space. 

Unit of work.—One foot-pound, i.e., a pressure of one pound exerted 
through a space of one foot. 

Horse-power,.—The rate of work. Unit of horse-power = 33,000 ft. - 
Ibs. pev minute. or 550 ft.-lbs. per second = 1,980,000 ft.-lbs. per hour. 

Weat unit = heat required to raise 1 Ib. of water 1° F, (from 39° to 40°), 


33000 
Horse-power expressed in heat units = org = 42.416 heat units per min- 


ute = .707 heat unit per second = 2545 heat units per hour. 
1 1b. of fuel per H. VP. per hour= \ 2" ae Se Parl. of fuel. 
1,900,000 ft.-Ibs. per lb. of fuel = 1.98 Ibs. of fuel per H. P. per hour. 
Velocity.-—Keet per second = a = = 


1760 11 
Gross tons per mile = iG = lbs. per yard (single rail.) 


French and British Equivalents of Compound Units, 


x miles per hour. 


FRENCH. BRITISH. 
1 gramme per square millimetre Ne Jbs. per square inc! Le 
M kilogramme per square be 1422. 32 
~ centimetre 14,223 ° si $ Ge 
Wah ss 


1 lb. per square inch. 
0.062428 lb. per cubie foot. 
7.2330 foot-pounds. 


1 10335 kg. as sq.cm, = 1 atmosphere 
0.070308 kilogramme per square centimetre 
1 grainme per litre 
1 kilogsrammetre 


Panwa 


98 ARITHMETIC, 


WIRE AND SHEET-METAL GAUGES COMPARED. 


———— eee 
































\ = ee B= “=> og eis 
le Se fa OS oIRriti jall= Rots 
o.  G28| oes Seo | 2 8 standard [SSees | 8 
BG ive & G25 wb hl SE H&S) Wire Gauge. Sparen ellie 
£5 | 885 | Feo £Ge 3\2a 22| (Legal Standard |3 63 S27| 25 
=e fee Do |S 8—5'H SO G| in Great Britain |. Fa 85 gs 
= Rem Sas DER Y~ © since Nw Paws | 5 
a mae qha 2 8\ March 1, 1884.) eee She|G 
~ > a No4—'sR 
inch. | inch. inch 
F500; Wie a7 5 (GA © 
.464 | 11.78 .469 6/0 — 
-432 | 10.97 438 5/0 
4 : 10.16 406 4/0 
37 ; 7 3/0 
: 344 2/0 
8.23 .313 0 
220 7.62 231 J 
£219 7.01 266 2 
212 6.4 625 3 
207 5.89 234 4 
.204 5.38 219 5 
201 4.88 .208 6 
199 4.47 188 7 
19% 4.06 172 8 
194 3.66 .156 9 
.191 3.25 141 10 
.188 2.95 125 11 
185 2.64 109 12 
.182 2.34 “094 13 
-180 2.03 0% 14 
178 1.83 07 15 
175 1.63 0625 16 
Fi) atic 12s -0563- 17 
.168 ieee .05 18 
.164 102 .0438 19 
-161 Ot 
15 : 
.155 : 
153 i 
-151 
148 
. 146 
143 
.189 
184 
127 
.120 
115 
.112 
.110 
.108 
.106 
.108 
101 
.099 
097 
-095 
092 
.088 
085 
.081 
07 
O77 
07 





WIRE GAUGE TABLES. 


29 


EDISON, OR CIRCULAR MIL GAUGE, FOR ELEC- 
TRICAL WIRES. 


SS) | | 


Gauge |,; Diam- 
Num- Sere eter 
ber. Us. | in Mils. 
8 3,000 | 54.78 
5 5,000 70: (2 
8 8,000 89.45 
12 12,000 | 109.55 
15 15,000 | 122.48 
20 20,000 | 141.43 
25 25,000 | 158.12 
30 30,000 | 173.21 
lis 35,000 | 187,09 
40 40,000 | 200.00 
45 45,000 | 212.14 
50 50,000 | 223.61 
55 55,000 | 234.58 
60 60,000 | 244.95 
65 65,000 | 254.96 


1% 
18 


: Diam- || Gauge 
Circular eter Tike 
* Jin Mils.|| ber. 
70,000 | 264.58 190 
75,000 | 273.87 200 
80,000 | 282.85 220 
85,000 | 291.55 240 
90,000 } 800.00 260 
95,000 | 808.23 280 
100,000 | 316.28 800 
110,000 | 831.67 320 
120,000° | 346.42 3840 
130,000 | 360.56 360 
140,000 74.17 
150,000 | 387.30 
160,000 | 400.00 
170,000 | 412.82 
180,000 | 424.27 








Circular 


Mils. 


190,000 
200,000 
220,000 
240,000 
260,000 


280,000 
300,000 
320,000 
340,000 
360,000 


Diam- 
eter 
in Mils. 


435.89 
447 .22 
469.05 
489.90 
509.91 


529.16 
547.78 
565.69 
583.10 
600.00 





TWIST DRILL AND STEEL WIRE GAUGE. 
(Morse Twist Drill and Machine Co.) 


















































No.| Size. ||No.| Size. || No.| Size. || No.| Size No.| Size. || No.| Size. 
inch. inch inch, inch inch. inch. 
1 . 2280 11 .1910 21 1590 31 ~1200 || 41 0960|| 51 | .0676 
2 »2210 || 12 .1890 || 2% 1570 || 82 1160 || 42 } .0985]| 52 |} .0635 
3 -2180 || 18 .1850 || 23 .1540 |} 33 .1180 || 48 | .0890]} 53 | .0595 
4 -2090 || 14 .1820 || 24 1520 || 34 1110 || 44 | .0860}| 54 | .0550 
5 .2055 15 .1800 20 1495 35 1100 |) 45 | .0820]) 55 | .0520 
6 - 2040 16 .1770 26 1470 36 1065 || 46 | .0810]) 56 0465 
7 .2010 || 17 .1730 || 27 1440 || 37 .1040 % 1 .0785|| 57 | .0480 
8 .1990 || 186) .1695 || 28 1405 || 38 .1015 || 48 | .0760)} 58 | .0420 
9 .1960 || 19 .1660 || 29 -1360 |! 39 .0995 || 49 730|| 59 | .0410 
10 -1935 || 20 -1610 || 30 -1285 || 40 -0980 |} 50 | .0700]) 6O | .0400 
STUBS’ STEEL WIRE GAUGE. 
(For Nos. 1 to 50 see table on page 28.) 
No.| Size No.| Size No.| Size. || No.| Size. || No.| Size. || No.| Size 
inch, inch. inch. inch. inch. inch 
Z .413 if 3823 F 2257 51 .066 61 | .038 |} 71 | .026 
Ni 404 O .3816 E 250 52 .063 62 | .037 ||. 72 | .024 
x 897 N .202 ||'D 246 53 .058 63 | .086 ||} 73 | .023 
WwW 386 M 2295 C 2242 54 .055 64 | .035 74 | .022 
V 37% L .290 B .238 55 050 65 | .033 || 75 | .020 
U 368 K 281 A 284 56 .045 66 | .082 || 76 | .018 
oT 358 J ere 1 See 57 .042 67 | .031.|| 77 | .016 
Ss 348 I 272 to |< page || 58 | .041 68 | .030 || 78 | .015 
1° 339 H .266 50 28 59 .040 69 | .029 || 79 | .014 
Q .382 G 261 60 .039 90 | .027 || 80} .013 
































The Stubs’ Steel Wire Gauge is used in measuring drawn steel wire or 
drill rods of Stubs’ make, and is also used by many makers of American 


drill r ods, 


30 ARITHMETIC. 


THE EDISON OR CIRCULAR MIL WIRE GAUGE. 


(For table of copper wires by this’gauge, giving weights, electrical resis\- 
ances, etc., see Copper Wire.) 

Mr. C. J. Field (Stevens Indieator, July, 1887) thus describes the origin of 
the Edison gauge: 

The Edison company experienced inconvenience and loss by not having a 
wide enough range nor sufficient number of sizes in the existing gauges. 
This was felt more particularly in the central-station work in making 
electrical determinations for the street system. They were compelled to 
make use of two of the existing gauges at least, thereby introducing a 
enpeL canoe. that was liable to lead to mistakes by the contractors and 
inemen. 

In the incandescent system an even distribution throughout the entire 
system and a uniform pressure at the point of delivery are obtained by cal- 
culating for a given maximum percentage of loss from the potential as 
delivered from the dynamo. In carrying this out, on account of lack of 
regular sizes, it was often necessary to use larger sizes than the occasion 
demanded, and even to assume new sizes for large underground conductors. 
It was also found that nearly all manufacturers based their calculation for 
the conductivity of their wire on a variety of units, and that not one used 
the latest unit as adopted by the British Association and determined from 
Dr. Matthiessen’s experiments ; and as this was the unit employed in the 
manufacture of the Edison lamps, there was a further reason for construct- 
ing a new gauge. The engineering department of the Edison company, 
knowing the requirements, have designed a gauge that has the widest 
range obtainable and a large number of sizes which increase in a regular 
and uniform manner. The basis of the graduation is the sectional area, and 
the number.ef the wire corresponds. A wire of 100,000 circular mils area js 
No. 100; a wire of one half the size will be No. 50; twice the size No. 200. 

In the older gauges, as the number increased the size decreased. With 
this gauge, however, the number increases with the wire, and the number 
multiplied by 1000 will give the circular mils. 

The weight per mil-foot, 0.00006302705 pounds, agrees with a specific 
gravity of 8.889, which is the latest figure given for copper. The ampere 
capacity which is given was deduced from experiments made in the com- 
pany’s laboratory, and is based on arise of temperature of 50° F. in the viire. 

In 1893 Mr. Field writes, concerning gauges in use by electrical engineers: 

The B. and S. gauge seems to be in general use for the smaller sizes, up 
to 100,000 c. m., and in some cases a little larger. From between one and 
two hundred thousand circular mils upwards, the Edison gauge or its 
ean Rien is practically in use, and there is a general tendency to designate 
all sizes above this in circular mils, specifying a wire as 200,000, 400,000, 500,- 
000, or 1,000,000 c. m. @ 

In the electrical business there is a large use of copper wire and rod and 
other materials of these large sizes, and in ordering them, speaking of them, 
specifying, and in every other use, the general method is to simply specify 
the circular milage, I think it is going to be the only system in the future 
for the designation of wires, and the attaining of it means practically the 
adoption of the Edison gauge or the method and basis of this gauge as the 
correct one for wire sizes, 


THE U. S. STANDARD GAUGE FOR SHEET AND 
PLATE IKON AND STEEL, 1893. 


There is in this country no uniform or standard gauge; and the same 
numbers in different gauges represent different thicknesses of sheets or 
plates. This ]\as given rise to much misunderstanding and friction between 
employers and workmen and mistakes and fraud between dealers and con- 
sumers. 

An Act of Congress in 1893 established the Standard Gauge for sheet iron 
and steel which is given on the next page. It is based on the fact thata 
cubic foot of iron weighs 480 pounds. 

A sheet of iron 1 foot square and 1 inch thick weighs 40 pounds, or 640 
ounces, and 1 ounce in weight should be 1/640 inch thick. The scale has 
been arranged so that each descriptive number represents a certain number 
of ounces in weight and an equal number of 640ths of an inch in thickness. 

The law enacts that on and after July 1, 1893, the new gauge shall be used 
in determining duties and taxes levied on sheet and plate iron and steel; and 
that in its application a variation of 244 per cent either way may be allowed, 


GAUGE FOR SHEET AND PLATE IRON. AND STEEL. 3] 


U. S&S. STANDARD GAUGE FOR SHEET AND PLATE 
IRON AND STEEL, 1893. 








a 












































Quakes Sia 2g rd aS sea | RSW eg Bh Oe gj ap | sue ays 
S. lse3.|Sag8 | 28 § (SS e5l 83a5 |Sselssaiseas 
oS |B$o5|E¢iuc| £2 2 lomo) Cees |be sce s|fo S 
d © far] i o'5 H_2 =n) ose Me Seat al ia 
es |RESa Resneg | Ses ess Ge opids sidetieoss 
Spe BOO 5 co SEM ae = BEO8 SAS siglese vets 
5 Sa) SsA08 i = S| ois SM Sos 
z |BEE*|EE°S | ES BZeREgS3 Eas ase 52% 
0000000; 1-2 |0.5 - PATE SEY)» eID. 9.072 |97.65.| 215.28 
000000} 15-382 |0.468%'5 11.90625 300 18.75 8.505 |91.55 | 201.82 
00000} 7-16 |0.4375 tes Leo: 280 17.50 7.938 |85.44 | 188.37 
0000) 138-32 | 0.40625 10.31875 260 16.25 7.371 |79.838 | 174.91 
000} 38-8 |0.37 9.525 240 15. 6.804 |73.24 | 161.46 
00) 11-82 | 0.34375 8.73125 220° 118.75 6.237 167.13 | 148 00 
0} 5-16 |0.3125 7.9875 200 12.50 5.67 1.03 | 184.55 
1) 9-82 | 0.28125 7.14375 18057 11225 5.103 [54.95 | 121.09 
2) 17-64 |0.265625 |6.746875 170 §=— 110.625 ~~ /4.819 |51.88 | 114.37 
Shot ea Obeb 6.35 160 —/|10: 4.536 |48.82 | 107.64 
4} 15-64 | 0.234375 5.953125 150 9.375 4.252" 145.77 | 100.91 
5) 7-382) | 0.21875 5.55625 140 8275 3.969 42.72 | 94.18 
6} 13-64 | 0.208125 5.159375 130 8.125 3.685 139.67 87.45 
"| 3-16 |0.1875 4.7625 120 7.5 3.402 |386.62 | 80.72 
8| 11-64 [0.171875 |4.365625 110 6.875 | 18.118 |38.57 | 74.00 
9| 5-82 | 0.15625 3.96875 100 6.25 2.835 |30.52 | 67.27 
10| 9-64 |0.140625 3.57187 90 5.625 2.552, (27.46 60.55 
11} 1-8 0.125 3.175 80 ‘aye 2.268: 124.41 53.82 
12} 7-64 |0.109875 |2.778125 70 4.875 1.984 }21.86 | 47.09 
13} 3-32 |0.09375 2.88125 60 3.75 1.701 |18.81 40.36 
14] 5-64 |0.078125 {1.984375 50 8.125 {1.417 |15.26 | 33.64 
15| 9-128 |0.0703125 |1.7859375 45 2.8125 |1.276 113.7: 30.27 
16] 1-16 |0.0625 1.5875 40 2.0 1.134 |12.21 26.91 
17| 9-160 | 0.05625 1.42875 36 Pe ds 1.021 |10.99 24.22 
18} 1-20 |0.05 1.27 32 26 0.9072) 9.765} 21.53 
19} 7-160 |0.04375 1.11125 28 1275 0.7938] 8.544) 18.84 
20; 3-80 |0.0375 0.9525 24 1.50 0.6804) 7.324) 16.15 
21} 11-820 | 0.034375 0.873125 22 1.3875 0.6237] 6.713) 14.80 
22) 1-382 | 0.08125 0.793750 20 1.25 0.567 | 6.103} 13 46 
23} 9-320 | 0.028125 0.714375 18 1.125 0.5103) 5.493) 12.11 
24) 1-40 |0.025 0.635 16 1” 0.4536] 4.882) 10.7 
25| 7-320 |0.021875 0.555625 14 0.875 0.3969} 4.272 9742 
26! 3-160 |0.01875 0.47625 13 0.95 0.3402) 3.662 8 U7 
27) 11-640 |0.0171875 |0.4365625 11 0.6875 |0.3119) 3.357 7.40 
28} 1-64 |0.015625 {0.396875 10 0.625 | /0.2835! 3.052; 6.73 
29) 9-640 |0.0140625 |0.3571875 9 0.5625 10.2551] 2.746) 6.05 
30) 1-80 | 0.0125 0.3175 8 0.5 0.2268} 2.441 5.38 
81] 7-640 |0.0109375 |0.2778125 hs 0.4875 |0.1984) 2.136 4.71 
32) 13-1280] 0.01015625 |0.25796875 614 | 0.40625 [0.1843] 1.988 4.37 
33} 3-320 |0.009875  |0.2388125 6 0.3875 |0.1701} 1.831] 4.04 
34] 11-1280] 0.00859375 |0.21828125 546 | 0.384375 10.1559} 1.67 3 70 
35] . 5-640 |0.0078125 |0.1984375 5 0.3125 |0.1417| 1.526 3.36 
36) 9~-1280) 0.00703125 |0.17859375 446 | 0.28125 |0.1276) 1.873 3.03 
37| 17-2560) 0.006640625|0.168671875 414 | 0.265625)0.1205) 1.297 2.87 
3 1-160 | 0.00625 0.15875 4 0.25 0.1184} 1.221 2.69 














: 





+ Seppe ees 





Die panel MATHEMATICS, ¥ 


4 


The Decimal Gauge.—The legalization of the standard sheet-metal 
gauge of 1893 and its adoption by some manufacturers of sheet iron have 
only added to the existing confusion of gauges. A joint committee of the 
American Society of Mechanical Engineers and the American Railway 
Master Mechanics’ Association in 1895 agreed to recommend the use of the 
decimal gauge, that is, a gauge whose number for each thickness js the 
number of thousandths of an inch in that thickness, and also to reeommend 
*“*the abandonment and disuse of the various other gauges now in use, as 
tending to confusion and error.” A notched gauge of oval form, shown in 
the cut below, has come into use as a standard form of the decimal gange. 

In 1904 The Westinghouse Electric & Mfg. Co. abandoned the use of gauge 
numbers in referring to wire, sheet metal, ete. 

Weight of Sheet Iron aU: Steel. Thickness by Decima} 
auge. 


Weis ht per 





2 Weight per ie @ 
a # Square Foot g 5B Square Foot 
; aS) ® in Pounds. * 2 ) in Pounds. 
ae 2 8 2. i = 
3 Sos Shy Wh get 5 © sap Ba 
Rh = p taal | =] 
Si} oPE LE PSR se | Sof Rese | ee lee 
° me st Ci aes | ° 
a KS cA Sh |Seat = og 8h |F oa 
g 3 fan} 3 STAs, ae 5 5 € tas} ce pes <2 J 
3 ES  |Sa/Sn0q 8 BS Ss | S&|2Ho 
(e) <q <q Rs} ND Q <{ <q & n 
0.002 1/500 0.05 | 0.08 | 0.082 & 0.060 1/16 — | 1.52 | 2.40 2.448 
0.004 1/250 0.10 {| 0.16 | 0.163 f 0.065 | 13/200 1.65 | 2.60 2.652 
0.006 3/500 0.15 | 0.24 | 0.245 9 0.07 7/100 1.78 | 2.80 2.856 
0.008 1/125 0.20 | 0.32 | 0.326 # 0.075 &/40 1.90 | 3.00 3.060 
0.010 1/100 0.25- | 0.40 | 0.408 g§ 0.080 2/25 2.03 | 38.20 8.264 
0.012 3/250 0.380 | 0.48 | 0.490 § 0.085 | 17/200 2.16 | 3.40 3.468 
0.014 7/500 6.386 | 0.56 | 0.571 § 0.090 9/100 2.28 | 3.60 S602 
0.016 | 1/64 + | 041 | 0.64 | 0.653 f 0.095 | 19/200 | 2.411 3.80] 3.87 
0.018 9/500 0.46 | 0.72 | 0.734 £§ 0.100 1/10 2.54 | 4.00 4.080 
0.020 1/50 0 51 | 0.80 | 0.816 # 6.110 | 11/100 2.79 | 4.40 4.488 
0.022 | 11/500 0.56 | 0.88 } 0 898 W 0.125 1/8 8.18 | 5.00 5.100 
0.025 1/40 0.64 | 1.00 | 1.020 f 0.125 | 27/200 3.43 | 5.40 5.508 
0.028 7/250 0.7 1.12 | 1.142 # 0.150 8/20 38.81 | 6.00 6.120 
0.032 1/32 +] 0.81 1.28 | 1.306 f 0.165 | 33/200 4.19 | 6.60 §.732 
0.036 9/250 0.91 1.44 | 1.469 & 0.180 9/50 4.57 | 7.20 7.844 
0.040 1/2 1,02 1.60 | 1.632 # 0.200 1/5 5.08 | 8.00 8.160 
0.045 9/200 1.14 | 1.80 | 1.8386 § 0.220 |} 11/50 5.59 | 8.80 8.976 
0.050 1/20 1.27 | 2 00 | 2.040 § 0.240 6/25 6.10 | 9.60 9.792 
0.055 | 11/200 1.40 | 2.20 | 2.244 § 0.250 1/4 6.35 110.00 ° 10.200 








HARTFORD, CONN. 
oie US.a 


Asreq-wecune® . 


N x 






ALGEBRA, og 


ALGEBRA. 


Addition.—Addaandb, Ans.a+b. Adda,b,and—c. Ans.a+b—e, 

Add’ 2a and —38a. Ans.—a, Add 2ab, —3ab, —c, —3c. Ans, — ab— 4e, 

Subtraction.—Subtract afrom >. Ans.b—a. Subtract — a from — b, 
Ans. —b+a. 

Subtract 6-++-c froma. Ans.a—b—c. Subtract 8a2b— 9c from 4a2b + ¢, 
Ans. @?2b.+.10c. Rue: Change the signs of the subtrahend and proceed as 
in addition. 

Multiplication.—Multiply a by b. Ans. ab. Multiply ab by a+b. 
Ans. @?b.-+ ab. 

Multiplya+obbya-+b. Ans. (a+ 6b)(a+b) = a+ 2ab + b?, 

Multiply —-a-by — b. Ans. ab. Multiply — aby 6. Ans.—ab. Like 
signs give plus, unlike signs minus. 

Powers of numbers.—the product of two or more powers of any 
number is the number with an exponent equal to the sum of the powers: 
a? x a8 = a5;. a2b? x ab = a3b3; — Tab x Zac = — 14 a2be. 

To multiply a polynomial by a monomial, multiply each term of the poly- 
nopiabhy the monomial and add the partial products: (6a — 3b) x 8c = 18ac 
— 9bc. 

To multiply two. polynomials, multiply each term of one factor by each 
term of the other and add the partial products: (5a — 6b) x (8a — 4b) = 
15a? — 38ab + 2462. 

The square of the sum of two numbers = sum of their squares + twice 
their product. 

The square.of the difference. of two numbers = the sum, of their squares 
— twice-their product. 

The product: of the sum and difference of two numbers = the difference 
of their squares: 

(a+b)? =a? +2ab+6?2; (a — b)? =a? — 2ab- b3; 
(a+b) x (a- b) =a? — b?, 
The square of half the sums of two quantities is equal to their product pius 
2 = 
the square of half their difference: (g 9 Shi ab 4- (2-" . 

The square of the sum of two quantities is equal to four times their prod: 
ucts, plus. the square of their difference: (a + b)2 = 4ab + (a — b)? 

The sum of the squares of two quantities equals twice their product, plus 
the square of their difference: a? + b2 = 2ab + (a -- b)?. 

The square of a trinomial = the square of each term + twice the product 
of each term by each of the terms that follow it: (a +b +c)? = a? + b2 + 
c? + 2ab + 2ac + 2bc; (a — b — c)? = a? 4+ b?2 4+ c2 — 2ab — 2ac + 2be. 

The square of (any number + 4) = square of the number + the number 
+14; =the number X (the number + 1) + 4; 

(a+ 4)? =a?+ a+, =aa+1)+. (446)2=42+4+34=4 X54 = 204, 

The product of any number -+ 4 by any other number + % = product of 
the numbers + half theirsum +4. (a+%) x 6+%) =ab-+ K(a+ b)+ \%. 
414 x 6144 = 4X 6414446) +14 = M4544 = 294. _ 

Square, cube, 4th power, ete., of a binomial a-+- b. 


(a +b)? =a? --2ab +02; (a +b)3 = a3 + 3% + 8ab2 +3; 
(a+ b)* = at +4u%b + 6a2d2 + 4ab3 + D4, 


In each case the number of terms is one greater than the exponent of 
the power to which the binomial is raised. 

2. In the first term the exponent of a is the same as the exponent of the 
power to which the binomial is raised, and it decreases by 1 in each succeed- 
ing term. 

3. b appears in the second term with the exponent 1, and its exponent 
inereases by 1 in each succeeding term. 

4, The coefficient of the first term is 1. 

5. The coefficient of the second term is the exponent of the power to 
which the binomial is raised. 

6. The coefficient of each succeeding term is found from the next pre- 
ceding term by multiplying its coefficient by the exponent of a, and divid- 
ing the product by a number greater by 1 than the exponent of b. (See 
Binomial Theorem, below.) 





34 ALGEBRA, 


Parentheses.—When a parenthesis is preceded by a plus sign it may be | 
removed without changing the value of the expression: a+b + (a+ 6) = 
2a + 2b. When a parenthesis is preceded by a minus sign it may be removed 
if we change the signs of all the terms within the parenthesis: 1 —(a —b 
—c)=1—a+6-+c. When a parenthesis is within a parenthesis remove 


the inner one first: a —[b-4e-(— | | =a-— [o—je-a+et | 


=a—[b—c+d-—e] =a—b+c--d-e. 

A multiplication sign, x, has the effect of a parenthesis, in that the oper- 
ation indicated by it must be performed before the operations of addition 
or subtraction. a+bxa-+b=a-+ab+b; while (a+ b) xX (a+ b)= 
a? + 2ab + b?, and (a+ 6b)xa+t+b=a?+ab+b. 

Division.—The quotient is positive when the dividend and divisor 
have like signs, and negative when they have unlike signs: abc =~ b = ac; 
abe = —b= — ac. 

To divide a monomial by a monomial, write the dividend over the divisor 
with a line between them. If the expressions have common factors, remove 
the common factors: 
aba ax. at Bt as 1 23. 
aby y’ a3 a5 a? 

To divide a polynomial by a monomial, divide each term of the polynomial 
by the monomial: (8ab — 12ac) + 4a = 2b — 8c. 

To divide a polynomial by a polynomial, arrange both dividend and divi- 
sor in the order of the ascending or descending powers of some common: 
letter, and keep this arrangement throughout the operation. 

Divide the first term of the dividend by the first term of the divisor, and 
write the result as the first term of the quotient. 

Multiply all the terms of the divisor by the first term of the quotient and 
subtract the product from the dividend. If there be a remainder, consider 
it as a new dividend and proceed as before: (a? — b?) + (a+ b). 


a? — b*| a+b. 


a*bx + aby = 








a?+ab|a-— b. 
— ab — b?, 
— ab — b*, 


The difference of two equal odd powers of any two numbers is divisible 
by their difference and also by their sum: 

(a3 — 63) + (a — b) = a2-+ ab+t b?; (a3 — 63) + (a+b) = a? — ab b?. 

The difference of two equal even powers of two numbers is divisible by 
their difference and also by their sum: (a? — 6?) + (a — b) =a-+b. 

The sum of two equal even powers of two numbers is not divisible by 
either the difference or the sum of the numbers; but when the exponent 
of each of the two equal powers is composed of an odd and an even factor, 
the sum of the given power is divisible by the sum of the powers expressed 
by the even factor. Thus x® 4+ y$ is not divisible by x + y or by x — y, but is 
divisible by #2 + y?. 

Simple equations.—An equation is a statement of equality between 
two expressions; as,a+b=c+d. 

A simple equation, or equation of the first degree, is one which contains 
only the first power of the unknown quantity. If equal changes be made 
(by addition, subtraction, multiplication, or division) in both sides of an 
equation, the results will be equal. 

Any term may be changed from one side of an equation to another, pro- 
vided its sign be changed: a+b=c+d; a=c+d-—b. To solve an 
equation having one unknown quantity, transpose all the terms involving 
the unknown quantity to one side of the equation, and all the other terms 
to the other side; combine like terms, and divide both sides by the coefficient 
of the unknown quantity. 

Solve 8a — 29 = 26 — 3%. 8a + 3H = 294 26; lla = 55; a” = 5, ans. 

Simple algebraic problems containing one unknown quantity are solved 
by making x = the unknown quantity, and stating the conditions of the 
problem in the form of an algebraic equation, and then solving the equa- 
tion. What two numbers are those whose sum is 48 and difference 14? Let 
x = the smaller number, 2-+ 14 the greater. a2+a4+14= 48, 2x7 = 34,2” 
= 17; «+ 14 = 31, ans. 

Find a number whose treble exceeds 50 as much as its double falls short 
of 40. Leta =thenumber, 3x — 60 = 40 = 2x; 54 = 90; 4 = 18, ans, Proy- 
ing, 54 — 50 = 40 — 36, re 


OLGEBRA. 3d 


Equations containing two unknown quantities.—If one 
equation contains two unknown quantities, # and y, an indefinite number of 
pairs of values of x and y may be found that will satisfy the equation, but if 
a second equation be given only one pair of values can be found that will 
satisfy both equations. Simultaneous equations, or those that may be satis- 
fied by the same values of the unknown quantities, are solved by combining 
the equations so as to obtain a single equation containing only one unknown 
quantity. This process is called elimination. : : 

Elimination by addition or subtraction.—Multiply the equation by 
such numbers as will make the coefficients of one of the unknown quanti- 
ties equal in the resulting equation. Add or subtract the resulting equa- 
tions according as they have unlike or like signs. 

24 -+ 38y = 7. Multiply by 2: 4a + 6y = 14 
Solve | 4% — 5y = 3. Subtract: 4a — By = 38 Lp asa Syst: 


Substituting value of y in first equation, 2a+3= 7; 4 = 2. 

Elimination by substitution.—From one of the equations obtain the 
value of one of the unknown quantities in terms of the other. Substitu- 
tute for this unknown quantity its value in the other equation and reduce 
the resulting equations. ; 





Solve / 2a + 3y = 8. (1). From (1) we find x = 8 et 
8a + Ty =%. (2). 
: . : 8 — 3y he . 
NSA nl ll a st + %y =7; = 4 — 94 14y = 14, 


whence y = — 2. Substitute this valuein (1): 2a —6=8;a”2=7. 

Elimination by comparison.—From each equation obtain the value of 
one of the unknown quantities in terms of the other. Form an equation 
from these equal values, and reduce this equation. 





Oye Uy ti. (Oy irom(yme inde at 
Solve | 744 
[ Be —4y=7. (2). From (2) we find «= 3 Z ; 
Equating these values of 2, plaid = seas be 19y = — 19; y= — 1. 


Substitute this value of yin (1): 22+9=11;”=1. 

If three simultaneous equations are given containing three unknown 
quantities, one of the unknown quantities must be eliminated between two 
pairs of the equations; then a second between the two resulting equations. 

- Quadratic equations.—A quadratic equation contains the square 
of the unknown quantity, but no higher power. A pure quadratic contains 
the square only; an affected quadratic both the square and the first power. 

To solve a pure quadratic, collect the unknown quantities on one side, 
and the known quantities on the other; divide by the coefficient of the un- 
known quantity and extract the square root of each side of the resulting 
equation. 


Solve 302 —-15=0. 842? = 15;22=5;a"= V5 


A root like “5, which is indicated, but which can be found only approxi: 
mately, is called a surd. 


Solve 822+-15=0. 3”? = —- 15;47=—5;4¢= Vy — 5. 

The square root of — 5 cannot be found even approximately, for the square 
of any number positive or negative is positive; therefore a root which is in- 
dicated, but cannot be found even approximately, is called imaginary. 

To solve an affected quadratic.—1. Convert the equation into the form 
a?e? + 2abx = c, multiplying or dividing the equation if necessary, so as 
to make the coefficient of x? a square number. 

2. Complete the square of the first member of the equation, so as to con- 
vert it to the form of a?x? + 2aba + b?, which is the square of the binomial 
ax + b, as follows: add to each side of the equation the square of the quo- 
tient obtained by dividing the second term by twice the square root of the 
first term. 

3. Extract the square root of each side of the resulting equation. 

Solve 3”? — 4a = 32. To make the coefficient of x? a square number, 
multiply by 3: 9x”? — 124 = 96; 12a + (2 x 387) = 2; 22 = 4: 

Complete the square: 9%? — 12~-+-4= 100. Extract the root: 37-—2=+ 


36 ALGEBRA. 


10, whence # = 4 or — 2 2/8. The square root of 100 is either + 10 or — 10, 
since the square of — 10 as well as + 10% = 100. 

Problems involving quadratic equations have apparently two solutions, as 
a quadratic has two roots. Sometimes both will be true solutions, but gen- 
erally one only will be a solution and the other be inconsistent with the 
conditions of the problem. 

The sum of the squares of two consecutive positive numbers is 481, Find 
the numbers. 

ven «x = one number, # + 1 the other. #?-+ (a+ 1)? = 481. 2a%7+ 2741 

x3 + x = 240. Completing the square, 2? + «+ 0.25 = 240.25. Extracting 
the root we obtain x + 0.5 = + 15.5; w = 15 or — 16. 

The positive root gives for the numbers 15 and 16. The negative root — 
16 is inconsistent with the conditions of the problem. 

Quadratic equations containing two unknown quantities require different 
methods for their solution, according to the form of the equations. For 
these methods reference must be made to works on algebra. 

- nw — 

Theory of exponents.—//a when n is a positive integer is one of n 

nH 


equal factors of a. V a” means @ is to be raised to the mth power and the 
nth root extracted. 


myo 
V a) means that the nth root of a is to be taken and the result 
raised to the mth power. 


n tp—-\m Le 
Va" = (y a ) = a”, When the exponent is a fraction, the numera- 
ste : 6 6 Capes 
tor indicates a power, and the denominator areot. a? = "A OS Sees Oe 


WV a3 = als, 
To extract the root of a quantity raised to an indicated power, divide 
the exponent by the index of the required root; as, 


n,— ssh ye 6 
Va™ ~ an’ Vas = a® =a. 
Subtracting 1 from the exponent of a is equivalent to dividing by a: 
a oe eas eae ee be 
a-l=q=a; Oh Be Oe oer mals Gs ibs Nae 1 Le ine Gs 
A number with a negative exponent denotes the reciprocal of the number 
with the corresponding positive exponent. ; 
A factor under the radical sign whose root can be taken may, by having 
the root taken, be removed from under the radical sign: 


Var = a? x fo=4 Vd. | 
A factor outside the radical sign may be raised to the corresponding 
power and placed under it: 


a 1d his vee Gaia 
(2-8 = sfx pal var aH 


Binomial Theorem.—To obtain any power, as the nth, of an ex- 
pression of the form a+ a 


(a+2)* =a" 4+ na"-) a+ 


etc. 
The following laws hold for any term in the expansion of (a + x)”. 
The exponent of x is less by one than the number of terms. 
The exponent of a is n minus the exponent of x. 
The last factor of the numerator is greater by one than the exponent of a, 
The last factor of the denominator is the same as the exponent of a. 
In the rth term the exponent of x will be r — 1. 
The exponent of a will be n — (r — 1), orn — r +1. 
The last factor of the numerator will be n — r + 2. 
The last factor of the denominator Be be =r —1. ‘ 

a 4 — nh ee ome 9° ot < 
Hence the rth term Se ee a eT ae? +1 grak 


n(n — 1 a%—? 


1.2 


Ee a n-8 





GEOMETRICAL PROBLEMS, 37 


GEOMETRICAL PROBLEMS. 





1. To bisect a straight line, 
or an are of a cirele (Fig. 1).— 
From the ends A, B. as centres, de- 
scribe ares intersecting at C and D, 
and draw a line through C and D 
which will bisect the line at # or the 
are at F. 


2. To draw a perpendicular 
to a straight lime, or a radial 
line to a circular are.—Same as 
in Problem 1. C Dis perpendicular to 
the line A B, and also radial to thearc. 


3. To draw a perpendicular 
toastraight line froma given 
point in that lime (Fig. 2).—With 
any radius, from the given point A in 
the line B C, cut the line at B and C. 
With a longer radius describe ares 
from B and C, cutting each other at 
D, and draw the perpendicular D A. 


4. From theend 4 ofa given 
line A D to erect a perpendic= 
ular A FE (Fig. 3).—From any centre 
F, above 4 D, describe a circle passing 
through the given point A, and cut- 
ting the given line at D. Draw D Ff 
and produce it to cut the circle at £, 
and draw the perpendicular A E. 

Second Method (Fig. 4).—From the 
given point A set off a distance A EH 
equal to three parts, by any scale; 
and onthe centres A and #, with radii 
of four and five parts respectively, 
describe aresintersecting at C. Draw 
the perpendicular A C. 

Notr.—This method is most useful 
on very large scales, where straight 
edges areinapplicable. Any multiples 
of the numbers 3, 4, 5 may be taken 
HAL the same effect as 6, 8, 10, or 9, 

15 


5. To draw a perpendicular 
to a straight lime from any 
point without it (Fig. 5.)—From 
the point A, with a sufficient radius 
cut the given line at # and G, and 
from these points describe ares cut- 
ung at ZH. Draw the perpendicular 
A EH. 


6. To draw a straight line 
parallel to a given line, ata 
given distance apart (Fig. 6).— 
From the centres A, Bb, in the given 
line, with the given distance as radius, 
describe arcs C, D, and draw the par- 
allel lines C D touching the arcs. 


38 


GEOMETRICAL PROBLEMS. 











Fig. 10. 
Cc 





7. fo divide a straight line 
into a number of equal parts 
(Fig. 7).—To divide the line 4 B into, 
say, five parts, draw the line A C at 
an angle from 4A; set off five equal 

arts; draw #6 5 and draw parallels to 
it from the other points of division in 
AC. These parallels divide A B as 
required. 

Notr.— By a similar process a line 
may be divided into a number of un- 
equal parts; setting off divisions on 
A C, proportional by a scale to the re- 
quired divisions, and drawing parallel 
cutting A B. The triangles A11, A422, 
A838, etc., are similar triangles. 


8. Upon a straight line to 
draw an angle equal to 2 
given angle (Fig. 8).—Let A be the 
given angle and #'G the line. From 
the point A with any radius describe 
the are DE. From F with the same 
radius describe J H. Set off the are 
I Hequal to D E,anddraw Ff H. The 
angle Fis equal to A, as required. 


9. To draw angles of 60° 
and 30° (Fig. 9).—From Ff’, with 
any radius FI, describe an are lH; 
and from J, with the same radius, cut 
the are at H and draw F'H to form 
the required angle] FH. Draw the 
perpendicular H K to the base line to 
form the angle of 30° F HK. 


10. To draw an angle of 45° 
(Fig. 10).—Set off the distance F'T; 
draw the perpendicular I H equal to 
JF, and join H F’ to form the angle at 
F. The angle at H is also 45°. 


11. To bisect an angle (Fig. 
11).—Let A C B be the angle; with 0 
as a centre draw an are cutting the 
sides at A, B. From A and B as 
eentres, describe arcs cutting each 
other at D. Draw C D, dividing the 
angle into two equal parts. 


12. Through two given 
points to describe an are of 
a circle with a given radius, 
(Fig. 12).—From the points A and B: 
as centres, with the given radius, de: 
scribe arcs cutting at C; and from, 
C with the same radius describe an 
are A B. 


GEOMETRIGAL PROBLEMS. : 39 


13. To find the centre ofa 
cirele or of am are of a circle 
(Fig. 13).—Select three points, A, B, 
C, in the circumference, well apart; 
with the same radius describe ares 
from these three points, cutting each 
other, and draw the two lines, D EH, 
F G, through their intersections. The 
point O, where they cut, is the centre 
of the circle or are. 

Wo describe a circle passing 
through three given points. 
—Let A, B, C be the given points, and 
Fic. 18 proceed as in last problem to find the 

I@. lo. centre O, from which the circle may 

be described. 


14. To deseribe an are of 
a cirele passing through 





af ; three given points when 
Gx xH . the centre is not available 
KK x (Fig.14).—From the extreme points 
estes od \ A, B, as centres, describe ares A H, 
IAL oS a BG. Through the third point C 
Pee OF draw AE, BF, cutting the ares. 


Divide A F'and B # into any num- 
ber of equal parts, and set off a 
series of equal parts of the same 
length on the upper portions of the 
ares beyond the points # F. Draw 
straight lines, B L, B M, etc., to 
the divisions in 4 F,and 4 I, A K, 
etc., to the divisionsin HG. The 
successive intersections JN, O, etc., 
of these lines are points in the 
circle required between the given 
points A and C, which may. be 
drawn in ; similarly the remaining 
part of the curve B C may be 
described. (See also Problem 54.) 


15. To draw a tangent to 
a circle from a given point 
in the circumference (Fig. 15). 
—Through the given point A, draw the 
radial line A C,and a perpendicular 
to it, FG, which is the tangent re- 
quired. 








16. To draw tangents to a 
circle from a point without 
it (Fig. 16).—From A, with the radius 
A O, describe an arc B C D, and from 
C. with a radius equal to the diameter 
of the circle, cut the arc at B D. Join 
BC, C D; cutting the circle at EF, 
and draw A EF, A F’,, the tangents. 

Norre.—When a tangent is already 
drawn, the exact point of contact may 
be found by drawing a perpendicular 
to it from the centre. 





Hie, 16. 


17. Between two inclined lines to draw a series Of cir= 
eles touching these lines and touching each other (Fig. 1%). — 
—Bisect the inclination of the given lines A B, CD, by the line N O. From 
a point P in this line draw the perpendicular P B to the line A B, and 


GEOMETRICAL PROBLEMS. 








Fig. 22, 


on P describe the circle B D, touching 
the lines and cutting the centre line 
at #. From E draw EF F perpendicular 
to the centre line, cutting A B at F, 
and from F' describe an are E G, cut- 
ting A Bat G. Draw G H parallel to 
B P, giving H, the centre of the next 
circle, to be described with the radius 
HE, and so on for the next circle IN. 

Inversely, the largest circle may be 
described first, and the smaller ones 
in succession. This problem is of fre- 
quent use in scroll-work. 


18. Between two inclined 
lines to draw a circular seg= 
ment tangent to the linesand 
passing through a point F 
on the line F C which bisects 
the angle of the lines (Fig. 18). 
—Through F' draw D A atright angles 
to FC; bisect the angles A and D, as 
in Problem 11, by lines cutting at C, 
and from C with radius C F#’ draw the 
are H F G required. 


19. To draw a circular are 
that will be tangent to two 
given lines 4 B and C Din-= 
clined to one another, one 
tangential point £ being 
given (Fig. 19).—Draw the centre 
line GF’. From E draw # F'at right 
to angles A B; then F' is the centre 
of the circle required. 


20. Ko deseribe a circular 
are joining two circles, and 
touching one of them at a 
given point (Fig. 20).—To join the 
circles A B, F’'G, by an are touching 
one of them at F, draw the radius FH F, 
and produceit both ways. Set off # H 
equal to the radius A CO of the other 
circle; join C A and bisect it with the 
perpendicular ZL J, cutting EF at I. 
On the centre J, with radius J F, de- 
scribe the arc F' A as required. 


21. Todraw a circle witha 
given radius & that will be 
tangent to two given cireles 
A and B (Fig. 21).—From centre 
of circle A with radius equal F plus 
radius of A, and from centre of B with 
radius equal to R + radius of B, draw 
two ares cutting each other in C, which 
will be the centre of the circle re- 
quired. 


22. To construct an equi- 
lateral triangle, the sides 
being given (Fig. 22).—On the ends 
of one side, A, B, with A Bas radius, 
describe. ares, cutting at C, and. draw 
AC,CB, 


@ROMETRICAL PROBLEMS. 41 


w 





Tig. 24. 
ecuaegl 
E F 


Fie. 25. 





Fic, 26. 
B 


aN 





23. To construct a triangle 
of umequal sides (Fig. 23).—On 
either end of the base A D, with the 
side B as radius, describe an arc; 
and with the side Cas radius, om the 
other end of the base as a centre, cut 
the arc at #. Join AH, DE. 


24. To construct a square 
on a given straight line 4 B 
(Fig. 24).—With A B asradius and A 
and B as centres, draw arcs A Dand B 
C, intersecting at H.- Bisect EF Bat F. 
With Has centre and E F'as radius. 
cut the ares A Dand B Cin D and C. 


‘Join A C, C D, and DB to form the 


square, 


25.To construct a rect= 
angie with given base H F 
and height EF 4A (Fig. 25).—On the 
base H F’'draw the perpendiculars HE H, 
F G equal to the height, and join G A. 


26. Vo describe a_ circle 
about a triangle (Fig. 26).— 
Bisect two sides A &, AC of the tri- 
angle at H Ff, and from these points 
draw perpendiculars cutting at kK. On 
the centre K, with the radius K 4A, 
draw the circle A B C, 


2%. Wo inscribe a circle in 
a triangie (Fig. 27).—Bisect two of 
the angles A, C, of the triangle by lines 
cutting at D; from D draw a per- 
pendicular D # to any side, and with 
D Hasradius describe a circle. 

When the triangle is equilateral, 
draw a perpendicular from one of the 
angles to the opposite: side, and from 
the side set off one third of the per- 
pendicular. 

8. To describe a circle 
about a square, and to in= 
scribe a square in a cirele (Fig. 
28).—To describe the circle, draw the 
diagonals A B, C D of the square, cut- 
ting at Z. Onthe centre FE, with the 
radius A E, describe the circle. 

To inscribe the square,— 
Draw the two diameters, A B, CD, at 
right angles, and join the points 4, B, 
C D, to form the square. 

Notr.—In the same way acircle may 
be described about a rectangle, 


GEOMETRICAL PROBLEMS. 








29. To inscribe a cirele in & 
square (ig. 29).—To inscribe the 
circle, draw the diagonals A B, C D 
of the square, cutting at H; draw the 
perpendicular H F to one side, and 
wae the radius E F describe the 
circle, 


30. To describe a square 
about a cirele (Fig. 30).—Draw two 
diameters 4 B, CD at right angles. 
With the radius of the circle and A, B, 
© and D as centres, draw the four 
half circles which cross one another 
in the corners of the square. 


31. To inscribe a pentagon 
im a cirele (Fig. 31).—Draw diam- 
eters 4 C, B D at right angles, cutting 
at o. Bisect Ao at H, and from #£, 
with radius £ B, cut A Cat &; from 
B, with radius B F, cut the circumfer- 
ence at G, H, and with the same radius 
step round the circle to Zand K; join 
the points so found to form the penta. 
gon. 


32. To construct a penta: 
gon on a given line 4 B (Fig. 
32).—From #& erect a perpendicular 
B Chalf the length of A B; join 4 C 
and prolong itto D, making CD=BC. 
Then B D is the radius of the circle 
circumscribing the pentagon. From 
A and Bascentres, with B D as radius, 
draw ares cutting each other in O, 
which is the centre of the circle. 


33. To construct a hexagon 
upon a given straight line 
(Fig. 33).—From A and B, the ends of 
the given line, with radius A B, de- 
seribe arcs cutting at g ; from g, with 
the radius g A, describe a circle; with 
the same radius set off the ares AG, 
GF,and BD. DE. Join the points so 
found to form the hexagon. The side 
of a hexagon = radius of its circum- 
scribed circle. 


34. To inscribe a hexagon 
in a circle (Fig. 34).—Draw a diam- 
eter 4 CB. From Aand# as centres, 
with the radius of the circle A C, cut 
the circumference at D, H, Ff, G, and 
draw A D,D E, etc., to form the hexa- 
gon. The radius of the circle is equal 
to the side of the hexagon; therefore 
the points D, EH, etc., may also be 
found by stepping the radius six 
times round the circle. The angle 
between the diameter and the sides of 
a hexagon and also the exterior angle 
between a side and an adjacent side 
prolonged is 60 degrees: thereforea 
hexagon may conveniently be drawn 
by the use of a 60-degree triangle, 


GEOMETRICAL PROBLEMS. 43 


35. Vo describe a hexagon 
about a circle (Fig. 35).—Draw a 
diameter A D B, and with the radius 
A D, on the centre A, cut the circum- 
ference at C; join A C, and bisect it 
with the radius D # ; through H draw 
F'G, parallel to A O, cutting the diam- 
eter at F, and with the radius D F' de- 
scribe the circumscribing circle F' H. 
Within this circle describe a hexagon 
by the preceding problem. A more 
convenient method is by use of a 60- 
degree triangle. Four of the sides 
make angles of 60 degrees with the 
diameter, and the other two are par- 
allel to the diameter. 


36. To describe an octagon 
on a given straight lime (fig. 
36).—Produce the given line 4 B both 
ways, and draw perpendiculars A £, 
B F; bisect the external angles A and 
B by the lines A A, B C, which make 
equalto 4 B. Draw C Dand HG par- 
allel to A EH, and equal to 4 B; from 
the centres G, D, with the radius A B, 
cut the perpendiculars at H, F, and 
draw E F to complete the octagon. 


37. To convert a square 
intoan octagon (lig. 37).—Draw 
the diagonals of the square cutting at 
e; from the corners A, B, C, D, with 
Aeas radius, describe ares cutting 
the sides at gn, fk, hm, and ol, and 
join the points so found to form the 
octagon. Adjacent sides of an octa- 
gon make an angle of 135 degrees. 


38. To inscribe an octagon 
im a cirele (Fig. 38).—Draw two 
diameters, 4 C, B D at right angles; 
bisect the ares A B, BC, ete., at ef, 
etc., and join 4 e,e B, etc., to form 
the octagon. 


39. To describe an octagon 
about a cirele (Fig. 38).—Describe 
a square about the given circle A B,; 
draw perpendiculars h k, etc., to the 
diagonals, touching the circle to form 
the octagon. 





Fie. 39. 


40. To describe a polygon of any number of sides upon 
*: given straight lime (fig. 40).—Produce the given line A B, and on 4, 


44 





Number 
of Sides. 


DIrornoo A 


GEOMETRICAL PROBLEMS. 


Fie. 48, 





with the radius A B, describe a semi- 
circle; divide the semi-cireumference 
into as many equal parts as there are 
to be sides in the polygon—say, in this 
example, five sides. Draw lines from 
A through the divisional points D, b, 
and c, omitting one point a; and on 
the centres B, D, with the radius A B, 
cut AbatHand Acat Ff. Draw DE, 
E F, F B to complete the polygon. 


41. To inscribe a cirele 
within a polygon (Figs. 41, 42).— 
When the polygon has an even number 
of sides (Fig. 41), bisect two opposite 
sides at 4 and B; draw A B, and biseet 
it at C by a diagonal D #, and with 
the radius C A describe the circle. 

When the number of sides is odd 
(Fig. 42), bisect two of the sides at 4 
and B, and draw lines A E, BD to the 
opposite angles, intersecting at C; 
from C, with the radius C A, describe 
the circle. 


42. Wo deseribe a_  cirele 
without a polygon (Figs. 41, 42). 
—Find the centre C as before, and with 
the radius C D describe the circle. 


43. To inscribe a polygon 
of any number of sides with 
im a cirele (Fig. 438).—Draw the 
diameter A & and through the centre 
£ draw the perpendicular EC, cutting 
the circle at F. Divide # F into four 
equal parts, and set off three parts 
equal to those from F' to C. Divide 
the diameter A B into as many equal 
parts as the polygon is to have sides:; 
and from C draw CD, through the 
second point of division, cutting the 
circle. at D. Then A D is equal to one 
side of the polygon, and by stepping 
round the circumference with the 
length A Dthe polygon may be com- 
pleted. 


TABLE OF POLYGONAL ANGLES. 





Angle 


at Centre. 


Degrees. 
1 





Number 
of Sides. 


No. 
9 


Angle Number Angle 
at Centre. of Sides. | at Centre. 


Degrees. No. Degrees, 
40 15 24 
z. | # |B 
32} 1 
iit 18 9 oo 
2725 19 19 





GEOMETRICAL PROBLEMS, 45 


In this table the angle at the centre is found by dividing 360 degrees, the 
aumber of degrees in a circle, by the number of sides in the polygon; and 
by setting off round the centre of the circle a succession of angles by means 
of the protractor, equal to the angle in the table due to a given number of 
Peay the radii so drawn will divide the circumference into the same number 
of parts, 

44. Vo describe an ellipse 
when the lengthand breadth 
are given (Fig. 44).—A B, transverse 
axis; C D, conjugate axis; FG, foci. 
The sum of the distances from C to 
Fand G, also the sum of the distances 
from F' and G to any other point in 
the curve, is equal to the transverse 
axis. From the centre C, with 4 Has 
radius, cut the axis A B at F'and G, 
the foci; fix a couple of pins into the 
axis at F’ and G, and loop on a thread 
or cord upon them equal in length to 
the axis A B, so as when stretched to 
reach to the extremity C of the con- 
jugate axis, as shown in dot-lining. 
Place a pencil inside the cord as at H, 
and guiding the pencil in this way, 
keeping the cord equally in tension, 
carry the pencil round the pins F, G, 
and so describe the ellipse. 

Notst.—This method is employed in 
setting off elliptical garden - plots, 
walks, ete. 

2d Method (Fig. 45).— Along the 
straight edge of a slip of stiff paper 
mark off a distance a c equal to A C, 
half the transverse axis; and from the 
same point a distance ab equal to 
CD, half the conjugate axis. Place 
the slip so as to bring the point b on 
the line 4 B of the transverse axis, 
and the point con the line DH; and 
Fic. 45 set off on the drawing the position of 

We as the point a. Shifting the slip so that 
the point b travels on the transverse 
axis, and the point c on the conjugate 
axis, any number of points in the 
curve may be found, through which 
4 the curve may be traced, 
| yf 3d Method (Fig. 46).—The action of 
| , 4 the preceding method may be em- 
_—= bodied so as to afford the means of 
7 Cc describing a large curve continuously 

by means of a bar m k, with steel 
points m, 1, k, riveted into brass slides 























S 


OH adjusted to the length of the semi- 
axis and fixed with set-screws. A 
Fig. 46. rectangular cross # G, with guiding- 


slots is placed, coinciding with the 
two axes of the ellipse 4 Cand BH. 
By sliding the points k, J in the slots, 
and carrying round the point m, the 
curve may be continuously described. 
A pen or pencil may be fixed at m. 
4th Method (Fig. 47).—Bisect the 
transverse axis at C,and through C 
draw the perpendicular D H, making 
CD and C E each equal to half the 
conjugate axis. From D or E, with 
the radius A C, cut the transverse 
axis at FH, FF’, for the foci. Divide 
AC into a number of parts at the 





46 


GEOMETRICAL PROBLEMS. 


points 1, 2, 8, etc. With the radins A J on F and F’ as centres, describe 
arcs, and with the radius BJ on the same centres cut these ares as shown. 





Repeat the operation for the other 
divisions of the transverse axis. The 
series of intersections thus made are 
points in the curve, turough which the 
curve may be traced. 

5th Method (Fig. 48).—On the two 
axes A B, D Fas diameters, on centre 
C, describe circles; from a number of 
points a, b, etc., in the circumference 
AFB, draw radii cutting the inner 
circle at a’, b’, etc. From a, Db. ete., 
draw perpendiculars to 4B; and from 
a’, b’, ete., draw parallels to A B, cut- 
ting the respective perpendiculars at 
n, o, ete. The intersections are points 
in the curve, through which the curve 
may be traced. 

6th Method (Fig. 49).— When the 
transverse and conjugate diameters 
are given, A B, C D, draw the tangent 
EF parallel to A&B. Produce CD, 
and on the centre G with the radius 
of half AB, describe a semicircle 
H DK; from the centre G draw any 
number of straight lines to the points 
EH, 7, ete., in the line # F, cutting the 
circumference at l, m, n, etc.; from 
the centre O of the ellipse draw 
straight lines to the points £, r, etc.; 
and from the points J, m, 7, ete., draw 
parallels to G C, cutting the lines O £, 
Ov, etc., at L, M, N, ete. These are 
points in the circumference of the 
ellipse, and the curve may be traced 
through them. Points in the other 
half of the ellipse are formed by ex- 
tending the intersecting lines as indi- 
eated in the figure. 

45. Vo describe an ellipse | 
approximately by means of 
eircular ares.—fiist.—With arcs 
of two radii (Fig. 50).—-Find the differ- 
ence of the semi-axes, and set it off 
from the centre O to a andcon OA 
and OC; draw ac, and set off half 
actod; draw di parallel to ac; set 
off O e equal to Od; join ei, and draw 
the parallels em, dm. From m, with 
radius m C, describe an are through 
C; and from 7 describe an are through 
D; from d and e describe arcs through 
A and B. The four arcs form the 
ellipse approximately. 

Notr.—This method does not apply 
satisfactorily when the conjugate axis 
is less than two thirds of the trans- 
verse axis. 

2d Method (by Carl G. Barth, 
Fig. 51).--In Fig. 51 a b is the major 
and cd the minor axis of the ellipse 
to be approximated. Lay off b e equal 
to the semi-minor axis c O, and use a e 
as radius for the arc at each extremity 
of the minor axis. Bisect e o at fand 
lay off e g equal to ef, and use g b as 
radius for the are at each extremity 
of the major axis, 


GEOMETRICAL PROBLEMS. 4" 


The method is not considered applicable for cases in which the minor 
axis is less than two thirds of the major. 

38d Method: With arcs of three radii 
(Fig. 52).—On the transverse axis A B 
draw the rectangle B G on the height 
OC; to the diagonal AC draw the 
perpendicular G H D; set off O K 
equal to OC, and describe a semi- 
circle on A K, and produce O Cto L; 
set off O M equal to C L, and from D 
describe an are with radius D M ; from 
A, with radius O L, cut A Bat N; from 
H, with radius HN, cut are ab at a. 
Thus the five centres D, a, 6, H, H’ 





a ' 
Sah are found, from which the ares are 
wM/ described to form the ellipse. 
D This process works well for nearly 
if all proportions of ellipses. It is used 
Fig. 52. in striking out vaults and stone bridges, 


4th Method (by F. R. Honey, Figs. 53 and 54).—Three radii are employed. 
With the shortest radius describe the two arcs which pass through the ver- 
tices of the major axis, with the longest the two arcs which pass through 
the vertices of the minor axis, and with the third radius the four arcs which 

connect the former. 
A simple method of determining the radii of curvature is illustrated in 
Fig. 538. Draw the straight 


lines a f and ac, forming any 

C angleata. Withaasa centre, 

and with radiiaband ac, re- 

e spectively, equal to the semi- 

1 minor and semi-major axes, 

g drawthearesbeandcd. Join 

ed, and through b and ¢ re- 

a epee trey ye! te g andcf 
arallel to e d, intersecting ac 


b at g, and af atf; af is the 
radius of curvature at the ver- 
tex of the minor axis; andag 
the radius of curvature at the 


Fig. 53. 


vertex of the major axis. 

Lay off d h (Fig. 53) equal to one eighth of bd. Joineh, and draw ck and 
bl parallel toeh. Take a k for the longest radius (= R), a l for the shortest 
radius (= r), and the arithmetical mean, or one half the sum of the semi-axes, 
for the third radius (= p), and employ these radii for the eight-centred oval 


as follows: 

Let a b and cd (Fig. 54) 
be the major and minor 
axes. Lay off ae equal 
to r, and af equal to p: 
also lay off c g equal to R, 
and ch equal to p. With 
gasa centre and ghas a 
radius, draw the arc hk; 
with the centre e and 
radius e f draw the are fk, 
intersecting hk atk. Draw 
the line gk and produce it, 
making gl equal to Rk, 
Draw ke and produce it, 
making k m equal to p. 
With the centre g and 
radius gc (=f) draw the 
are cl; with the centre k 
and radius kl (=p) draw 
the arc 1m, and with the 
centre e and radius em 
(= r) draw the are ma. 

The remainder of the 
work is symmetrical with 
respect to the axes, 





48 GEOMETRICAL PROBLEMS. 





46. The Parabola.—aA parabola 
(D A C, Fig. 55) is a curve such that 
every point in the curve is equally 
distant from the directrix K Land the 
focus F#.. The focus lies in the axis 
A B drawn from the vertex or head of 
the curve A, so as to divide the figure 
into two equal parts. The vertex A 
is equidistant from the directrix and 
the focus, or Ae= AF. Any line 
parallel to the axis isa diameter. A 
straight line, as HG or DC, drawn 
across the figure at right angles to the 
axis is a double ordinate, and either 
half of itis an ordinate. The ordinate 
to the axis H F' G, drawn through the 
focus, is called the parameter of the 
axis. A segment of the axis, reckoned 
from the vertex, is an abscissa of the 
axis, and it is an apscissa of the ordi- 
nate drawn from the base of the ab- 
scissa. Thus, 4 B is an abscissa of 
the ordinate B C. 


Abscisse of a parabola are as the squares of their ordinates. 

To describe a parabola when an abscissa and its ordi- 
nate are given (lig. 55).—Bisect the given ordinate B Cat a, draw Aa, 
and then ab perpendicular to it, meeting the axis at b. Set off Ae, AF, 
each equal to Bb; and draw Ke JL perpendicular to the axis. Then K L is 


the directrix and F' is the focus. 


Through F and any number of points, o, 0, 


etc., in the axis, draw double ordinates, n 0 n, etc., and from the centre F, 
with the radii F’e, o e, ete., cut the respective ordinates at H, GY, n, n, etc. 
The curve may be traced through these points as shown. 


& 


Fig. 56. 








2d Method: By means of a square 
and a cord (Fig. 56).—Place a straight- 
edge to the directrix H N, and apply 
to it a square L HG. Fasten to the 
end G one end of a thread or cord 
equal in length to the edge H G, and. 
attach the other end to the focus #’; 
slide the square along the straight- 
edge, holding the cord taut against the 
edge of the square by a pencil D, by 


-which the curve is described. 


8d Method: When the height and 
the base are given (Fig. 57).—_Let A B 
be the given axis, and CD a double 
ordinate or base; to describe a para- 
bola of which the vertex is at A, 
Through A draw # F parallel to C D, 
and through OC and D draw C # and 
D F parallel to the axis. Divide BC 
and BD into any number of equal 
parts, say five, at a, b, etc., and divide 
CH and D F into the same number of 
parts. Through the points a, b, c,d in 
the base OC Don each side of the axis 
draw perpendiculars, and through 
a,b,c, d@in CHand D F draw lines te 
the vertex A, cutting the perpendicu- 
lars at e, f,g,h. These are points in 
the parabola, and the curve C 4 D may 
pe traced as shown, passing througb 
them. 


GEOMETRICAL PROBLEMS, 49 


47. The Myperbola (Fig. 58).—A hyperbola is a plane curve, such 
that the difference of the distances from any point of it to two fixed points 
is equal toa given distance. The fixed 
points are called the foci. 

To construct a hyperbola, 
—Let F’ and F' be the foci, and #’” F# 
the distance between them. Take a 
ruler longer than the distance FY’ F, 
and fasten one of its extremities at the 
focus #’. At the other extremity, H, 
attach a thread of such a length that 
the length of the ruler shall exceed 
the length of the thread by a given 
distance A B. Attach the other ex- 
tremity of the thread at the focus F’. 

Press a pencil, P, against the ruler, 
and keep the thread constantly tense, 
while the ruler is turned around #” as 
a centre. The point of the pencil will 
describe one branch of the curve. 

2d Method: By points (Fig, 59).— 
From the focus #” lay off a distance 
FF” N equal to the transverse axis, or 
distance between the two branches of 
the curve, and take any other distance, 
as F’H, greater than FN. 

With #” as a centre and #'’A as a 
radius describe the arc of a circle. 

Fie, 59. Then with Fas a centre and NH asa 

radius describe an arc intersecting 

the arc before described at p and q. 

These will be points of the hyperbola, for F’ q — F'q is equal to the trans- 
verse axis A B. 

If, with # as a centre and A” H as a radius, an are be described, and a 
second arc be described with F” as a centre and N H as aradius, two points 
in the other branch of the curve will be determined. Hence, by changing 
the centres, each pair of radii will determine. two points in each branch. 

The Equilateral Hyperbola.—tThe transverse axis of a hyperbola 
is the distance, on a line joining the foci, between the two branches of the 
curve. The conjugate axis is a line perpendicular to the transverse axis, 
drawn from its centre, and of such a length that the diagonal of the rect- 
angle of the transverse and conjugate axes is equal to the distance between 
the foci. The diagonals of this rectangle, indefinitely prolonged, are the 
asynuptotes of the hyperbola, lines which the curve continually approaches, 
but touches only at an infinite distance. If these asymptotes are perpen- 
dicular to each other, the hyperbola is called a rectangular or equilateral 
hyperbola. It is a property of this hyperbola that if the asymptotes are 
taken as axes of a rectangular system of codrdinates (see Analytical Geom- 
etry), the product of the abscissa and ordinate of any point in the curve is 
equal to the product of the abscissa and ordinate of any other point; or, if 
p is the ordinate of any point and v its abscissa, and p, and v, are the ordi- 
nate and abscissa of any other point, puv=p, v,; or pv = a constant. 

48. The  Cycloid 
(Fig. 60).—If a circle 4d 
be rolled along a straight 
line 46, any point of the 
circumference as A will 
deseribe a curve, which is 
ealled a cycloid. The circle 
is called the generating 
circle, and A the generat- 








A i 





ing point. 
23 4 5 6 Wo draw a cycloid. 
Fie. 60. —Divide the circumference 


of the generating circle into an even number of equal parts, as A 1, 12, etc., 
and set off these distances on the base. Through the points 1, 2, 3, etc., on 
the circle draw horizontal lines, and on them set off distances la = Al, 
2b = A2, 8c = A3, etc. The points A, a, b,c, etc., will be points in the cycloid, 
through which draw the curve. 


5d GEOMETRICAL PROBLEMS, 


49. The Epicycloid (Fig. 61) is 
generated by a point D in one circle 
D C rolling upon the circumference of 
another circle A C B, instead of on a 
flat surface or line; the former being 
the generating circle, and the latter 
the fundamental circle. The generat- 
ing circle is shown in four positions, in 
which the generating point 1s succes- 
sively marked D, D’, D’, D’’. AD’ B 
is the epicycloid. 


50. The Hypocyeloid (Fig. 62) 
is generated by a point in the gener. 
ating circle rolling on the inside of the 
fundamental circle. 

When the generating circle = radius 
of the other circle, the hypocycloid 
becomes a straight line. 





51. The Tractrix or 
Schiele’s anti-friction curve 
(Fig. 63).—R is the radius of the shaft, 
OC, 1, 2, ete., the axis. From O set off 
on R a small distance, oa; with radius 
F and centre a cut the axis at 1, join 
a1, and set off a like small distance 
ab; from b with radius RF cut axis at 
2, join 6 2, and so on, thus finding 
points 0, a, b,c, d, etc., through which 
the curve is to be drawn, 





Fie. 63. 

52. Whe Spiral.—tThe spiral is a curve described by a point which 
moves along a straight line according to any given law, the line at the same 
time having a uniform angular motion. The line is called the radius vector. 

If the radius vector increases directly 

as the measuring angle, the spires, 

or parts described in each revolution, 
' thus gradually increasing their dis; 
tance from each other, the curve is 
known as the spiral of Archimedes 

(Fig. 64). 

This curve is commonly used for 
cams. To describe it draw the radius 
vector in several different directions 

Fie. 64. around the centre, with equal angles 
between them; set off the distances 1, 2,3, 4, etc., corresponding to the scale 
upon which the curve is drawn, as shown in Fig. 64. 

In the common spiral (Fig. 64) the pitch is uniform; that is, the spires are 

equidistant. Such a spiral is made by rolling up a belt of uniform thickness, 





To construct a spiral with 
four centres (Fig. 65).—Given the 
pitch of the spiral, construct a square 
about the centre, with the sum of the 
four sides equal to the pitch. Prolong 
the sides in one direction as shown; 
the corners are the centres for each 
arc of the external angles, forming a 
quadrant of a spire. 








GEOMETRICAL PROBLEMS. AL 


53. To find the diameter of a circle into whicn a certain 
number of rings will fit on its inside (Fig. 66).—For instance, 
What is the diameter of a circle into which twelve 44-inch rings'will fit, as 
per sketch? Assume that we have found the diameter of the required 
circle, and have drawn the rings inside 
of it. Join the centres of the rings 
by straight lines, as shown; we then 
obtain a regular polygon with 12 
sides, each side being equal to the di- 
ameter of a given ring. We have now 
to find the diameter of a circle cir- 
cumscribed about this polygon, and 
add the diameter of one ring toit; the 
sum will be the diameter of the circle 
into which the rings will fit. Through 
the centres A and D of two adjacent 
rings draw the radii CA and CD; 
since the polygon has twelve sides the 
angle 4 C D=30° and AC B= 15°. 
One half of the side A D is equal to 
AB. We now give the following pro- 
portion: The sine of the angle ACB 
is to AB as 1 is to the required ra- 
dius. From this we get the following 
ruz2: Divide A B by the sine of the angle ACB; the quotient will be the 
radius of the circumscribed circle ; add to the corresponding diameter the 
diameter of one ring ; the sum will be the required diameter FG. 

54. To describe an are of a cirele which is too large to 
be drawn by a beam compass, by means of points in the 
are, radius being given.—Suppose the radius is 20 feet and it is 
desired to obtain five points in an are whose half chord is 4 feet. Draw a 
line equal to the half chord, full size, or on a smaller scale if more con- 
venient, and erect a perpendicular at one end, thus making rectangular 
axes of codrdinates. Erect perpendiculars at points 1, 2, 3, and 4 feet from 
the first perpendicular. Find values of y in the formula of the circle. 
a? + y? = RF? by substituting for x the values 0, 1, 2, 3, and 4, etc.. and for FR? 
the square of the radius, or 400. The values will be y= VR? — x2 = V 400, 
7399, V396, V391, “384; = 20, 19.975, 19.90, 19.774, 19.596. 

Subtract the smallest, 

or 19.596, leaving 0.404, 03879, 0.3804, 0.178, 0 feet. 

Lay off these distances on the five perpendiculars, as ordinates from the 
half chord, and the positions of five points on the are will be found. 
Through these the curve may be 
drawn. (Seealso Problem 14.) 

55. Whe Catenary is the curve 
assumed by a perfectly flexible cord 
when its ends are fastened at two 
points, the weight of a unit length 
being constant. 

The equation of the catenary is 





aw 1G 
a oe Co © ° . 
y= cleats aj, in which e is the 
~ 


base of the Naperian system of log- 
arithms. 

To plot the catenary.—Let o 
(Fig. 67) be the origin of coordinates. 
Assigning to a any value as 3, the 
equation becomes 


xv x 


ye 
y=5(e +6 s). 





| 
! 
\ 
\ 
1 
' 
1 
\ 
! 
! 
1 
! 
4. 


Fic. 67. 
To find the lowest point of the curve. 


0) saeew 
Put x = 0; .°. y = 3(¢ +e ) =8ayn=3 


52 GEOMETRICAL PROBLEMS. 


a52 
Then put « = 1; .". y=8 (e+e ') = 3 (1396 4. 0.717) = 8.17, 


2 


P afaop- 8) a3 
Gi, ane aes 35 +e = 5 (148 + 0.513) = 3.69. 


Put x = 3, 4, 5, etc., etc., and find the corresponding values of y. For 
‘each value of y we obtain two symmetrical points, as for example p and p!. 

In this way, by making a@ successively equal to 2, 3, 4, 5, 6, 7, and 8, the 
curves of Fig. 67 were plotted. 

In each case the distance from the origin to the lowest point of the curve 
is equal toa ; for putting = 0, the general equation reduces to y = a, 

For values of a = 6,7, and 8 the catenary closely approaches the parabola. 
For derivation of the equation of the catenary see Bowser’s Analytic 
Mechanics. For comparison of the catenary with the parabola, see article 
by F. R. Honey, Amer. Machinist, Feb. 1, 1894. 

56. The Involute is a name given to the curve which is formed by 

the end of a string which is unwound 
b from a cylinder and kept taut; con- 
sequently the string as it is unwound 
bi will always lie in the direction of a 
tangent to the cylinder. To describe 

4 be the involute of any given circle, Fig. 

68, take any point A on its circum- 

bs ference, draw a diameter 4 B, and 

from B draw B b perpendicular to AB. 

ag 64 Make Bb equal in length to half the 


pulee hy g of the Cited: Divide 
Bb and the semi-circumference into 
a2 A\ Lee the same number of equal parts, 

| B say six. From each point of division 


1 1, 2, 3, ete., on the circumference draw 
lines to the centre C of the circle. 
Then draw 1a perpendicular to C1; 
2a, perpendicular to C2; and so on. 
Fig. 68. Make: 1 a equal to 6b,; 2a, equal 
to b bg; 8a, equal to b bg 3; and so on. 
Join the points A, a,', dg, dz, ete., by a curve; this curve will be the 
required involute. 
_ 57. Method of plotting angles without using a protrac= 
tor.—The radius of a circle whose circumference is 360 is 57.23 (more ac- 
eurately 57.296). Striking a semicircle with a radius 57.3 by any scale, 
spacers set to 10 by the same scale will divide the are into 18 spaces of 10° 
each, and intermediates can be measured indirectly at the rate of 1 by scale 
for each 1°, or interpolated by eye according to the degree of accuracy 
required. The following table shows the chords to the above-mentioned 
radius, for every 10 degrees from 0° up to 110°. By means of one of these, 


As 


Angle Chord. Angle Chord 
li eAceos OSCR OCR aes 0.999 loaner Sos had: 57.296 
VO oi aE Oe ee Se 9.988 D1 EE CSA TES Se 65.727 
QOS He seatetsis a tsls bed «cles 19.899 SOM oiieies noreyaier eyed fs ekouteets 73.658 
SOS Pialere anceps: aieanhie.< 6.0.48" 29.658 LOS NC RSE Ales ie: 81.029 
1A are sek ods SUA AOS 39.192 100° Sige dw itearey as ene 87.782 
OT cd veneer a aetna ie eis ois is 48.429 A COL era i eS BIE he. 93.869 


a 10° point is fixed upon the paper next less than the required angle, and 
the remainder is laid off at the rate of 1 by scale for each degree. 


GEOMETRICAL PROPOSITIONS. 53 


GEOMETRICAL PROPOSITIONS. 


In a right-angled triangle the square onthe hypothenuse is equal to the 
sum of the squares on the other two sides. 

If a triangle is equilateral, it is equiangular, and vice versa. 

If a straight line from the vertex of an isosceles triangle bisects the base, 
it bisects the vertical angle and is perpendicular to the base. 

If one side of a triangle is produced, the exterior angle is equal to the sum 
‘of the two interior and opposite angles. 

If two triangles are mutually equiangular, they are similar and their cor- 
responding sides are proportional. 

If the sides of a polygon are produced in the same order, the sum of the 
exterior angles equals four right angles. (Not true if the polygon has re- 
entering angles.) 

In a quadrilateral, the sum of the interior angles equals four right angles. 

In a parallelogram, the opposite sides are equal; the opposite angles are 
equal; it is bisected by its diagonal, and its diagonals bisect each other. 

If three points are not in the same straight line, a circle may be passed 
through them. ; 

If two arcs are intercepted on the same circle, they are proportional to 
the corresponding angles at the centre. 

If two arcs are similar, they are proportional to their radii. 

The areas of two circles are proportional to the squares of their radii. 

If a radius is perpendicular to a chord, it bisects the chord and it bisects 
the arc subtended by the chord. 

A straight line tangent to a circle meets it in only one point, and it is 
perpendicular to the radius drawn to that point. 

If from a point without a circle tangents are drawn to touch the circle, 
there are but two; they are equal, and they make equal angles with the 
chord joining the tangent points, 

If two lines are parallel chords or a tangent and parallel chord, they 
intercept equal ares of a circle. 

If an angle at the circumference of a circle, between two chords, is sub- 
tended by the same arc as an angle at the centre, between two radii, the 
angle at the circumference is equal to half the angle at the centre. 

If a triangie is inscribed in a semicircle, it is right-angled. 

If two chords intersect each other ina circle, the rectangle of the seg- 
ments of the one equals the rectangle of the segments of the other. 

And if one chord is a diameter and the other perpendicular to it, the 
rectangle of the segments of the diameter is equal to the square on half the 
other chord, and the half chord is a mean proportional between the seg« 
ments of the diameter. . 

If an angle is formed by a tangent and chord, it is measured by one half 
of the arc intercepted by the chord; that is, it is equal to half the angle at 
the centre subtended by the chord. 

Degree of a Railway Curve.—This last proposition is useful in staking out 
railway curves. A curve is designated as one of so many degrees, and the 
degree is the angle at the centre subtended by a chord of 100 ft. ‘To lay out 
a curve of n degrees the transit is set at its beginning or “ point of curve,” 
pointed in the direction of the tangent, and turned through 4n degrees; a 
point 100 ft. distant in the line of sight will be a point in the curve. The 
transit is then swung 44n degrees further and a 100 ft. chord is measured 
from the point already found to a point in the new line of sight, which is a 
second point or ‘‘ station ’’ in the curve. 

The radius of a 1° curve is 5729.65 ft., and the radius of a curve of any 
degree is 5729.65 ft. divided by the number of degrees. 


54 MENSURATION. 


MENSURATION. 


PLANE SURFACES. 


Quadrilateral.—A four-sided figure. 

Parallelogram,—aA quadrilateral with opposite sides parallel. 

Varieties.—Square: four sides equal, all angles right angles. Rectangle: 
opposite sides equal, all angles right angles. Rhombus: four sides equal, 
opposite angles equal, angles not right angles. Rhomboid: opposite sides 
equal, opposite angles equal, angles not right angles, 

Tra pezium,—A quadrilateral with unequal sides. ’ } 

Trapezoid.—A quadrilateral with only one pair of opposite sides 
paraliel. i pb Sn seep WAP DD ty lla tae ae tea 


. Diagonal of a square = 4/2 X side? = 1.4142 x side. 


Diag. of a rectangle = 4/sum of squares of two adjacent sides. 


Area of any parallelogram = base X altitude. 

Area of rhombus or rhomboid = product of two adjacent sides 
x sine of angle included between them. 

Area of a trapezium = half the product of the diagonal by the sum 
of the perpendiculars let fall on it from opposite angles. 

Area of a trapezoid = product of half the sum of the two parallel 
sides by the perpendicular distance between them. 

To find the area of any quadrilateral figure.—Divide the 
quadrilateral into two triangles; the sum of the areas of the triangles is the 
area. 

Or, multiply half the product of the two diagonals by the sine of the angle 
at their intersection. 

To find the area of a quadrilateral inscribed ina circle. 
—From half the sum of the four sides subtract each side severally; multi- 
plv the four remainders together; the square root of the product is the area. 

TWriangle.—A three-sided plane figure. 

Varieties.—Right-angled, having one right angle; obtuse-angled, having 
one obtuse angle ; isosceles, having two equal angles and two equal sides; 
equilateral, having three equal sides and equal angles. 

The sum of the three angles of every triangle = 180°. 

The sum of the two acute angles of a right-angled triangle = 90°. 

Hypothenuse of a right-angled triangle, the side opposite the right angle, 
= Ysum of the squares of the other two sides. If @ and b are the two sides 
and c the hypothenuse, c? = a? + b2; a = #/c? — b? = (e+ b)(c — Dd). 

To find the area of a triangte ; 

Ruut 1. Multiply the base by half the altitude. 

RuLeE 2. Multiply half the product of two sides by the sine of the included 
angle. 

Rue 3. From half the sum of the three sides subtract each side severally; 
multiply together the half sum and the three remainders, and extract the 
square root of the product. 

The area of an equilateral triangle is equal to one fourth the square of one 


V: 
of its sides multiplied by the square root of 3, = sa a being the side; or 


a? X 433013. 

Hypothenuse and one side of right-angled triangle given, to find other side, 
Required side = Vhyp? — given side?, 

If the two sides are equal, side = hyp + 1.4142; or hyp X .7071. 

e ae of a triangle given, to find base: Base = twice area + perpendicular 
eight 

Area of a triangle given, to find height: Height = twice area + base, 

Two sides and base giver, to find perpendicular height (in a triangle in 
which both of the angles at the base are acute). 

Ru.zt.—As the base is to the sum of the sides, so is the difference of the 
sides to the difference of the divisions of the base made by drawing the per- 
pendicular. Half this difference being added to or subtracted from half 
the base will give the two divisions thereof. As each side and its opposite 











PLANE SURFACES. 55 


{ wision of the base constitutes a right-angled triangle, the perpendicular is 


ascertained by the rule perpendicular = Vhyp? — base?. 

Polygon, — A plane figure having three or more sides. Regular or 
irregular, according as the sides or angles are equal or unequal. Polygons 
are named from the number of their sides and angles. 

To find the area of an irreguiar polygon.—Draw diagonals 
Satagate the polygon into triangles, and find the sum of the areas of these 
triangles. 

To find the area of a regular polygon: 

RoLe.—Multiply the length of a side by the perpendicular distance to the 
centre; multiply the product by the number of sides, and divide.it by 2. 
Or, multiply half the perimeter by the perpendicular let fall from the centre 
on one of the sides. 

The perpendicular from the centre is equal to half of one of the sides of 
phe polygon multiplied by the cotangent of the angle subtended by the halt 
side. 

The angle at the centre = 360° divided by the number of sides. 


TABLE OF REGULAR POLYGONS. 


Radius of Cir- 





cumscribed | gq cai “ 
° "Ce e oe f 
g Circle z° = “ Fs = 
~ e o ° 
5 l de Zo |32.. 1.3 3 
wa S) pace ah Cee ® Pa} 
o Pu 3 = Il DN | ay e) SH 
z a |  » ah; ey ae | toce XS o 
a re) 77) ee n® | qa°2 oS 2s 
oan o « oe Ul 570 nO 0 oo 
° g s 20 ro) sal OSs "ep "Sb 3 
6 a x 5O s gO |} o09) «& == 
7, J 4 Ay 1) fae} 4 <q < 
3 | Triangle .4380127 | 2 5773 | .2887} 1.732° | 120° 60° 
4 | Square In 1.414 707 5 1.4142 | 90 90 
5 | Pentagon 1.7204774 | 1.288 | .8506 | .6882) 1.1756 | % | 108 
6 | Hexagon 2.5980762 | 1.155 | 1. .866 | 1. 60 120 
7 | Heptagon 3.6339124 | 1.11 | 1.1524 | 1.03883} .8677 | 51267] 128 4-7 
8 | Octagon 4.8284271 | 1.083 | 1.3066 |} 1.2071] .7653 | 45 135 
9 }/ Nonagon 6.1818242 | 1.U64 | 1.4619 | 1.38737] .684 40 140 
10 ; Decagon ¢.6942088 | 1.051 | 1.618 | 1.5388) .618 36 144 
11 | Undecagon| 9.3656399 | 1.042 | 1.7747 | 1.7028] .5634 | 3243’) 1473-11 
12 | Dodecagon | 11.1961524 | 1.037 | 1.9319 | 1.866 .5176 | 30 150 





To find the area of a regular polygon, when the length 
of a side only is given: 

RuLE.—Multiply the square of the side by the multiplier opposite to the 
name of the polygon in the table. ; 

To find the area of an ir- 
regular figure (Fig. 69).—Draw or- 
dinates across its breadth at equal 
distances apart, the first and the last 
ordinate each being one half space 
from the ends of the figure. Find the 
average breadth by adding together 
the lengths of these lines included be- 
tween the boundaries of the figure, 





and divide by ea ticaree of tue lines piaet3) 4 5 O70 esi ae 
added; multiply this mean breadth by ees Sen ethi see el 
the length. The greater the number cee at 

of lines the nearer the approximation. Fia. 69. 


In a figure of very irregular outline, as an indicator-diagram from a high- 
speed steam-engine, mean lines may be substituted for the actual lines of the 
figure, being so traced as to intersect the undulations, so that the total areg 
ie spaces cut off may be compensated by that of the extra spaces in- 
closed. 


56 MENSURATION, 


2d Method: Tut TRAPEZzoIDAL Rute. — Divide the figure into any suffi. 
cient number of equai parts; add half the sum of the two end ordinates te 
the sum of all the other ordinates; divide by the number of spaces (that is, 
one less than the number of ordinates) to obtain the mean ordinate, and 
multiply this by the length to obtain the area. 

3d Method: Simpson’s RuLe.—Divide the length of the figure into any 
even number of equal parts, at the common distance D apart, and draw or- 
dinates through the points of division to touch the boundary lines. Add 
together the first and last ordinates and call the sum A; add together the 
even ordinates and call the sum 4; add together the odd ordinates, except 
the first and last, and call thesum C. Then, 

area of the figure = arietit x D. 


4th Method : DuRAND’s RuLE.—Add together 4/10 the sum of the first aud 
last ordinates, 11/10 the sum of the second and the next to the last (or the 
penultimates), and the sum of all the intermediate ordinates. Multiply the 
sum thus gained by the common distance between the ordinates to obtain 
the area, or divide this sum by the number of spaces to obtain the mean or- 
dinate. 

Prof. Durand describes the method of obtaining his rule in Engineering 
News, Jan.18, 1894. He claims that it is more accurate than Simpson’s rule, 
and practically as simple as the trapezoidal rule. He thus describes its ap. 
plication for approximate integration of cifferential equations. Any defi 
uite integral may be represented graphically by an area. Thus, let 


Q= fudz 


be an integralin which wu is some function of x, either known or admitting of 
computation or measurement. Any-curve plotted with x2 as abscissa and u 
as ordinate will then represent the variation of w with a2, and the area be- 
tween such curve and the axis X will represent the integral in question, no 
matter how simple or complex may be the real nature of the function w. 

Substituting in the rule as above given the word ‘‘ volume” for ~ area” 
and the word ‘‘ section’ for ‘*‘ ordinate,’’ it becomes applicable to the deter- 
mination of volumes from equidistant sections as well as of areas from 
equidistant ordinates. 

Having approximately obtained an area by the trapezoidal rule, the area 
by Durand’s rule may be found by adding algebraically to the sum of the 
ordinates used in the trapezoidal rule (that is, half the sum of the end ordi- 
nates + sum of the other ordinates) 1/10 of (sum of penultimates—sum of 
first and last) and multiplying by the commor distance between the ordi- 


nates. 

5th Method —Draw the figure on cross-section paper. Count the number 
of squares that are entirely included within the boundary; then estimate 
the fractional parts of squares that are cut by the boundary, add together 
these fractions, and add the sum to the number of whole squares. The 
result is the area in units of the dimensions of the squares. The finer the’ 
ruling of the cross-section paper the more accurate the result. 

6th Method.—Use a planimeter. 

Sth Method.—With a chemical balance, sensitive to one milligram, draw 
the figure on paper of uniform thickness and cut it out carefully: weigh the 
pi2ce cut out, and compare its weight with the weight per square inch of the 
paper as tested by weighing a piece of rectangular shape. 


THE CIRCLE. 57 


THE CIRCLE. 
Circumference = diameter x 3.1416, nearly; more accurately, 3.14159265359, 
Approximations, ° = 3.148; = = 3.1415929. 
The ratio of circum. to diam. is represented by the symbol a (called Pi), 


. 7T 
Multiples of z. Multiples of r 


1m = 3.14159265359 ” = .7853982 
Qn = 6.28318530718 “ 4% 2=1.5707963 
8m = 9.42477796077 “© x 3 = 2.3561945 
4m = 12.56637061436 & x 4 = 3,1415927 
Bm = 15.70796326795 «© x 5 = 8.9269908 
6x = 18 84955592154 © x 6 = 4.7123890 
Tm = 21.99114857513 | “ y 7 =5.4977871 
8m = 25.13274122872 «© 48 = 6,2831853 
Gm = 28.27433388231 © x 9 = 70685035 
Ratio of diam. to circumference = reciprocal of 7 = 0,3183099. 
ecees ink 10), rene 8 1a 
Reciprocal of 7 = 1.27324. sas 2.22817 jo 0.261799 
Multiples ot 1 8 = 2.54648 =— = 0.0087266 
ates = se 360 
360 
hs 8188 ® _ 9 g6479 eer = 114.5915 
Tv 7 wT 
P= .63662 19 = 3.18310 n= 9.86960 
7 7 
1 
3 95498 12 _ 3 81972 — = 0.101321 
T Tv us 
£ = 1.27324 = 1.570796 Var = 1.772458 
: : vA 1— 0.564189 
~ = 1.59155 sm = 1.047197 7 
= 0.49714987 
< = 1.90986 ” = 0.523598 tar tei 


| Log 7 = 1.895090 


Diam. in ins. = 13.5405 Varea in sq. ft. 
Area in sq. ft. = (diam. in inches)? x .0054542, 
D=diameter, R=radius, C=circumference, <A = area, 


4A 


C= 7Dj= 2R; = 3 =2VrA;=3.545V 43 
2 CD 
A= D2? x .7854; no es = 4R? x .7854; =7R2; BEAR iat = i = .07958C?; = 7 - 
2 4 4 4 


A a 
D=~=; = 0.318310; aay 4, = 1,12838 V4; 


A ee 
R= 5; = 01501550; = ee = 0.564189 VA. 


Areas of circles are to each other as the squares of their diameters. 
To find the length of an are of a circle: 


RULE 1. As 360 is to the number of degrees in the are, so is the cireum- ~~ 


ference of the circle to the length of the are. 
RULE 2. Multiply the diameter of the circle by the number of degrees in 
the are, and this product by 0.0087266, 


es 


58 MENSURATION. 


Belations of Arc, Chord, Chord of Half the Are, 
Versed Sine, etc. 
Let Rk = radius, D = diameter, Arc = length of arc, 
Cd = chord of the are, ch = chord of half the are, 
V = versed sine, or height of the are, 








8ch —-Cd _ VCd? +42 x 1072, , 

Are —-—~,—- (very,nearly), = ~~ aaa 3302 -+ 2ch, nearly. 
2ch x 10V 

Arc = 60D + 2ch, nearly. 


Chord of the are =2Vch?—V2; = VD? —(D—2V)?; = 8ch = 8Are. 
=2VR?—(R—V)?; =2V(D—V) x V. 
Chord of half the are, ch = 54 OP AV; LV Dg Va 


8 
an _ Gouytr? 


Diameter La ee CE We te 
: gl sy ee: 
Versed sine Suiat kweli V D?— Cd?) 


(or 5D + VD? — Cd*), if Vis greater than radius 


Half the chord of the arc is a mean proportional between the versed sine 
and diameter minus versed sine: 144Cd = VV x(D—V) 

Length of the Chord subtending an angle at the centre = twice the 
Sing of haf the aigte, (see able of Sines, p. 157.) 


Length of a Circular Arc.—Huyghens’s Approximation. 
Let C represent the length of the chord of the are and c the length of the 
chord of half the arc; the length of the arc 


8c —C 

L ea 
Professor Williamson shows that when the are subtends an angle of 30°, the 
radius being 100,000 feet (nearly 19 miles), the error by this formula is about 
two inches, or 1/600000 part of the radius. When the length of the arc is 
equal to the radius, i.e., when it subtends an angle of 57°.3, the error is less 
than 1/7680 part of the radius. Therefore, if the radius is 100,000 feet, the 


0000 / ‘ : 
error is less than “7680 = 13 feet. The error increases rapidly with the 


increase of the angle subtended. 

In the measurement of an are which is described with a short radius the 
error is so small that it may be neglected. Describing an arc with a radius 
of 12 inches subtending an angle of 30°, the error is 1/50000 of aninch. For 
57°.3 the error is less than 0/’.0015. 

In order to measure an are when it subtends a large angle, bisect it and 
measure each half as before—in this case making B = length of the chord of 
half the are, and b= length of the chord of one fourth the arc; then 

16b — 2B 
L — ae e 
Relation of the Circle to its Equai, Inscribed, and Cir= 
curmsceribed Squares, 
Diameter of circle <1 88623) eaieeee as Sm 
Circumference of circle x .28209 t = side of equal square. 
Circumference of circle x 1.1284 = perimeter of equal square, 








THE ELLIPSE. 59 


Diameter of circle x .7071 , 
Circumference of circle x .22508} = side of inscribed square. 
Area of circle x .90031+ diameter 


Area of circle x 1.2732 = area of circumscribed square, 
Area of circle x .68662 = area of inscribed square. 
Side of square x 1.4142 = diam. of circumscribed circle. 
a oh le; 4.4428 = circum. bi ‘i i 
“ OP ee 1.1284 = diam. of equal circle. 
by eee . 3.5449 = circum. ay 
Perimeter of square x 0.88623 = a se ‘s 
Square inches x 1.27382 = circular inches. 


Sectors and Segments.—To find the area of a sector of a circle. 

Kuie 1. Multiply the are of the sector by half its radius. 

Rue 2. As 360 is to the number of degrees in the arc, so is the area of 
the circle to the area of the sector. 

Rute 3. Multiply the number of degrees in the arc by the square of the 
radius and by .008727. 

To find the area of a segment of a circle; Find the area of the sector 
which has the same arc, and also the area of the triangle formed by the 
chord of the segment and the radii of the sector, 

Then take the sum of these areas, if the segment is greater than a semi- 
circle, but take their difference if it is less. 

Another Method; Area of segment = 4%R(are — sin A), in which A is the 
central angle, R the radius, and arc the length of arc to radius J. 

To find the area of a segment of a circle when its chord and height only 
are given. First find radius. as follows: 


ER: 17 square of half the chord 
ei | height 





3 a height |. 


2. Find the angle subtended by the are, as follows: half chord + radius = 
sine of half the angle. Take the corresponding angle from_a table of sines, 
and double it to get the angle of the are. 

3. Find area of the sector of which the segment is a part; 


area of sector = area of circle x degrees of are + 360. 
4, Subtract area of triangle under the segment}: 
Area of triangle = half chord x (radius — height of segment). 


The remainder is the area of the segment. 

When the chord, arc, and diameter are given, to find the area. From the 
length of the are subtract the length of the chord. Multiply the remainder 
by the radius or one-half diameter; to the product add the chord multiplied 
by the height, and divide the sum by 2. 

Given diameter, d, and height of segment, h. 


When h is from 0 to 14d, area = hV1.766dh — h?; 
we ee Vd todéd, area = hV0.017d? -+-1.7dh — h? 


(approx.). Greatest error 0.23%, when h = 14d. 

To_find the chord: From the diameter subtract the height; multiply the 
remainder by four times the height and extract the square root. i 

When the chords of the are and of half the arc and the rise are given: To 
the chord of the are add four thirds of the chord of half the are, multiply 
the sum by the rise and the product by .40426 (approximate). 

Circular Ring.—To find the area of @ ring included between the cir- 
cumferences of tivo concentric circles; Take the difference between the areas 
of the two circles; or, subtract the square of the less radius from the square 
of the greater, and multiply their difference by 3.14159. 

The area of the greater circle is equal to 7R?; 
and the area of the smaller, wr2, 
Their difference, or the area of the ring, is r(R?2 — r?). 
The Ellipse.—Area of an ellipse = product of its semi-axes x 3.14159 
= product of its axes x .785398. 


VBT® py mad 





The Ellipse.—Circumference (approximate) = 3.1416 


being the two axes. , 
Trautwine gives the following as more accurate: When the longer axis D 
is not more than five times the length of the shorter axis, d, 


60 MENSURATION, 


( ILq (DD 

Circumference = 8.1416 eee teeta 
When D is more than 5d, the divisor 8.8 is to be replaced by the following : 
For D/d= 6. ¢ 8 9 10 12-14 16 18 20 30 40 5 

Divisoy: =/9°9.2-9.38., G00, 9.4, 9.590926) 0.68. 69.75) 9.8.9.0 908 bee 
An accurate formula is C = r(a + oy a + a eR se i 

3 e form = (0 ad 6 tong taesert e+): in 

which 4 = “= 

Carl G. Barth (Machinery, Sept., 1900) gives as a very close approximation 

to this formula 
64 — 3A4 


C= m(a + b) B46 40" 


Area of a segment of an ellipse the base of which is parallel to one of 
the axes of the ellipse. Divide the height of the segment by the axis of 
which it is part, and find the area of a circular segment. in a table of circu- 
lar segments, of which the height is equal to the quotient; multiply the area 
thus found by the product of the two axes of the ellipse. 

Cycloid.—A curve generated by the rolling of a circle on a plane. 


Length of a cycloidal curve = 4 x diameter of the generating circle. 
Length of the base = circumference of the generating circle. 
Area of a cycloid == 3 X area of generating circle. 


Welix (Screw).—A line generated by the progressive rotation of a 
point around an axis and equidistant from its centre. 

Length of a helix.—To the square of the circumference described by the 
generating-point add the square of the distance advanced in one revolution, 
and take the square root of their sum multiplied by the number of revolu- 
tions of the generating point. Or, 


V(c? + h?)n = length, n being number of revolutions. 


Spirals,.—Lines generated by the progressive rotation of a point around 
a fixed axis, with a constantly increasing distance from the axis. 

A plane spiral is when the point rotates in one plane. 

A conical spiral is when the point rotates around an axis at a progressing 
distance from its centre, and advancing in the direction of the axis, as around 
a cone. 

pera of a plane spiral line-—When the distance between the coils is 
uniform. 

RuLe.—Add together the greater and less diameters; divide their sum by 
2; multiply the quotient by 3.1416, and again by the number of revolutions. 
Or, take the mean of the length of the greater and less circumferences and 
multiply it by the number of revolutions. Or, 


a’ 





° -—Ingenieurs Taschenbuch, 1896. 





length = 7 = ,d and d’ being the inner and outer diameters. 


2 

Length of a conical spiral line.—Add together the greater and less diam- 
eters; divide their sum by 2 and multiply the quotient by 3.1416. To the 
square of the product of this circumference and the number of revolutions 
of the spiral add the square of the height of its axis and take the square 


root of the sum. 
d+d’\2 
Or, length = 4/ (on 5 ) +h, 


SOLID BODIES. 


The Prism.—To find the surface of a right prism : Multiply the perim- 
eter of the base by the altitude for the convex surface. To this add the 
areas of the two ends when the entire surface is required. 





Volume of a prism = area of its base x its altitude. 


The pyramid.—Convex surface of a regular pyramid = perimeter of 
its base < half the slant height. To this add area of the base if the whole 
surface is required. 


Volume of a pyramid = area of base X one third of the altitude. 


SOLID BODIES. 61 


To find the surface of a frustum of a regular pyramid : Multiply half the 
slant height by the sum of the perimeters of the two bases for the convex 
aan To this add the areas of the two bases when the entire surface is 
required, 

To find the volume of a frustum of a pyramid: Add together the areas of 
the two bases and a@ mean proportional between them, and multiply the 
sum by one third of the altitude. (Mean proportional between two numbers 
<= square root of their product.) 

Wedge.—A wedge is a solid bounded by five planes, viz.: a rectangular 
base, two trapezoids, or two rectangles, meeting in an edge, and two tri- 
angular ends. The altitude is the perpendicular drawn from any point in 
the edge to the plane of the base. ; 

To find the volume of a wedge: Add the length of the edge to twice the , 
Jength of the base, and multiply the sum by one sixth of the product of the 
height of the wedge and the breadth of the base. 

Rectangular prismoid.—aA rectangular prismoid is a solid bounded 
by six plaues, of which the two bases are rectangles, having their corre- 
spon as sides parallel, and the four upright sides of the solids are trape- 
zoids. 

To find the volume of a rectangular prismoid: Add together the areas of 
the two bases and four times the area of a parallel section equally distant 
from the bases, and multiply the sum by one sixth of the altitude. 

Cylinder.—Convex surface of a cylinder = perimeter of base x altitude. 
To this add the areas of the two ends when the entire surface is required. 


Volume of a cylinder = area of base X altitude. 


Cone,.—Convex surface of a cone = circumference of base X half the slant 
side. To this add the area of the base when the entire surface is required. 


Volume of a cone = area of base X one third of the altitude. 


To find the surface of a frustum of a cone; Multiply half the side by the 
Sum ot the circumferences of the two bases for the convex surface; to this 
add the areas of the two bases when the entire surface is required. 

To find the volume of a frustum of a cone? Add together the areas of the 
two bases and a mean proportional between them, and multiply the sum by 
one third of the altitude. Or, Vol. = 0.2618a(62 + c2-+ bc); a = altitude; 
b and c, diams. of the two bases. 

Sphere.—To find the surface of a sphere: Multiply the diameter by the 
circumference of a great circle; or, multiply the square of the diameter by 
8.14159. 


Surface of sphere = 4 X area of its great circle. 
* “eS = convex surface of its circumscribing cylinder. 


Surfaces of spheres are to each other as the squares of their diameters, 

To find the volume of a sphere: Multiply the surface by one third of the 
radius; or, multiply the cube of the diaineter by 7/6; that is, by 0.5236, 

Value of 7/t to 10 doc nal pices = .5235987756. 

The volume of a sphere = 2/3 the volume of its circumscribing cylinder, 

Volumes of spheres are to each other as the cubes of their diameters. 

Spherical triangle.—To find the area of a spherical triangle : Com- 
pute the surface of the quadrantal triangle, or one eighth of the surface of 
the sphere. From the sum of the three angles subtract two right angles; 
divide the remainder by 90, and multiply the quotient by the area cf the 
quadrantal triangle. 

Spherical polygon.—To find the area of a spherical polygon: Com- 
nute the surface of the quadrantal triangle. From the sum of all the angles 
subtract the product of two right angles by the number of sides less two; 
divide the remainder by 90 and multiply the quotient by the area of the 
quadrantal triangle. 

The prismoid.—The prismoid isa solid having parallel end areas, and» 
may be composed of any combination of prisms, cylinders, wedges, pyra- 
mids, or cones or frustums of the same, whose bases and apices lie in the 
end areas. 

Inasmuch as cylinders and cones are but special forms of prisms and 
pyramids, and warped surface solids may be divided into elementary forms 
of them, and since frustums may also be subdivided into the elementary 
forms, it is sufficient to say that all prismoids may be decomposed into 
prisms, wedges, and pyramids. If a formula can be found which is equally 
applicable to all of these forms, then it will apply to any combination of 
them, Such a formula is called 


62 MENSURATION. 


The Prismoidal Kormuia. 


Let A = area of the base of a prism, wedge, or pyramid; 
A,, Ag, Am = the two end and the middle areas of a prismoid, or of any af 
its elementary solids; 


h = altitude of the prismoid or elementary solid; 
V = its volume; 


h 
w= 6 (41 +44,, + Ag). 


For a prism, 4,, Am and A, are equal, = 4; V= ; x64 =A. 





1 ] he 
For a wedge with parallel ends, 4, = 0, 4m = at Sa Ae 5 (At +2A4)) = sen 
1 h- I 
For a cone or pyramid, 4A, = 0, Am = gA13 V= GA +A4,)= “f 


The prismoidal formula is a rigid formula for all prismoids. The onlv 
approximation involved in its use is in the assumption that the given solid 
may be generated by a right line moving over the boundaries of the end 
areas. 

The area of the middle section is never the mean of the two end areas if 
the prismoid contains any pyramids or coues among its elementary forms. 
When the three sections are similar in form the dimensions of the middle 
area are always the means of the corresponding end dimensions. This fact 
often enables the dimensions, and hence the area of the middle section, to 
be computed from the end areas, 

Polyedroms.—aA polyedron is a solid bounded by plane polygons. A 
regular polyedron is one whose sides are all equal regular polygons. 

To find the surface of a regular polyedron.—Multiply the area of one of 
the faces by the number of faces; or, multiply the square of one of the 
edges by the surface of a similar solid whose edge is unity. 


A TABLE OF THE REGULAR POLYEDRONS WHOSE EDGES ARE UNITY. 


Names. No. of Faces. Surface. Volume. 
MetraAe aroma atts Hiei woe lee os ee 4 1.7320508 9.1178513 
HexaAcdnOn dei Phe eee ee i AEN te ane S 6 6 .0060000 1.0000000 
MCtACUrOnu:ciucace woe ees Meats Soe 8 3.4641016 0.4714045 
Dodecaedron serra cae Boerne wart ed 20.6457288 7 6631189 
TCOSHEATOD Aas FEE seeuieiene Be Oe 20 8.6602540 2.1816950 


To find the volume of a regular polyedron.— Multiply the 
surface by one third of the perpendicular let fali from the centre on one of 
the faces; or, multiply the cube of one of the edges by the solidity of a 
similar polyedron whose edge is unity. ' 

Solid of revolution.—The volume of any solid of revolution is 
equal to the product of the area of its generating surface by the length of 
the path of the centre of gravity of that surface. 

The convex surface of any solid of revolution is equal to the product of 
the perimeter of its generating surface by the length of path of its centre 
of gravity. 

Cylindrical ring.—Let d= outer diameter; d’= inner diameter ; 

1 
4 
eter = M; wt = circumference of section; 7M = mean circumference of 
: 1 
ring; surface =at X 7M; = 47° (d2 — d/2); = 9.86965 t M; = 2.46741 (d2 —d’?); 


J 1 
5 (d — d’) = thickness = ¢; 7 at? = sectional area ; 3 (a+ d’) = mean diam- 


J 
volume = 47 2 Ma; = 2.467410? M. 


Spherical zone.—Suwifuce of a sphericat zone or segment of a sphere 
= its altitude x the circumference of a great circle of the sphere. A great 
circle is one whose plane passes through the centre of the sphere. 

Volume of a zone of a sphere.—To the sum of the squares of the radii 
of the ends add one third of the square of the height ; multiply the sum 
by the height and by 1.5708. ‘ 

Spherical segment,.—Volume of aspherical segment with one base.— 


SOLID BODIES. 68 


Multiply half the height of the segment by the area o. uhe base, and the 
cube of the height by .5236 and add the two products. Or, from three times 
the diameter of tne sphere subtract twice the height of the segment; multi- 
ply the difference ty the square or the height and by .5286. Or, to three 
times the square of the radius of the base of the seginent add the square of 
its height. and multiply the sum by the height and by .5236. 

Spheroid or ellipsoid.—Wben the revolution of the spheroid is about 
the trausverse diameter it is prolate, and when about the conjugate it is 
oblate. 

Convex surface of a segment of a spheroid.—Square the diameters of the 
spheroid, and take the square root of balf their sum ; then, as the diameter 
from which the segment is cut is to this root so is the height of the 
segment to the proportionate height of the segment to the mean diameter. 
Multiply the product of the other diameter and 3.1416 by the proportionate 
height. 

Contex surface of a frustum or zone of a spheroid.—Proceed as by 

revious rule for the surface of a segment, and obtain the proportionate 

eight of the frustum. Multiply the product of the diameter parallel to the 
base of the frustum and 3.1416 by the proportionate height of the frustum. 

Volume of a spheroid is equal to the product of the square of the revolving 
axis by the fixed axis and by .5236. The volume of a spheroid is two thirds 
of that of the circumscribing cylinder. 

Volume of a segment of a spheroid.—l. When the base is parallel to the 
revolving axis. multiply the difference between three times the fixed axis 
and twice the height of the segment, by the square of the height and by 
5236. Multiply the product by the square of the revolving axis, and divide 
by the square of the fixed axis. 

2. When the base is perpendicular to the revolving axis, multiply the 
difference between three times the revolving axis and twice the height of 
the segment by the square of the height and by .5236. Multiply the 
product by the length of the fixed axis, and divide by the length of the 
revolving axis. 

Volume of the middle frustum of a spheroid.—1. When the ends are 
circular, or parallel to the revolving axis: To twice the square of the 
middle diameter add the square of the diameter of one end ; multiply the 
sum by the length of the frustum and by .2618. 

2, When the ends are elliptical, or perpendicular to the revolving axis: 
To twice the product of the transverse and conjugate diameters of the 
middle section add the product of the transverse and conjugate diameters 
of one end ; multiply the sum by the length of the frustum and by .2618. 

Spindies.—Figures generated by the revolution of a plane area, when 
the curve is revolved about a chord perpendicular to its axis, or about its 
double ordinate. They are designated by the name of the are or curve 
from which they are generated, as Circular, Elliptic, Parabolic, ete., etc. 

Convex surface of a circular spindle, zone, or segment of it —Rule: Mul- 
tiply the length by the radius of the revolving arc; multiply this arc by the 
central distance, or distance between the centre of the spindle and centre 
of the revolving are; subtract this product from the former, double the 
remainder, and multiply it by 3.1416 ; 

Volume of a circular spindle.—Multiply the central distance by half the 
area of the revolving segment; subtract the product from one third of the 
cube of half the length, and multiply the remainder by 12.5664. 

Volume of frustum or zone of a circular spindle.—From the square of 
half the length of the whole spindle take one third of the square of half the 
length of the frustum, and multiply the remainder by the said half length 
ot the frustum ; multiply the central distance by the revolving area which 
generates the frustum ; subtract this product from the former, and multi- 
ply the remainder by 6.2832. 

Volume of a segment of a circular spindle.—Subtract the length of the 
segment from the half leugth of the spindle ; double the remainder and 
ascertain the volume of a middle frustum of this length; subtract the 
result from the volume of the whole spindle and halve the remainder. 

Volume of a cycloidal spindle = five eighths of the volume of the cireum- 
scribing cylinder.—Multiply the product of the square of twice the diameter 
of the generating circle and 3.927 by its circumference, and divide this pro- 
dnet by 8. 

Parabolie conoid.—Volume of a parabolic conoid (generated by the 
revolution of a parabola on its axis).—Multiply the area of the base by half 


the height, 


64 MENSURATION. 


ans multiply the square of the diameter of the base by the height and by 
.8927. 


Volume of a frustum of a parabolic conoid.—Multiply half the sum of 
the areas of the two ends by the height. 

Volume of a parabolic spindle (generated by the revolution of a parabola 
fans easing nps ee the square of the middle diameter by the length 
and by .4189. 

The volume of a parabolic spindle is to that of a cylinder of the same 
height and diameter as 8 to 15. 

Volume of the middle frustum of a parabolic spindle.—Add together 
8 times the square of the maximum diameter, 3 times the square of the end 
diameter, and 4 times the product of the diameters. Multiply the sum by 
the length of the frustum and by .05236. 

: This rule is applicable for calculating the content of casks of parabolic 
orm. 

Casks.—'o find the volume of a cask of any form.—Add together 39 
times the square of the bung diameter, 25 times the square of the head 
diameter, and 26 times the product of the diameters. Multiply the sum by 
the length, and divide by 31,773 for the content in Imperial gallons, or by 
26,470 for U.S. gallons. 

This rule was framed by Dr. Hutton, on the supposition that the middle 
third of the length of the cask was a frustum of a parabolic spindle, and 
each outer third was a frustum of a cone. 

To find the ullage of a cask, the quantity of liquor in it when it is not full. 
1. For a lying cask: Divide the number of wet or dry inches by the bung 
diameter in inches. If the quotient is less than .5, deduct from it one 
fourth part of what it wants of .5. If it exceeds .5, add to it one fourth part 
of the excess above .5. Multiply the remainder or the sum by the whele 
content of the cask. The product is the quantity of liquor in the cask, in 
gallons, when the dividend is wet inches; or the empty space, if dry inches. 

2. For a standing cask: Divide the number of wet or dry inches by the 
length of the cask. If the quotient exceeds .5, add to it one tenth of its 
excess above .5; if less than .5, subtract from it one tenth of what it wants 
of 5. Multiply the sum or the remainder by the whole content of the cask. 
The product is the quantity of liquor in the cask, when the dividend is wet 
inches; or the empty space. if dry inches. 

Volume of cask (approximate) U. 8. gallons = square of mean diam. 
x length in inches x .0034. Mean diam. = half the sum of the bung and 
head diams. 

Volume of an irregular solid.—Suppose it divided into parts, 
resembling prisms or other bodies measurable by preceding rules. Find. 
ae sae oa of each part; the sum of the contents is the cubic contents of 

e solid. 

The content of a small part is found nearly by multiplying half the sum 
of the areas of each end by the perpendicular distance between them. 

The contents of small irregular solids may sometimes be found by im- 
mersing them under water in a prismatic or cylindrical vessel, and observ- 
ing the amount by which the level of the water descends when the solid is 
withdrawn. The sectional area of the vessel being multiplied by the descent 
of the level gives the cubic contents. 

Or, weigh the solid in air and in water; the difference is the weight of 
water it displaces. Divide the weight in pounds by 62.4 to obtain velume in 
cubic feet, or multiply it by 27.7 to obtain the volume in cubic inches. 

When the solid is very large and a great degree of accuracy is not 
requisite, measure its length, breadth, and depth in several different 
places, and take the mean of the measurement for each dimension, and 
multiply the three means together. a 

When the surface of the solid is very extensive it is better to divide it 
into triangles, to find the area of each triangle, and to multiply it by the 
mean depth of the triangle for the contents of each triangular portion; the 
contents of the trianguiar sections are to be added together, 

The mean depth of a triangular section is obtained by measuring the 
depth at each angle, adding together the.three measurements, and taking 
one third of the sum. 





PLANE TRIGONOMETRY. 65 


PLANE TRIGONOMETRY. 


Trigonomeiricai Functions. 


Every triangle has six parts—three angles and three sides. When any 
three of these parts are given, provided one of them is a side, the other 
parts may be determined. By the solution of a triangle is meant the deter- 
mination of the unknown parts of a triangle when certain parts are given. 

The complement of an angle or arc is What remains after subtracting the 
angle or are from 90°. 

In general, if we represent any are by A, its complement is 90° — A. 
Hence the complement of an are that exceeds 90° is negative. 

Since the two acute angles of a right-angled triangle are together equal to 
aright angle, each of them is the complemeut of the other. 

The supplement of an angle or arc is what remains after subtracting the 
angle or are from 180°. If A is an arc its supplement is 180° — A. The sup- 
plement of an are that exceeds 180° is negative. 

The sum of the three angles of a triangle is equal to 180°. Either angle is 
the supplement of the othertwo. Ina right-angled triangle, the right angle 
being equal to 90°, each of the acute angles is the complement of the other. 

In all right-angled triangles having the same acute angle, the sides have 
to ee other the same ratio. These ratios have received special names, as 
follows: 

If Ais one of the acute angles, a the opposite side, b the adjacent side, 
and c the hypothenuse. 

Whe sime of the angle A is the quotient of the opposite side divided by the 


a 
hypothenuse. Sin. A= 8 
Whe tangent of the angle A is the quotient of the opposite side divided by 


a 
the adjacent side. Tang. A= in 


Mhe secant of the angle Ais the quotient of the hypothenuse divided by 
c 
the adjacent side. Sec. A= i 

The cosine, cotangent, and cosecant of an angle are respec- 
tively the sine, tangent, and secant of the complement of that angle. The 
terms sine, cosine, etc., are called trigonometrical functions. 

In acircle whose radius is unity, the sime of an arc, or of the angle at the 
centre measured by that arc, is the perpendicular let fall from one extrem- 
ity of the are upon the diameter passing through the other extremity. 

The tangent of anarcis the line which touches the circle at one extrem- 
ity of the arc, and is limited by the diameter (produced) passing through 
the other extremity. 

Whe secant of anarcis that part of the produced diameter which is 
intercepted betireen the centre und the tangent. 

Whe versed sine of an arc is that part of the diameter intercepted 
between the extremity of the arc and tiie foot of the sine, 

In a circle whose radius is not unity, the trigonometric functions of anare 
will be equal to the lines here defined, divided by the radius of the circle. 

If IC A (Fig. 70) is an angle in the first quadrant, and C #'= radius, 

FG Cane CG KF 
Rad.’ a ads aaa 

IA S t Cr we DL. 
Tener Rad gue > Rademe oo Rad, 









The sine of the angle = 


> Tangent 


CL ‘ GA 
Cosec. = aq. Versin, = Rad. B 


If radius is 1, then Rad. in the denominator is 
omitted, and sine = FG, ete. 

The sine of an are = half the chord of twice the 
arc, 

The sine of the supplement of the arc is the same sy 
as that of the arc itself. Sineofarc BDF=FG= ~- , 
sin arc F' A. Fig. 70, 


66 PLANE TRIGONOMETRY. 


The tangent of the supplement is equal to the tangent of the arc, but with 
acontrary sign. Tang. BDF= B M. 

The secant of the supplement is equal to the secant of the arc, but witha 
contrary sign. Sec. BD F=C M. 

Signs of the functions in the four quadrants.—If we 
divide a circle into four quadrants by a vertical and a hvrizontal diame- 
ter, the upper right-hand quadraut is called the first, the upper left the sec- 
ond, the lower left the third, and the lower right the fourth. The signs of - 
the functions in the four quadrants are as follows: 


First quad, Second quad. Third quad. Fourth quad. 
Sine and cosecant, + -- -- — 
Cosine and secant, + _ _ + 
Tangent and cotangent, + - + — 


The values of the functions are as follows for the angles specified: 

















° ° ° ° fo} ° ° ° ° ° ° 
Aine le ae teh tie’ at clare 0}; 380 45 | 60 }90) 120 135 150 = |180/270/360 
V3 V3 
Sia skint) ban Wipes Pea MEE pial rei P ea allay 
V3 1 1 1 1 V3 
dea aera Wilh 5 ees fh 288 ashy > 
Cosine......... Suse fll 2 Ve 12 3 ¥a\ 2 1}0/1 
PNSRYT OU byes goa ae atts assis Oil aes 1 08) Fis Woo ited dines Aj 
‘ V3 ES U.et care) 
1 1 V3 
Cotangent..... ....J0) yz bs es Py ee 1 
i V3 noe — V3 12/0 |o 
2 le am 1] ye | “2 [2 ]o}—2 J-vg |-— |-tle|a 
V3 
Cosecant........... wo] 2 Aa rah iS 
V3 V3 V2 ec) OO. ed Oe 
a V8) > _. > 9 3 
Versed sine jae. ii. OeG.s oS Eee bh | a V2+4 oT V3 ° 
2 72 |2 2 a 








TRIGONOMETRICAL FORMULAE, 


The following relations are deduced from the properties of similar tri 
angles (Radius = 1): 


cos A: sin A : 1: tan A, whence tan 4 = ales 
cos A’ 
sin A:cos 4:1:cot 4, “ eotan A= COE oy 
sin A 
cos A: 1 sol'sisee 4007 Poy need. 
cos A 

br 1 
sin 4:1 1: cosec A, ‘* cosec A = ——3 
+ sin A 

1 
e ee e 6é — as 
tan A:1 : 1: cot 4 tan A= 


The sum of the square of the sine of an are and the square of its cosine 
equals unity. Sin? A+ cos? 4 = 1, 

Also, 1+ tan? A = sec? A: 1 + cot? A = cosec? A. 

Functions of the sum and difference of two angles: 

Let the two angles be denoted by A and #, their sum 4 -+ 6 = C, and 
their difference A — B by D. 


sin(4+ B)=sin AcosB+cosAsinB; . . .-» (I) 





TRIGONOMETRICAL FORMULA. 67 


cos (A +B) = cos A.cos B —sin\A sin By.) 5. . - (2) 
sin (A — B) =sin AcosB—cos Asin B; . . ... (8) 
cos (4 — B) =cosAcosB+sin Asin Bo... (4) 
From these four formule by addition and subtraction we obtain 
sin (4 + B)-+sin(4 —- B)=2sin AcosB;. .... (5) 
sin (4+ Bb) — sin (A — B) = cos A sin 18, afte wert ehh CG) 
cos (A +- B) + cos(A — B)=2cos4AcosB;..... (7) 
cos (A — B) — cos (Act A) =.2 81 ASIN Be oie sjyey he fs vC8) 
If we put 4+ B= C,and 4— B= D,then 4=%(C+D)andB= kK(C-. 
D), and we have 
sin C+ sin D = 2sinl4(C+ D)cosl4(C— D);.... (9) 
sin C — sin D= 2 cos (C+ D)sin B(C— D); . . . « (10) 
cos C+ cos D = 2 cos &(C+ D)cos&(C — D);... . (11) 
cos.D —cos C= 2sin 4(C + D)sink(C— D). . . . . (12) 
Equation (9) may be enunciated thus: The sum of the sines of any two 
anyles is equal to twice the sine of half the sum of the angles multiplied by 
the cosine of half their difference. These formule enable us to transform 
asum or difference into a product. 


The sum of the sines of two angles is to their difference as the tangent of 
half the sum of those angles is to the tangent of half their difference. 


sin A+sinB_ 2sin (4+ B) cos WA — B)_ tanl&(A +B) - (13) 
sin 4d—sin B” 2coslé(A + B) sin 4(A — B)” tan K(A — BY 


The sum of the cosines of two angles is to their difference as the cotangent 
of half the sum of those angles is to the tangent of half their difference. 


cos A-+cos B _ 2 cos (A + 8) cos H(A — B) _ cot 46(A + B) (14) 
cosB—cosA” 2siu 144(4 + B)sin k(A — B) ~ tan K(4 — BY 
The sine of the sum of two angles is to the sine of their differenee as the 
sum of the tangents of those angles is to the difference of the tangents. 
sin(A + B)_ tan A+ tan B, 
pin (Ai 2) ew ptanlc4 as tans ily eet eke 


tan 4+tan B. 























(15} 


sin (A +) _ tan 4+tanB; | iA EN yh EN 





cos A cos B — tan A tan B’ 
sin (A — B) tan A —*tan’B 

LS eat al pS — tan B: t Ry ce . 
cos A cos B PU eae zs see eae 1+ tan A tan B’ 
cos (AP Bt ys A tan 8: Bab C4 py ook dicot Bins b 





cos Acos B cot B+ cot 4:* 


eos (A — B) : _ cot Acot B+1 
Reuse ee SA est hs cot B — cot A’ 


Functions of twice am angle: 








sin 24 = 2sin A cos A; cos 24 = cos? A — sin? 4; 
: 2tan A a ent? 4 — 1 
peice ane h Se eect 
Functions of half an angle: 
sin 4d = 4 4/184, cosa= 2 4/ ESSA, 


1 —cos A /1 + cos A 
= ene |) WwvA= + aoe 
tanlg4 = + 3 mare cot 4 + 1/ mugs 


68 PLANE TRIGONOMETRY. 


Solution of Plane Right-angled Triangles, 


Let 4 and B be the two acute angles and C the right angle, and a, b, and 
c the sides opposite these angles, respectively, then we have 
a 
B? 
b 


2. cos A = sin Bx; 4, cot A = tanB=~. 


1. sin A= cosB x5; 8, tan A =cotB= 


1. In any plane right-angled triangle the sine of either of the acute angles 
is equal to the quotient of the opposite leg divided by the hypothenuse. 

2. The cosine of either of the acute angles is equal to the quotient of the 
adjacent leg divided by the hypotbenuse. 

3. The tangent of either of the acute angles is equal to the quotient of the 
opposite leg divided by the adjacent leg. 

4. The cotangent of either of the acute angles is equal to the quotient of 
the adjacent leg divided by the opposite leg, 

5. The square of the hypothenuse equals the sum of the squares of the 
other two sides. 


Solution of Gblique-angled Triangles, 


The following propositions are proved in works on plane trigonometry. In 
any plane triangle— 

Theoren 1. The sines of the angles are nroportional to the opposite sides. 

Theorem 2. The sum of any two sides is to their difference as the tangent 
of half the sum of the opposite angles is to the tangent of half their differ- 
ence: 

Theorem 3. If from any angle of a triangle a perpendicular be drawn to 
the opposite side or base, the whole base will be to the sum of the other twa 
sides as the difference of those two sides is to the difference of the segments 
of the base. 

Cask I. Given two angles and a side, to find the third angle and the other 
two sides. 1. The third angle = 180° — sum of the two angles. 2. The sides 
may be found by the following proportion : 

The sine of the angle opposite the given side is to the sine of the angle op- 
posite the required side as the given side is to the required side. 

Case II. Given two sides and an angle opposite one of them, to find the 
third side and the remaining angles. 

The side opposite the given angle is to the side opposite the required angle 
as the sine of the given angle is to the sine of the required angle. 

The third angle is found by subtracting the sum of the other two from 180°, 
and the third side is found as in Case I. 

CasE II. Given two sides and the included angle, to find the third side and 
the remaining angles. 

The sum of the required angles is found by subtracting the given angle 
from 180°. The difference of the required angles is then found by Theorem 
ll. Half the difference added to half the sum gives the greater angle, and 
half the difference subtracted from half the sum gives the less angle. The 
third side is then found by Theorem I. 

Another method ; 

Given the sides c, 0, and the included angle JA, to find the remaining side a 
and the remaining angles B and C. 

From either of the unknown angles, as B, draw a perpendicular B e to the 
opposite side. : 

Then 


Ae=ccosA, Be=csinA, eC=b—Ae, Be+eC= tan. 


Or, in other words, solve Be, Ae and B e Cas right-angled triangles. 
CasE IV. Given the three sides, to find the angles. 4 
Let fall a perpendicular upon the longest side from the opposite angle, 
dividing the given triangle into two right-angled triangles. The two seg- 
ments of the base may be found by Theorem III. There will then be given 
_ the bypothenuse and one side of a right-angled triangle to find the angles, , 
For areas of triangles, see Mensuration. 


ANALYTICAL GEOMETRY. 69 


ANALYTICAL GEOMETRY. 


Analytical geometry is that branch of Mathematics which has for 
its object the determination of the forms and magnitudes of geometrical 
magnitudes by means of analysis. 

Ordinates and abscissas,.—In analytical geometry two intersecting 
lines YY’, XX’ are used as cvudrdinate axes, 
XX’ being the axis of abszissas or axis of X, 
and YY’ the axis of ordinates or axis of Y. 
A, the intersection. is called the origin of co- 
Grdinates. The distance of any point P from 
the axis of Y measured parallel to the axis of 
X is called the abscissa of the point, as AD or 
OP, Fig. 71. Its distance from the axis of X, 
measured parallel to the axis of Y, is called 
the ordinate,as AC or PD. Theabscissa ard 
ordinate taken together are called the coér- 
dinates of the point P. The angie of intersec- 
tion is usually taken as a right angle, in which 
case the axes of X and Y are called vectangu- 
lar coordinates. 

The abscissa of a point is designated by the letter x and the ordinate by y. 

The equations of a point are the equations which express the distances of 
the point from the axis. Thus «=a, y=b are the equations of the point P. 

Equations referred to rectangular coérdinates,.—The equa- 
tion of a line expresses the relation which exists between the codrdinates of 
every point of the line. 

Kquation of a straight line, y= ax + b, in which a is the tangent of the 
angle the line makes with the axis of X, and b the distance above A in which 
the line cuts the axis of Y. 

Every equation of the first degree between two variables is the equation of 
a en line, as 4y + Bx+ C= 0, which can be reduced to the form y = 
ax + b. 

Equation of the distance between two points: 


D= Val = aE EO =F, 


in which 2’y’, x’’y’’ are the coérdinates of the two points. 
Equation of a line passing through a given point; 





y—y' = ae — 2’), 


in which «’y’ are the codrdinates of the given point, a, the tangent of tuw 
angle the line makes with the axis of w, being undetermined, since any num- 
ber of lines may be drawn through a given point. 

_ Equation of a line passing through two given points: 


yy’ : 
, y; 
{— FY oS C— V'). 
US Ueiss spear an ) 





Equation of a line parallel to a given line and through a given point. 
y—y’ = ae — x’). 

Equation of an angle V included between two given lines: 

a’ —a 

in which a and a’ are the tangents of the angles the lines make with the 


axis of abscissas. 
If the lines are at right angles to each other tang V = », and 


1+a/a=0. 
Equation of an intersection of two lines, whose equations are 


tang V = 


ys=arn+b, and y=a’x+D’, 
b — b’ abt — a/b 
= Tees Gy a00 ys 


70 ANALYTICAL GEOMETRY. 


Equation of a perpendicular from a given point to a given line: 
ups S 1 / 
ek dimers don 


Equation of the length of the perpendicular P: 


The circle.—Equation of a circle, the origin of codrdinates being at the 
ventre, aud radius = R 


Er Oi) fll a 
If the origin is at the left extremity of the diameter, on the axis of X: 
y? = 2Rhae — 22, 
If the origin is at any point, and the codrdinates of the centre are a’y’: 
(x4— x)? +y—y')? = R. 


Equation of a tangent to a circle, the codrdinates of the point of tangency 
being a’’y’’ and the origin at the centre, 


yy! -- ea! = Rt, 


The ellipse.—Equation of an ellipse, referred to rectangular coérdi- 
nates with axis at the centre: 


A2y? + Bre? = A2B2, 


in which 4 is half the transverse axis and B half the conjugate axis. 
Equation of the ellipse when the origin is at the vertex of the transverse 
axis: 


2 
y? = (ede a x2), 


The eccentricity of an ellipse is the distance from the centre to either 
focus, divided by the semi-transverse axis, or 


4 A? — B2 
cay Witag 


The parameter of an ellipse is the double ordinate passing through the 
focus. Itis a third proportional to the transverse axis and its conjugate, or 
2B2 


24:2B::2B: parameter; or parameter = RT 


Any ordinate of a circle circumscribing an ellipse is to the corresponding 
ordinate of the ellipse as the semi-transverse axis to the semi-conjugate. 
Any ordinate of a circle inscribed in an ellipse is to the corresponding ordi- 
nate of the ellipse as the semi-conjugate axis to the semi-transverse. 

Equation of the tangent to an ellipse, origin of axes at the centre > 


Atyy? —-- Bieta. 42 fs, 


y''x'’ being the codrdinates of the point of tangency. 
Equation of the normal, passing through the point of tangency, and per- 
pendicular to the tangent: 


ei 


A 4} 

y ae wi 7 Saat ia i). 

The normal bisects the angle of the two lines drawn from the point of 
tangency to the foci. 

The lines drawn from the foci make equal angles with the tangent. 

Whe parabola.—Equation of the parabola referred to rectangular 
coérdinates, the origin being at the vertex of its axis, y? = %px, in which 2p 
is the parameter or double ordinate through the focus. 


ANALYTICAL GEOMETRY. "1 


The parameter is a third proportional to any abscissa and its corresponding 
ordinate, or 
ep DET RTA Ser 
Equation of the tangent: 
yy” = pa +x"), 


ya’? being codrdinates of the point of tangency. 
Equation of the normal: 


1) pees y” vr 
y-y Maan age )s 


The sub-normal, or projection of the normal on the axis, is constant, and 
equal to half the parameter. 5 : ‘ 

The tangent at any point makes equal angles with the axis and with the 
line drawn from the point of tangency to the focus. 

The hyperbola.—Equation of the hyperbola referred to rectangular 
coérdinates, origin at the centre: 


Aty? — Bry? = — A?B?, 


in which <A is the semi-transverse axis and B the semi-conjugate axis. 
Equation when the origin is at the right vertex of the transverse axis: 


B? . 
y= qarAx + x). 


Conjugate and equilateral hyperbolias.—If on the conjugate 


axis, as a transverse, and a focal distance equal to /A2-+ B?, we construct 
the two branches of a hyperbola, the two hyperbolas thus constructed are 
called conjugate hyperbolas. If the transverse and conjugate axes are 
equal, the hyperbolas are called equilateral, in which case y? — #2 = — A? 
when A is the transverse axis, and #2 — y2 = — 62 when B is the trans- 
verse axis. 

The parameter of the transverse axis is a third proportional to the trans- 
verse axis and its conjugate. 


2A: 2B ::2B : parameter. 





The tangent to a hyperbola bisects the angle of the two lines drawn from 
the point of tangency to the foci. 

The asymptotes of a hyperbola are the diagonals of the rectangle 
described on the axes, indefinitely produced in both directions, 

In an equilateral hyperbola the asymptotes make equal angles with the 
transverse axis, and are at right angles to each other. 

The asymptotes continually approach the hyperbola, and become tangent 
to it at an infinite distance from the centre. 

Conie sections.—Every equation of the second degree between two 
variables will represent either a circle, an ellipse, a parabola or a hyperbola. 
These curves are those which are obtained by intersecting the surface of a 
cone by planes, and for this reason they are called conic sections. 

Logarithmie curve.—A logarithmic curves one in which one of the 
coérdinates of any pointisthe logarithm of the other. 

The codrdinate axis to which the lines denoting the logarithms are parallel 
is called the axis of logarithms, and the other the axis of numbers. If y is 
the sat of logarithms and @# the axis of numbers, the equation of the curve 
is 7 = log a. 

If the base of a system of logarithms is a, we have aY = x, in which y is the 
logarithm of a. 

Each system of logarithms will give a different logarithmic curve. If y= 
0,2 =1. Hence every logarithmic curve will intersect the axis of numbers 
at a distance from the origin equal to 1. 


2 DIFFERENTIAL CALCULUS. 


DIFFERENTIAL CALCULUS. 


The differential of a variable quantity is the difference between any two 
of its consecutive values; hence it is indefinitely small. It is expressed by 
writing d before the quantity, as dz, which is read differential of x. 


The term wy is called the differential coefficient of y regarded as a func. 
tion of x. 


The differential of a function is equal to its differential coefficient mul. 
tiplied by the differential of the independent variable; thus, Yaw = Oy: 


The limit of a variable quantity is that value to which it continually 
ee so as at last to differ from it by less than any assignable quan- 
ity. 

The differential coefficient is the limit of the ratio of the increment of the 
independent variable to the increment of the function. 

The differential of a constant quantity is equal to 0. 

The differential of a product of a constant by a variable is equal to the 
constant multiplied by the differential of the variable. 


Tf (= Any duis Adv. 


In any curve whose equation is y= f(x), the differential coefficient 
at = tan a; hence, the rate of increase of the function, or the ascension of 
the curve at any point, is equal to the tangent of the angle which the tangent 
line makes with the axis of abscissas. 

All the operations of the Differential Calculus comprise but two objects: 

1. To find the rate of change in a function when it passes from one state 
of value to another, consecutive with it. 

2. To find the actual change in the function: The rate of change is the 
differential coefficient. and the actual change the differential. 

Differentials of algebraic functions.—The differential of the 
sum or difference of any number of functions, dependent on the same 
variable, is equal to the sum or difference of their differentials taken sepa- 


rately: 
vf If uwu=yt2z2—w, du=dy+t dz—duw. 


The differential of a product of two functions dependent on the same 
variable is equal to the sui of the products of each by the differential of 


the other: 
d(awv) eae 


Uv uU v- 





d(uv) = vdu + udv. 


The differential of the product of any number of functions is equal to the 
sum of the products which arise by multiplying the differential of each 
function by the product of all the others: 


d(uts) = tsdu + usdt + utds. 


The differential of a fraction equals the denominator into the differential 


of the numerator minus the numerator into the differential of the denom- 
inator, divided by the square of the denominator : 


dt =a(%) =u aud 


ye 
: : vau du 
If the denominator is constant, dv = 0, and dt = a 
: udv 
If the numerator is constant, du =0, and dt = — er 


The differential of the square root of a quantity is equal to the differen- 
tial of the quantity divided by twice the square root of the quantity: 
If v=ui, or v= Vu, LS = 1 y-tau, 
2Vu 2 





DIFFERENTIAL CALCULUS. "3 


The differential of any power of a function is equal to the exponent multi- 
plied by the function raised to a power less one, multiplied by the differen- 
tial of the function, d(w") = nu” — Idu. 

Formulas for differentiating algebraic functions, 


1a d,(a\— 0; 6.a() __ ydu — xdy 
y y? 
2. d (ax) = adx. Lb ge Bei eed ae ele 
3.d (a+ y) =da+dy. = Sper lg 
8. d(x sats 
4.d(x— y)=dx—dy. r r 
CNR 
9d \x =-—-2 dx. 


5. d (xy) = ady + yda. 


To find the differential of the form u = (a-+ ba”): 

Multiply the exponent of the parenthesis into the exponent of the varia- 
ble within the parenthesis, into the coefficient of the variable, into the bi- 
nomial raised to a power less 1, into the variable within the parenthesis 
raised to a power less 1, into the differential of the variable. 


du = d(a + ba”)™ = mnb(a + ba”)™— * ae - Tae, 


To find the rate of change for a given value of the variable: 
Find the differential coefficient, and substitute the value of the variable in 
the second member of the equation. v 
Uw 


Exampue.—lIf x is the side of a cube and w its volume, u = 23, re 3202, 
Hence the rate of change in the volume is three times the square of the 
edge. If the edge is denoted by 1, the rate of change is 3. 

Application. The coefficient of expansion by heat of the volume of a body 
is three times the linear coefficient of expansion. Thus if the side of a cube 
expands .001 inch, its volume expands .003 cubic inch. 1.0013 = 1.003003001. 

A partial differential coefficient is the differential coefficient of 
a function of two or more variables under the supposition that only one of 
them has changed its value. 

A partial differential is the differential of a function of two or more vari- 
ables under the supposition that only one of them has changed its value. 

The total differential of a function of any number of variables is equal to 
the sum of the partial differentials. 


If u =f (ay), the partial differentials are wae, cdg. ae, 
du du du 
— 72 Sis = — pass —dz: = . 2 = 4 
If u= x? -+ y3 — 2, du an” -+- aye ok a dz; = 2xdx +. 3y2dy — dz 


Imtegrals.—An integral is a functional expression derived from a 
differential. Integration is the operation of finding the primitive function 
from the differential function. It is indicated by the sign /, which is read 
“the integral of.”’ Thus f2xdx = «#2 ; read, the integral of 2ada equals a°. 

To integrate an expression of the form ma”™~ "da or ada, add 1 to the 
exponent of the variable, and divide by the new exponent and by the differ- 
ential of the variable: / 3x*da = x3. (Applicable in all cases except when 


-1 
iy ee he For fv dx see formula 2 page 78.) 


The integral of the product of a constant by the differential of a vari- 
able is equal to the constant multiplied by the integral of the differential: 


Saw da =a/a™dx = oy gm +3, 


The integral of the algebraic sum of any number of differentials is equal to 
the algebraic sum of their integrals: 4 
du = 2ax*da — bydy — 22dz; fdu= aes ~ oy? - = 

Since the differential of a constant is 0, a constant connected with a vari- 
able by the sign + or — disappears iu the differentiation; thus d(a+2™) = 


da” = mx” ~*dw, Hence in integrating a differential expression we must 


74. DIFFERENTIAL CALCULUS, 


annex to the integral obtained a constant represented by C to compensate 
for the term which may have been lost in differentiation. Thus if we have 
dy =adx; fdy=afdx, Integrating, 


y= a0 = 'C: 


The constant CO, which is added to the first integral, must have such a 
value as to render the functional equation true for every possible value that 
may be attributed to the variable. Hence, after having found the first 
integral equation and added the constant C, if we then make the variabls 
Boe to zero, the value which the function assumes will be the true value 
of C. 

An indefinite integral is the first integral obtained before the value of the 
constant C is determined. 

A particular integral is the integral after the value of C has been found. 

A see integral is the integral corresponding to a given value of the 
variable. 

Integration between limits.—Having found the indefinite inte- 
gral and the particular integral, the next step is to find the definite integral, 
and then the definite integral between given limits of the variable. 

The integral of a function, taken between two limits, indicated by given 
values of a, is equal to the difference of the definite integrals correspond- 
ing to those limits. The expression 


0 
J ayaa f as 
a’ 


is read: Integral of the differential of y, taken between the limits v7’ and w’’- 
the least limit, or the limit corresponding to the subtractive integral, being 
placed below. 

Integrate du = 9x°dxz between the limits x = 1 and x = 3, u being equal te 
81 when x=0. fdu = /9x2dx = 843+ C; C=81 when x2 = 0, then 


c=38 
a du = 3(8)8 + 81, minus 3(1)? + 81 = 78, 


ie Ent 
Entegration of particular forms, 
To integrate a differential of the form du = (a+ ba")™g” ~ 1qy, 


1. If there is a constant factor, place it without the sign of the integral, 
and omit the power of the variable without the parenthesis and the differ. 
ential; 

2. Augment the exponent of the parenthesis by 1, and then divide this 
quantity, with the exponent so increased, by the exponent of the paren- 
thesis, into the exponent of the variable within the parenthesis, into the co- 
efficient of the variable. Whence 


Br Pie dl ee =i 
(m+ 1)nb 


The differential of an arc is the hypothenuse of a right-angle triangle of 
which the base is dw and the perpendicular dy. 


If zisanare,dz= Vdx?+dy? z=/f Vda? + dy?. 


Quadrature of a piane figure. 
“he differentiul of the area of a plane surface is equal to the ordinate into 
the differential of the abscissa. 
Gs Yyoae 


To apply the principle enunciated in the last equation, in finding the area 
of any particular plane surface : 

Find the value of y in terms of a, from the equation of the bounding line; 
substitute this value in the differential equation, and then integrate between 
the required limits of x. 

Area of the parabola,—Tlind the area of any portion of the com- 
mon parabola whose equation is 


y?= 2px; whence y = 4/2pa. 


~3 
Cr 


DIFFERENTIAL CALCULUS. 


Substituting this value of y in the differential equation ds = yda gives 


oul 2 2 4/2p 
fwaf Var = Vip | tidx= 3 x3 + C; 


24/20e x LH 2 
or, pee ae = ryt C. 


Tf we estimate the area from the principal vertex, v= 0. y= 0, and C=0; 





and denoting the particular integral by s’, s’ = 3 eY- 


That is, the area of any portion of the parabola, estimated from the ver- 
tex, is equal to % of the rectangle of the abscissa and ordinate of the extreme 
point. Thecurve is therefore quadrable. 

Quadrature of surfaces of revolution. — The differential of a 
surface of revolution is equal to the cireumference of a circle perpendicular 
to the axis into the differential of the are of the meridian curve. 


ds = 2ny4/dx? + dy?; 


in which y is the radius of a circle of the bounding surface in a plane per- 
pendicular to the axis of revolution, and w is the abscissa, or distance of the 
plane from the origin of coédrdinate axes. 

Therefore, to find the volume of any surface of revolution: 

Find the value of y and dy from the equation of the meridian curve in 
terms of « and dx, then substitute these values in the differential equation, 
and integrate between the proper limits of x, 

By application of this rule we may find: 

The curved surface of a cylinder equals the product of the circumference 
of the base into the altitude. 

The convex surface of a cone equals the product of the circumference of 
the base into half the slant height. 

The surface of a sphere is equal to the area of four great circles, or equal 
to the curved surface of the circumscribing cylinder. 

Cubature of volumes of revolution.—aA volume of revolution 
is a voluine generated by the revolution of a plane figure about a fixed line 
called the axis. 

If we denote the volume by V, dV = ry? dx. 

The area of a circle described by any ordinate y is wy?; hence the differ- 
ential of a volume of revolution is equal to the area of a circle perpendicular 
to the axis into the differential of the axis. 

The differential of a volume generated by the revolution of a plane figure 
about the axis of Y is 7x?dy. 

To find the value of V for any given volume of revolution : 

Find the value of y? in terms of x from the equation of the meridian 
curve, Substitute this value in the differential equation, and then integrate 
between the required limits of x. 

By application of this rule we may find: 

si acaaiy of a cylinder is equal to the area of the base multiplied by the 
altitude. 

A ye Cae of a cone is equal to the area of the base into one third the 
altitude. ‘ 

The volume of a prolate spheroid and of an oblate spheroid (formed by 
the revolution of dan ellipse around its transverse and its conjugate axis re- 
spectively) are each equal to two thirds of the circumscribing cylinder. 

If the axes are equal, the spheroid becomes a sphere and its volume = 


o 
suk? De 5nDS; R being radius and D diameter. 


The volume of a paraboloid is equal to half the cylinder having the same 
base and altitude. 

The volume of a pyramid equals the area of the base multiplied by one 
third the altitude. 

Second, third, etc., differentials,—The differential coefficient 
being a function of the independent variable, it may be differentiated, and 
we thus obtain the second differential coefficient: 

* ; 
d (= = —. Dividing by dx, we have for the second differential cocti- 


76 DIFFERENTIAL CALCULUS, 


2 
cient “™, which is read: second differential of u divided by the square of 
the differential of a (or dx squared). 
The third differential coefficient a is read: third differential of w divided 


by da cubed. k f 
The differentials of the different orders are obtained by multiplying the 
3 


differential coefficients by the corresponding powers of dw; thus ee da = 


third differential of w. i 2 
Sign of the first differential coefficient.—If we have a curve 
whose equation is y= fa, referred to rectangular codrdinates, the curve 


: ly, We 
will recede from the axis of X when =e is positive, and approach the 


axis when it is negative, when the curve lies within the first angle of the 
coérdinate axes. For all angles and every relation of y and a the curve 
will recede from the axis of X when the ordinate and first differential co- 
efficient have the same sign, and approach it when they have different 
signs. If the tangent of the curve becomes parallel to the axis of X at any 


point ay =0. If the tangent becomes perpendicular to the axis of X at any 


d 
point = = 0, 

Sign of the second differential coefficient.—The second dif- 
ferential coefficient has the same sign as the ordinate when the curve is 
convex toward the axis of abscissa and a contrary sign when it is concave. 

Maclaurin’s Theorem,—For developing into a series any function 
of a single variable as u = A+ Bu + Cx? -+ Davi + Het, etc., in which A, B, 
CO, etc., are independent of w: 

) , i ay 1 Hat 

= == x+-—( — ue? + ——__ {| —— 3. 

a Sd gS TTB data no MIN ee 


In applying the formula, omit the expressions # = 0, although the coeffi- 
cients are always found under this hypothesis. 
EXAMPLES: 


(ata) = moa mgm —ly 4 MH (m ay 1) m= 2 


‘2 


pede 
m (m —1)(m—2) mes, 
EE 7 3 3 a3 + ete. 
1 1 x , x3 28 cb 
a--% a a? aMeAL Py uae take 


Waylor’s Theorem,—For developing into a series any function of the 
sum or difference of two independent variables, as w’ = f(a + y): 
d?u y? Bu y® 
dat 1.2 deit.2.3° 


du , du’ 
i 1s what - becomes when 
de da 


du 
a | | 
ie maa he 


in which u is what w’ becomes when y= 0 


= Oete, . ‘ 

A Maxima and minima,.—To find the maximum or minimum value 
of a function of a single variable: 

1. Find the first differential coefficient of the function, place it equal to 0, 
and determine the roots of the equation. 

2. Find the second differential coefficient, and substitute each real root, 
in succession, for the variable in the second member of the equation. Each 
root which gives a negative result will correspond to a maximum value of 
the function, and each which gives a positive result will correspond to a 
minimum value. 

ExampLe.—To find the value of a which will render the function y a 
maximum or minimum in the equation of the circle, y2 + v7? = R*; 


dy x : CU so 
da ae making — ie 0 givesx = 0. 





DIFFERENTIAL CALCULUS, 92 


aty 2 y2 


The second d#ferential coefficient is: — = — ——.—, 
; j dx? ys 
When a2 = 0, y= R; hence ot mips which being negative, y is a2 maxi- 


mum for £& positive. 

In applying the rule to practical examples we first find an expression for 
the function which is to be made a maximum or minimum. 

2. If in such expression a constant quantity is found asa factor, it may 
be omitted in the operation, jor the product will be a maximum or a mini- 
mum when the variable factor is a maximum or a minimum. 

3. Any value of the independent variable which renders a function a max- , 
imum or a minimum will render any power or root of that funetion a 
maximum or minimum; hence wc may square both members of an equa- 
tion to free it of radicals before differentiating. 

By these rules we may find: 

The maximum rectangle which can be inscribed in a triangle is one whose 
altitude is half the altitude of the triangle. 

The altitude of the maximum cylinder which can be inscribed in a cone is 
one third the altitude of the cone. 

The surface of a cylindrical vessel of a given volume, open at the top, isa 
minimum when the altitude equals half the diameter. 

The altitude of a cylinder inscribed ina sphere when its convex surface is 


a maximum isr 4/2. 1 = radius. 
The altitude of a cylinder inscribed in a sphere when the volume is a 
maximum is 27 + 7/3. 
(For maxima and minima without the calculus see Appendix, p. 1080.) 
Differential of an exponential function, 


Efe; a ae fo Semel ons ot a Oe Bel tom ele GG) 
then du = da” =a%k dx, oe @ © @ © © @ (2) 


m which & is a constant dependent on a. 
1 


The relation between a and kis a® = e; whencea=e*%, ..... (3) 


in which e = 2.7182818 . . . the base of the Naperian system of logarithms. 
Logarithms,.—The logarithms in the Naperian system are denoted by 
i, Nap. log or hyperbolic log, hyp. log, or log,; and in the common system 

always by log. 
k= Nap. lopias dog as blove.. se «1. - ee 


The common logarithm of e, = log 2.7182818 . . . = .4842945 .. . , is called 
the modulus of the common system, and is denoted by M. Hence, if we have 
tne Naperian logarithm of a number we can find the common logarithm of 
the same number by multiplying by the modulus, Reciprocally, Nap. 
log = com, log x 2.3025851. 

If in equation (4) we make @ = 10, we have 


1=kloge, or i = loge = M. 


That is, the modulus of the common system is equal to 1, divided by the 
Naperian logarithm of the common base. 
rom equation (2) we have 


x 
a a a = kdx. 
bgt 
If we make a = 10, the base of the common system, x = log u, and 
dui 1. du 


d{log u) = dw=—- x7 = x M. 


K 


That is, the differential of a common logarithm of a quantity is equal to the 
differential of the quantity clivided by the quantity, into the modulus. 
If we make a = e, the base of the Naperian system, « becomes the Nape- 


V8 DIFFERENTIAL CALCULUS, 


rian logaritnm of u, and k becomes 1 (see equation (3)); hence M = 1, and 


d(Nap. log u) = dx = —3; =—. 


That is, the differential of a Naperian logarithm of a quantity is equal to the 
differential of the quantity divided by the quantity; and in the Naperian 
system the modulus is 1. 


Since k is the Naperian logarithm of a, du=a” ladx. That is, the 


differential of a function of theform a” is equal to the function, into the 
Naperian logarithm of the base a, into the differential of the exponent. 

If we have a differential in a fractional form, in which the numerator is 
the differential of the denominator, the integral is the Naperian logarithm 
of the denominator. Integrals of fractional differentials of other forms are 
given helow: 

Differential forms which have known integrals; ex= 
ponential functions. (/ = Nap. log.) 


1. J tiade= 08 +05 
d 
Re Wo fawn = W403 
3. fer ay $F iy x dx) = y® + C; 
4 dx — 
° == = l(a + /x? + a2) +0; 
Wx? + a? 
dx —_—__—. 
5. ———- ) Wa tat f/x? + 2027) 4-0; 
Vcc ( Vv )+¢; 
2ada ata 
6. Be Ween l pi 
eter aces 
%. 2adx wy 
22 — G2 [eaalee 


























8, lope 2 (FE ca 
x 4/02 + x73 a? fatta 
9. fade a) a— Var — x? +6: 
xa — x at Yaur— o : 
—2 dx 1 1 Qy2 
10, ee as be 
WV ata- x ua 


_Cireular functions, —Let z denote an arc in the first quadrant, y its 
sine, x its cosine, v its versed sine, and ¢ its tangent; and the following nota- 
tion be employed to designate an are by any one of its functions, viz., 


sin ~} y denotes an are of which y is the sine 
cos~!a *“ “wil 66h) 146 ig the Cosine, 
tan ee oc 6 t is the tangent 





DIFFERENTIAL CALCULUS. 49 


(read ‘‘are whose sine is y,”’ etc.),—-we have the following differential forms 
which have known integrals (7 = radius): 
} 




















<) 
i coszdz =sinz+0; [x z dz = ver-sin z + C; 
inzd C; ee eit fen Cr 
—sinzdz=cosz+C; Coe) een ; 
dy + — i | ’ rd KD) ( 
yi-P 7 = sin y+ C; 7a = ver-sin ~*v-+-C; 
pee ret =i 
pas Oe = cos~!a +0; mE 1 £4 Leah eee ea oo 
3 1 — a2 2 ? + t 
d 
|. ver-sin 1» + 0; pee 
dt vas a7 ‘ lcd A ne. —1¥ r 
of ite =: tan 71¢-++- C; dE Wipe cos + C; 
rdy eet! y du penny u 
—— = sin y+C; aa, eee ee — VEISID me hee 
Vr—y 2au — u? a 
— rdx {tits * adu . U 
ap) = COR CE pees ake j 
Vitna “us a. pu tan~* = + C. 


Whe cycloid.—lIf a circle be rolled along a straight line, any point of 
the circumference, as P, will describe a curve which is called a cycloid. The 
circle is called the generating circle, and P the generating point. 

The transcendental equation of the cycloid is 


y nh neler 
x = ver-sin—1 2 — Very — 7%, 
yan 
Voy —y 


ae area of the cycloid is equal to three times the area of the generating 
circle. ; 

The surface described by the are of a cvcloid when revolved about its base 
is equal to 64 thirds of the generating circle. 

The volume of the solid generated by revolving a cycloid about its base is 
equal to five eighths of the circumscribing cylinder. 

Integral caleulus.—In the integral calculus we have to return from 
the differential to the function from which it was derived. A number of 
differential expressions are given above, each of which bas a known in- 
tegral corresponding to it, and which being differentiated, will produce the 
given differential. 

In all classes of functions any differential expression may be integrated 
when it is reduced to one of the known forms; and the operations of the 
integral calculus consist mainly in making such transformations of given 
differential expressions as shall reduce them to equivalent ones whose in- 
tegrals are known. 

For methods of making these transformations reference must be made to 
che text-books on differential and integral calculus. 


and the differential equation is dx = 


80 


MATHEMATICAL TABLES. 


RECIPROCALS OF NUMBERS. 





No. 


—_— 


or P= is©) 
IATA WMROOMOVRATIAPWNHWHOUOOIHGorPwwoe 


OoPOworeoao@e= 


D 
Wm OOO 


Recipro- 


| 


cal. 


1 |1.00000000 


.50000000 


. 


33333333 


25000000 
. 20000000 
. 16666667 
14285714 
. 12500000 
elisha Viet 
. 10000000 
.09090909 
083333383 
07692308 
07142857 
.06666667 
06250000 
05882353 
05555556 
.05263158 
.05000000 
04761905 
04545455 
. 04347826 
-04166667 


.04000000): 


.03846154 
03703704 
.03571429 
03448276 
03333333 
03225806 
.03125000 
03030303 
02941176 
02857143 
02777707 

.02702708 
.02631579 
02564103 
.02500000 
02439024 
02380952 
02325581 
02272727 
02222222 
02173913 
.02127660 
02083333 
.02040816 
. 02000000 
.01960784 
.01923077 
.01886792 
.01851852 
.01818182 
.01785714 
.01754386 
01724138 
.01694915 
.01666667 
.01639344 
.01612903 
.01587302 


| 


ior) 


oe] 
WW OM OWIOOe 


(2) 








le} 
SO DWIBDWMIPC WOK OCOMOMVIRDOTRWNWH OOM IMs 


i 
S 


SOI QOS COW 





Recipro- 
eal. 


.01562500 
.01588461 
.01515151 
.01492537 
.01470588 
-01449275 
01428571 
.01408451 
.01388889 
.01369863 
.01351351 
01333333 
.01315789 
01298701 
01282051 
01265823 
01250000 
.01234568 
.01219512 
.01204819 
.01190476 
.01176471 
.01162791 
01149425 
.01136364 
.01123595 
-01111111 
.01098901 
.01086956 
01075269 
.01063830 
01052682 
.01041667 
.01030928 
.01020408 
.01010101 
.01000000 
.00990099 
00980392 
.00970874 
00961538 
00952381 
00943396 
.00934579 
00925926 
.00917431 
. 00909091 
.00900901 
00892857 
. 00884956 
00877193 
00869565 
.00862069 
.00854701 
.00847458 
00840336 
00883333 
.00826446 
00819672 
.00813008 
. 00806452 
.00800000 
.00793651 








No. 





i 
co 
Qopwore+owo =} 


ren 
te 


— 
v 








SOSMOIHTP WW GDODMIAoPOOWH OOMs? 


i 
fop) 


= 
=3 





re 
: ie.2) 
DOVIODUPWMWH OO MAIMDUPWWH OO OIDs wwe 








Recipro- 
cal. 


00787402 
.00781250 
00775194 
.00769231 
.00763359 
00757576 
.00751880 
.00746269 
.00740741 
00735294 
.00729927 
00724638 
00719424 
.00714286 
00709220 
00704225 
.00699301 
.00694444 
. 00689655 
.00684931 
.00680272 
00675676 
.00671141 
.00666667 
.00662252 
.00657895 
00653595 
.00649351 
00645161 
.00641026 
.00636943 
.0063291 1 
. 00628931 
00625000 
.00621118 
.00617284 
.00613497 
. 00609756 
.00606061 
.00602410 
. 00598802 
.00595238 
.00591716 
.00588235 
00584795 
00581395 
00578035 
00574713 
.00571429 
00568182 
.0056497'2 
00561798 
00558659 
00555556 
00552486 
00549451 
00546448 
00543478 
.00540540 
00537634 
.00534759 
.00531914 
-00529100 


No. 


| 





OUR 0 DH © 





WO MOIMDUP WWH OO MID 


220 


rw) 
ow 








rw) 
— 


rw) 
or 
WH OOMONDUBRWNWHOODMDIRDMNPWMWOH ODO MIMI WMH 





Recipro- 
cal. 


.00526316 
00523560 
00520833 
.00518135 
-00515464 
-00512820 
00510204 
-00507614 
00505051 
00502513 
00500000 
00497512 
00495049 
00492611 
-00490196 
.00487805 
00485437 
00483092 
-00480769 
.004%8469 
.00476190 
.00473934 
00471698 
00469484 
00467290 
00465116 
00462963 
00460829 
.00458716 
00456621 
00454545 
00452489 
00450450 
00448430. 


00446429 | 


00444444 
00442478 
00440529 
00438596 
00436681 
00434783 
.00432900 
-00431034 
00429184 
00427350 
00425532 
00423729 
00421941 
.00420168 
.00418470 
00416667 
.00414938 
00413223 
00411523 
. 00409836 
-00408163 
.00406504 
-00404858 
00403226 
-00401606 
- 00400000 
.00398406 





396825 | 


No. 


rw) Cw) a 
(o2) =3 for) 
SOMDIDTPRWWH SO DIDO WWH OO WDIADTAWNHWH OO MOIAAA 


ri) 
le} 


ie) 
S 





BSH OOo IOorpr wwe 


QoOVWoHoP Oo 


Recipro- 
cal. 


00395257 — 


.00393701 

.00392157 
00390625 
.00889105 
.00387597 
.00386100 
.00384615 
.00383142 
.00381679 
00380228 
00378788 
.00377358 
.00375940 
00374532 
.00373134 
.00371747 
.00370370 
.00369004 
00367647 
.00366300 
-00364963 
00363636 
.00362319 
.00361011 
.00359712 
.00358423 
.00857143 
-00355872 
.00354610 
- 00353357 
.00352113 
-00850877 
.00349550 
00348432. 
00347222 
.00346021 
00344828 
00343643 
00342466 
.00341297 
.00340136 
-00338983 
00337838 
.00336700 
.00335570 
00334448 
00333333 

00832226 

00331126 

.00330033 

.00328947 

00327869 

00326797 

00325733 

-00324675 

- 00323625 

00322581 

00321543 

00320513 

00319489 

.00318471 

.00317460 





Sd ‘ 
BWW OMMOVIRHTAWWHOOMW-I Goh WMH 


oe 





S 
DMIDOHWNWH OW MAIRBOLWWHSCOM*IDOORWNWH OOM Do 


=~) 


ee 


Recipro- 
cal, 


.00316456 
-00315457 
.00314465 
.00318480 
00312500 
00311526 
.00310559 
00309597 
.00308642 
00307692 
.00306748 
00305810 
.00304878 
.00303951 
.00303030 
00302115 
.00301205 
00300300 
00299401 
.00298507 
00297619 
00296736 
00295858 
.00294985 
.00294118 
.00293255 
00292398 
.00291545 
. 00290698 
00289855 
00289017 
.€0288 184 
.00287356 
00286533 
00285714 
.00284900 
.00284091 
00283286 
00282486 
. 00281690 
. 00280899 
.00280112 
.00279330 
00278551 
00277778 
.00277008 
00276243 
00275482 
00274725 
00273973 
00273224 
00272480 
00271739 
. 00271003 
00270270 
00269542 
.00268817 
. 00268096 
00267380 
. 00266667 
00265957 
00265252 
.00264550 
.00263852 
00263158 

















RECIPROCALS OF NUMBERS. 


381 


HFM OU CM 


iS) 
oO 


~ 
> 
WOMIMDOIPWWHOOMDNMDOUPWMH OO 


a 
co 


— 
r—~ 
OUR 09 WH OO MAIDOP WW OM MINHA COW eH 





Recipro- 


cal. 


00262467 


.00261780 
.00261097 
.00260417 
.00259740 
.00259067 
.00258398 
00257732 
00257069 
.00256410 


.00255754 | 


00255102 
00254453 
.00253807 
00253165 
.00252525 
.00251889 
00251256 
.00250627 
.00250000 
00249377 
00248756 
.00248139 
00247525 
.00246914 
00246305 
00245700 
.00245098 
. 00244499 
00243902 
.00243309 
.00242718 
.00242131 
00241546 
.00210964 
00240385 
. 00239808 
.00239234 
. 00238663 
00238095 
.00237530 
00236967 
00236407 
00235849 
.00235294 
00234742 
00234192 
.00233645 
00233100 
- 00232558 
.00282019 
00231481 
00230947 
.00230415 
-00229885 
00229358 
.00228833 
-00228310 
00227790 
.00227273 
00226757 
00226244 
00225734 
00225225 


0022471911 51 


jor) 


DBNIODoRwnwo-+DdoCt=t 





= 


(oo) 
SIOUBRWMWHOOWMAIDOKWNWH OO 





ie) 





50 


Ow WMH OO MOAIS 


4 


2 


8 
9 
0 
1 
2 
3 
5 
6 
7 
8 
9 
0 
1 
3 
4 
5 
6 
7 
8 
9 
0 





Recipro- 


eal. 


.00224215 


00223714 
.00223214 
.00222717 
00222222 
.00221729 
00221289 
.00220751 
00220264 
.00219780 
00219298 
-00218818 
00218341 
.00217865 
00217391 
.00216920 
60216450 
.00215983 
.00215517 
.00215054 
00214592 
.002141383 
.00213675 
.00213220 
00212766 
.00212314 
.00211864 
-00211416 
.00210970 
-00210526 
00210084 
.00209644 
00209205 
00208768 
00208333 
00207900 
.00207469 
-00207039 
00206612 
.00206186 
00205761 
00205339 
.00204918 
.00204499 
00204082 
-00203666 
.00203252 
-00202840 
00202429 
-00202020 
.00201618 
00201207 
.00200803 
.00200401 
-00200000 
.00199601 
.00199203 
.00198807 
.00198418 
00198020 
.00197628 
. 00197239 
- 001968 « 
.00196464 
.00196078 











= 
NOP wWMmWmReOODIMDOLRWWHOOCOMRDUP WW 


cr 


or 


TR WWE CUOMO RATUIPWNWHOUMSIAIKWWrHOOD 





fer) 


=F 








cal, 


.00195695 
.00195812 
.001 94932 
.00194552 
00194175 
.00193798 
001938424 
-00193050 
.00192678 
.00192308 
-00191939 
.0019157 1]! 
.00191205 
.00190840 
00190476 
.00190114 
.00189753 
.00189394 
.00189036 
.00188679 
.00188324 
.00187970 
.00187617 
.00187266 
.00186916 
.00186567 
00186220 
.00185874 
00185528 
.00185185 
.C0184843 
00184502 
00184162 
.00183828 
00183486 
.00183150 
-00182815 
.00182482 
.00182149 
.00181818 
.00181488 
.00181159 
-00180832 
00180505 
.00180180 
-00179856 
.00179533 
00179211 
.00178891 
00173571 














.001 78253 
.00177936 
.00177620 
00177305 
00176991 
.00176678 
.00176367 
00176056 
00175747 
00175439 
.00175131 
.00174825 
-00174520 








.00174216 
00173918 


576 


or 
(os) 
SOO =3 


Pm 09 DO RS 


or 
io) 
OOF Od OUR 09D Ht OO WFO OF 


S 
S 


CO GO =F Od OF fe CO WE © 


oO 
ww 
SSOIAOK WMH COMOVWIRWMWWwWNwe 


or) 
re 





81 


Recipro- NA Recipro- 


cal. 


-00173611 


.00113310 
.00173010 
.00172712 
.00172414 
-00172117 
.00171821 
.00171527 
00171253 
.00170940 
.00170648 
.00170358 
.00170068 
.00169779 
.00169491 
00169205 
.00168919 
.00168634 
.00168350 
.00168067 
.00167785 
.00167504 
.00167224 
.00166945 
.00166667 
.00166389 
.00166118 
.00165837 
.00165563 
. 00165289 
.00165016 
.00164745 
.001644'74 
.00164204 
.00163934 
.00163666 
.00163399 
.001631382 
.00162866 
.00162602 
.00162388 
.00162075 
.00161812 
.00161551 
.00161290 
.00161031 
.0016077' 

.00160514 
.00160256 
.00160000 
.00159744 
.00159490 
.00159236 
.00158982 
.00158730 
.00158479 
.00158228 
00157978 
.001577:29 
.00157480 
-00157233 
.00156986 
.00156740 
.00156494 
.00156250 


nme 


utr 


MID BD WW OO MIG USC 


jor) for) 
=} lr) 
FS SI OTA DWH SO MDIDOTPUWHOSODIAMBWWHSO 


TOU ewweHS 


=} 


AWM Seca 





Recipro- Recipro- |'. | Recipro- Recipro- 
‘| eal. No.) “eal. NO.) cal, No.| "cal. ||No- 


.00156006 
.00155763 
.00155521 
.00155279 
.00155039 
-00154799 
.00154559 
00154321 
.00154088 
.00153846 
.00153610 
.001538374 
.00153140 
.00152905 
.00152672 
.00152439 
.00152207 
.00151975 
.00151745 
.00151515 
.00151286 
00151057 
.00150830 
.00150602 
00150376 
.00150150 
.00149925 
.00149701 
.00149477 
.00149254 
.00149031 
.00148809 
.00148588 
.00148368 
.00148148 
00147929 
.00147710 
.00147493 
.00147275 
00147059 
.00146848 
-00146628 
.00146413 
.00146199 
.00145985 
00145773 
.00145560 
00145349 
.00145137 
.00144927 
-00144718 
.00144509 
.00144300 
.00 144092 
.00143885 
00143678 
.00143472 
00143266 
.00143061 
00142857 
.00142653 
00142450 
.00142247 
.00142045 
00141844 


.00141643 
.00141443 
.00141248 
.00141044 
.00140845 
.00140647 
.00140449 
.00140252 
.00 140056 
.00139860 
.00139665 
00139470 
0013927 
00139082 
00138889 
.00 138696 
00138504 
.00138318 
.00138121 
.00137931 
.00137741 
.00 137552 
00137363 
00137174 
.00136986 
.00136799 
.00136612 
.00136426 
.CO136240 
.00136054 
.00 135870 
00135685 
.00185501 
.00135318 
.00135135 
.00134953 
00184771 
.00134589 
.00134409 








CSrHIDosp cc wre Csr 


=-2 


Sv) 
mwrmreoeo 


= 
a 
AHO BP MO] OO O2I QD 





.00133690 


=F 


or 


SOOVIAO POW H OOD 


.00132626 
.00132450 





.00132100 


00131752 
(00131579 
00131406 
00131234] 
-00131062 
-00130890) 
-00130719 
“00130548 
00130378 
.00: 30208 
00130039 


ler) 


bad 





SOMI9 oT PRowrmwu 


2 
=> 


eal 


.00134228 
.001341048 
.00133869 





=? 
Mt or tom ++ 


@ 
S&wwmre coo 


=? 


i 


DOAWWHOSOMISM 


OOsDURPWMW*OUM= 





.00133511 
001333383 
.00133156 
00132979 
.00132802 


00132275 
.00131926 





oa) 


ww 5 
SOO MOIHoOTA Woe 


a 
~ 








00129870 


ah oO? 


00129702 
00129534 | 
00129366 
00129199 
00129032 | 
00128866 
00128700 
00128535. 
00128370 
00128205 
00128041 
00127877 
00127714 
00127551 
00127388 
00127226 
00127065 
00126904 
00126743 
00120582 
00126422 
00126263 
00126103 
00125945 
00125786 
00125628 
00125470 
00125313 
00125156 
00125000) 
00124844 
00124688 
00124533 
00124378 
00124224 
00124069 
001239 16 
00123762 
00123609 
00123457 
00123305 
00123153. 
00123001 
00122850 
00122699 
00122549 
.00122349 
00122249 
0022100 
.00121951 
00121803 
00121654 
00121507 
.00121359 
.00121212 
00121065 
00120919 
00120773 
00120627 
00120482 
00120837 
00120192 
00120048 
00119904 


00119760 


PD 
rs 
role oat 


" 


oo 
IDRWUWHOCMIMSUAwWwH 





=} 


WHODMIMDTA WWHOWMsID 


(ee) 
STROM WNW HOO O37 OTP CO 


Sc 0 











WOPRIWoMK wwWH 


ie) 
cS 
j=) 


MATHEMATICAL TABLES, 


.00119617 


.00119474 
.00119832 
.00119189 
.00119048 
.00118906 
.00118765 
.00118624 
.00118483 
.00118343 
.00118208 
.00118064 
.00117924 
00117786 
00117647 
.00117509 
.00117371 
00117233 
.00117096 
.00116959 
.00116822 
.00116686 
.00116550 
.00116414 
.00116279 
.00116144 
.00116009 
.00115875 
.00115741 
00115607 
.00115473 
.00115340 
00115207 
.00115075 
.00114942 
.00114811 
.00114679 
.00114547 
.00114416 
.00114286 
-00114155 
.00114025 
.00113895 
00113766 
.00113686 
00118507 
.00113379 
.00113250 
.00113122 
.00112994 
.00112867 
.00112740 
.00112613 
.00112486 
.00112360 
00112233 


.00112108 


00111982 
00111857 
00111732 
00111607 
00111483 
00111359 


-00111235 
00111111 





OOI Doh Cw — 





te 
OOD WH COMA DOP WH 


eo) 
ree 


SSO Oop eww OoM=ID 


fe) 
or 


SwODMROowWwWIADH 


co 
jor) 





Ori 09 2D 


Recipro- 
cal. 


.00110988 


00110865 
00110742 
00110619 
00110497 
00110375 
00110254 
00110132 
00110011 
-0109890 
00109769 
00109649 
00109529 
00109409 
00109290 
00109170 
(00109051 
00108932 
00108814 
00108696 
00108578 
00108460 
00108342 
00108225 
-00108108 
00107991 
00107875 
00107759 
00107643 
00107527 
00107411 
00107296 
00107181 
00107066 
00106952 
0106838 
00106724 
00106610 
00106496 
00106383 
0010627 
00106157 
00106044 
00105932 
00105820 
00105708 
00105597 
00105485 
00105374 
00105263 
00105152 
00105042 
.00104932 
00104822 
00104712 
00104602 
00104493 
00104384 
00104275 
.0010416% 
00104058 
00103950 
00103843 
00108734 


5| 00108627 


3 
3D 


AIO CMH COL 


(2) 
He 05 DO Ht OS CO OC 


IP OR WN OOOO ESS SSS 


(ve) 
AR Ae Pn A 


OMI DUP OM SOM 





SOMVIDOP WOH 


pte O- 
cal. 


.00103520 
00103413 
00103306 
.00103199 
00103093 
.00102987 
.00102881 
.0010277 
00102669 
.00102564 
.00102459 
.00102854 
.00102250 
.00102145 
.00102041 
.00101937 
.00101833 
.00101729 
.00101626 
.00101523 
.00101420 
.00101317 
.00101215 
.0010i112 
.00101010 
00100908 
.00100806 
.00100705 
.00100604 
.00100502 
.00100402 
.00100301 
00100200 
.0V100100 
.00100000 
.000999001 


.000998004| 


000997009 
000996016 
. 000995025 
.000994036 
.600993049 
.000992063 
000991080 
.000990099 
.000989120 
.000988142 


3] .000987167 


.000986193 


5] .000985222 
3} .000984252 


.000983284 
.000982318 
000981354 


20} 000980392 


.000979432 
000978474 
.000977517 
.000976562 
.0009756 10 
. 000974659 
.000973710 
.000972763 
.000971817 
. 000970874 





RECIPROCALS OF NUMBERS. 


1031 


Co 09 


104 


OUR CS WH OO MONIOOR 


105 


wWrHOO MAIC 


106 


— 
S 


108 


S29 42 2e Ses. 


109 


OB WMH OOS 


. 000930233 
. 000929368 
000928505 
.000927644 
.000926784 
.000925926 
. 000925069 
-000924214 
000923361 
. 000922509 


000920810 
.00091 99683 
.000919118 


.000917431 
.000916590 
.000915751 
.000914913 
.000914077 
000913242 





Recipro- 


cal. 


.000969932 
. 000968992 
. 000968054 
.000967118 
000966184 
.000965251 
.000964320 
.000963391 
.000962464 
.000961538 
.000960615 
. 000959693 
000958774 
.000957854 
.000956938 
.000956023 
.000955110 
.000954198 
.000953289 
.000952381 
000951475 
.000950570 


000949668 
000948767 
000947867 
000946970 
000946074 
000945180 
000944287 
000943396 
000942507 
€00941620 
000940734 
000939850 
000938967 
000938086 
000937207 
000936330 
000935454 
000934579 
000933707 
000932836 
000931966 
000931099 


000921659 


000918274 











No. 


1096 





FIO OTH GOD 


113 


AIQOTR CH WH OO 


foaole 2) 


114 





11é 


1 
2 
3 
4 
5 
6 
7 
8 
9 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
0 


116( 








000899281 
.000898473 | 
000897666 
000896861 
000896057 | 
000895255 
000894454 
000893655 
000892857 
000892061 
000891266 
000890472 
000889680 | 
000888889 | 
000888099 | 
000887311 | 
000886525 
000885740 
000884956 
000884173 
000883392 
000882612 
000881834 
000881057 
000880282 
000879508 
000878735 
000877963 
000877193 
000876424 
000875657 
000874891 
000874126 
000873362 
.000872600 
.000871840 
000871080 
000870322 
.000869565 
000868810 
000868056 
000867303 
000866551 
000865801 
000865052 
000864304 
000863558 
000862813 
000862069 






Recipro- 


cal. 


000912409 
| .000911577 | 
000910747 
000909918 
000909091 
000908265. 
000907441 | 
000906618 
000905797 | 
000904977 | 
006904 159 
000903342 
000902527 
000901713 
000900901 


000900090 


No. 


117 








118 





119 





ig OOD =F OFS COW 


O DMIRDOAH OWE OS 


IO OTR C9 DH © 





ATOR WOH OOM 


OO IHOMA WIM SOD 





83 








Recipro- |x His) Reeipro 
Cal. : 
. 000861326 |1226} .000815661 
.O00860585 7) 000814946 
000859845 8] 000814332 
000859106 9] 000813670 
. 000858369 |1230] .000813008 
- 000857683 1} .000812348 
.QU0856598 9) .0V0811688 
000856164 3] .00081 1080 
.UUU855432 4} .000810373 
.000854701 5] .000869717 
.000858971 6] .000809061 
.000858242 7| .000S08407 
000852515 8} .000807754 
. 000851789 9} .000807'102 
.00085 106414240] . 000806452 
.0U0850340 1|.000805802 
000849618 2] 000805153 
.000848896 8} .000804505 
000848176 4} .000803858 
.000847457 5|.000803213 
.000846740 6| .000802568 
.000846024 | 000801925 
.000845308 8} .000801282 
000844595 9} .000800640 
.000843882 }1250} .000800000 
.000843170 1) 000799360 
.000842460 2] .000798%'22 
.000841751 8) .000798085 
000841043 4| .000797448 
.00084033€ 5} 000796813 
000839631 6} .000796178 
000838926 %| 000795545 
000838222 8} .000794913 
000837521 9} 000794281 
.000836820 | 1260} 000793651 
.000836120 1} .000793021 
000835422 2) 000792393 
.000834724 3} .000791766 
.000834028 4| 000791139 
000833833 5} .000790514 
, 000832639 6| .000789889 
.00083 1947 | 000789266 
000831255 8} .0007 88643 
.000830565 9| 000788022 
.000829875 |1270] .000787402 
. 000829187 1| .0007867 82 
. 000828500 2} 000786163 
.000827815 3| .000785546 
. 000827130 4| .000784929 
.000826446 5|.000784314 . 
. 000825764 6} .000782699 
. 000825082 7| .000788085 
.000824402 8} 000782473 
000823723 9} .000781861 
.000823045 |1280} .000781250 
.000822368 1} .000786640 
.000821693 2} 000780031 
.000821018 8] .000779423 
.000820344 4| .000778816 
.000819672 5} .000778210 
.000819001 6] 000777605 
. 000818331 % .000777001 
.000817661 8} .0007'76397 
.000816993 9} .0007°75795 
.000816326 112901 .000775194 


84 


MATHEMATICAL TABLES. 





J 
No. Recipro- No. 


rer 
= 
CO OIMOR WMH OOOO oP 65 


_— 
(SU) 
cs 


134 


: el 
oo 
or - 
CHR WWH OO MOMAIASOBRWNWH OC MAAR WHWH COMMAS WMWH 


000774593 
:000773994)| 7 
.000773395|| 8 
000772797 
00 
000771605 
000771010) 
000770416 
000769823 
000769231 
000768639 
000768049 
000767459 
000766871 
000766283 
000765697 
000765111 
000764526 
000763942 
000763359 
1| 000762776 
000762195 
000761615. 
000761035 
000760456 
000759878, 
000759301 | 
000758725 
000758150 
00075757 
000757002 | 
000756430. 
000755858 
000755287 
000754717 
000754148 
000753579 
000753012 
000752445, 
000751880 
000751315 
000750750 
000750187 
000749625 
000749064 | 
000748503 
000747943 
000747384 | 
000746826 
000746269 
000745712 
000745156, 
.000744602) 
000744048) 
000743494 
000742942 
000742390 
000741840 
000741290, 
000740741. 
000740192 
000739645. 
000739098. 
000738552, 





eal 


1856 


72201 


SCOOIOUPwWWeH 


137 


138 


139 


—_ 
> 
OOMIAOM BS W WH OO MIMS WWHOUWMVIHMOTPRWWH SOOM WWE 





"0007380071]1420 


.000737463 
000736920) 
000736377 | 
9} .000735835 
.000785294 
.000734754 
.000734214 
.000733676 
.000733138 
.00073 2601 
.000732064 
.00078 1529 
.000730994 
.000730460 
.000729927 
.000729395 
.000728863 
.000728332 
.000727802 
.000727273 
.000726744 
.0007 26216: 
.000725689 
.000725163 
.000724638 
.000724113 
.000723589 
.000723066 
.000722543 
.000722022 
.000721501 
.000720980 
.000720461 | 
.000719942 
.000719424 
.000718997 
.000718391 
.000717875 
.000717360 
.000716846 
.000716832 
.000715820 
.000715808 
.000714796 
.0007 14286 
.000713776 
.000713267 
.000712758 
.000712251 
.000711744 
.000711238 
.0007 10732 
.000710227 
.C00709723 
.000709220 
. 000708717 
.000708215 
.060707714 
.000707214 
. 0007067 14 
.000706215 
.000705716 
.000705219 
9} .000704722 
.000764225! 








Recipro- 
cal, 





SO OID OUR 69 0 


143 


144 


COR WMH OOOH WOH 


145 


146 


147 


ROwre 


148 


Orie Cot 


bh SO OHIO 








i 
Recipro- 


cal. 


000703780 
-000708235 
000702741 
000702247 
.000701754 
-000701262 
- 00070077 

- 000700280 
-000699790 
-000699301 
. 000698812 
-000698324 
000697837 
-0006973850 
. 000696864 
000696379 
000695894 
.000695410 
000694927 
000694444 
.000693962 
.000693481 
.000693001 
.000692521 
.000692041 
.000691563 
000691085 
000690608 
.000690131 
000689655 
.000689180 
.000688705 
.000688231 
000687758 





000687285 
. 000686813 
.000686341 
.000685871 
.000685401 
| .000684932 
.000684463 
. 000683994 
.000683527 
.000683060 
. 000682594 
.0006821 28 
. 000681663 
000681199 
, 000680735 
000680272 


INo. 


150 


WerCOMNVIAO A wwe 


OM 2D OT CO 











.000679810 
| .000679348 
| .000678887 
. 000678426 
.000677966 
000677507 
.000677048 
.000676590 
.000676132 
, 000675676 
.000875219 
000674764 
. 000674309 





000678854 


000673401 | 


He 9 0D et 


158 


154 


ATIREORPWUWHCOMONAUTRARWNWHFOCOMNIOH 


oF o) 


155 





00067 2948 
7| 000672495 
000672043 
000671592 
.000671141 
.000670691 
000670241 
000669792 
000669344 
.000668896 
000668449 
.000668008 
.000667557 
.000667111 
000666667 
000666223 
000665779 
000665336 
000664894 
000664452 
000664011 
000663570 
000663130 
000662691 
000662252 
J} .000661813 
.000661376 
000660939 
000660502 
000660066 
000659631 
000659196 
000658761) | 
. 000658328 
000657895 
000657462 
000657030 
000656598 
000656168 
000655738) 
000655308 
.000654879 
.000654450 
000654022 
000653595) 
.000653168' 
. 000652742) 
.000652316! 
000651890, 
000651466 | 
000651042 
.000650618, 
000650195: 
000649773 
000649351 
.000648929 
000648508 
000648088 
.000647668 
000647249. 
000646830 
000646412 
000645995 
000645578 
000645161 





Recipro- 
cal. 


No. 


SCOMNIOOP Ww 


156 


= 
3 
ow, 
WWRrHOOCMVIRHOPWDH 


SCODNIOO 


158 








OUR Cote 


159 


NOTA WOH OOM VS: 





_ 
> 
NOwKWSOH 


Recipro- 
eal. 


000644745 
000644330 
000643915 
000643501 
000643087 
000642673 
000642261 
000641848 
000641437 
000641026 
000640615 
000640205 
000639795 
000639386 
000638978 
00063857 

000638162 
000637755 
000637319 
000636943 
000636537 
000636132 
000635728 
000635324 
000634921 
000634518 
000634115 
000633714 
000633312 
000632911 
000632511 
000632111 
' 000631712 
000631313 
000630915 
000630517 
000630120 
000629723 
000629327 
000628931 
000628536 
-000628141 
000627746 
000627353 
000626959 
000626566 
000626174 
000625782 
000625391 
000625000 
000624219 
000623441 
000622665 
.000621890 
000621118 


2| .000620347 


.000619578 
.000618812 
.000618047 
000617284 


2| .000616523 


.000615763 
.000615006 


8} .000614250 


.000613497 


RECIPROCALS OF NUMBERS, 


85 





No. 


— 
St 
DBDOLWOOMD*PLW 


1700 
4 





Recipro- 
cal, 


000612745 
000611995 
000611247 


006610500 


.000609756 
. 000609013 
. 000608272 
.000607533 
.000606796 
.000606061 
.000605327 
.000604595 
.000603865 
. 000603 136 
000602410 
.000601685 
00600962 
. 000600240 
. 000599520 
.000598802 
2} .000598086 
.000597371 
.000596658 
.000595947 
.000595238 


000594530 


000593824 
000593 120 
.000592417 
.000591716 
.000591017 
000590319 
000589622 
.000588928 
.000588235 
2} 000587544 
.000586854 


| 
Recipro- 
| No. bal. No. 


1706} .000586166 
8} .000585480 


— 
—F 
wo 


_ 
“J 
ro 


_ 
=3 
lor) 


a 
=} 
Ra 


3 
or 
BOL KMOCAARNWOABDRAWOMABRNOCMAARNWOWDAALW 





000584795 
.000584112 
000583430 
.000582750 
000582072 
000581395 
.000580720 
.000580046 
000579374 
000578704 | 
- 000578035 
000577367 
.060576701 
000576037 
.000575374 
.000574713 
.000574053 
.000573394 
000572737 
.000572082 
-00057 1429 
.000570776 
0005701 25 
.000569476 
.000568828 | 
.000568182 
000567537 
000566893 
.000566251 
.000565611 
000564972 
.000564334 
.000563698 
000563063 





. 000562430 





_ 
bea’ J 
co 


re 
~“ 
ile) 
WOWSKHLNWSCBARLWO 


e2korn ws 





BOO e 


000561798 
000561167 
.000560538 
000559910 
000559284 
000558659 
000558035 
000557413 
000556793 
000556174 
000555556 
000554939 
.000554324 
000553710 
000553097 
000552486 
000551876 
000551268 
000550661 
0003550055 
000549451 
.000548848 
000548246 
.000547645 
000547046 
000546448 
|,000545851 
000545255 
| 000544662 
8) .000544069 
000543478 
000542888 
000542299 
000541711 
000541125 
000540540 
000539957 





Recipro- Recipro- 
No, cal, No, cal, 
1854) .000539374 | |1928] 000518672 
6|.000538793) 1930] 000518135 
8} .000538213 2} .000517599 
1860) .000537634|} 4] .000517063 
2).000537057 6} 000516528 
4| .000536480 8} .000515996 
6| .000535905!|1940) .000515464 
8} .000535332 2} 000514933 
1870} .000534759 4! .000514408 
2) .000534188 6} .000513874 
4} .000538618 8} .000513347 
6| .000583049) | 1950} .0005 12820 
8} .00053248 1 2} 000512295 
1880} .000531915 4} 00051177 
2} .000531350 6] .000511247 
4| .000530785 8} 000510725. 
6} .000530222| |1£60) .000510204 
8} .000529661 2} 000509684 
18 90} .000529100 4} .000509165 
2} .000528541 6| .000508647 
4) 000527983 | 8) .000508130 
6} .000527426) 1970} .000507614 
8] .000526870 2} .000507099 
1900} .000526316}}. 4} .00V506585 
2} .000525762 6] .000506073 
4} 000525210 8} .000505561 
6} 000524659! | 1980) .000505051 
8} .000524109 2) .000504541 
19 10) .000528560 4} .000504032 
12] .000528012 6) .0005038524 
14} .000522466 8) .000503018 
16} .000521920) | 1990) .000502513 
18) .000521376) 2} .000502008 
1920} .000520833 4} .000501504 
2} .000520291 6} .000501002 
4} .000519750) 8} .000500501 
6! .000519211!|/2000| .000500000 























Use of reciproecals.—Reciprocals may be conveniently used to facili- 
Instead of dividing as usnal, multiply 


tate computations in long division. 
the dividend by the reciprocal of the divisor. 


The method is especially 


useful when many different dividends are required to be divided by the 


same divisor. 


reciprocal of 1638 is .000610500, 


In this case find the reciprocal of the divisor, and make a 

small table of its multiples up to 9 times, and use this as a multiplication- 

table instead of actually performing the multiplication in each case. 
EXAMPLE.— 9871 and several other numbers are to be divided by 1638. The 


Multiples of the 





reciprocal: 
1. .0006105 The table of multiples is made by continuous addition 
2. .0012210 of 6105. The tenth line is written to check the accuracy 
8. 0018315 of the addition, but it is not afterwards used. 
4. .0024420 Operation: 
5, .0030525 Dividend 9871 
6. .0036630 Take from table 1........ 0006105 
7%, .0042735 Misdedindes 0.042735 
8. .0048840 Sons 00.48840 
9. .0054945 Dee we 5)-5 005.4945 
10. .0061050 —— 
Quotient........ 6.0262455 
Correct quotient by direct division........ 6.0262515 


The result will generally be correct to as many figures as there are signifi- 
cant figures in the reciprocal, less one, and the error of the next figure will in 
general not exceed one. In the above example the reciprocal has six sig« 
nificant figures, 610500, and the result is correct to five places of figures. 


56 


pS (Pe | ee a | | (pe ee ee 


.B162 
38873 
4472 
.500 

5477 


.5916 
6325 
.6708 
COT 


7416 


7746 
.8062 
8367 
. 8660 
8944 


. 9219 
9487 
9747 


No. |Square. 
aL 01 
15} .0225 
2 04 
:20| .0625 
3 .09 
.80| 21225 
4 .16 
-45) =. 2025 
4 .20 
.55} 8025 
ae eet oe 
.65]  .4225 
uff .49 
75} 5625 
| .64 
~80] - . (225 
al 81 
.95| .9025 

bi he ea he 

1.05] 1.1025 

sea Nea i By 

1.15} 1.8225 

1.2 | 1.44 

1.25) 1.5625 

1.3 | 1.69 

1.35) 1.8225 

aL 96 

1.45) 2.1025 

1.5 | 2.25 

1.55] 2.4025 

1.6 | 2.56 

1.65} 2.7225 

Lge lnesdo 

1.75] 3.0625 

1.8 | 8.24 

1.85} 3.4225 

1.9 | 3.61 

1.95) 3.8025 

Ee ee 
.1 | 4.41 
.2 | 4.84 
AS | kop e8) 
4 | 5.76 
Fon TOLeo 
SONG. 1G 
Ba ier 2) 
8 | 7.84 
9 | 8.41 

3. | 9. 


MATHEMATICAL TABLES. 


SQUARES, CUBES, SQUARE ROOTS AND CUBE 











ROOTS OF NUMBERS FROM .1 TO 1600. 





Cube. 


-001 

0034 

-008 
0156 
027 


0429 
064 
0911 
125 
1664 


>216 


Sq. 


Root. 





hk ek ek 


ee ee 











Sayargearqarwar agar areas — ee ee 
Ci et Lee ees Bi Ree, sag eS Shy es Lae 
©, 


eager ar 


Cube 





“ SD-ID Tmwom 


"COON TR WW "COIR URW “ OBONAR oRwWWE 


COIR om OWION 








Boog: : No, |Square. 


9.61 
10.24 
10.89 
11.56 
12.25 


12.96 
13.69 
14.44 
15.21 
16. 


16.81 
17.64 
18.49 
19.36 


20.25 


21.16 











Cube. 


29.791 
32.768 
35 937 
39.304 
42.875 


46.656 
50.653 
54.872 
59.319 
64. 


68.921 
74.088 
79.507 
85.184 
91.125 


97.336 
103.823 
110.592 
117.649 
125. 


132.651 
140.608 
148.877 
157.464 
166.375 


75.616 
185.193 
195.112 
205.379 
216. 


226.981 
238 .82 
250.047 
262.144 
74.625 


287.496 
800.763 
314.432 
328.509 
343. 


857.911 
313.248 
389.017 
405.224 
421.875 


438.976 
456.533 
474.552 
493.039 


MW WWK BW ee 


Sq. 
Root. 











Se 


| ll ee 


WWM WM Ww WWWW WWW WC 


to 09 0 €9 0 0D 1D UW 


WWwWWKO 


10 0 


161 














peek eh peek pet peek 


Pm mek ek ek ek 


ee ek et 


SQUARES, CUBES, SQUARE AND CUBE'ROOTS. 587° 












































Sq. Cube 3 Sq. Cube 

No. |Square.| Cube. | pols | Root, PNO- |Sauare.| Cube. Rove. Root. 

8. 64 512. 2.8284 |2 nH 45 8025 91125 6.7082) 3.5569 
cd 65.61 531.441)2.846 |2 008 & 46 2116 97336 6.7823] 3.5830 
32 67 .24 551.368/2.864 (2.017 § 47 2209 103823 6.8557| 3.6088 
BS 68.89 571.787/2.881 (2 025 & 48 2304 110592 6.9282) 3.6342 
4 70.56 592.704/2.898 {2.033 § 49 2401 117649 is 3.6593 
5 eds) 614.125)/2.915 |2.041 4 50 2500 125000 7.0711) 3.6840 
.6 73.96 636 .056/2.9383 {2.049 51 2601 132651 7.1414) 3.7084 
ar 75.69 658.503/2.950 {2.057 § 52 2704 140608 7 QW Ea tae: 
8 77.44 681 .472/2. 966 2.065 § 53 2809 148877 7.2801) 3.7563 
9 79.21 704.969|2.983 |2.072 § 54 2916 157464 7.3485) 3.7798 

9 81. 729. 3. 2.0801 55 3025 166375 7.4162] 3.8030 

1 $2.81 753.571/38.017 |2.088 6 56 3136 175616 7.4833) 3.8259 
2 84.64 778.688/8.033 |2.095 #& 57 3249 185193 7.5498] 3.8485 
3 86.49 804 .357/3.050 12.103 58 3364 195112 7.6158] 3.8709 
4 88.36 830.584/3.066 |2.110 59 3481 205379 7.6811) 3.8930 
5 90.25 857.375/3.082 {2.118 #4 60 8600 216000 7.7460) 3.9149 
6 92.16 884.736/38.098 /2.125 61 3/21 269381 7.8102| 3.9365 
(4 94.09 912 .673/38.114 |2 13838 § 62 3844 238328 7.8740) 3.957 
8 96.04 941 .192/3.180 }2.140 63 3969 250047 7.9373) 3.9791 
9 98.01 970.29913.146 |2.147 @ 64 4096 262144 8, 4, 

10 | 100 1000 3.1623 |2.1544 ; 65 4225 274625 8.0623] 4.0207 
11 | 121 1381 8.3166 (2.2240 § 66 4356 287496 8.1240) 4.0412 
12 | 144 1723 3.4641 12.2894 § 67 4189 3800763 8.1854] 4.0615 
13 | 169 2197 3.6056 |2.3513 g 63 4024 314432 8.2462] 4.0817 
14 | 196 2744 3.7417 |2.4101 9 69 4761 328509 8.3066] 4.1016 
5 Lo ke P45) 3375 3.8730 |2.4662 & 70 4900 343000 8 3666] 4.1213 
16 | 256 4096 4. 2.5198 8 71 5041 357911 8 4261] 4.1408 
17 | 289 4913 471231925713) 472 5184 373248 8.4853] 4.1602 
18 | 324 5832 4.2426 |2.6207 p73 5329 3889017 8.5440) 4.1798 
19 | 361 6859 4.3589 |2.6684 F q 5476 405224 8.6023] 4.1983 
20 | 400 8000 As4721 1207144 Vis) 5625 421875 8.6603) 4 2172 
21} 441 9261 4.5826 |2 7589 76 5776 438976 8.7178) 4.2858 
22 | 484 10648 4.6904 |2.8020 Ge 5929 456533 8.7750) 4.2543 
83 | 529 12167 4.7958 |2.8429 78 6084 47,4552 8.8318) 4.2727 
24 | 576 138824 4.8990 12.8845 79 6241 493039 8.8882] 4.2908 
25 | 625 15625 is 2.9240 80 6400 512000 8.9443] 4.3089 
26 | 676 17576 5.0990 |2.9625 9 81 6561 531441 9. 4.3267 
OF Hh 29 19683 5 1962 13. y 82 6724 551368 9 0: 4.3445 
98 | 784 21952 5.2915 138 03866 # 83 6889 571787 9. 4.8621 
29 | 841 24389 5.3852 13.0723 -§ 84 7056 592704 9, 2). 4.3795 
30 | 900 27000 5 4772 (3.1072 85 225 614125 9.2 4.3968 
31 | 961 29791 5.5678 (3.1414 §& 86 7396 636056 9... 4.4140 

~ 82 11024 82768 5.6569 13.1748 7 9569 658503 9 3276] 4.4310 
33 11089 35937 5.7446 13.2075 88 4744 681472 9.¢ 4.4480 
34 11156 39304 5.8310 |3.2396 89 7921 704969 9.4: 4.4647 
85 |1225 49875 5.9161 |3.2711 90 8100 729000 9. 4.4814 
36 11296 46656 |6. 3.3019 91 8281 45357 9.5: 4.4979 

7 11369 50653 6.0828 13.3322 92 8464 778688 95s 4.5144 
88 |1444 54872 6.1644 !3.3620 93 8649 804357 9 4.5307 
39 11521 59319 6.2450 (3.3912 94 8836 830584 9.6 4.5468 
40 |1600 64000 6.3246 13 4200 95 9025 857375 9 4.5629 
41 |1681 689221 6 .4031 18.4482 96 9216 884736 9. 4.5789 
42 \1764 74088 6.4807 {3.4760 § 97 9409 912673 9. 4.5947 
43 |1849 79507 '6.5574 13.5034 9G 9604 941192 9.8995] 4.6104 
44 11936 85184 ‘6.6332 13.5303 99 9801 970299 9.9499) 4.6261 


BB MATHEMATICAL TABLES, 








Sq. | Cube 


r Sq. 
No. |Square.| Cube. | pods | Root, JNO: |Sauare.| Cube. | pole 








155 | 24025 | 8723875 |12.4499) 5.3717 
9156 | 24836 | 38796416 12.4900) 5.3832 
3157 | 24649 | 3869893 12.5300) 5.3947 
58158 | 24964 | 3944312 |12.5698! 5.4061 
159 | 25281 | 4019679 {12.6095) 5.4175 


4 
4 
4 
4 
105 | 11025 | 1157625 |10.2470) 4 ¥ 160 | 25600 | 4096000 12.6491) 5.4288 
106 | 11236 1191016 10.2956] 4. B161 | 25921 4178281 |12.6886) 5.4401 
107 | 11449 | 1225043 |10.3441) 4.74759 162 | 26244 | 4251528 |12.7279) 5 4514 
t 
4 
4 
4 
4 
4 
4 


100.| 10000 | 1000000 |10. 4.6416} 
101 | 10201 1030301 |10.0499 
102 | 10404 | 1061208 |10.0995 
103 | 10609 | 1092727 |10.1489 
104 | 10816 | 1124864 |10.1980 





108 | 11664 | 1259712 10.3928 9163 | 26569 | 4830747 [12.7671] 5.4626 
109 | 11881 1295029 10.4403 #164 | 26896 | 4410944 [12.8062] 5.4737 


110 | 12100 | 13831000 /10.4881 R165 | 27225 | 4492125 12.8452) 5.4848 
111 | 12321 1367631 |10.5357 $166 | 27556 | 4574296 |12.8841) 5.4959 
112 | 12544 =| 1404928 |10.5830 8167 | 27889 | 4657463 12.9228) 5.5069 
113 | 12769 | 1442897 |10.6301} 4.83461168 | 28224 | 47416382 |12.9615| 5.5178 
114 | 12996 | 1481544 {10.677 .8488 7169 | 28561 | 4826809 [18.0000] 5.5288 


115 | 18225 | 1520875 |10.7238) 4.86298170 | 28900 | 4913000 |138.0884| 5.5397 
116 | 18456 | 1560896 {10.7703 R171 | 29241 | 5000211 |138.0767) 5.5505 
117 | 138689 | 1601613 |10.8167 fiv2 | 29584 | 5088448 138.1149) 5.5613 
118 | 18924 | 1643032 |10.8628 4173 | 29929 | BITTT1T §=|18.1529) 5.5721 
119 | 14161 1685159 {10.9087} 4.9187 9174 | 80276 | 5268024 |13.1909] 5.5828 


120 | 14406 | 1728000 10.9545 8175 | 80625 | 58593875 |18.2288) 5.5934 
121 | 14641 1771561 |11.0000 R176 | 8097 5451776 = |138.2665) 5.6041 
122 | 14884 | 1815848 |11.0454 B1T7 | 813829 | 5545283 |18.38041) 5.6147 
123 | 15129 | 1860867 |11.0905 178 | 31684 | 5639752 |18.3417| 5.6252 
124 | 153876 | 1906624 |11.1355 p179 | 32041 5735389 |18.3791| 5.6357 


H180 | 32400 | 5882000 |13.4164] 5.6442 
181 | 32761 5929741 |13.4536) 5.6567 
g182 | 838124 | 6025568 |13.4907] 5.6671 


125 | 15625 | 1953125 /11.1803 
126 | 15876 | 2000876 |11.2250 
127 | 16129 | 20483883 {11.2694 








(=) N 
[sy] 
< 
3 








128 | 16884 | 2097152 |11.31387 979183 | 88489 | 6128487 |13.5277| 5.6774 
129 | 16641 | 2146689 /11.3578) 5.0528 9184 | 33856 | 6229504 |13.5647] 5.6877 
130 | 16900 | 2197000 |11.4018) 5.06589185 | 34225 | 6331625 |13.6015} 5.6980 
131 | 17161 | 2248091 |11.4455) 5.07888186 | 34596 | 6434856 [13.6382] 5.7083 
132 | 17424 | 2299968 /|11.4891 09169187 | 34969 | 6539203 |13.6748| 5.7185 
133 | 17689 | 2352637 |11.5326) 5.10458 188 | 35344 | 6644672 |13.7113] 5.7287 
134 | 17956 | 2406104 {11.5758} 5.11729189 | 85721 | 6751269 13.7477) 5.7388 
135 | 18225 | 2460375 |11.6190} 5.1299%190 | 36100 | 6859000 {13.7840} 5.7489 
136 | 18496 | 2515456 |11.6619) 5.14269191 | 386481 | 6967871 13.8203) 5.7590 
137 | 18769 | 2571353 /11.7047) 5.15519 192 | 36864 | 7077888 |138.8564) 5.7690 
138 | 19044 | 2628072 [11.7473) 5.16769193 | 37249 | 7189057 113.8924] 5 7790 
139 | 193821 | 2685619 /11.7898) 5.18019 194 | 37636 | 7301384 [13.9284] 5.7890 
140 | 19600 | 2744000 /|11.8322) 5.19254195 | 38025 | 7414875 |13.9642) 5.7989 
141 | 19881 | 2808221 |11.8743) 5.20489196 | 88416 | 7529536 14.0000} 5.8088 
142 | 20164 | 2863288 |11.9164) 5.21719 197 | 88809 | 7645373 14.0357) 5.8186 
143 | 20449 | 2924207 111.9583} 5.22939198 | 39204 762392 114.0712) 5.8285 
144 | 20736 | 2985984 {12.0000| 5.24159§199 | 39601 | 7880599 |14.1067) 5.8383 
145 | 21025 | 3048625 |12.0416) 5.2536%200 | 40000 | 8000000 {14.1421} 5.8480 
146 | 21316 | 31121386 |12.0830) 5.2656 @201 | 40401 | 8120601 |14.1774| 5.8578 
147 | 21609 | 31765238 412.1244) 5.2776 § 202 | 40804 | 8242408 |14.2127| 5.8675 
148°] 21904 | 3241792 |12.1655| 5.28968 203 | 41209 | 8365427 114.2478) 5.8771 
149 | 22201 | 3307949 [12.2066] 5.30159 204 | 41616 | 8489664 |14.2829) 5.8868 
150 | 22500 | 3375000 |12.2474| 5.3133 9205 | 42025 | 8615125 14.3178] 5.8964 
151 | 22801 | 3442951 |12.2882| 5.3251 § 206 | 42436 | 8741816 14.5527) 5.9059 





207 | 42849 | 8869743 |14.3875) 5.9155 
208 | 43264 | 8998912 |14.4222] 5.9250 
209 | 43681 9129329 114.4568! 5.9845 


152 | 23104 | 3511808 |12.3288 
153 | 23409 | 3581577 '12.3693 
154 | 23716 | 3652264 112.4097 





ororororor 
“owe 
Ww 
cS 
Ce 





No. |Square. 


210 
211 
212 
213 
214 


215 
216 
217 
218 
219 


220 
221 





SQUARES, CUBES, SQUARE AND CUBE ROOTS, 


44100 


44521 
44944 
45369 
45796 


46225 
46656 
47089 
47524 
47961 


48400 
48841 
49284 
49729 
50176 


50625 
51076 
51529 
51984 
52441 


52900 
53361 
53824 
54289 
54756 


55225 
55696 
56169 
56644 
57121 


7600 
58081 
58564 
59049 
59536 


60025 
60516 
61009 
61504 
62001 


62500 
63001 
63504 
64009 
64516 


65025 
65536 
66049 
66564 
67081 


67600 
68121 
68644 
69169 
69696 


Cube. 


9261000 
9393931 
9528128 
9663597 
9800344 


993837 
10077696 
10218313 
10360232 
10503459 


10648000 
10793861 
10941048 
11089567 
11239424 


113890625 
11543176 
11697083 
11852352 
12008989 


12167000 
12326391 
12487168 
12649337 
12812904 


12977875 
13144256 
13312053 
13481272 
13651919 


13824000 
13997521 
14172488 
14348907 
14526784 


14706125 
14886936 
15069223 
15252992 
15438249 


15625000 
15818251 
16008008 
16194277 
16387064 


16581375 
16777216 
16974593 
17173512 
17373979 


17576000 
17779581 
17984728 
18191497 
18399744 











Sq. 
Root. 





14.4914 
14.5258 


15.8114 
15.8430 
15.8745 
15.9060 
15.9374 


15.9687 
16.0000 
16.0312 
16.0624 
16.0935 


16.1245 
16.1555 
16.1864 
16.2173 
16.2481 





Cube 
Root. 





5. 9439 
5.9538 
5.9627 
5.9721 


5.9814 : 


5.9907 


6.0000 ff: 





265 
266 


B17 
318 











No. |Square.| Cube. Pe 
70225 18609625 |16.2788 
90756 18821096 |16.8095 
7128y 19034163 |16.3401 
71824 19248832 116.3707 
72361 19465109 |16.4012 
72900 19683000 |16 4817 
73441 19902511 |16.4621 
73984 20128648 |16.4924 
74529 203846417 |16.5227 
75076 20570824 |16.5529 
75625 90796875 116.5831 
76176 21024576 |16.6132 
76729 21258933 |16.6433 
T7284 21484952 116.6733 
T7841 21717689 |16.70383 
78400 21952000 |16.73832 
78961 22188041 |16.7631 
79524 22495768 116.7929 
80089 22665187 |16.8226 
80656 22906304 |16.8523 
81225 93149125 (16.8819 
81796 23393656 116.9115 
82369 23639908 |16.9411 
82944 23887872 |16.9706 
88521 | 241387569 117.0000 
84100 24389000 |17.0294 
84681 24642171 117.0587 
85264 24897088 |17.0880 
85849 208bacbe, \17. 1172 
86436 25412184 117.1464 
87025 95672375 117.1756 
87616 25984336 117.2047 
88209 26198073 |17.2337 
88804 26463592 |17.2627 
89401 26730899 |17.2916 
90000 27000000 |17.3205 
90601 27270901 |17.3494 
91204 27543608 117.3781 
91809 27818127 117.4069 
92416 28094464 |17 4856 
93025 28372625 117.4642 
93636 28652616 117.4929 
94249 28934443 117.5214 
94864 29218112 117.5499 
95481 29503629 117.5784 
96100 29791000 |17.6068 
96721 80080231 117.6352 
97344 30371328 117.6635 
97969 30664297 117.6918 
98596 30959144 |17.7200 
99225 81255875 117.7482 
99856 31554496 |17.7764 

100489 31855013 17.8045 
101124 32157432 117.8326 
101761 32461759 117.8606 


319 





89 


Cube 
Root. 





6.4232 
6.4312 
6.4893 
6.4473 
6.4553 
6.4683 
6.4718 
6.4792 


‘| 6.4872 


6.4951 


6.5030 
6.5108 
6.5187 
6.5265 
6.5343 
6.5421 
6.5499 
6.5577 


5] 6.5654 


6.5731 


6.5808 
6.5885 
6.5962 
6.6039 
6.6115 


6.6191 
6.6267 
6.6343 
6.6419 
6.6494 


6.6569 
6.6644 
6.6719 
6.6794 
6.6869 


6.6943 
7018 
7092 
7166 
7240 


7313 
(387 
7460 
7533 
7606 


7679 
775 
7824 
(897 
7969 


6.8041 
6.8118 
6.8185 
6.8256 
6.8328 


OO OO & fo erlorlorsor) Oa C2 Od 


90 


No. |Square. 





320 
321 
322 
» 823 
324 


825 
326 


nw 6 
328 
329 


330 
331 











102400 


103041 
103684 
104329 
104976 


105625 
106276 
106929 
107584 
108241 


108900 
109561 
110224 
110889 
111556 


112225 
112896 
118569 
114244 
114921 


115600 
116281 
116964 
117649 
118336 


119025 
119716 
120409 
121104 
121801 


122500 
123201 
123904 
124609 
125316 


126025 
126736 
127449 
128164 
128831 


129600 
130321 
131044 
131769 
132496 


133225 
133956 
134689 
135424 
186161 


136900 
137641 
138384 
139129 
139876 


Cube. 


82768000 


33076161 
33386248 
33698267 
34012224 


34328125 
34645976 
34965783 
35287552 
35611289 


35937000 
36264691 
36594368 
386026037 
372597 04 


87595375 
37933056 

38272753 
38614472 
83958219 


39304000 
39651821 
40001688 
40353607 
40707584 
41063625 
41421736 
41783923 


42144192. 


42508549 


42875000 
43243551 
43614208 
43986977 
44361864 


44738875 
45118016 
45499293 
45882712 
46268279 


46656000 
47045881 
47437928 
47832147 
48228544 


48627125 
49027896 
49430863 
49836032 
50243409 


50653000 
51064811 
51478848 
51895117 
52313624 


Ee 


118.4932 





Sq. 
Root. 





17.8885 
17.9165 
17.9444 
17.9722 
18.0000 


18.0278 
18.0555 
18.0831 
18.1108 
18.1384 


18.1659 
18.1934 
18.2209 
18.2483 
18.2757 


18.3030 
18.3303 
18.3576 
18.3848 
18.4120 


18.4891 
18. 4662 


18.5203 
18.5472 


18.5742 
18.6011 
18.6279 
18.6548 
18.6815 


18.7083 
18.7850 
18.7617 
18.7883 
18.8149 


18.8414 
18.8680 
18.8944 
18 9209 
18.9473 


18.9737 
19.0000 
19.0263 
19 .0526 
19.0788 


19.1050 
19.1311 
19.1572 
19.1833 
19.2094 


19.2354 
19.2614 








19. 19.3391; | 


Cube 
Root. 


6.8399 
6.8470 
6.8541 
6.8612 §: 
6.8683 


6.8753 
6.8824 fl: 
6.8894 f 
6.8964 f 38: 














. Square. 


140625 


141376 
142129 
142884 
143641 


144400 
145161 
145924 
146659 
147456 


148225 
148996 
149769 
150544 
151621 


152100 
152881 
158664 
154449 
155286 


156025 
156816 
157609 


; 158404 


159201 


160000 
160801 
161604 
162409 
1638216 


164025 
164836 
165649 
166464 
167281 


168100 
168921 
169744 
170569 
171396 


172225 


179776 


180625 
181476 
182329 
183184 


29 | 184041 











MATHEMATICAL TABLES. 


Cube. 


52784375 
53157376 
58582633 
54010152 
54439939 


54872000 
55806341 
55742968 
56181887 
56623104 


7066625 
57512456 
57960603 
58411072 
58563869 


59319000 
59776471 
60236288 
60698457 
61162984 


61629875 
62099136 
62570773 
63044792 
68521199 


64000000 
64481201 
64964808 
65450827 
659389264 


66430125 
66923416 

7419143 
67917312 
68417929 


68921000 
69426531 
69934528 
70444997 
70957944 


71473375 
71991296 
72511718 
738034632 
73560059 


74088000 
74618461 
75151448 
75686967 
76225024 


76765625 


77308776 |: 


77854483 
78402752 


78953589 |2 





Sq. 
Root. 





19.3649 
19.3907 
19.4165 
19.4422 
19.4679 


19.4936 
19.5192 
19.5448 
19.5704 
19.5959 


19.6214 
19.6469 
19.6723 
19.6977 
19.4231 


19.7484 
19.7737 
19.7990 
19.8242 
19.8494 


19.8746 
19.8997 
19.9249 
19.9499 
19.9750 


20.0000 
20.0250 
20.0499 
20.0749 
20.0998 


20.1246 
20.1494 
20.1742 
20.1990 
20.2237 


20.2485 
20.2731 
20.2978 
20.3224 
20.8470 


20.3715 
20.3961 
20.4206 
20.4450 
20.4695 


20.4939 
20.5183 
20.5426 
20.5670 
20.5913 


20.6155 








Cube 
Root, 





.2112 
each 
2240 
2304 
.2308 


2432 
2495 
2558 
2622 
2685 


2748 
2811 
2874 
2936 
2999 


8061 
3124 
3186 
3248 
3310 


3372 
3434 
3496 
3558 
3619 


7.3681 
7.38742 
7.3808 
7 

7 


TPAWAIWVIAF WII 


NQF tt = 


NINN 


WII 


. 3864 
3925 


7.3986 
7.4047 
7.4108 
7.4169 
7.4229 


7.4290 
7.4350 
7.4410 
7.4470 
7.4580 


7.4590 
7.4650 
7.4710 
7.477 
7 


4829 


% 4889 
7.4948 
7.5007 
7.5067 
7.5126 
7.5185 
7.5244 
7.5302 
7.5361 
7.5420 


No. |Square. 


oe 


430 
431 








SQUARES, CUBES, SQUARE AND CUBE ROOTS. 


184900 


185761 
186624 
187489 
188356 


189225 
190096 
190969 
191844 
192721 


193600 
194481 
195364 
196249 
197136 


198025 
198916 
199809 
200704 
201601 


202500 
203401 
204304 
205209 
206116 


207025 
207936 
208349 
209764 
210681 


211600 
212521 
213444 
214369 
215296 


216225 
217156 
218089 
219024 
219961 


220900 
221841 
222784 
2237129 
224676 


225625 
226576 
227529 
228484 
229441 


230400 
231361 
232324 
233 /89 
234256 








Cube. 


79507000 


80062991 
80621568 
$1182737 
81746504 


82312875 
82881856 
83453453 
84027672 
84604519 


85184000 
85766121 
86350888 
86938307 
87528384 


88121125 
88716536 
89314623 
89915392 
90518349 


91125000 
91733351 
92345408 
92959677 
93576064 


94196375 
94818316 
95443993 
96071912 
96702579 


97336000 
97972181 
98611128 
99252847 
99897344 


100544625 
101194696 
101847563 
102503232 
103161709 


103823000 
104487111 
105154048 
105823817 
106496424 


107171875 
107850176 
108531333 
109215352 
109902239 


110592000 
111284643 
111980168 
112678587 
113379904 


Sq. 
Root, 





20.7364 
20.7605 
20.7846 
20.8087 
20.8327 





20.8567 
20.8806 
20.9045 
20.9284 
20.9523 


me 











21 


.2132 
2363 
2603 
2833 
80731 


.8307 | 
0042 
8176 
-4009 
. 4248 


4476 
4709) 
4942 
.5174 
5407 


.5639 


.6102 
6333 
. 6564 


6795 
7025 
7256 
F486 


T715 


7945 
.8174 
. 8403 


9317 
9545 
9773 
22.0000 


20. 9762 
. 0000 
0238 
.0476 
0718 


.0950 
culbdeyy 
1424 
. 1660 
1896 


5870 





8632 


8861 


9089 








HF J 3-2-3 


APAVOD ABABA PAVAT ABA PBI MMINMIWNRIW’ BWNVNAH 


IVI 


2 =e aT-3 





. |Square. 


235225 
236196 
237169 
238144 
239121 


240100 
241081 
242064 
243049 
244036 


245025 
246016 
247009 
248004 
249001 


250000 
251001 
252004 
253009 
254016 


255025 
256036 
257049 
258064 
209081 


260100 
261121 
262144 
263169 
264196 


265225 
266256 
267289 
268324 
269361 


270400 
271441 
272484 
273529 
274576 


275625 
276676 
207729 
278784 
279841 


280900 
281961 
283024 
284089 
285156 


2RBH225 
237296 
288369 
289444 


By 290521 


Cube. 


114084125 
114791256 


115501303 |: 


116214272 


116930169 |; 
117649000 


118370771 
119095488 
119823157 
120553784 


121287375 


123505992 
124251499 


|125000000 
125751501 
126506008 
127263527 


128024064 


128787625 
129554216 
130328843 
131096512 
131872229 


132651000 
133432831 
134217728 
135005697 
135796744 


136590875 
187388096 
138188413 
138991832 
139798359 


140608000 
141420761 
142236648 
143055667 
148877874 


(144703125 
(145531576 
146363183 
1147197952 
| 148035889 


1488777000 
149721291 
(150568768 
151419437 
152273304 


153130375 
153990656 
154854153 
1155720872 





156590819 


122023936 |: 
122763473 |2: 





Sq. 
Root. 


22.0227 
22. 0454 


22.3159 


22.3607 
22.3830 
22.4054 
22.4277 
22.4499 


22.4722 
22.4944 
22.5167 
22.5389 
22.5610 


22.5832 
22.6053 
22.6274 
22.6195 
22.6716 


22.6936 
22.7156 
22.7376 
22.7396 
22.7816 


22.8035 
22.8254 
22.8473 
22.8692 
22.8910 


22.9129 
22.9347 
22.9565 
22.9783 


123.0000 


23 0217 
23.0434 
23.0651 
23 0868 
23.1084 


23.1307 
23.1517 
23.1733 
23.1948 
23.2164 








92 





No. |Square, 


540 
541 











291600 
292681 
298764 
294849 
295936 


297025 
298116 
299209 
800304 
301401 


802500 
305601 
804704 
305809 
306916 


808025 
809186 
810249 
811864. 
312481 


313600 
314721 
315844 
816969 
818096 


319225 

20356 
321489 
822624 
323761 


824900 
326041 
827184 
828329 
829476 


330625 
331776 
832929 
334084 
335241 


336400 
337561 
338724 
339889 
841056 


842225 
343396 
844569 
345744 
846921 


348100 
349281 
350464 
351649 
352836 











MATHEMATICAL TABLES. 


Cube. 


157464000 


158340421 
159220088 
160103007 
160989184 


161878625 
162771336 
163667323 
164566592 
165469149 


166375000 
167284151 
168196608 
169112377 
170031464 


170953875 
171879616 
172808693 
1738741112 
174676879 


75616000 
176558481 
177504328 
178453547 
179406144 


180362125 
181321496 
182284263 


183250432 


184220009 


185193000 
186169411 
187149245 
188132517 
189119224 


190109375 
191102976 
192100033 
193100552 
194104539 


195112000 
196122941 
197137368 
198155287 
199176704 


200201625 
201280056 
2022620038 
203297472 
204336469 


205379000 
206425071 
207474688 
208527857 
209584584 








Sq. 
Root. 





23.2379 
23.2594 
23.2809 
23.3024 
23.8238 


23.3452 
23.3666 
23.3880 
23.4094 
23.4807 


23.4521 
23.4734 
23.4947 
23.5160 
23.5372 


28.5584 
23.5797 
23.6008 
23.6220 
23.6482 


23.6643 
23.6854 
23.7065 
23.7276 


28.7487 


23.7697 
23.7908 
23.8118 
23.8328 
23.8537 


23.8747 
23.8956 
23.9165 
23.9874 
23.9585 


23.9792 
24.0000 
24.0208 
24.0416 
24.0624 


24.0832 
24.1039 
24.1247 
24.1454 
24.1661 


24.1868 
24.2074 
24 2281 
24.2487 
24.2693 


24.2899 
24 3105 
24.3811 
24.3516 
24.3721 

















No, |Square. 


854025 


355216 
856409 
357604 
358801 


360000 
361201 
862404 
863609 
364816 


866025 
867236 
368449 
369664 
370881 


372100 
818821 
874544 

75769 
376996 


878225 
879456 
380689 
381924 
383161 


884400 
380641 
386884 
388129 
389376 


890625 
391876 
898129 
894384 
395641 


896900 
598161 
899424 
400689 
401956 


403225 
404496 
405769 
407044 
408321 


409600 
410881 
412164 
413449 
414736 


416025 
417316 
418609 
419904 
421201 





Cube. 


210644875 


211708736 
212776178 
218847192 
214921799 


216000000 
217081801 
218167208 
219256227 
220348864 


221445125 
222545016 

23648543 
224755712 
225866529 


226981000 
228099131 
229220928 
230346397 
281475544 


232608375 
233744896 
234885113 
236029032 
237176659 


238328000 
239483061 
240641848 
241804367 
242970624 


244140625 
245314376 
246491883 
247673152 
248858189 


250047000 
251259591 
252435968 
258636137 
254840104 


256047875 
257259456 
258474853 
259694072 
260917119 


262144000 
263374721 
264609288 
265847707 
267089984 


268336125 
269586136 
270840023 
272097792 
2733859449 





Sq. 
Root. 





24.3926 
24.4131 
24.4336 
24.4540 
24.4745 


24.4949 
24.5153 
24.5857 
24.5561 
24.5764 


24.5967 
24,6171 
24.6374 
24.6577 
24.677 


24 6982 
24.7184 
24.7386 
24.7588 
24.7790 


24.7992 
24.8193 
24.8395 
24.8596 
24.8797 


24.8998 
24.9199 
24.9399 
24.9600 
24.9800 


25.0000 
25.0200 
25.0400 
25.0599 





25.0799 


25.0998 
25.1197 
25.1396 
25.1595 
25.1794 


25.1992 
25.2190 
257 2389 
25.2587 
25.2784 


25.2982 
25.3180 
25.3377 
25.8574 
25.3772 


25.3969 
25.4165 
25.4862 
25.4558 
25.4755 











Cube 
Root. 





8.4108 
8.4155 
8.4202 
8.4249 
8.4296 


8 4343 
8.4890 
8.4437 
8.4484 
8.4530 


8.4577 
8.4623 
8.4670 
8.4716 
8.4763 


8.4809 
8.4856 
8.4902 
8.4948 
8.4994 


8.5040 
8.5086 
8.5132 
8.5178 
8.5224 


8.5270 
8.53816 
8.5362 
8.5408 
8.5453 


8.5499 
8.5544 
8.5590 
8.5635 
8.5681 


8.5726 
8.5772 
8.5817 
8.5862 
8.5907 


8.5952 
8.5997 
8.6043 
8.6088 
8.61382 


8.6177 
8.6222 
8.6267 
8.6312 
8.6357 


8.6401 
8.6446 
8.6490 
8.6535 
8.6579 





SQUARES, CUBES, SQUARE AND CUBE ROOTS. 


93 





No. |Square. 


650 
651 
652 
653 
654 





422500 
423801 
425104 
426409 
427716 


429025 
430336 
431649 
432964 
434281 


435600 
436921 
438244 
439569 
440896 


442225 
443556 
444889 
446224 
447561 


448900 
450241 
451584 
452929 
45427 


455625 
456976 
458329 
459684 
461041 


4621400 
463761 
465124 
466489 
467856 


469225 
470596 
471969 
473344 
474721 


76100 
477481 
478864 
480249 
481636 


483025 
484416 
485809 
487204 
488601 


490000 
491401 
492804 
494209 
495616 











Cube, 


274625000 
275894451 
277167808 
278445077 


281011375 
282300416 
283593393 
284890312 
286191179 


287496000 
288804781 
290117528 
291434247 
292754944 


296740963 
298077632 
299418309 


300763000 
302111711 
303464448 


807546875 


311665752 
313046839 


314432000 
315821241 
317214568 
318611987 
320018504 


321419125 
322828856 
324242703 
325660672 
327082769 


328509000 
329939371 
331373888 
332812557 
334255384 


335702375 
337153586 
338608873 
340068392 
341582099 


343000000 
344472101 
345948408 
347428927 
348913664 


279726264 |: 


294079625 |: 
295408296 |2 





304821217 |2: 
806182024 |. 





Sq. 


Root. 


25.4951 
25.5147 
25.5343 
5539 
.57384 


5.5930 
6125 
. 6320 
.6515 
.6710 


.6905 
7099 
7294 


26.2298 
26.2488 


26.2679 
26.2869 
26.3059 
26.3249 
26.3439 


26.8629 
26.3818 
26.4008 
26.4197 
26.4386 


26.4575 


26.4764! | 


26.4953 
26.5141 
26.5330 











. (Square. 


497025 
498436 
499849 
501264 
502681 


504100 
505521 
506944 
508369 
509796 


511225 
512656 
514089 
515524 
516961 


518400 
519841 
521284 
522729 
524176 


525625 
527076 
528529 
529984 
531441 


532900 
534361 
585824 
587289 
538756 


540225 
541696 
543169 
544644 
546121 


547600 
549801 
550564 
552049 
558536 


555025 
556516 
558009 
559504 
561001 


562500 
564001 
565504 
567009 
568516 


570025 

71536 
573049 
574564 
576081 


Cube. 


351895816 
358393243 
354894912 
356400829 


357911000 
359425431 
360944128 
362467097 
363994344 


365525875 
367061696 
368601818 
370146232 
371694959 


373248000 
374805361 
376367048 
3779383067 
379503424 


381078125 
382657176 
384240583 
385828352 
887420489 


889017000 
390617891 
392223168 
393832837 
395446904 


897065375 
398688256 
400315553 
401947272 





403583419 


405224000 
406869021 
408518488 
410172407 
411830784 


413493625 
415160936 
416832723 
418508992 
420189749 


421875000 
423564751 
425259008 
426957777 
428661064 


430868875 
432081216 
433798093 
435519512 
437245479 


350402625 


Sq. 
Root. 





26.5518 
26.5707 
26.5895 
6083 
3.6271 


6458 
.6646 
26.6833 
D. 7021 
7208 


7395 
1582 





7769 
26.7955 
26.8142 


26.8328 
26.8514 
26.8701 
26.8887 
26.9072 


26.9258 
26.9444 
26.9629 
26.9815 
27.0000 


27 0185 
27.0370 
27.0555 
27.0740 
27.0924 


27.1109 
27.1298 
27.1477 
27.1662 
27.1846 


27.2029 
27.2213 
27.2397 
27.2580 
2164 


27.2947 
27.3180 
27.3313 
27.3496 
27.8679 





27.3861 
27.4044 


Cube 
Root. 





8.9001 
8.9043 
8.9085 
8.9127 
8.9169 


8.9211 
8.9253 
8.9295 
8.9837 
8.9378 


8.9420 
8.9462 





8.9503 
8.9545 
8.9587 


8.9628 
8.9670 
8.9711 
8.9752 
8.9794 


8.9835 
8.9876 
8.9918 
8.9959 
9.0000 


9 0041 
9.0082 
9.0128 
9.0164 
9.0205 


9.0246 
9.0287 
9.0328 
9.0369 
9.0410 


9.0450 
9.0491 
9.0532 
9.057% 

9.0613 


9.0654 
9.0694 
9.0735 
9.0775 
9.0816 


9.0856 
9.0896 








27.4226 
27.4408 
27.4591 


27.4773 
27.4955 
27.5136 
27.5818 
27 5500 


9.0937 
9.0977 
9.1017 


9.1057 
- 9.1098 
9.1138 
9.1178 
9.1218 








94 


No.|Square. 


760 
761 
762 


577600 
579121 
580644 
582169 
583696 


585225 
3} 586756 
588289 
589824 
591361 


592900 
594441 
595984 
597529 
599076 


5} 600625 
6| 60217 
77| 603729 
8 605284 
9} 600841 


608400 
609961 
611524 
613089 
614656 


616225 
617796 
619369 
620944 
622521 


624100 
625681 
627264 
628849 
630436 


632025 

333616 
635209 
636804 
638401 


640000 
641601 
643201 
644809 
646416 


648025 
649636 
651249 
652864 
654481 


656100 
657721 
659344 
660969 

662596 

















438976000 


MATHEMATICAL TABLES, 


Sq. 
Cube. Root. 


No. Square. 





27.5681 
44071 1081)27 5862 
442450728 }27 6043 
444194947/27 6225 
445943744/27 6405 


447697125) 2". 6586 
449455096)}27 6767 
451217663)27 6948 
45298483227 .7128 
454756609/27 . 7308 


456538000/27 . 7489 
458314011)27.7669 
460099648 /27. 7849 
461829917|27 8029 
463684824 /27 8209 
465484375/27 8388 
467288576)/ 27.8568 
469097433127 8747 
470910952 27.8927 
472729139 27.9106 


474552000'27 . 9285 
476379541127 .9464 
478211768127. 9643 
480048687 [27.9821 
48 1890304 28 . v000 
483736625|28 0179 
485587656, 28. 0357 
487443403 |28 .0585 
489303872) 28.0713 
491169069\28 .0891 


493039000 28.1069 
494918671 /23.1247 
496793088 20.1425 
49867725728. 1603 
500566184 /28.1750 


502459875 28. 
504358336 |28 2135 
506261573 28.2312 
508169592 28.2489 
510082399 28. 


512000000 28. 
513922401 /28.3019 
515849608 /28.. 
51778162728 3373 
519718464 |28. 3549 


521660125; 28.3725 
523606616) 28. 3901 
525557943 28. 4077 
527514112 28.4253 
529475129 28.4429 


53144100028. 4605 
533411731 28.4781 
535387328 28.4956 
537367797 28.5132 
539353144 28.5307 

















| 


1957, 


2666, 
2843 
3196 





9) 206 


SS © 3 8S *O wore 


polelie) 
wR 


f 815) 
H 816) 
‘ 819, 


584 820. 
A S821 





664225 
665856 
667489 
669124 
670761 


72400 
674041 
675684 
677329 


817) 
818 


y 824) 678976 


680625 
682276 
683929 
685584 
687241 


688900 
690561 
692224 
693889 
695556 


697225 
698896 
700569 
702244 
703921 


705600 
707281 
708964 
710649 
712336 


714025 
715716 
717409 
719104 
720801 


722500 
724201 
725904 
727609 
729316 


731025 
3} 782786 
734449 
3} 736164 
7387881 


739600 
741321 
743044 
744769 
746496 


748225 
749956 
751689 
753424 
755161 














541343375 





Sq. 


Cube. Root. 





543838496 
545338513 
547343482 
549353259 


551368000 
593387661 
555412248 
557441767 
559476224 


561515625 
563559976 
565609283 |28 . 757 
567663552/28 . 7750 
569722789 |28 . 792 


571787000/28 .8097 
573856191 |28.8271 
5759380368 |28 .8444 
578009587 |28 .8617 
580093704 |28 . 8791 


28.5657 
28 .5832 


28.6182 


28.6356 
28.6531 
28 .6705 
28 . 6880 
28.7054 


28 .7228 
28.7402 





582182875|28 8964] § 


584277056 /28 . 9137 


58637 6253}28 9310) § 


588480472 /28 . 9482 


590589719}28.9655] § 


592704000/28 . 9828 
594823321 /29 .0000 
596947688}29 0172 
599077107 /29 .0345 
601211584 29.0517 


603351125 /29 .0689 
605495736 |29 .0861 
607645428 129.1033 
609800192 29.1204 
611960049 29.1876 


614125000,29.1548 
616295051 /29.1719 
618470208) 29.1890 
620650477 |29 . 2062 
622835864) 29 2233 


625026875 | 29.2404 
6272220)6/29 .2575 
6294227 93/29 .2746 
631628712/29.2916 
688839779) 29 . 38087 


636056000) 29 8258 
688277381/29 3428 
640503928) 29. 8598 
642735647) 29.3769 
644972544 29.3939 


647214625 29.4109 
649461896) 29.4279 
651714363 29.4449 
65397 2032/29 .4618 
656234909!29 4788 





28.5482! $ 


28.6007) § 








SQUARES, CUBES, SQUARE AND CUBE ROOTS. 95 


Sq. | Cube § 


No.|Square.}| Cube. | post. | Root. | bea ede Cube. Sq. | Cube 


Root. | Root. 











925} 855625 | 791453125 30.4138) 9.7435 
8 926) 857476 | 794022776 30.4302) 9.7470 
H 927) 859329 | 796597983 30.4467) 9.755 
# 928) 861184 | 799178752 380.4631) 9 7540 
§ 929) 863041 | 801765089 30.4795) 9.7575 


9 
9 
9 
9 
9 H 930) 864900 | 804357000 30.4959} 9.7610 
876) 767376 | 672221876)29.5973) 9 34 931) 866761 | 806954491 30.5123) 9.7645 
877| 769129 | 674526133) 29.6142) 9.57199 9382) 868624 | 809557568 30.5287) 9 TSU 
78] 770884 | 676836152)29.6311 atl 933) 870489 | 812166237 30.5450] 9.7715 

iS) 

9 

9 

a 

9 








70} 756900 | 658503000/29.4958) 9.5464 
71} 758641 | 660776311/29.5127 
872} 760384 | 663054848 /29.5296 
73| 762129 | 665338617)/29.5466 
74| 763876 | 667627624)29 5635 


875) 765625 | 669921875/29.5804 








9 
879] 772641 | 679151439/29. 6479 934) 872356 | 814780504 30.5614) 9.7750 
1 935] 874225 | 817400375 30.577 Wisi) 


880} 774400 | 681472000'29.6648 
4 7819 


76161 | 683797841/29.6516 
882) 777924 | 686128968)}29 6985 
883} 779689 | 688465387)/29.7153 
884} 781456 | 690807104/29.7321 


885} 783225 | 693154125)29.7489| 9.6010 
886) 784996 | 695506456)29.7653) 9.6046 8 
887) 786769 | 697864103)29.7825| 9.6082 f 
888} 788544 | 700227072/29.7993| 9.6118 5 
839} 790321 | 702595369)29.8161} 9.6154 F 


890} 792100 | 704969000 29.8329) 9.6190 
891) 1933831 | 707347971/29.8496| 9.62265 
892! 795664 | 709732288)29.8664| 9.6262 F 
893} 797449 | 712121957|29.8831| 9.6298 
894) 7992386 | 714516984/29.8998) 9.6334 § 


895} 801025 | 716917375 29.9166) 9.6370) 
896! 802816 | 719323136)/29.9333) 9.6406 
897| 804609 | -721734273)29.9500| 9.6442; 
898) 806404 | %'24150792)29. 9666) 9.6477 

899} 808201 | 726572699 29.9838) 9 65134 


900} 810000 | %29000000'30 0000} 9.6549 
901} 811801 | 731432701/30.0167| 9.6585} 
902} 813694 | 733870808/30.0233} 9.6620 
903] 815409 | 736314327/80.0500} 9.6656 
904} 817216 | 7388763264/30.0666} 9.6692 


905} 819025 | 741217625/30.0832} 9.6727 % 
906} 820836 | 743677416/30.0998] 9.6763 
907} 822649 | 746142643/30.1164| 9.6799 9 
9U8| 824464 | 748613312/30.1330} 9.6334 | 
909} 826281 | 751089429/30.1496} 9.6870 | 


910} 828100 | 753571000/30.1662| 9.6905 ¢ 
911) 829921 | 756058031/30.1828) 9.6941 f 
912) 831744 | 758550528/30.1993] 9.6976 | 
913, 833569 | 761048497/30.2159] 9.7012 
914) 835396 | 763551944)30.2324! 9.7047 


915} 837225 | 766060875/30.2490) 9.7082 
916) 839056 | 768575296/30. 2655) 9.7118 
917) 840889 | 771095213}30. 2820] 9.7153 | 
913, 842724 | 773620632/30.2985) § 
919) 844561 | 776151559/30.3150 


9 

4) 
320} 846400 | 778688000) 30.3315} 9 ; 
92%) 848241 | 781229961 /30.3480) 9.7294 § 

9 

9 


9 
936) 876096 | 820025856 30.5941} 9 
1 937| 877969 | 822656953 30.6105] 9.7854 
§ 938) 879844 | 825293672/30.6268| 9.7889 
W 939, 881721 | 827936019 30.6431] 9.7924 
9 
9 
y 


$40, 883600 | 830584000 30 6594 
941} 885481 | 833237621 30.6757! 9.7995 
942) 887364 | 835896888 30.6920] 9.8028 
943] 889249 | 838561807/30 7083, 9.8063 
944) 891186 | 841232384 30.7246) 9 8097 


945! 893025 | 843908625'30.7409| 9.8132° 
946| 894916 | 846590536'30.7571| 9 8167 
947| 896809 | 849278123!30.7734| 9.8201 
948) 898704 | 851971292'30.7896| 9.8236 
949 900601 eee | 8270 


9 
9 
950 902500 | 857375000 30.8221] 9.8305 
9 
9 


7959 











951) 904401 | 860085351 |80.8383) 9.8339 
952; 906304 | 862801408 80.8545; 9.8374 
953 908209 | 86552317730 8707) 9.8408 
954, 910116 | 868250664 30.8869) 9.5443 


955, 912025 | 870983875 30.9031] 9.8477 
956' 913936 | 873722816 380 9192) 9.8511 
957) 915849 | 876467493 30.9351) 9.8546 
958) 917764 | 879217912/380.9516} 9.8580 
959} 919681 | 881974079|}30.9677) 9.8614 


960} 921600 | 884736000/30. 9839) 9.8648 
961) 923521 | 887503681/31.0000} 9.8683 
962} 925444 | 890277128'31.0161) 9 8717 
963} 927369 | 893056347)31.0322) 9.8751 
964) 929296 | 895841344/31.0483) 9.8785 


965} 931225 | 898632125/31.0644) 9 8819 
966} 933156 | 901428696)31.0805| 9.8854 
967) 935089 | 904231063)31.0966} 9.8888 
968} 937024 | 907039282/31.1127| 9.8922 
969} 938961 | 909853209)31.1208) 9.8956 


9 
9 
9 
9 
9 
97'0| 940900 | 912673000/31.1448) 9.8990 
971} 942841 | 915498611/31.1609) 9.9024 
972| 944784 | 918380048/31.1769 A aes 
9 
9 
9 
9 
9 
9 








973) 946729 | 921167317/81.1929} 9.9092 
974] 948676 | 924010424)51.2090) 9.9126 


9.9160 
9194 
92. 
9261 
9295 


4 975) 950625 | 926859375] 31.2250 
976! 952576 | 9297'14176/31.2410] -§ 
Vt) 954529 | 932574833] 31. 257 
978| 956484 | 935141352/31.2730 
979) 958441 0383 13739' 31.2890 





922| 850084 | 7837'77448/30 . 3645 
923) 851929 | 786330467/30.3809) 9. 
924) 853776 —'788889024130.3974! 9.7400 























36 MATHEMATICAL TABLES. 





Cube. No. 


No.|Square.| Cube. Bae Root. Cube. Sq. Cuba 


Square. Root. | Root, 








960400} 941192000/31 .3050| 9.9329 $1035) 1071225)1108717875/32.1714)10.1153 
962361) 944076141/31.3209] 9.9363 § 1036} 1073296/1111934656/32.1870]10.1186 
964324) 946966168/31.3369] 9.9396 f 1037) 1075369)1115157653 32, 2025)10.1218 
966259] 949862087/31.3528] 9.9430 #10388} 1077444) 1118386872 32.2180) 10.1251 
968256) 952763904)31.3688} 9.9464 9 10389) 1079521/1121622319) 32.2335) 10.1288 


9497 #1040} 1081600)1124864000 32 .2490]10.1316 
9531 #1041) 1083681)1128111921'32. 2645/10. 1348 
9565 f 1042) 1085764/ 1181866088 32. 2800)10.1381 
9598 § 1048) 1087849) 1134626507 82 .2955/10.1413 
9632 § 1044) 1089936/1187893184 32.3110) 10.1446 


980100} 970299000)31.4643) 9.9666 #1045) 1092025)1141166125 32.3265)]10.1478 
982081} $73242271)/31.4802] 9.9699 #1046} 1094116) 1144445336'32.3419}10.1510 
984064} 976191488/31.4960} 9.9733 #1047) 1096209)1147730823 82 3574/10.1543 
986049} 979146657/31.5119} 9.9766 91048} 1098804] 1151022592 32.3728] 10.1575 
988036] 982107784/31.5278) 9.9800 #1049} 1100401] 1154320619 32.8883] 10. 1607 


990025) 985074875 /31 5436) 9.9833 91050) 1102500) 1157625000 32.4037/10 1640 
992016] 988047936)31.5595| 9.98668 1051) 1104601) 1160935651 /32.4191110.1672 
994009] 991026973)31.5753} 9.9900 #1052] 1106704]1164252608 32.4345] 10.1704 
996004} 994011992/31.5911{ 9 9933 #1053) 1108809)1167575877 32. 4500}10. 1736 
998001} 997002999/31.6070} 9.9967 #1054) 1110916) 1170905464/32 4654]10.1769 


1000000) 1000000000) 31.6228) 10.0000 g 1055} 1113025) 1174241375 /32. 4808] 10. 1801 
1002001 |1003003001|31.6386| 10.0033 § 1056) 1115186) 1177582616 32.4962/10.1833 
1004004) 1006012008) 31 .6544/10.0067 § 1057) 1117249) 1180932193 /32.5115]10. 1865 
1006009] 1009027027 /31 .6702] 10.0100 § 1058) 1119264) 1184287112/32.5269)10.1897 
1008016}1012048064/31.6860) 10.0183 § 1059) 1121481|1187645379/32.5423]10.1929 


1010025] 1015075125) 31.7017) 10.0166 ¢ 1060} 1123600) 1191016000/32 5576)10 1961 
1012036] 1018108216] 31.7175) 10.0200 #1061) 1125721) 1194389981 |32.5730)10.1993 
1014049] 1021147343)31.7333)10 0233 § 1062) 1127844) 119777C328/32 5883] 10.2025 
1016064|1024192512/31.7490) 10.0266 #1063) 1129969) 1201157047 |32.6036)10 2057 
1018081] 1027243729) 31.7648/10.0299 f 1064) 1182096) 1204550144/382.6196) 10.2089 


1020100]1030801000) 31.7805) 10.0332 # 1065) 1184225) 1207949625/32. 6343] 10.2121 
1022121 | 1033364331/31.7962)10.0365 #1066} 1186356) 1211855496 /32. 6497} 10.2153 
1024144) 1036433728) 31.8119) 10.0398 #1067} 1138489) 1214767763)32 6650]10.2185 
1026169} 1039509197/31.8277] 10.0431 #1068) 1140624 1218186432/382.6803)10.2217 
1028196} 1042590744 /31.8434 10.0465 $1069) 1142761/1221611509/ 82. 6956/10. 2249 


1080225] 1045678375 )/31. 8591) 10.0498 § 1070} 1144900) 1225043000/32.7109| 10.2281 
1032256} 1048772096 31 .8748)10.0531 #1071} 1147041) 1228480911/32.7261/10.2313 
1084289] 1051871913/51.8904)10.0563 #1072) 1149184 1231925248/32.7414|10.2345 
1036324] 1054977832/31 .9061|10.0596 91073) 1151329) 1235376017/32. 7567) 10.2376 
1038361 |1058089859)}31.9218) 10.0629 § 1074) 1153476) 12388833224 /32.7719)10. 2408 


1040400] 1061208000/31 . 9374) 10.0662 1075} 1155625) 1242296875/32.7872/10.2440 
1042441} 1064332261 31.9531) 10.0695 § 1076) 1157776) 1245766976 |32 8024) 10. 2472 
1044484] 1067462648) 31.9687) 10.0728 # 1077] 1159929) 1249243533)/32 8177/10. 2503 
1046529] 1070599167)31.9844)10.0761 § 1078] 1162084) 1252726552/82.8329)10.2535 
1048576] 1073741824 /32.0000) 10.0794 § 1079} 1164241| 1256216039)32.8481 10.2567 


1050625] 1076890625|32.0156]10.0826 # 1080) 1166400/ 1259712000|32.8634|10.2599 
1052676] 108004557632. 0312/10.08594 1081! 1168561/1263214441/32. 8786110. 2630 
1054729] 1083206683|32 0468] 10.0892 4 1082) 1170724) 1266723368122 8938110 2662 
1056784|1086373952|32 0624/10 0925 #1083] 1172889] 127023878732. 9090/10. 2693 
1058841 |1089547389|32. 0780| 10.0957 f 1084} 1176056|1273760704/ 32. 9242110. 2725 


1060900] 1092727000|32. 0936] 10.0990 § 1085} 1177225/127'7289125/32. 9393110. 2757 
1062961|1095912791|32, 1092/10 10234 1086] 1179396 1280824056!32.9545/10.2788 
1065024 | 1099104768]32. 1248) 10.1055 # 1087 1181569| 1284365503) 32. 9697|10. 2820 
1067089] 1102302937/32. 1403] 10.1088 1088} 1183744] 1287913472/32 9818/10 2851 
1069156] 1105507304132. 1559/10. 112181089! 1185921|1291467969133.0000110 2883 








970225) 955671625}31 3847 
972196} 958585256/ 31.4006 
974169} 961504803/31.4166 
976144] 964430272)31 , 4825 
978121] 9673861669/31 4484 





loko) Woes wo Nejeiioile) 


















































SQUARES, CUBES, SQUARE AND CUBE ROOTS. 9% 


No. |Square. 


— | — |__| | ———_—__——_ * ———_— | — | | 


10.2914} 
10.2946 F 
10.2975 


1090 
1091 
1092 
1093 
1094 


1095 
1096 
1097 
1098 
1099 


1100 
1101 
1102 
1103 
1104 


1105 
1106 
1107 
1108 
1109 


1110 
1111 
1112 
1113 
11i4 


1115 
1116 
P11 
1118 
1119 


1120 
1121 
1122 
1123 
1124 


1125 
1126 
1127 
1128 
1129 


1130 
1131 
1132 
1133 
1134 


1135 
1136 
1137 
1138 
1139 


1140 
1141 
1142 
1143 
1144 





1188100 
1190281 
1192464 
1194649 
1196836 


1199025 
1201216 
1203409 
1205604 
1207801 


1210000 
1212201 
1214404 
1216609 
1218816 


1221025 
1223236 
1225449 
1227664 
1229881 


1232100 
1234321 
1236544 
1238769 
1240996 


1243225 
1245456 
1247689 
1249924 
1252161 


1254400 
1256641 
1258884 
1261129 
1263376 


1265625 
1267876 
1270129 
1272384 
1274641 


1276900 
1279161 
1281424 
1283689 
1285956 


1288225 
1290496 
1292769 
1295044 
1297821 


1299600 
1301881 
1804164 
1306449 








§q. 


Cube. Host: 


1295029000 
1298596571 
1302170688 
1205751357 
1309338584 


1312932375 
1316532736 
1320139673 
1823753192 
1827378299 


1331000000)33. 
13484633301 
1338273208 
1341919727 
1845572864 


1349232625 
1352899016 
1356572043 
1360251712/33 2866 
1363938029 /33.3017 


1367631000 33.3167 
13871330631 33.3317 
1375036928 33,3467 
1378749897 |33 3617 
1882469544 /33.3766 


1386195875 /33.3916 
1389928896 33. 4066 
1393668613 38.4215 
1897415032/33 .4365 
1401168159 33.4515 


1404928000 33.4664 
1408694561 |383.4813 
1412467848 33.4963 
1416247867 33.5112 
1420034624 33.5261 


1423828125 33.5410 
1427628376 33.5559 
1431435383 33.5708 
1435249152 33.5857 
1489069689 33.6006 


1442897000 33.6155 
1446731091|33 6303 
145057196833, 6452 
1454419637/33.6601 
1458274104| 33.6749 


1462135375/33.6898 
1466003456/33 .7046 
1469878353) 33.7174 
1473760072) 338 .7342 
1477648619)33.7491 


1481544000) 33.7639 
148544622133, 7787 
1489355288) 33.7935 
14938271207/33.8083 


38.0151 
33.0308 
33.0454 
33.0606 
33.0757 


33.0908 
33.1059 
33.1210 
33,1361 


33.1964 
33,2114 
33.2264 
33.2415 


33.2566 
33.2716 

















Cube § no. |Square. 


Root. 


10.8009 


10.3040 § 
10.3071} 


10.3108 
10.3134 


10.3165 % 
38.1512/10.3197 § 


1662} 10.3228 } 
33.1813)10.8259 | 


10.3290 
10.3322 


10.3353 § 
10.3384 | 


10.5 


10,4097 § 
10.4127} 


10.4158 


1308736! 1497193984133.8231110. 4586 











1311025 
1813316 
1315609 


| 1317904 


1320201 


1322500 
1324801 
1827104 
1329409 
1331716 


1334025 
1336336 
1338649 
1340964 
1843281 


1345600 
1347921 
1350244 
1352569 
1354896 


1357225 
1359556 
13861889 
1304224 
1366561 


1368900 
1371241 
1373584 
1375929 
1378276 


1380625 
1382976 
1385329 
1387684 
1390041 


1392400 
1394761 
1397124 
1399489 
1401856 


1404225 
1406596 
1400369 
1411344 
1413721 


1416100 
1418181 
1420864 
1423249 
1425636 


1428025 
1430416 
1432809 
1435204 








Cube. 


1501123625 
1505060136 
1509003523 
1512953792 
1516910949 


1520875000 
1524845951 
1528823808 
1532808577 
1536800264 


1540798875 
1544804416 
1548816893 
1552836312 
1556862679 


1560896000 
1564936281 
1568983528 
1573087747 
1577098944 


1581167125 


1585242296) 


1589324463 
1593413632 
1597509809 


1601613000 
16057238211 
1609840448 
1618964717 
1618096024 


1622234375 
1626379776 
1630532233 
1634691752 
1638858339 


1643032000 
1647212741 
1651400568 
1655595487 
1659797504 


1664006625 
1668222856 
1672446203 
1676676672 
1680914269 


1685159000 
1689410871 
1693669888 
1697936057 
1702209384 


1706489875 
1710777536 
1715072873 
1719874892 





Cube 
Root. 


Sq. 
Root. 





33.8378 
33.8526 
33.8674 
33.8821 
33.8969 


33.9116 
33.9264 
33.9411 
33.9559 
33.9706) 10.4890 


83.9853)10.4921 
34 .0000)10.4951 
34.0147)10.4981 
34.0294)10.5011 
34.0441) 10.5042 


34.0588) 10.5072 
84.0735/10.5102 
34.0881) 10.5182 
34, 1028}10.5162 
34,1174} 10.5192 


84.1321)10.5223 
34, 1467/10 .5253 
34,1614) 10.5283 
34.1760} 10.5313 
34.1906) 10.5343 


34.2053) 10.5373 
34.2199)10.54038 
34.2345) 10.5433 
34.2491/10.5463 
34.2637) 10,5493 


24 .2783)10.5523 
34.2929] 10,5553 
34,3074| 10.5583 
34,8220) 10,5612 
34.3366) 10.5642 


34.3511)10,5672 
84,3657/ 10.5702 
34,3802)10.5732 
34.3948/10 5762 
34.4093) 10.5791 


34.4238!10.5821 
34.4384] 10.5851 
34.4529110.5881 
34.4674/10.5910 
34,4819| 10.5940 


34. 4964)10.5970 
84.5109]10.6000 
34.5254/10. 6029 
84.5398)10.6059 
84.5543] 10.6088 


34.5688} 10.6118 
34,5832|10.6148 
84.5977) 10.6177 
84,6121/10.6207 


10.4617 
10.4647 
10.4678 
10.4708 
10.4739 


10.4769 
10.4799 
10.4830 
10.4860 





-143760111728683599 34. 6266110. 6236 


98 


MATHEMATICAL TABLES, 


Cube 
Root. 


No 


Sq. 
No.|Square.| Cube. | poot. 
1200} 1440000] 1728000000 34.6410 





3} 1552516/1984434936 





1442401 1782323601 34.6554 
1444804]1736654408 34.6699 
1447209]1740992427 34.6843 
1449616/1745337664 34.6987 


1452025}1749690125/34.7131 
1454436 }1754049816)34.7275 
1456849]1758416743'34.7419 
1459264 /1762790912/34 . 7563 
1461681 /1767172329/34. 7707 


1464100]1771561000)34.7851 
1466521]1775956931|34.7994 
1468944 }1780360128); 
1471369 )1784770597 
1473796 |1789188344 


1476225/1793613375 
1478656] 1798045696 
1481089/1802485313 
1483524) 1806932232 
1485961 /1811386459 


1488400} 1815848000 
1490841 |18203 16861 
1493284 /}1824793048 
1495729 | 1829276567 
1498176) 18383767424 


1500625 |1838265625 
1503076)1842771176 
1505529/1847284083 
1507984 }18518043852 
1510441)1856831989 


1512900]1860867000 
1515361/1865409391 
1517824/1869959168 
1520289} 1874516337 
1522756)}187 9080904 


1525225 |1883652875 
1527696) 1888232256 
1530169} 1892819053 
15382644) 1897413272 
1535121/1902014919 


153760011906624000 
1540081|1911240521 
1542564! 1915864488 
1545049] 1920495907 
1547536] 1925184784 


1550025 /1929781125 


34.8425 


34.8569 
34.8712 
34.8855 
34.8999 
34.9142 


34.9285 
34.9428 
34.9571 
34.9714 
34.9857 


35.0000 
35.0143 
35.0286 
35.0428 
35.0571 


35.0714 
35.0856 
35.0999 
35.1141 
30.1283 


85.1426 
35.1568 
35.1710 
35.1852 
35.1994 


30.2136 
35 .2278 
35.2420 
35 .2562 
35.2704 


35.2846 
85.2987 
1555009 |1939096223)385 .3129 
1557504] 1943764992) 35.3270 
1560001 |1943441249)/ 35.3412 


1562500 | 1955125000) 35 3553 
1565001 |1957816251 |85.3695 
1567504|1962515008/ 35.3836 
1570009}1967221277) 35.3977 








1572516|1971935064!35.4119: 





10.6266 
10.6295 
10.6825 
10.6354 
10.6384 


10.6413 
10.6448 
10.6472 
10.6501 
10.6530 


10.6560 
10.6590 
10.6619 
10.6648 
10.6678 


10.6707 
10.6736 
10.6765 
10.6795 
10.6824 


10.6853 
10.6882 
10.6911 
10.6940 
10.6970 


10.6999 
10.7028 
10.7057 
10.7086 
10.7115 


10.7144 
10.7173 
10.7202 
10.7281 
10.7260 


10.7289 
10.7318 
10.7347 
10.7376 
10.7405 


10.7434 
10.7463 
10.7491 
10.7520 
10.7549 


10.7578 
10.7607 
10.7635 
10.7664 
10.7693 


10. 
10. 
10.777 
10 7808 
10.78 


7722 


.|Square. 











Cube. Sq. 








Cube 


Root. | Root. 





1575025)}1976656375 35.4260) 10.7865 
1577536 }1981385216 35.4401]10.7894 
1580049)1986121593 385 .4542)10.'7922 


1582564|1990865512 35.4683 
158508) Frans os 
1587600}200037'6000 35.4965 
41590121 |2005142581 35.5106 
1592644/2009916728 35.5246 
1595169)2014698447 35.5387 
1597696 |2019487744 35.5528 


1600225 12024284625 35.5668 
1602756 |2029089096'35 .5809 
1605289 |2033901163}35 .5949 
1607824 |2038720832)35 6090 
1610361 |2043548109|35 . 6230 


1612900}2048383000/35 .6371 
1615441 }2053225511|35.6511 
1617984 |2058075648/35 . 6651 
1620529 )}2062933417|35 .6791 
1623076} 2067798824 35.6931 


1625625} 2072671875 |35 . 7071 
1628176 '2077552576/35.7211 
1630729 )2082440933)35 . 7351 
1638284 |2087336952|85 .7491 
1685841 |2092240639|35 .7631 


1638400|2097152000135 7771 
1640961 }2102071041|35.7911 
164352412106997768/35 . 8050 
1646089 |2111932187/35 .8190 
1648656 |2116874304)35 .8329 


1651225 ]2121824125)|35 .8469 
1653796 |2126781656/35 .8608 
1656369)}2131746903 35.8748 
1658944 2136719872135 . 8887 
1661521 }2141760569) 35. 9026 


1664100)2146689000)35 .9166 
1666681 |2151685171}35.9305 
1669264 |2156689088)35 . 9444 
1671849 |2161700757|35 . 9583 
1674486 


1677025 
1679616 
1682209 
1684804 
1687401 


1690000 
1692601 
1695204 
1697809 





2171747375)35.9861 
2176782336 /36 0000 
2181825073/36.0189 
218687559236 . 027; 
2191933899 /36 .0416 


2197000000/86 .0555 
2202073901 |36 0694 
2207155608) 36 . 0832 
2212245127|36.0971 
1700416 | 2217342464 |36.1109 


1703025 | 2222447625/36. 1248 
1705636 /2227560616)36 . 1386 
1708249 223268 1443/36 1525 
1710864 223781011236 .1663 





1713481 2242946629136. 1801 








10,7951 
10.7980 


10.8008 
10.8037 
10.8065 
10.8094 
10.8122 


10.8151 
10.8179 
10 8208 
10.8236 
10.8265 


10.8298 
10.8822 
10.8350 
10 8378 
10.8407 


10.8435 
10.8463 
10.8492 
10.8520 
10.8548 


10.8577 
10.8605 
10.8633 
10.8661 
16.8690 


10.8718 
10.8746 
10.877 

10.8802 
10.8831 


10.8859 
10.8887 
10.8915 
10.8942 


2166720184 |35 .9722!10.8971 


10.8999 
10.9027 
10.9055 
10.9083 
10.9111 


10.9139 
10.9167 
10.9195 
10.9223 
10.9251 


10.9279 
10.9807 
10.9335 
10.9363 


10.9391 


SQUARES, CUBES, SQUARE AND CUBE ROOTS. 99 


CO 


Sq. Cube 


enter Cube. Rone Root: Cube 


.;Square.| Cube. poe Root 


SSS ee ee ee eS eee = 


1310] 1716100 2248091000/36. 1939/10.9418 1863225 | 2543302125 /36 . 9459] 11.0929 
1311) 1718721 2253243231/36. 2077/10. 9446 1865956 | 2548895896 |36 . 9594/11 .0956 
1312] 1721344 2258403328/36 221510. 9474 1868689} 2554497863 36 . 9730) 11.0983 
1313) 1723969 2263571297 |36 .2353)10.9502 1871424|2560108032/36 . 9865/11 .1010 
1314] 1726596 2268747144) 36.2491|10.9530 1874161 |2565726409/37 .0000/ 11.1037 


1315 1729995 2973030875 36 .2629/10.9557 

1316] 1731856 2279122496/36.2767| 10.9585 § 1: 
1817| 1734489 2284322013]36 . 2905] 10.9613 
1318} 1787124 2289529432/36 .38043/10.9640 
1319) 1739761 /2294744759/36 3180/10. 9668 § 


1320} 1742400 2299968000) 36 .3318/10.9696 § 
1321) 1745041)2305199161|36 3456) 10.9724 
1322] 1747684]2310438248]36 . 3593) 10.9752 
1323] 1750329)/2315685267]36 .3731/10.9779 | 
1324| 175297 6/2820940224/36 .3868) 10.9807 


1325] 1755625/2326203125/36 .4005) 10.9834 
1326) 1758276]2331473976/36.4143! 10. 9862 g 1 
1327) 1760929)2336752783| 36.4280) 10.9890 } 
1328] 1763584}2342039552|36.4417/10.9917 
1329] 1766241]2347331289)36 4555) 10.9945 


» 1330) 1768900/2352637000/36 . 4692) 10.9972 # 
© 1831) 1771561]2357947691|36 4829) 11.0000 ¢ 1: 
1582] 1774224 /2363266368/36 .4966) 11.002 
1833] 1776889]2368593037 |36 .5103) 11.0055 # 1: 
1334| 1779556}2373927704/36 5240) 11.0088 § 


1335| 1782225/2379270375|36 .5377| 11.0110] 
1336| 1784896 /2384621056/36 .5513)11.0138 5 
| 1337| 1787569/2389979753| 36.5650) 11.0165 § 1392 
1338] 1790244]2305346472|36 5787/11 0193 | 
1339| 1792921|2400721219) 36.5923) 11.0220 5 


1340} 1795600|2406104000) 36.6060) 11.0247 § 
1341| 1798281]2411494821/36.6197)11.0275 § 1 
1342; 1800964/2416893688]36 . 6333) 11.0302 
1343] -1803649/2422300607|36 .6469) 11.0330 § 
1344] 1806336]}2427715584| 36.6606) 11.0357 § 


1345} 1809025)2433138625)36 . 6742) 11.0384 § 
1346) 1811716}2438569736) 36 .6879/ 11.0412 | 
1347| 1814409}2444008923/36 .7015} 11.0429 § 
1348) 1817104/2449456192/36.7151) 11.0466 § 
1349| 1819801|2454911549]36.7287/11.0494 § 


1350] 1822500}2460375000) 36 .7423/11.0521 | 
1351} 1825201)2465846551) 36.7560) 11.0548 } 
1352} 1827904/2471326208) 36 . 7696) 11.0575 | 
1353) 1830609}2476813977|36.7831|11.0603 | 
1854] 1833316/2482309864| 36.7967) 11.0680 


1355| 1836025)2487'813875) 36.8103) 11.0657 

1356] 1838736]2493326016|36 8239) 11.0684 
1357| 1841449/2498846293136 .8375/11.0712 
1358) 1844164]2504374712)/36.8511/11.0739 } 
1359] 1846881)2509911279)36.8646/11.0766 } 


1360] 1849600]2515456000) 36.8782: 11.0793 k 
1361] 1852321/2521008881|36.8917)11.0820 § 
1362! 1855044]2526569928) 36.9053) 11.0847 § 
1363) 1857769]/2532139147|36 .9188)11.0875 § 
1364| 1860496|]2537716544/36.9324'11.0902 § 


1876900) 2571353000) 37 0135] 11.1064 
1879641] 2576987811 |37.0270}11.1091 
1882384 | 25826308 418}37 .0405]11.1118 
1885129} 258828211737 .0540}11.1145 
1887876} 2593941624/37 .0675/11.1172 


1890625 | 2599609375 }37.0810|11.1199 
1893376) 260528537637 0945 11.1226 
1896129/2610969633/37 . 1080/11 . 1253 
1898884) 2616662152/87.1214/11.1280 
1901641) 2622362939/37.1349}11.1307 


1904400) 262807200037 .1484)11. 1334 
1907161) 2633789341 |37.1618)11.1361 
1909924/ 2639514968 )/37.1753/11.1387 
1912689] 2645248887 |37.1887)11.1414 
1915456) 2650991104/37 .2021]11.1441 


1918225) 2656741625 |87 .2156) 11.1468 
1920996} 2662500456 |37 .2290)11.1495 
1923769) 2668267603 |37 .2424)11. 1522 
1926544] 2674043072 |87 .2559|11.1548 
1929321) 2679826869 37 .2693/11.1575 


1932100) 2685619000|37 .2827')11.1602 
1934881) 2691419471 [37 .2961)11.1629 
1937664) 2697228288 |37 . 3095/11. 1655 
1940449) 2703045457 |37 .3229| 11.1682 
1943236/ 2708870984 |37 .3363/11.1709 


1946025/2714704875|37 .38497/11.1736 
1948816] 2720547136)37.38631)11.1762 
1951609) 2726397773 |37 .3765|11.1789 
1954404 | 2732256792 |37 3898) 11.1816 
1957201) 2738124199 |37.4032)11.1842 


1960000) 2744000000)37 4166) 11.1869 
1962801) 2749884201 )37.4299/ 11.1896 
1965604) 2755776808 87 .4433)11.1927 
1968409/276 1677827 37.4566) 11.1949 
1971216/2767587264 [37 .4700)11.1975 


1974025]27735051 25/37 .4833/11 . 2002 
1976836|2779431416/37 .4967|11.2028 
1979649) 2785366143/37 .5100)11.2055 
1982464/2791309312/37 .5233)/11.2082 
1985281 | 279726092937 .5366| 11.2108 


1988100) 2803221 000)37 .5500)11.2135 
1990921) 2809189531 |387 .5633 11.2161 
1993744|2815166528]37 .5766]11.2188 
1996569) 2821151997/37 .5899)}11 .2214 
1999396] 282714594437 .6032)11.2240 


9002225 2833148375137 .6165]11. 2267 
2005056] 2839159296/37 .6298/11 2293 
2007889] 2845178713/37 .6431)11 2320 
2010724) 2851206632137 .6563'11.2346 
2013561!2857243059/37 .6696'11 . 2373 









































100 


MATHEMATICAL TABLES. 





No.|Square, 





Cube. 





2016400}2863288000 
2019241 |2869341461 
2022084 |2875403448 
2024929 |2881473967 
2027776 | 2887553024 


2030625 |2893640625 
2033476 }2899736776 
2036329|2905841483 
2039184 12911954752 
2042041 12918076589 


2044900}2924207000 
2047761}2930345991 
2050624 |2936493568 
2053489 2942649737 
2056356 }2948814504 


2059225 
2062096|2961 169856 
2064969) 2967360453 
2067844 | 2973559672 


2070721 |2979767519 


2073600 |2985984000 
2076481 12992209121 
2079364 |2998442888 
2082249 }3004685307 
2085136 |80109363884 


2088025}38017196125 
2090916) 8028464536 





2093809} 3029741623 


2096704| 3036027392 
2099601 | 3042321849 


2102500/8048625000 
2105401 | 3054936851 
2108304|306] 257408 
2111209/3067586677 
2114116/30738924664 


2117025| 3080271375 
21199386|3086626816 
2122849)3092990993 
2125764/30993639 12 
2128681 |3105745579 


2131600/3112136000 
2134521/3118535181 
2187444/ 3124943128 
2140369) 3131359847 
2143296) 31387785344 


2146225|3144219625 
2149156/3150662696 
2152089} 3157114563 
2155024 /3163575232 
2157961 | 3170044709 


2160900) 3176523000 
2163841 |3183010111 
2166784/3189506048 





87.9737 
(37.9868, 


Sq. 
Root. 





27 6829/11. 
'37.6962|11. 
37.7094/11. 
87.7227|11. 
37.7359/11. 


37.7492)11. 
37.7624}11, 
87 775711, 
87.7889] 11. 
87 .8021)11. 


37.8153/11. 
37 8286/11. 
37.8418)11. 
87.8550}11. 
37, 8682/11. 


37.8946/11. 
'37.9078/11. 
'37.9210|11. 
'37.9342/11. 


87 .9473}11. 
87.9605}11. 
11 
11 
88.0000,11 


98.0132/11 
38.0263) 11 
38 .0395|11 
38.0526) 11 
38.0657) 11. 


38.0789) 11 
88.0920) 11. 
38.1051) 11. 
38.1182) 11 
38.1814)11 


38.1445/11. 
38.1576) 11 
38.1707|11 
38. 1838/11. 
88.1969) 11 


38.2099) 11 
88 .2230/11 
38 .2361)11, 
88. 2492/11 
38 .2623/11. 


88.2753 11 
38.2884/11. 
88.3014/11. 
38.3145) 11 
88.3275|11 


38.3406) 11 
38.3536] 11 








38.3667/11. 


Cube 
Root. 





2399 
2425 
2452 
2478 
2505 


2531 
2557 
2583 
2610 
2636 


2662 
2689 
2715 
2741 
2767 


2954987875 87.8814) 11.2793 


2820 
2846 
2872 
2898 


2924 
2950 


Pas 
. 3003 
. 3029 


8055 
8081 
8107 
8133 


3159 


38185 


211 
3237 


8263 
8289 


3315 


8341 
.8367 


3393 


38419 


8445 
.B471 


3496 


.B022 


3548 


8574 


3600 
3626 


. 8652 
3677 


8703 
8729 


8755 


2169729 
2172676 








3196010817/38 3797 
3202521424138.8927| 


11.8780 
11.8806 





.|Square, 





Cube. 


Sa. 
Root. 





Cube 
Root. 





2175625 |3209046875|38. 4057/11. 3832 


2178576 |3215578176 38 .4187)11. 
88.4318) 11. 
38 .4448)11. 
38.4578}11. 


88.4708) 11. 
88.4838} 11. 
38.4968/11. 
88.5097} 11. 
88.5227/11. 


38 5357/11. 
38.5487 /11. 
88.5616/11. 
38.5746/11. 
88.5876} 11. 


38.6005}11. 
38.6135)11. 
38 .6264}11. 
38.6394}11. 
38. 6523/11. 


38.6652|11. 
11. 
11. 


2181529|32221 18333 
2184484 |3228667352 
2187441 138235225289 


2190400|8241792000 
2193361 |8248367641 
2196324 13254952168 
2199289 |3261545587 
2202256/38268147904 


2205225 18274759125 
2208196|3281379256 
2211169}3288008303 
2214144}3294646272 
2217121 |8301293169 


2220100}3307949000 

223081 |8314613771 
2226064 18321287488 
2229049 /3327970157 
2238203612334661784 


2235025 | 3341862375 
2238016/3348071936 
2241009/3354790473 
2244004) 3361517992 
2247001)3368254499 


3375000000 
3381754501 
8388518008 
3895290527 
3402072064 


3408862625 
3415662216 
3422470843 
3429288512 
3436115229 


3442951000 
3449795831 
3456649728 
3463512697 
3470384744 


3477265875 
3484156096 
8491055413 
3497963832 
8504881359 


3511808000 
85187438761 
3525688648 
8532642667 
8539605824 


3546578125 
2328676 | 855355907 

2331729) 38560550183 
2334784) 3567549952 
2837841' 3574558889 





2250000 
2253001 
2256004 
2259009 
2262016 


2265025 
2268036 
2271049 
2274064 

277081 


2280100 
2283121 
2286144 

289169 
2292196 


2295225 
2298256 
2301289 
2304324 
2307361 


2310400 
2313441 
2316484 
2319529 
2822576 


2825625 














88.6782 
38.6911 
38.7040 
38.7169 


38.7298 
88.7427 
38.7556 
88.7685 
38.7814 


38.7943 
38.8072 
38.8201 
38.8330 
38.8458 


38.8587 
38.8716 
388 8844 
38.8973 
88.9102 


38.9230 
388.9358 





38 .9487|11. 
38.9615\11. 
38.9744/11. 


38. 9872/11. 
89 .0000)11. 
39 .0128/11. 
89. 0256/11. 
39 .0384/11. 


39.0512)11. 
39.0640}11. 
39.0768}11 . 
39 .0896|11 . 
89.1024 11. 


SQUARES, CUBES, SQUARE AND CUBE ROOTS. 


No. |Square. 


NS ee ee a 


2340900 
2343961 
2347024 
2350089 
2353156 


2356225 
3} 2359296 
2362369 
2365444 
2368521 


2371600 
2374681 
2377764 
23805849 
23838936 


2387025 
2390116 
2393209 
2396304 
2399401 


2402500 
2405601 
2408704 
2411809 
2414916 


2418025 
3) 2421136 
2424249 
2427364 
2430451 


2433600 
2436721 
2439844 
2442969 
2446096 





SQUARES AND CUBES 





Cube. 


3581577000 
3588604291 
8595640768 
3602686437 
3609741304 


3616805375 
3623878656 
3630961153 
3638052872 
3645153819 


3652264000 
3659383421 
3666512088 
3673650007 
3680797184 


36879538625 
3695119336 
3702294323 
3709478592 
3716672149 


3723875000 
3731087151 
3738308608 
3745539377 
3752779464 


3760028875 
3767287616 


3774555693 | 


3781833112 
3789119879 


3796416000 
3803721481 
3811036328 
3818360547 
3825694144 


101 





39.1152 
189.1280 
39.1408 
39.1535 
39.1663 


39.1791 
39.1918 
39.2046 
89.2178 
|39.2301 


39.2428 
39.2556 
39. 2683 
39.2810 
\39.2938 


39.3065 
139.3192 
39.3319 
39.3446 
39.357 


39.3700) 
39.3827 
39.3954} 
39.4081 

39.4208 


39.4335 
39.4462 
39.4588 
39.4715 
39.4842 


39 4968) 
39. 5095| 
39.5221 11 
39.5348) 11 
39.5474 








| 


aie 
Bi 


ii 
Be 
de 
1 
ible 


i 
aby i 
1 
1 
stile 


ab he 
11.6 
6027 
6052 
11.6077 


Cube 


.|Square. 


2493241 


2496400. 
2499561) 
2502724 
2505889 
2509056, 


2512225) 
2515396 
2518569) 
2521744 
2524921 


2528100 
2531281 
2534464 | 
2537649 
2540836 


2544025 
2547216 
2550409 
2553604) 
2556801 





Cube. 


2449225 ' 38330371 25)/39.5601 
2452356 | 3840889496 |39.5727 
2455489 3847751 263/39 .5854 
2458624 3855123482139. 
2461761 3862503009/39. 


2464900 3869893000)39. 
2468041 3877292411 /39. 
2471 184/3884701248/39. 
2474329 3892119517)39. 
2477476 8899547224) 39. 


2480625 3906984375139. 
3] 2483776 3914430976]39. 
2486929 3921887033! 39. 
2490084 | 3929352552) 39. 
3936827539| 39. 


3944312000]39. 


3651805941 
3959309368 
3966822287 
3974344704 


8981876625 
3989418056 
3996969008 
4004529472 
4012099469 


4019679000 
4027268071 
4034866688 
4042474857 
4050092584 


4057719875 
4065356736 
4073003173 
4080659192 
4088324799 





2560000 


4096000000 


Sq. 
Root. 





11 
5980 
6106 


6232 
6358 
6485 
6611 
6737 


6863 
6989 
7115 
7240 
7366 


7492 
7618 
(744) 11 
39.7869] 11 
389.7995) 11 


39.8121|11 


11 
11 


39. 
39. 





39.8748, 
39.8873. 
39.8999! 
39,9124) 
39.9249 


39.9375, 
39.9500) 
39,9625 
39.9750) 
39.9875 








40.0000 


OF DECIMALS, 


abibs 
11. 


1h. 
1. 


Cube 
Root. 





6102 
6126 
-6151 
6176 
6200 


6225 
6250 
6274 


6299 
63824 


6348 
6873 
6398 
(6422 
6447 


6471 
.6496 
. 6520 
.6545 
6570 


6594 
39.8246 11. 
39.8372 11. 
39.8497 11. 
39.8623 11.6 


1}. 
TY, 
1a 
1d, 
11. 


1h. 
11. 
1 
ilite 
11.6 


py 





No.|Square. 


——— | | —__—______ S| | — | —_— 


.000 001 
.000 008 
.000 027 
.000 064 
.000 125 
.000 216 
.000 343 
.000 512 
.000 729 
.001 000 
.001 728 


SODVWATAR WOH 


1 


1.2} 1.44 


Cube. 


Square, 


Cube. 





‘00 O1 44 


.000 000 001 
-000 000 008 
.000 000 027 
.000 000 064 
.000 000 125 
.000 G00 216 
.000 000 343 
.000 000 512 
.000 000 729 
.000 001 000 
.000 001 728 


Note that the square has twice as many decimal places, and the cube three 
times as many decimal places, as the root. 


102 MATHEMATICAL TABLES. 


FIFTH ROOTS AND FIFTH POWERS, 
(Abridged from TRAUTWINE.) 























Sa Ss 5 63 os 
6 o| Power. [66] Power. [65| Power. [ 66} Power. | ¢6| Power. 
7, CG 7 cag 7,04 Aaa 
10 .0000104 3.7 693.440} 9.8} 90392 $21.8) 4923597 | 40 | 102400000 
15 000075 | 3.8 792.8521 9.9 95099 22.0) 5153632 41 | 115856201 
.20 .000320f 3.9 902.242910.0] 100000 922.2) 5392186 # 42 | 130691232 
$29 000977} 4.0} 1024.00 410.2) 110408 22.4} 56389493 43 | 1470084438 
.30 002430} 4.1 1158.56 $10.4) 121665 22.6} 5895793 44 | 164916224 
.3d .0052524 4.2} 1306.91 910.6} 13838238 22.8] 61613827 | 45 | 184528125 
.40 .010240] 4.3} 1470.08 [10.8] 1469383 23.0) 6436343 | 46 | 205962976 
.45 018453} 4.4] 1649.16 411.0) 161051 23.2 (21093 47 | 229345007 
.50 .031250] 4.5] 1845.28 411.2] 176234 $23.4) 7015834 | 48 | 254803968 
.05 .0503828) 4.6] 2059.63 $11.4) 192541 28.6} 73820825 49 | 282475249 
.60 077760 4.7] 2293.45 111.6} 210084 §238.8) 7636332 I 50 } 812500000 
.65 21160294 4.8] 2548.04 §11.8) 22877 24.0) 7962624 51 | 845025251 
. 40 168070} 4.9] 2824.75 $12.0] 248882 24.2) 8299976 52 | 380204082 
Sts .2373054 5.0] 8125.00 $12.2) 27027 24.4) 8645666 53 | 418195493 
.80 0206807 5.1] 3450.25 912.4) 293163 24.6) 9008978 54 | 459165024 
.85 -4437054 5.2) 8802.04 912.6) 317580 924.8) 93881200 55 | 5082843875 
.90 .590490] 5.3) 4181.95 [12.8] 3438597 §25.0 765625 56 | 550781776 
£95 7737819 5.4) 4591.65 $138.0) 371298 25.2) 10162550 § 57 | 601692057 
1.00 1.000004 5.5] 5082.84 7138.2) 400746 425.4) 1057227 58 | 656356768 
1.05 1.276287 5.6) 5507.52 918.4] 482040 425.6] 10995116 59 | 714924299 
1.10 1.610514 5.7] 6016.92 313 6] 465259 425.8) 114381377 60 | 777600000 
ry es) 2.011351 5.8] 6563.57 [13.8] 500490 26.0) 11881376 61 | 844596301 
1.20) 2.488321 5.9] 7149.24 $14.0) 587824 [26.2] 12845437 | 62 | 916132882 
1.25} 3.051762 6.0] 7776.00 $14.2) 577353 126.4) 12828886 ] 63 | 992436543 
1.30 8.71293F 6.1 8445.96 $14.4) 619174 $26.6) 18317055 64 |1078741824 
1.35 4.48403) 6.2} 9161.38 [14 6] 663383 § 26.8) 18825281 65 |1160290625 
1.40] - 5.878249 6.8] 9924.87 914.8] 710082 [27.0| 14848907 { 66 |1252332576 
1.45 6.409734 6.4] 10787 15.0) 759375 27.2) 14888280 67 11850125107 
1.50 7.593754 6.5 | 11603 15 2) 811868 27.4) 15448752 68 |1458933568 
den) 8.94661} 6.6] 12523 15.4) 866171 27.6) 16015681 69 11564081349 
1.60} 10.4858 § 6.7) 138501 15.6] 9238896 27.8) 16604430 7O {1680700000 
.1.65} 12.2298 | 6.8] 14539 15.8] 984658 $28.0) 17210368 71 11804229851 
1.70) 14.1986 § 6.9] 15640 16.0} 1048576 28.2) 17&383868 %2 119384917632 
Ol petGn 4 Leal 7.0] 16807 16.2] 1115771 28.4) 184753809 73 |2073071593 
1.80) 18.8957 # 7.1] 18042 16.4] 1186867 28.6) 19185075 74 12219006624 
1.85} 21.6700 # 7.2] 19349 16.6] 1260493 $28.8) 19813557 75 |23878046875 
1,90} 24.7610 § 7.3) 20731 16.8] 13838278 29.0) 20511149 76 |2535525376 
1.95) 28.1951 7.4] 22190 17.0} 1419857 29.2) 21228253 9% 12706784157 
2.00} 32.0°00 § 7.5 | 28730 17.2] 15053866 $29.4] 21965275 § 78 |2887174368 
2.05). 36.2051 7.6| 253855 17.4] 1594947 29 .6| 22722628 79 |8077056399 
2.10) 40.8410 # 7.7 | 27068 17.6] 1688742 $29.8] 28500728 | 80 |38276800000 
2.15) 45.9401 7.8 | 28872 17.8] 1786899 30.0) 24800000 81 |8486784401 
220) 51.5363 | 7.9] 30771 18.0) 1889568 430.5] 26398634 | 82 |3707398432 
2.25] 57.6650 | 8.0) 32768 18.2} 19969038 81.0} 28629151 83 |3939040643 
2.30} 64.3634 — 8.1] 384868 18.4] 2109061 81.5] 31018642 84 |4182119424 
2.35) 71.6703 | 8.2| 87074 18.6] 2226203 82.0} 83554432 85 14437058125 
2.40) 79.6262 § 8.38] 39390 18.8} 2348493 32.5} 86259082 86 14704270176 
2.45) 88.2735 § 8.4] 41821 19.0] 2476099 83.0} 39135393 87 14984209207 
2.50) 97.6562 § 8.5] 443871 19.2} 2609193 83.5} 42191410 | 88 |5277819168 
2.55] 107.820 8.6] 47048 19.4] 2747949 34.0} 45435424 89 15584059449 
2.60) 118.814 8.7] 49842 19.6] 2892547 §34.5) 48875980 | 90 |5904900000 
2.70] 148.489 8.8] 52773 19.8] 3043168 85.0) 52521875 91 16240321451 
2.80) 142.104 8.9] 55841 20.0} 8200000 85.5} 56382167 92 |165908152382 
2.90) 205.111 9.0| 59049 20.2] 3363232 86.0) 60466176 93 16956883693 
3.00} 243.000 9.1} 62403 20.4] 38558059 86.5) 64783487 94 |7339040224 
8.10} 286.292 9.2] 65908 20.6} 38709677 $37.0! 69343957 # 95 |77378093875 
3.20) 385.544 9.3 | 69569 20.8) 8898289 87.5) 74157715 96 |81538726976 
3.30} 391.354 9.4] 73390 21.0} 4084101 88.0) 79285168 97 18587340257 
8.40) 454.354 9.5) 77378 21.2] 4282322 88.5] 84587005 98 |9039207968 
3.50} 525.219 9.6] 81587 21.4] 4488166 739.0) 90224199 § 99 |950990U4y9 
. 8.60) 604.662 9.7] 85873 21.6} 4701850 §39.5] 96158012 | 





ees 


—_ 


CIRCUMFERENCES AND AREAS OF CIRCLES. 103 


CIRCUMFERENCES AND AREAS OF CIRCLES. 


Diam.|Circum. 





© Ok Or C9 0D et 


10 





3.1416 

6.2832 

9.4248 
12.5664 
15.7080 
18.850 
21.991 
25.133 
28.274 
31.416 
34.558 
37.699 
40.841 
43.982 
47.124 
50.265 
53.407 
56.549 
59.690 
62.832 


Area. 


0.7854 
8.1416 
7.0686 
12.5664 
19,635 
28 274 
388 .485 
50.266 
63.617 
78.540 
95.033 
113.10 
132.73 
153.94 
176.71 
201.06 
226.98 
254.47 
283.53 
814.16 
346.36 
880.18 
415.48 
452.39 
490.87 


Diam.|Circum. 





Area. 


3318.31 


3421.19 
8525.65 
3631.68 
3739.28 
3848, 45 
3959.19 
4071.50 
4185.39 
4300 .84 
4417.86 
4536.46 
4656.63 
4778.36 
4901.67 
5026.55 
5153.00 
5281.02 
5410.61 
5541.77 
5674 50 
5808.80 
5944.68 
6082.12 
6221.14 
6361.73 
6503.88 
6647.61 
6792.91 
6939.78 
7088.22 
7238 . 23 
7389.51 
7542.96 
7697 .69 
7853.98 
8011.85 
8171.28 
8332.29 
8494.87 
8659.01 
8824.73 
8992.02 
9160.88 
9331.82 
9503 .32 
9676.89 
9852.03 
10028.75 
10207 .03 
10386 89 
10568. 32 
10751 .32 
10935.88 
11122.02 
11309.73 
11499.01 
11689.87 
11882 .29 
12076 .28 
12271.85 
12468 .98 
12667.69 
12867 .96 





Diam.)Circum. 





129 | 405.27 
130 | 408.41 
131 | 411 55 
132 | 414.69 
133 | 417.83 
134 | 420.97 
135 | 424.12 
136 | 427.26 
137 | 430.40 
138 | 433.54 
139 | 436.68 
140 | 439.82 
141 | 442.96 
142 | 446.11 
143 | 449.25 
144 | 452.39 
145 | 455.53 
146 | 458.67 
147 | 461.81 
148 | 464.96 
149 | 468.10 
150 | 471.24 
151 | 474.38 
152 | 477.52 
153 | 480.66 
154 | 483.81 
155 | 486.95 
156 | 490.09 
157 | 493.23 
158 | 496.37 
159 | 499.51 
160 | 502.65 
161 | 505.80 
162 | 508.94 
163 | 512.08 
164 | 515.22 
165 | 518.36 
166 | 521.50 
167 | 524.65 
168 | 527.79 
169 | 530.93 
170 | 534.07 
171 | 537.21 
172 | 540.35 
73 | 543.50 
74 | 546.64 
175 | 549.78 
176 | 552.92 
177 | 556.06 
178 | 559.20 
79 | 562.35 
180 | 565.49 
181 | 568.63 
182 | 571.77 
183 | 574.91 
184 | 578.05 
185 | 581.19 
186 | 584.34 
187 | 587.48 
188 | 590.62 
189 | 593.76 
190 | 596.90 
191 | 600.04 
192 | 603.19 








Area, 





13069.81 
138273 .23 
13478 .22 
13684 78 
13892 .91 
14102.61 
14313.88 
14526. 7 
14741.14 
14957 .12 
15174.68 
15393 .80 
15614.50 
15836 .77 
16060. 61 
16286. 02 
16513.00 
16741 .55 
16971 .67 
17203. 

17436 . 62 
17671 .46 
17907 .86 
18145.84 
18385. 39 
18626 .50 
18869.19 
19113.45 
49359 . 28 
19606.68 
19855 .65 
20106.19 
20358 .31 
20611.99 
20867 . 24 
21124.07 
21382.46 
21642.43 
21903 97 
22167 08 
22431.7 

22698 . 01 
22965 .83 
23235 .22 
23506 .18 
23778 .7 

24052. 82 
24328 .49 
24605 .74 
24884 .56 
25164.94 
25446 90 
25730.43 
26015 .53 
26302. 20 
26590.44 
26880 .25 
27171.63 
27464.59 
27759 11 
28055 .21 
28352 87 
28652 .11 
28952 .92 


(SS a Te EY 


104 


MATHEMATICAL TABLES. 





Diam.|Circum. 





193 | 606.33 
194 | 609.47 
195 | 612.61 
196 | 615.75 
197 | 618.89 


Area, 


29255. 30 


29559 ..25 
29864 .77 
80171 .86 
80480 .52 
30790. 75 
81102.55 
31415.93 
81730.87 
82047 .39 
32865.47 
82685.13 
88006. 36 
88329 .16 
83653 .53 
83979 .47 
34306.98 
84636 .06 
84966. 71 
85298 . 94 
85632.73 


389057 .07 
89408. 14 
39760.78 
40115.00 
40470.78 
40828 .14 
41187 .07 
41547 .56 
41909 .63 
42273 27 
42638 .48 
43005 .26 
43373 .61 
43743 .54 
44115.03 
44488 .09 
44862 .73 
45238 .93 
45616.71 
45996 .06 
46376 .98 
46759 .47 
47143 .52 
47529 .16 
47916.36 
48305 .138 
48695 .47 
49087 .39 
49480 .87 
49875 .92 
50272 .55 
50670.75 
51070.52 
51471 .85 
51874.76 
52279, 24 
52685 .29 


Diam, 


260 
261 
262 
263 
264 
265 
266 
267 
268 
269 

270 








Cireum, 


Area. 


53092 .92 


53502.11 
58912.87 
54325 .21 
54739 .11 
55154 .59 
55571 .63 
55990. 25 
56410.44 
56882 .20 
57255 .58 
57680 .43 
58106. 90 
58584 .94 
58964.55 
59595 . 74 
59828 .49 
60262. 82 
60698. 71 
61136.18 
61575 .22 
62015 .82 
62458 .00 
62901 .7 

63347 .07 
63793 .97 
64242.43 
64692.46 
65144 .07 
65597 .24 
66051 .99 
66508 . 30 
669€6 .19 
67425 .65 
67886 .68 
68349 . 28 
68813 .45 
69279.19 
69746 .50 
70215 . 38 
70685 . 83 
71157 .86 
71631 .45 
72106 .62 
725838 .36 
78061 .66 
73541 .54 
74022 .99 
74506 .01 
74990 . 60 
75476. 76 
75964 .50 
76453. 80 
76944. 67 
77437 12 
77931 .18 
78426 .72 
78923 .88 
79422 .60 
79922 .90 
80424 .7% 
80928 .21 
81433 22 
81939 .80 
82447 .96 
82957 68 
83468 .98 


Diam.!Circum. 





327 
828 





1027.80 
1030.44 
1033 .58 
1036.73 
1039.87 
1043.01 
1046.15 
1049.29 
1052.43 
1055.58 
1058.72 
1061.86 
1065 .00 
1068.14 
1071.28 
1074.42 
1077.57 
1080.71 
1083.85 
1086.99 
1090.13 
1093.27 
1096.42 
1099.56 
1102.70 
1105.84 
1108.98 
1112.12 
1115.27 
1118.41 
1121.55 
1124.69 
1127.88 
1130.97 
1134.11 
1137.26 
1140.40 
1143.54 
1146.68 
1149.82 
1152.96 
1156.11 
1159.25 
1162.39 
1165.53 
1168.67 
1171.81 
1174.96 
1178.10 
1181.24 


1184.38) 
t 1187.52} 


1190.66 
1193.81 
1196.95 
1200.09 
1203.23 


1206.37} 


1209.51 
1212.65 
1215.80 
1218.94 
1222.08 
1225.22 
1228 .36 
1231.50 
1234.65 


83981 .84 


Area. 


= 


84496.28 
85012.28 
85529. 86 
86049.01 
86569.73 
87092 .02 
87615.88 
88141.31 
88668. 31 
89196. 88 
89727 .03 
90258 .74 
90792 .03 
91326.88 
91863.31 
92401.81 
92940.88 
93482 .02 
94024 .73 
94569.01 
95114.86 
95662 .28 
96211.28 
96761.84 
97313.97 
7867.68 
98422. 96 
98979 .80 
99538.22 
100098 .21 
100659.77 
101222. 90 
101787. 60 
102353.87 
102921 .72 
103491 .13 
104062.12 . 
104634 .67 
105208 . 80 
105784.49 
106361 .76 
106940. 60 
107521 .01 
108102 .99 
108686 .54 
109271 .66 
109858 . 35 
110446. 62 
111036.45 
111627 .86 
112220 .838 
11281588 
113411.49 
114009 .18 
114608 .44 
115209 27 
115811 .67 
116415.64 
117021 .18 
117628 .30 
118236 .98 
118847 .24 
119459 .06 
120072 .46 
120687 42 
121803 .96 





Te si 


CIRCUMFERENCES AND AREAS OF CIRCLES. 1085 





Diam.|Circum. 





1237.79 
1240.93 
1244.07 
1247.21 
1250.35 
1253.50 
1256.64 
1259.78 
1262.92 
1266.06 
1269.20 
1272.35 
1275.49 
1278.63 
1281.77 
1284.91 
1288.05 
1291.19 

204.34 
1297.48 
1300.62 
1303.76 
1306.90 
1310.04 
1313.19 





Area, 


121922. 


122541. 
1231638. 
123785. 
124410. 
125036. 
125663. 
126292. 
126923. 
127555. 
128189. 
128824. 
129461. 


130100. 4: 
130740.: 


131382. 
132025. 


132670.°* 


133316. 
133964. 
134614. 


135265 .2 


135917. 
136572. 
137227. 


137885.2 


138544, 


139204 .76 


139866. 
140530. 
141195. 
141862 

142530. 
143200. 


143872.: 


144545. 
145220. 
145896. 
146574. 
147253. 
147934. 


148616.$ 


149301. 
149986. 
150673. 
151362. 
152053. 
152745. 
153438 

154133: 
154830. 
155528. 
156228. 
156929. 
157632. 
158337 

159043. 
159750. 
160459. 
161170. 
161883. 
162597. 
163312. 
164029. 
164748. 
165468. 
166190. 


Ov 
75 
00 
§2 
21 


Ont OQH 
Ge Ores GQ 


02 
53 
60 
25 
47 
26 
62 
55 
06 
13 
77 
99 
V7 
13 
05 
55 
62 
26 
47 
25 


Diam.|Cireum. 








1448 .27 
1451.42 
1454.56 
1457.70 
1460.84 
1463.98 
1467.12 
1470.27 
1473.41 
1476.55 
1479.69 
1482.83 
1485.97 
1489.11 
1492.26 
1495.40 
1498.54 
1501.68 
1504.82 
1507.96 
1511.11 
1514.2 

1517.39 


1520.53 


1523.67 
1526.81 


1529.96 


1533.10 
1536.24 
1539.38 
1542.52 
1545.66 
1548.81 
1551.95 
1555 09 
1558.23 
1561.37 
1564.51 


1639.91 
1643.05 
1646.19 
1649.34 
1652.48 





Area. 


166913.60 


167638 53 
168365. 02 
169093 .08 
169822 .72 
170553 .92 
171286.7 

172021 .05 
172756. 97 
173494..45 
17423351 
174974.14 
175716 .35 
176460 12 
177205. 46 
177952 .37 
178700.86 
179450.91 
180202 .54 
180955 .74 
181710.50 
182466. 84 
183224 .75 
183984 .23 
184745 .2 

185507 90 
186272.10 
187037 . 86 
187805 .19 
188574.10 
189344 .57 
190116.62 
190890. 24 
191665 .43 
192442.18 
193220.51 
194000 .41 
194781.89 
195564 .93 
196349 54 
197135.7 

197923 .48 
198712.80 
199503 .7 

200296 .17 
201090.20 
201885.81 
202682 .99 
203481. 74 
204282 .06 
205083 .95 
205887 .42 
206692 .45 
207499 .05 
208307 .23 
209116 .97 
209925 .29 
210741.18 
211555.63 
212371.66 
213189. 26 
214008.43 
214829 17 
215651 .49 
216475 .37 
217300 .82 


1655. 62! 218127.85 


Diam.|Cireum. 








1658.76 
1661.90 
1665.04 
1668.19 
1671.33 
1674.47 
1677.61 
1630.75 
1683.89 
1687.04 
1690.18 
1693.32 
1696.46 
1699.60 
1702.74 
1705.88 
1709.08 
HW or 
1715.31 
1718.45 
1721.59 
1724.7 
1727.88 

2 








Area. 


218956. 44 


219786 .61 
220618. 34 
22145165 
222286. 53 
22312298 
223961 00 
224800.59 
225641 .75 
226484 48 
227328 ..7 

228174 66 
22902210 
229871. 12 
230721.71 
231573 .86 
23212759 
233282 89 
234139.76 
234998 20 
235858.21 
236719 .'79 
237582. 94 


2} 238447. 67 
3} 239313.96 


240181.83 
241051 .26 
241922 27 
242794.85 
243668 .99 
244514.71 
245422 00 
246300. 86 
247181.30 
248063 .30 
248946 .87 


3} 24983201 


250718 73 
251607.01 
252496. 87 
253388 . 30 
254281 .29 
25517586 
256072 .00 
256969.71 
257868. 99 
258769 . 85 
259672 27 


5} 260576 . 26 


261481 .83 
262388 . 96 
2638297 .67 


2} 264207. 94 


265119.79 
266033 .21 
266948 20 
267864 .76 ° 
26878289 


‘| 269702.59 


270623 .86 
271546.70 
272471 12 
273397 .10 
274324 66 


| 275253 .78 


276184.48 
277116.75 


106 


MATHEMATICAL TABLES. 





Diam. 
595 
596 
597 
598 
599 
600 
601 
602 
603 
604 
605 
606 
607 
608 
609 
610 
611 
612 
613 
614 
615 
616 
617 
618 
619 
620 
621 
622 
623 
624 
625 
626 
627 
628 
629 
630 
631 
632 
633 
634 
635 
636 
637 
638 
639 
640 
641 
642 
643 
644 
645 
646 
647 














Cirecum. 


1869.25 
1872.39 
1875.53 
1878. 6% 
1881.81 
1884.96 
1888 . 10 
1891.24 
1894.38 
1897.52 
1900.66 
1903.81 
1906.95 
1910.09 
1913.23 
1916.37 
1919 51 
1922.65 
1925.80 
1928.94 
1932.08 
1935.22 
1938.36 
1941.50 
1944.65 
1947.79 
1950.93 
1954.07 
1957.21 
1960.35 
1963.50 
1966.64 
1969.78 
1972.92 
1976.06 
1979.20 
1982.35 
1985 .49 
1988.63 


1991.77] & 


1994.91 
1998.05 
2001.19 
2004.34 
2007.48 
2010.62 
2013.76 
2016.90 
2020.04 
2023.19 
2026.33 
2029.47 
2032.61 
2035.75 
2038.89 
2042.04 
2045.18 
2048.32 
2051.46 
2054.60) 
2057.74 
2060.88 
2064.03 
2067.17 
2070.31 
2073.45 
2076.59 
2079.73 





Area, 


278050 .58 


278985 .99 
279922 .97 
280861 .52 
281801 65 
282743 .34 
283686 .60 
284631 .44 
285577 . 84 
286525 .82 
28747536 
288426 .48 
289379 .17 
290383 .43 
291289 . 26 
292246. 66 
293205 .63 
294166.1% 
295128 .28 
296091 .97 
297057 .22 
298024 .05 
298992 .44 
299962.41 
300933 .95 
301907 .05 
302881 . 7: 
3803257 .98 
304835. 80 
3805815 .20 
306796 .16 
307778 . 69 
308762.7 

309748 .47 
310735.71 
Sllietene 
312714.92 
3813706.88 


823712.85 
324722 .09 
825732. 89 
3826745. 27 
827759 .22 
828774. 74 
329791 .83 
830810.49 
331830. 72 
332852.5 

333875 .90 
334900. 85 
335927 . 36 
336955 .45 
337985 .10 
339016 .33 
840049 .13 
341083 ..50 
342119.44 
843156 .95 
344196 .03 


Diam’ 
663 


664 
665 
666 
667 
668 
669 
670 
671 











Cireum. 


2082.88 
2080.02 
2089 .16 
2092.30 
2095.44 
2098 .58 
2101.73 
2104.87 
2108.01 
2111.15 
2114.29 











Area. Diam: 
345236.694 731 
346278.91f1 732 
347322.70 733 
348368.07 ff 734 
349415.008 735 
350463.514 736 
351513.598 737 
352565.24— 738 
353618.45— 739 
354673 24 740 
355729.60f 741 
356787.54 8 742 
357847.04 743 
358908.119 744 
359970.75 8 745 
361034.978 746 
362100.75—| 747 
363168.11f, 748 
364237.04 8 749 

‘| 365307.5498 750 
366379.60f1 751 
367453.24 91 52 
B68528.458 753 
369605.23 8 754 
370683.599  T55 
371763.519 456 
372845.008 57 
373928.079 758 
375012.70f 759 
376098.91 8 760 
377186. 688 761 
378276 .03 8 762 

79366.959 763 
380459.449 764 
381553.50f1 765 
382649.13% 766 
383746.338 767 
384845.10$ 768 
385945.448 769 
387047.268 770 
388150.848 771 
889255.908 772 
390362.524 773 
391470.728  V74 
392580.498 “75 
393691 .828 776 
394804.738 777 
395919.218 578 
397035 26H 779 
398152.898 780 
399272.08f 7x1 
400392.84—8 782 
401515.188 783 
402639.0898 784 
403764.568 4785 
404891.608 786 
406020.228 787 
407150.419 88 
408282.179 789 
409415.50f 790 
410550.40f 791 
411686.879 92 
412824.91f 793 
413964.528 794 
415105.71 1 795 
416248.469 796 
417392.799 797 
418538.68 798 








Circum. 


2296 50 


2299.65 
230204 
2305 93 
2309.04 
Rolo 
2315.85 
2318.50 
2321.64 
2324.7 
2327 92 
2231.06 
2aade20) 
2337.34 
2340.49 
2343.63 
£346.77 
2349.91 
2353.05 
2356.19 
ROOT OA 
2362.48 
2365.62 
2368.76 
2371.90 
2375.04 








Area. 


419686 .15 


420835 .19 
421985.79 
423137 .97 
42429] .72 
42544704 
426603 .94 
427762.40 
428922 .43 
430084 .08 
431247 .21 
4382411.95 
433578. 27. 
434746.16 
435915. 62 
437086 . 64 
438259 .24 
439433. 41 
440609 16 
441786 .47 
442965 .35 
444145.80 
445827 83 
446511 .42 
447696.59 
448883 32 
450071 .63 
451261.51 


"| 452452.96 


45364598 
454840.57 
456036 . 7 
457234 .46 
458483 .77 
459634. 64 
460837 .08 
462041.10 
463246 .69 


471729.7 

472947 .92 
474167.65 
475358 . 94 
476611 .81 
477836 .24 
47 9062.25 
480289 .83 


‘| 481518 .97 


482749. 69 
483981 .98 
485215 .84 
486451 .28 
487688 . 28 
488926 .85 
490166.99 
491408.71 
492651 .99 
493896 . 85 
495143 .28 
496391 .27 
497640 .84 
498891 .98 
500144 .69 







































CIRCUMFERENCES AND AREAS OF CIRCLES. 107 
Diam.|Circum.|; Area. Diam. Circum.| Area. Diam.|Circum.| Area. 
799 | 2510.13) 501898.97 | 867 | 2723.76) 590375.168 935 | 2937.39, 686614. 71 
800 | 2518.27) 502654.82 | 868 | 2726.90) 591787.83§ 936 | 2940.53, 688084.19 
801 | 2516.42) 508912.25} 869 | 2730.04) 593102 06% 937 | 2943.67) 689555 .24 
802 | 2519.56] 505171.24 | 870 | 2733.19) 595167.87 9 938 | 2946 81) 691027.86 
803 | 2522.70} 506431.80 |) 871 | 2736.33) 595885.25f 939 | 2949.96) 692502.05 
804 | 2525.84] 507693.94] 872 | 2739.47) 597204.209 940 | 2953.10) 693977 .82 
805 | 2528.98) 508957.64} 873 | 2742.61) 598574.72 8 941 | 2956.24) 695455.15 
806 | 2532.12) 510222.92} 874 | 2745.75) 599946.81 ff 942 | 2959.38) 696934.06 
807 | 2535.27) 511489. 77 75 | 2748.89) 601320 479 943 | 2962.52) 698414.53 
808 | 2538.41] 512758.19 76 | 2752.04] 602695.70f 944 | 2965.66) 699896.58 
809 | 2541.55) 514028.18 (7 | 2755.18) 604072.50 945 | 2968.81} 701380.19 
810 | 2544.69) 515299.7 878 | 2758.32] 605450.88 fF 946 | 2971.95) 702865 .38 
811 | 2547.83) 516572.87 | 879 | 2761.46) 606820.82§ O47 | 2975.09) 704352. 14 
812 | 2550.97] 517847.57| 880 | 2764.60) 608212.34 948 | 2978.23) 705840. 47 
813 | 2554.11) 519123 84] 881 | 2767.74) 609595.429 949 | 2981.87) 707330 .37 
814 | 2557.26] 520401.68] 882 | 2770.88) 610980.08f 950 | 2984.51) 708821.84 
815 | 2560.40) 521681.10] 883 | 2774.03) 612366.31 951 | 2987.65} 710314.88 
816 | 2563.54] 522962.08} 884 | 2777.17) 613754.11§ 952 | 2990.80) 711809.50 
817 | 2566.68) 524244.63| 885 | 2780.31] 615143.48§ 953 | 2993.94) 713305.68 
818 | 2569.82} 525528.76 | 886 | 2783-45) 616534.42§ 954 | 2997.08) 714803.43 
819 | 2572.96] 526814.46 | 887 | 2786.59) 617926.939 955 | 3000.22) 716302.76 
820 | 2576.11) 528101.7 888 | 2789.73) 619321.01 956 | 3003.36) 717803.66 
821 | 2579.25) 529390.56} 889 | 2792.88) 620716 669 957 | 3006.50) 719306 12 
22 | 2582.39) 530680.97) 890 | 2796.02) 622118.898 958 | 38009 65) 720810.16 
823 } 2585.53) 531972.95 | 891 | 2799.16) 628512.68§ 959 | 8012.79) 722315.7 
824 | 2588.67) 533266.50) 892 | 2802.30) 624913.049 960 | 8015 93) 723822.95 
825 | 2591.81) 534561.62] 893 | 2805.44] 626314.98§ 961 | 8019.07) 725331.70 
826 | 2594.96) 535858.32} 894 | 2808.58) 627718.49§ 962 | 8022.21) 726842.02 
827 | 2598.10) 537156.58} 895 | 2811.73) 629123.568 963 | 8025.35) 728353.91 
828 | 2601.24) 538456 41} 896 | 2814.87) 630530.21§ 964 | 3028.50) 729867 .37 
829 | 2604.38) 539757.82 | 897 | 2818.01) 631938.439 965 | 8031.64) 731382.40 
830 | 2607.52) 541060.7 898 | 2821.15] 633348.228 966 | 8034.78) 732899.01 
831 | 2610.66) 542365.34] 899 | 2824.29) 634759.538 967 | 8037.92) 734417.18 
832 | 2613.81] 543671.46| 900 | 2827.43) 6386172.51 968 | 8041.06) 735936.93 
883 | 2616.95) 544979.15| 901 | 2880.58) 637587.01 969 | 3044.20) 737458.24 
834 | 2620.09) 546288.40] 902 | 2833.72) 639003.099 97 3047.34) 738981.13 
835 | 2623.23) 547599.23| 903 | 2836.86) 640420. 7: 971 | 8050.49) 740505.59 
836 | 2626.37) 548911.63] 904 | 2840.00) 641839.95 72 | 3053.63) 742031 .62 
8387 | 2629.51) 550225.61] 905 | 2843.14] 643260.73 § 73 | 8056.77) 74355922 
888 | 2632.65) 551541.15 | 996 | 2846.28) 644683.099 974 | 8059.91) 745088 .39 
839 | 2635.80) 552858.26| 907 | 2849.42) 646107.01 975 | 3063.05) 746619. 13 
$40 | 2635.94] 55417694} G08 | 2852.57) 647532.51f 976 | 3066.19) 748151 .44 
841 | 2642.08) 555497.20) 909 | 2855.71) 648959.589 977 | 3069.34! 749685.32 
842 | 2645.22) 556819.02 | 910 | 2858.85) 650388.226 978 | 8072.48) 751220.7§ 
843 | 2648 36) 558142.42} 911 | 2861.99) 651818.43g 979 | 8075.62) 752757.80 
844 | 2651.50) 559467.39] 912 | 2865.13) 653250.218 980 | 3078.76 754296 40 
845 | 2654.65] 560793.92] 913 | 2868.27) 654683.568 981 | 38081 90) 745836.56 
846 | 2657.79) 562122.03| 914 | 2871.42) 656118.489 - 982 | 3085.04) 757378.30 
847 | 2660.93) 563451.71] 915 | 2874.56) 657554.98 9 983 | 3088.19) 75k921.61 
848 | 2664.07) 564782.96 | 916 | 2877.70) 658993.049 984 | 3091.33) 760466 48 
849 | 2667.21) 566115.7 917 | 2880.84) 660432.688 985 | 3091.47) T6201z2.93 
850 | 2670.35) 567450.17] 918 | 2883.98] 661873 HBF 986 | 8097.61) 7135'0 95 
851 | 2673.50) 568786.14] 919 | 2887.12) 663316 669 987 | 3100.75! 765110 54 
852 | 2676.64) 570123.67 | 920 | 2890.27] 661761.019 988 | 3103.89 76661.7 
853 | 2679.78) 571462.77 | 921 | 2893.41] 666206.929 9°9 | 3107.04 THk214.44 
854 | 2682 92) 572803.45] 922 | 2896.55) 667654.41 ff 990 | 3110.18 769768. 74 
855 | 2686.06] 574145.69 | 923 | 2899.69} 669103.47@ 991 | 3113.32 771324 61 
856 | 2689.20] 575489.51 | 924 | 2902.83) 670554.108 992 | 3116.46) 772882 06 
857 | 2692.34) 576834.90} 925 | 2905.97) 672006.309 993 | 8119 60 174441.07 
858 | 2695.49) 578181.85 | 926 | 2909.11) 673460.089 994 | 3122.7 | ©6007. 66 
859 | 2698.63) 579530.38) 927 | 2912.26) 674915 429 995 | 3125.88) 777563. 82 
860 | 2701.77} 580880.48) 928 | 2915.40) 676872 339 996 | 3129.03! 77912754 
861 | 2704.91) 582232.15] 929 | 2918.54) 677s30.82R 997 3132.17) TSO0692.. 84 
862 | 2708.05) 583585.89} 980 | 2921.68) 679250.87 8 998 | 3135.31; 782259 71 
863 | 2711.19} 584940.20| 931 | 2924.82) 680752.509 999 | 3138.45) 783828.15 
864 | 2714.34] 586296.59] 932 | 2927.96} 682215.699 1000 | 3141.59) 78539816 
865 | 2717.48) 587654.54] 933 | 2931.11] 683680 .46 | 
866 | 2720 62] 589014.07| 934 | 2934.25] 68514680 











108 


MATHEMATICAL TABLES. 


CIRCUMFERENCES AND AREAS OF CIRCLES 
Advancing by Highths,. 





Diam. 


1/64 
1/32 
3/64 
1/16 
3/32 
% 
5/32 
3/16 
7/32 











Circum, 


04909 
.09818 
£14726 
. 19635 
29452 
89270 
.49087 
.58905 
68722 


. 78540 
88357 
.98175 
0799 
1781 
.2763 
8744 
726 


708 
. 6690 
1671 
8653 
. 9635 
0617 
1598 


ee eee ee 


WDD Hee 





Area. 





.00019 





Diam. 





2 34 
"7/16 


78, 
9/16 
56 
11/16 
34 
18/16 
% 
15/16 


3. 
1/16 


8 
3/16 
1 


Circum., 


9.2284 


9.4248 
9 6211 
9.8175 
10.014 








Area. 





aN 
AN 
w 
i) 
pa 


pert 
or 
aon 
ee 


WOOOMMOMDMMIGVIS OOO Pp 
S 
oO 
ie2) 
o 


Dian. 





Circum. 








CIRCUMFERENCES AND AREAS OF CIRCLES. 109 








Diam, | Circum.| Area. § Diam.| Cireum. | Area. # Diam.| Cirecum.| Area, 














1356 | 42.804 |145.80 [2174 | 68.722 [375.83 18014 | 94.640 | 712.76 
34 | 43.197 [148.49 | 22. 69.115 [380.13 14 | 95.033 | 718.69 
g 43.590 |151.20 1g | 69.508 |884.46 8% | 95.426 | 724.64 
14. 43.982 153.94 14 | 69.900 |388.82 i | 95.819 | 730.62 
1g | 44.375 |156.7 8 | 70.293 |393.20 64 | 96.211 | 736.62 
4% | 44.768 |159.48 ig | 70.686 [397.61 34 | 96.604 | 742.64 
86 | 45.160 162.30 5g | 71.079 |402.04 % | 96.997 | 748.69 
14 | 45.553 1165.13 & | 71.471 1406.49 931 97.389 | 754.77 
56 | 45.946 [167.99 % | 71.864 [410.97 14 | 97.782 | 760.87 
84 | 46.338 |170.87 [23. 72.257 1415.48 ig | 98.175 | 766.99 
Ye ( 46.731 |173.78 14 | 72.649 [420.00 && | 98.567 | 773.14 
15. 47.124 |176.71 14 | 73.042 1424.56 ig | 98.960 | 779.31 
1g | 47.517 |179.67 8% | 73.435 [429.13 D 99.358 | 785.51 
14 | 47.909 |182.65 6 | 73.827 [433.74 &% | 99.746 | 791.73 
8% | 48.302 |185.66 5 74.220 [438.36 % | 100.138 | 797.98 
ig | 48.695 |188.69 8 | 74.613 [443.01 932 100.581 | 804.25 
66 | 49.087 [191.7 % | 75.006 |447.69 100.924 | 810.54 
84 | 49.480 |194.83 924. 75.398 [452.39 14 | 101.316 | 816.86 
% | 49.873 {197.93 1g | 5.791 1457.11 8 | 101.709 | 823.21 
16. 50.265 |201.06 14 | 76.184 |461.86 1 | 102.102 | 829.58 


NG 
Or 
oo 
o 
w 
Ci) 
CX) 
NO) 
oO 
co 
or 
bo 
or 
I 
CO 
or 
oe 

yO 
rs 
co 
= 
(ee) 
~ 

NS 
—_ 
ce] 
pig 
oe 
or 
@ 
(e.2) 
ior) 
io 2) 
co 
—_ 


14 | 54.192 [233.71 14 | 80.111 [510.71 $4 | 106.029 | 894.62 





lg 54.978 |240.53 34 80.896 [520.77 fS4. 106.814 | 907.92 
6 55.371 |243.98 % 81.289 |525.84 1g | 107.207 | 914.61 
34 55.763 [247.45 926. 81.681 |530.93 44 | 107.600 | 921.82 
% 56.156 |250.95 ¥ 82.074 [536.05 3g | 107.992 | 928.06 
1s. 56.549 [254.47 4 82.467 |541.19 46 | 108.3885 | 934.82 











2 91.499 666.23 J 94 | 117.417 [1097.1 
21. | 65.973 [346/36 91.892 671.96 | ig | 117.810 |1104.5 
66.366 350.50 | 9% | 92.084 lerr.71 | 5g | 118.202 |1111.8 

: i, | 92.677 |683.49 | $4 | 118.596 [1119.2 

6, | 93.070 689.30 | % | 118.988 |1126.7 

44 | 67.544 [303105 | $4 | 93.462 (695.18 #38. | 119.381. [1134.1 

| [367 % | 93.855 (700.98 | 34 | 119.778 [1141.0 

34 | 68.330 !371.54 130. | 94.248 ros.86 § 14 | 190.166 {1149.1 


56.941 |258.02 86 | 82.860 1546.35 5g | 108.778 | 941.61 
14 | 57.334 1261.59 i4 | 83.252 [551.55 $4 | 109.170 | 948.42 
8 | BT.727 1265.18 56 | 88.645 556.7 % | 109.563 | 955.25 
14 | 58.119 1268.80 84 | 84.038 [562.00 [85 109.956 | 962.11 
66 | 58.512 [272.45 % | 84.430 [567.27 1g | 110.348 | 969.00 
34 | 58.905 [276.12 27. 84.823 [572.56 14 | 110.741 | 975.91 
% | 59.298 [279.81 1g | 85.216 |577.87 $4 | 111.134 | 982.84 
19 59.690 1283.53 14 | 85.608 |583.21 6 | 111.527 | 989.80 
14 | 60.083 1287.27 84 | 86.001 |588.57 56 | 111.919 | 996.78 
i 60.476 |291.04 ig | 86.394 |593.96 112.312 |1003.8 
$6 | 60.868 [294.88 6% | 86.786 [599.37 %4 | 112.705 [1010/8 
14 | 61.261 [298.65 84 | 87.179 [604.81 986. 113.097 1017.9 
6% | 61.654 [302.49 % | 87.572 |610.27 1g | 113.490 |1025.0 
34 | 62.046 |306.35 [28. 87.965 |615.75 14 | 113.883 |1032.1 
% | 62.439 [810.24 88.357 621.26 8% | 114.275 |1039.2 
20. 62.832 |314.16 14 | 88.750 |626.80 ¥4 | 114.668 |1046.3 
63.225 |B18.10 86 | 89.143 |632.36 6% | 115.061 [1053.5 
14 | 63.617 |322.06 46 | 89.535 |637.94 34 | 115.454 |1060.7 
86 | 64.010 [326.05 64 | 89.928 [643.55 % | 115.846 {1068.0 
14 | 64.403 |330.06 §{ | 90.321 |649.18 187; 116.239 |1075.2 
6 64.795 834.10 % | 90.713 |654.84 14 | 116.632 {1082.5 
84 | 65.188 |338.16 [29 91.106 |660.52 14 | 117.024 {1089.8 
% | 65.581 |342.25 1 
V4 





40. 


41. 


42 


45. 


cs 
f=} 
SeaNGR  ONMNGR 


a 


MATHEMATICAL TABLES. 





Circum. | Area, Diam.| Circum, | Area. [ diam. | Circum. 























120.559 | 1156.64465g | 146.477 | 1707.4 172.395 
120.951 | 1164.2] 34 | 146.869 | 1716.5 172.788 
121.344 | 1171.79 2% | 147.262 | 1725.7 178.180 
121.737 | 1179.39.47. 147.655 | 1734.9 173.573 
122.129 | 1186.99 14 | 148.048 | 1744.2 173.966 
122.522 | 1194.68 44 | 148.440 | 1753.5 174.358 
122.915 | 1202.38 3g | 148.933 | 1762.7 174 751 
123.308 | 1210.08 44 | 149.226 | 1772.1 175.144 
123.700 | 1217.7] 5g | 149.618 | 1781.4 175 536 
124.093 | 1225.4 84 | 150.011 | 1790.8 175.929 
124.486 | 1233.2 % | 150.404 | 1800.1 176.322 
124.878 | 1241.09 48. 150.796 | 1809.6 176.715 
125.271 | 1248.8) 44 | 151.189 | 1819.0 177 107 
125.664 | 1256.68 14 | 151.582 | 1828.55 177.500 
126.056 | 1264.59 86 | 151.975 | 1837.9] 177 893 
126.449 | 1272.4 14 | 152.367 | 1847.5] 178.285 
126.842 | 1280.3] 5% | 152.760 | 1857.0 178.678 
127.235 | 1288.2 84 | 153.153 | 1866.5 179.071 
127.627 | 1296.2] 7% | 158.545 | 1876.1 179.463 
128.020 | 1304.29 49. 153.988 | 1885.7 179.856 
128.413 | 1312.2] 14 | 154.331 | 1895.4 180.249 
128.805 | 1320.3) 14 | 154.723 | 1905 0 180.642 
129.198 | 1328.3] 8 | 155.116 | 1914.7 181.034 
129.591 | 1336.4f 4% | 155.509 | 1924.4 181.427 
129.983 | 1344.5 5 | 155.902 | 1984.2 181.820 
130.376 | 1352.7] 34 | 156.294 | 1943.9 182.212 
130.769 | 1360.8] % | 156 687 | 1953.7 182.605 
131.161 | 1269.09.50. 157.080 | 1963.5 182.998 
131.554 | 1377.29 14 | 157.472 | 1973.3 183.390 
131.947 | 1385 4 14 | 157.865 | 1983.2 183.783 
132.340 | 1393.79 8 | 158.258 | 1993.1} 184.176 
132.732 | 1402.0f 44 | 158.650 | 2003.0} 184.569 
133.125 | 1410.3 5g | 159.043 | 2012.9| 184.961 
133.518 | 1418.6 84 | 159.436 | 2022.89.59. 185.354 
133.910 | 1427.09 7 | 159.829 | 2032.8 185.747 
134.303 | 1435.49.51. 160.221 | 2042.8] 186.139 
134.696 | 1443-8 14 | 160.614 | 2052 81 186.532 
135.088 | 1452.29 14 | 161.007 | 2062.9 186. 925 
135.481 | 1460.7] 8% | 161.399 | 2073.08 18hB1F 
135.874 | 1469.19 46 | 161.792 | 208319 187.710 
136.267 | 1477.6) 5% | 162.185 | 2098 29 188.103 
136.659 | 1486.2f 84 | 162.577 | 2103.39.60. 188.496 
137.052 |1494.7f % | 162.970 | 2113.5 188.88 
137.445 | 1503.3)52- 163.363 | 2128.7 189.281 
137.837 | 1511.9] 14 | 163.756 | 2133.9] 189.674 
138.230 | 1520.5f 14 | 164.148 | 2144.2 190.066 
138.623 | 1529.20 3g | 164.541 | 2154.5 190.459 
139.015 | 1537.99 14 | 164.934 | 2164.8 190.852 
139.408 | 1546.6 5g | 165.326 | 2175.1 191.244 
139.801 | 1555.38 34 | 165.719 | 2185.49.61. 191 637 
140.194 | 1564.0] 2% | 166.112 | 2195.8] 192 030 
140.586 | 1572.89 53. 166.504 | 2206.25 192.423 
140.979 | 1581.69 1% | 166.897 | 2216.6 192.815 
141.372 | 1590.4f 14 | 167.290 |. 2227.0 193 208 
141.764 | 1599.3) 3g | 167:683 | 2237.5] 193.60] 
142.157 | 1608.2 46 | 168.075 | 2248.0} 193.993 
142.550 | 1617.08 5% | 168.468 | 2258.5 194.386 
142.942 | 1626.08 34 | 168.861 | 2269.1 194.77 
143.335 | 1634.99) % | 169.253 | 2279.6 195.171 
143.728 | 1643.99 54. 169.646 | 2290.2 195.564 
144.121 | 1652.9] 4% | 170.039 | 2300.8 195.957 
144.513 | 1661.9] 14 | 170.481 | 2311.5] 196 350 
144.906 | 1670.91 3% | 170.824 | 2322.1 196.742 
145.299 | 1680.0) 46 | 171.217 | 2332.8 197.135 
145.691 | 1689.1) 5g | 171.609 | 2343.5 197.528 
146.084 | 1698.20 84 | 172.002 | 9354.31 68: 197.920 











¢ 
WEAWONAGCHCKENIGMUUNIUIMNEBHCOCKHVISWNDWOMROROWHLOMNHIWROCOREN DOOR WWHOCOSCOUREWUAE 





CIRCUMFERENCES AND AREAS OF CIRCLES. 





Diam. 


Circum. | Area. 


Cireum. 


Circum. 


111 


| FC |) sd —————_ ) —o———————————_. | ————_ |] 


Gt. 


66. 


67. 


48. 


69. 


198.313 
198.706 
199.098 
199.491 
199.884 
200.277 
200.669 
201.062 
201.455 
201.847 
202.240 
202.633 
203 .025 
203.418 
203.811 
204.204 
204.596 
204.989 
205.382 
205.774 
206.167 
206.560 
206.952 
207.345 
207.738 
208.131 


3129.6 
3142.0 
3154.5 
3166.9 
8179.4 
3191.9 
3204.4 
8217.0 
3229.6 
3242.2 
8254.8 
3267.5 
8280.1 
8292.8 
3305.6 
3318.3 
33314 
3343.9 
3356.7 
3369.6 
8382.4 
3395.3 
3408.2 
3421.2 
3134.2 
8447.2 
3460.2 
3473.2 
3486.3 
8499.4 
3512).5 
302D F 
8538.8 
8552.0 
3565. 
3D7 
8591. 
8605. 
3618. 
3631. 
3645. 
3658. 
8671. 
3685. 
3698. 
3712. 
3725. 
3739. 
STD. 
3766. 
2780. 
3793. 
3807. 
3821. 
3834. 
8°48. 
3862. 
8876. 
3889. 
3903. 
3917. 
3931. 
3945. 
3959. 
3973. 
3987, 


HH WWREADONWMNVIOWNVOKRMwWRWwUWHRONMOREYW 


76. 


77. 


78. 








224.281 
224.624 
225.017 
225.409 
225.802 
226.195 
226.587 
226.980 
227 373 
227.765 
228.158 
228.551 
228.944 
29.336 
229.729 
230.122 
230.514 
230,907 
231.300 
231.692 
232.085 
232.478 
232.871 
233.263 
233 .656 
234.049 
234.441 
234 834 
235 .227 
235.619 
236.012 
236.405 
236.798 
287.190 
237.583 
237.976 
238.368 
238.761 
239.154 
239.546 
239.939 
240.332 
240.725 
241.117 
241.510 
241.903 
242.295 
242.688 
243.081 
243.473 
243.866 
244.259 
244.652 
245.044 
245 437 
245.830 
246.222 
246.615 
247.008 
247.400 
247.793 
248.186 
248.57 
248.971 
249 364 
249 757 


ro 
lon 
tw 
- Py lor) > ‘ rs 
NQOOPOHNHLHWUWHOMDUEHLWWEKOLOMINnGSTWKOOHO 


— Co 

Ne) 90 

= ie. 
on in 
Ee a Ew) 


81. 


83. 


250.149 
250.542 
250.935 
251.327 
251.720 
252.118 
252.506 
252.898 
253.291 
258 . 684 
294.076 
254.469 
254.862 
255.254 
255.647 


5558.3 





MATHEMATICAL TABLES. 


Diam.| Circum. | Area. 





877% | 276,067 
88. 276.460 
1g | 276.858 
14 | 977.246 


86 | 277.638 
t4 | 278.031 
56 | 278.424 
34 | 2781816 
% | 279.209 
89: | 279.602 
14 | 279.994 
14 | 280.387 
$6 | 280.780 
16 | 281.173 
6%: | 281.565 
84 | 281.958 
% | 282.351 
90° | 282.743 
1g | 283.136 
14 | 288.529 
84 | 283.921 
te | 284.314 
5% | 284.707 
84 | 285.100 


¥% | 285.492 


915° | 285.885 
1g | 286.278 
14 | 286.670 
$6 | 287.063 
44 | 287.456 
6% | 287.848 
34 | 288.241 
% | 288.634 








Diam. 
nade | al 
6082.1 4 
6099.4 14 
6116.7 38 
6134.1 14 
Blt 54 
6168.8 34 
6186.2) 9% 
6203.79 938. 
6221.1 vA 
6238.6 14 
6256.1 34 
6273.78 
6291.29 54 
6 08.8 34 
6326.49 % 
6344.18 94. 
6361.78 % 
6379.49 14 
6397.19 3 
6414.9 WA 
6432.6 54 
6450.49 34 
6468.2 % 
6486.09 95. 
6503.9 1% 
6521.89 14 
6539.7 34 
6557.6 6 
6575.5 54 
6593.5 34 
6611.5 % 
6629.68 96. 





Cireum. 


289.027 
289.419 
289.812 
290.205 
290.597 
290.990 
291.888 
291.775 
292.168 


801.200 
801.593 


Area, 





6647.6 





Circum. 


301.986 
302.378 





Area. 





(207.1 
7276.0 
7294.9 
7313.8 
7382.8 
7851.8 
7370.8 
7389.8 
7408.9 
7428 .0 
7447 1 
7466 2 
7485.3 
7504 5 
7523.7 
7543.0 
7562.2 
7581.5 
7600.8 
7620.1 
7639.5 
7658.9 


DECIMALS OF A FOOT EQUIVALENT TO INCRES 














AND FRACTIONS OF AN INCH, 

Inches. 0 1% 14 36 1% 54 34 % 
0 0 -01042 | .02083 | .08125 | ,04167 | .05208 | .06250 | .07292 
1 .0838 | .0938 vh042 101146 |) < £250 .1354 | .1458 1563 
2 ehboY | V177h 1875 .1979 2083 -2188 soode 2396 
3 .2500 | .2604 -2708 -2813 2917 8021 3125 8229 
4 .0038 | .34388 3042 . 3646 .3750 . 8854 3993 -4063 
5 «4167 | .4271 43875 .4479 .4583 .4688 4792 -4896 
6 5000 | .5104 .5208 .5313 5417 .5521 5625 5729 
7 58338 | .5938 .6042 | .6146 | .6250 | .6354 | .6458 6563 
8 6667 | .6771 .6875 .6979 . 7083 .7188 (292 .7396 
9 .7500 | .7604 (408  tieiSlo Lethal ~ S021 8125 8229 

10 . 8333 | .8438 .8542 .8646 8750 8854: .8958 . 9063 
11 9167 | .9271 .93875 | .9479 9583 | .9688! | .9792 | .9896 





113 


CIRCUMFERENCES OF CIRCLES. 





‘Mp gover gol 


Ye oor 
AL 16 
BAIL 8&6 
S401 06 
CR 10) 
Veg 
Gg I 
84g 8h, 
86. gy 


|YAIL Tt 


VOL 89 
4 cg 
29 69 
34g 6S 
Sie 9g 
Yel gg 
0 0S 





"HO LAM VIG ‘NE IL ‘Ea CF OF HONE T WO 








840 O0r! 











LoS BOY 
Yeq 66 
Sp 696 
See G6 
Yo 06 
Bie 
YG 8 
36) 08 
Bg Lb 
wp 2 
He OL 
Yeo 89 
S4tL #9 
846 «19 
ver 3g 
9 og 
Vip 
See «OP 
40 6 OF 
VAIL GP 
46 «68 
Veh 98 
8419 «6S 
Sep 08 
Vee LB 
LG. 
SELL 08 - 
866 LT 
4 = PT 
TAG LL 
“Pp 8 
we Ss 
BL 83 
‘ul “I 
‘al 8 








Sep 201 |AL sor |Sor Tor |%49 


84s «66 
[e536 
VAIL 6 
%6 «68 
34), 98 
349 «8 
Sep 08 
vee LD 
cat 7 
Sell OL 
346 LY 
g £9 
Wg 19 
“Hp gg 
Me gg 
SL ag 
AIL SP 
Veg oh 
348 «GP 
849 «68 
Sep 98 
€ 8 
YL 08g 
ot 
26 
4g (08 
9 LI 
vep FL 
at a Hl 
SE § 
Sell Ff 
OL T 
‘ul ‘3 
‘ul 2 














Sit 96 (848 96 |S 
veg 96 [849 G6 \%Ee 
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Seg «68 «|MeE) «68=«C| 40 
Yep 98 [Ser 98 |8<0r 
€ 88 |%ir 38 ks 
WL os or 6L L 
S6IL 94 |%8 91 [84 
360 ($1 He9 e848 
ws on |849 04 |S 
“9 19 |Se 29 |KO 
%p £9 [Ser £9 |MOl 
Se «19 0 19 |g 
Se. gg |KOL 2¢ | 
Vel FG [Seg Fo [Mg 
Ok Ig |%9 Te lee 
86g Sp |S4¢ SP re 
89 Gp ie cr |%0 
Sp Sb iver sb |Seol 
we 68 |80 68 6 
Gl 9g |80r ce | 
Bir se |g ee | 
S40L 66 L 63 |e 
8S 9c [KG 98 |e 
veg «6 ge [8k kes« 80 
G 06 |%I oe |ol 
Se LL |KO Lt 6 
Sel FL |SOL SI D 
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VOL & fois de p 
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‘al 90 [Ul “Ia [UT 
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vee LOL 
Se «86 
360 6-6 
YEO 16 
6 88 
YL 8B 
86g 88 
ye bL 
Be OL 
40 68h 
Veol 69 
846 99 
Ser $9 
veg 09 
patie 
WYSE FG 
840 «Tg 
Ok LP 
Ye OP 
A aa 8 
Ves 88 
“Pp ce 
Seg GE 
VEO 66 
2c 
YE ke 
86, 61 
we OL 
wp St 
ZOOL 
Veo ob 
SIL 8 
366 
‘al “WH 
‘ul g 





840 TOI 
Il 26 
YG 6 
“ 16 
Bg 68 
Hp 38 
ya Ages 
Yeo 62, 
tt ot 
846 BL 
86) 69 
9 99 
Wp $9 
3 09 
0 6LG 
SIT es 
6 0G 
ve, bp 
9° -tP 
Sep IP 
848 88 
i> 3 
KIL 1g 
865 86 
hr 
39 
“Pp 61 
Vee OL 
St «St 
Bell 6 
86 9 
8 & 
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‘Ul Z 











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WMA SHIOUO FO GWONDHAHAMW AOE 





114 MATHEMATICAL TABLES. 


LENGTHS OF CIRCULAR ARCS. 
(Degrees being given. Radius of Circle = 1.) 
8 1415927 


180 
Ru.e.—Multiply the factor in table for any given number of degrees by 
the radius. 


EXAMPLE.—Given a curve of a radius of 55 feet and an angle of 78° 2. 
What is the length of same in feet ? 


Factorfronr table tor 76° rsee. ces cess cen oa telco OleDos 
Factor from table for 2U’........... RD hoocee BOUDSL TS 


Factor..... Dice CG Se oe ON Oe ok Siete se cate as LOOM V4O 
1.3671746 < 55 = 75.19 feet. 


ForMuLA.—Length of are = < radius X number of degrees. 




















Degrees. Minutes. 

A) .0174533 61 1.0646508 121 2.1118484 1 - 0002909 

2 .0349066 62 1.0821041 12 2.1293017 2 .0005818 

3 .0523599 63 1.0995574 123 2.1467550 3 .0008727 

4 - 0698132 64 1.1170107 124 2.1642083 4 - 0011636 

5 .0872665 65 1.1344640 125 2.1816616 5 -0014544 

6 . 1047198 66 1.1519173 126 2.1991149 6 - 9017453 

ff .1221730 67 1.1693706 127 2.2165682 7 -0020362 

8 -1396263 68 1.1868239 128 2. 2340214 8 -0023271 

9 - 1570796 69 1.2042772 129 2.2514747 9 -0026180 
10 .1745329 70 1.2217305 130 2. 2689280 10 -0029089 
11 - 1919862 71 1.2391838 131 2.2863813 11 -0031998 
12 - 2094395 72 1.2566371 132 2.3038346 12 -0034907 
13 - 2268928 1@3 1.2740904 133 2.3212879 13 -0037815 
14 - 2443461 74 1.2915436 134 2.3387412 14 -0040724 
15 - 2617994 75 1.3089969 135 2.3561945 15 -0043633 
16 -2792527 76 1.3264502 136 2.3736478 16 -0046542 
17 - 2967060 77 1.3439085 137 2.3911011 17 -0049451 
18 -8141593 78 1.3613568 138 2.4085544 18 -0052360 
19 .3316126 79 1.3788101 139 2.4260077 19 -0055269 
20 . 3490659 80 1.3962634 140 2.4434610 20 -0058178 
21 . 38665191 81 1.4137167 141 2.4609142 21 -0061087 
22 . 8839724 82 1.4311700 142 2.4783675 22 -0063995 
23 4014257 83 1.4486233 143 2.4958208 23 -0066904 
24 -4188790 84 1.4660766 144 2.5132741 24 -0069813 
25 . 4363323 85 1.4835299 145 25307274 25 0072722 
26 . 4537856 86 1.5009832 146 2.5481807 26 -0075631 
27 -4712389 87 1.5184364 147 2.5656340 27 -0078540 
28 - 4886922 88 1.5358897 148 2.583873 28 -0081449 
29 - 9061455 89 1.5533430 149 2.6005406 29 .0084358 
30 - 5235988 90 1.5707963 150 2.6179939 30 -0087266 
31 -5410521 91 1.5882496 151 2.6354472 31 .0090175 
32 -5585054 92 1.6057029 152 2.6529005 32 .0093084 
33 . 5759587 93 1.6231562 153 2.6703538 33 - 0095993 
34 - 5934119 94 1.6406095 154 2.6878070 34 -0098902 
35 - 6108652 95 1.6580628 155 2.7052603 35 .0101811 
36 -6283185 96 1.6755161 156 2.7227136 36 .0104720 
37 -6457718 97 1.6929694 157 2.7401669 37 - 0107629 
38 - 6632251 98 1.7104227 158 2.7576202 38 .0110538 
39 - 6806784 99 1.7278760 159 2.7750735 39 -0113446 
40 -6981317 100 1.7453293 160 2.7925268 40 0116355 
41 . 7155850 101 1.7627825 161 2.8099801 41 -0119264 
42 - 7330383 102 1.7802358 162 2.8274334 42 -0122173 
43 -7504916 103 1.7976891 163 2.8448867 43 -0125082 
44 - 7679449 104 1.8151424 164 2.8623400 44 - 0127991 
45 - 7853982 105 1.8325957 165 2.8797933 45 - 0130900 
46 -8028515 106 1.8500490 166 2.8972466 46 - 0133809 
47 -8203047 107 1.8675023 167 2.9146999 47 - 0136717 
48 .8377580 108 1.8849556 168 2.9321531 48 - 0139626 
49 - 8552113 109 1.9024089 169 2.9496064 49 - 0142585 
50 -8726646 110 1.9198622 170 2.9670597 50 - 0145444 
51 . 8901179 111 1.9378155 171 2.9845130 51 . 0148355 
52 - 9075712 112 1. 9547688 172 3.0019663 52 -0151262 
53 - 9250245 113 1.9722221 173 3.0194196 53 -6154171 
54 - 9424778 114 1.9896753 174 3.0368729 54 - 0157080 
55 - 9599311 115 2.0071286 175 3.0543262 55 . 0159989 
56 - 9773844 116 2 .0245819 176 3.0717795 56 - 0162897 
57 - 9948377 117 2 0420552 177 3.0892328 57 . 0165806 
58 . 1.0122910 118 2.0594885 178 3.1066861 58 -0168715 
59 1.0297443 119 2.0769418 179 3.1241394 59 -0171624 
60 1.0471976 120 2.0943951 180 3.1415927 60 -0174£22 








a 


LENGTHS OF CIRCULAR ARCS. 115 


LENGTHS OF CIRCULAR ARCS, 


‘(Diameter =1. Given the Chord and Height of the Arc.) 


RULE FOR USE OF THE TABLE.—Divide the height by the chord. Findin the 
column of heights the number equal to this quotient. Take out the corre- 
sponding number from the column of lengths. Multiply this last number 
by the length of the given chord; the product will be length of the arc. 

If the arc is greater than a semicircle, first find the diameter from the 
formula, Diam. = (square of half chord + rise) + rise; the formula is true 
whether the are exceeds a semicircle or not. Then find the circumference. 
From the diameter subtract the given height of arc, the remainder will be 
height of the smaller arc of the circle; find its length according to the rule, 
and subtract it from the circumference. 












































Hegts.| Lgths. ||Hgts.| Lgths. ||Hgts.| Lgths. ||Hgts.) Lgths. ||Hgts.| Lgths. 
| 
.001 | 1.00002\) .15 | 1.05896]|} .288 | 1.14480)| .3826 | 1.26288]| .414 | 1.40788 
.005.| 1.00007|| .152 | 1.06051|| .24 1.14714]| .828 | 1.26588)| .416 | 1.41145 
01 1.00027|} .154 | 1.06209}) .242 | 1:14951]) .33 1.26892)| .418 | 1.41508 
.015 | 1.00061|} .156 | 1.06368)| .244 | 1.15189]) .8382 | 1.27196|| .42 1.4186! 
.02 1.00107|| .158 | 1.06530)| .246 | 1.15428)| .334 | 1.27502)| .422 | 1.42221 
.025 | 1.00167)| .16 1.06693)| .248 | 1.15670) .336 | 1.27810)| .424 | 1.42583 
.03 1.00240,| .162. | 1.06858) .25 1.15912)) .338 | 1.28118}]| .426 | 1.42945 
.035 | 1.00327)| .164 | 1.07025|| .252 | 1.16156)) .34 1.28428] .428 | 1.43309 
-04 1.00426)} .166 | 1.07194)| .254 | 1.16402)}| .842 | 1.28739)| .43 1.436738 
.045 | 1.00539 | .168 | 1.07365)| .256 | 1.16650|) .3814 | 1.29052/| .432 | 1.44039 
.05 1.00665 | .17 1.07537)| .258 | 1.16899)} .346 | 1.29366]] .434 | 1.44405 
.055 | 1.00805'} .172 | 1.07711] .26 | 1.17150)| .848 | 1.29681|| .436 | 1.4477. 
.06 | 1.00957|| .174 | 1.07888]|} .262 | 1.17403)| .385 | 1.29997]| .488 | 1.45142 
.065 | 1.011238} .176 | 1.08066|| .264 | 1.17657|| .852 | 1.30315]|| .44 1.45512 
.07 1.01302 | .1% 1.08246|| .266 | 1.17912|| .854 | 1.30684]} .442 | 1.45863 
.075 | 1:01493]| .18 1.08428} .268 | 1.18169 | .856 | 1.30954]| .444 ; 1.46255 
.08 1.01698} .182 | 1.08611] .27 1.18429 | .3858 | 1.31276]| .446 | 1.46628 
-085 | 1.01916]} .184 | 1.08797) .272 | 1.18689 | .36 1.81599|| .448 | 1.47002 
.09 1.02146|| .186 | 1.08984) .274 | 1.18951 | .3862 | 1.31923)| .45 1.4737 
.095. | 1.02389|| .188 | 1.09174] .27 1.19214 | .864 | 1.382249)! .452 | 1.47753 
.10 1.02646}/ .19 1.09365) .278 | 1.19479 | .366 | 1.82577)! .454 | 1.48131 
.102 | 1:02752)| .192 | 1.09557) » .28 1.19746 | .868 | 1.382905]| .456 | 1.48509 
.104 | 1.02860}} .194 | 1.09752) .282 | 1.20014] .37 1.33234|| .458 | 1.48889 
.106 | 1.02970}} .196 | 1.09949] .284 | 1.20284 | .3872 | 1.33564|| .46 1.4926 
,108 | 1.03082}} .198 | 1.10147) .286 | 1.20555 | .874 | 1.33896)| .462 | 1.49651 
.11 | 1.03196}! .20 | 1.103471 .288 | 1.20827 | .876 | 1.34229|| .464 | 1.50033 
o112 | 1.03812)}| .202.) 1.10548] .29 1.21102 | .378 | 1.34563]| .466 | 1.50416 
.114 | 1-038430]| .204 | 1.10752] .292 | 1.21377 | .88 | 1.34899)| .468 | 1.50800 
.116 | 1.03551}} .206 | 1.10958) .294 | 1.21654 | .882 | 1.35287|| .47 1.51185 
.118 | 1.038672) .208-) 1.11165]  .296 | 1.21983-) .884 | 1.35575|| .472 | 1.51574 
12 1.03797)| £21 1.11874) .298 | 1.22218 | .3886 | 1.35914/| .474 | 1.51958 
.122 | 1.038923}| .212 | 1.11584] .30 1.22495 | .888 | 1.86254!) .476 | 1.52346 
.124 | 1.04051}) .214 | 1.11796) .802 | 1.2277 .39 1.36596|| .47 1.52736 
.126 | 1.04181]}| .216 | 1.12011] .304 | 1.23063 | .392 | 1.36989)| .48 1.55126 
.128 | 1.04313]| .218 | 1.12225) .806 | 1.23349 | .394 | 1.37283]! .482 | 1.53518 
.13 1.04447}| .22 1.12444) .308 | 1.28636] .896 | 1.37628|| .484 | 1.F3910 
.182 | 1.04584]| .222 | 1.12664]| .31 | 1.23926] .398 | 1.3797 486 | 1.54302 
6134 | 1.04722;| .224 | 1.12885], .312 | 1.24216 | .40 | 1.38322|| .488 | 1.54696 
.136 | 1.04862}| .226 | 1.13108]) .314 | 1.24507 | .402 | 1.38671 49 1.55091 
.188 | 1.05003}| .228 | 1.13331]) .816 | 1.24801 | .404 | 1.39021 492 | 1.55487 
.14 1.05147}| .23 1.13557)| .3818 | 1.25095 | .406 | 1.39372]| .494 | 1.55854 
.142 | 1.05293]} .282 | 1.18785]| .32 1.25391 | .408 | 1.89724]| .496 | 1.56282 
.144 | 1.05441|| .234 | 1.14015}| .322 | 1.25689] .41 | 1.40077)| .498 | 1.56681 
-146 | 1.05591}} .236 | 1.14247), .824 | 1.25988 | .412 | 1.40432)| .50 1.57080 
-148 | 1.05743 








pe A a a a 2 a SE ee eens tee eee tS 


116 MATHEMATICAL TABLES. 


AREAS OF THE SEGMENTS OF A CIRCLE. 


(Diameter = 1; Rise or Height in parts of Diameter being 
given.) 

RvLE FOR USE OF THE TABLE. —Divide the rise or height of the segment by 
the diameter. Multiply the area in the table corresponding to the quotient 
thus found by the square of the diameter. 

If the segment exceeds a semicircle its area is area of circle — area of seg- 
ment whose rise is (diam. of circle — rise of given segment) 

Given chord and rise, to find diameter. Diam = (square of half chord + 
rise) +rise The half chord is a mean proportional between the two parts 
into which the chord divides the diameter which 1s perpendicular to it. 

Rise Rise Rise Rise 

a Area, oo Area. =f Area. i Area, 

Diam. Diam. i Diam 


-001 | .00004 |} .054 | .01646 |} .107 | .04514 || .16 .08111 || .218 | .12235 


Rise 
= Area. 
Diam. 











.002 | .00012 || .055 | .01691 |} .108 | .0457 -161 | .08185 || .214 | .12317 
-003 | .00022 || .056 | .01737 || .109 | .04638 || .162 | .08258 || .215 | .12399 
.004 | .00034 |} .057 | .01783 || .11 04701 .163 | .08882 |} .216 | .12481 
-005 | .00047 || .058 | .01830 |) .111 | .04763 |} .164 | .08406 |] .217 | .12563 
006 | .00062 |} .059 | .01877 |[ .112 | .04826 
.007 | .00078 || .06 .01924 |f .113 | .04889 
.008 | .00095 |} .061 | .01972 || .114 | .04953 
-009 | .00113 |} .062 | .02020 || .115 | .05016 
-O1 .00133 |} .063 | .02068 |} .116 | .05080 
O11 | .00153 || .064 | .O2117 || .117 | .05145 
-012 | .00175 |} .065 | .02166 || .118 | .05209 
-013 | .00197 |} .066 | .02215. |} .119 | .05274 
.014 | .0022 .067 | ,02265 || .12 05338 
.015 | .00244 || .068 } .02315 || .121 | .05404 
.016 | .00268 || .069 | .02866 |} .122 | .05469 
-017 | .00294 || .07 | -.02417 || .123 | .05535 
.018 | .0032 .O71 | .02468 || .124 | .05600 
.019 | .00347 |} .072 | .02520 || .125 | .05666 
-02 | .00375 || .073 | .O2571 |) .126 | .05733 
.021 } .00403 || .074:| .02624 |} .127 | .05799 
-022 | .00432 || .075 | .02676 || .128 | .05866 
.023 | .00462 || .076 | .02729 || .129 | .05933 
-024 | .00492 || .07 .02782 || .13 .06060 
-025 | .00523 |) .078 | .02886 |} .131 | .06067 
-026 | .00555 || .07 .02889 |} .132 | .06135 
-027 | .00587 || .08 .02943 |} .138 | .06203 
.028 | .00619 |} .081 | .02998 |} .184 | .06271 
.029 | .00653 |} .082 | .03053 |} .185 | .06339 
-03 | .00687 |} .083 | .03108 |} .186 | .06407 
.031 | .00721 ||: .084 | .03163 |} .187 | .06476 
.032 | .00756 || .085 | .03219 || .188 | .06545 
-033 | .00791 || .086 | .03275 |} .1389 | .06614 
-034 | .00827 || .087 | .03331 || .14 .06683 
-085 | .00864 |{ .088 | .03387 || .141 | .06753 
-036 | .00901 || .089 | .03444 |} .142 | .06822 
-037 |, .0093 -09 | .08501 || .143 | .06892 
.088 | .00976 || .091 | .03559 |; .144 | .06963 
.0389 | .01015 }} .092 | .03616 |} .145 | .07033 
.04 | .01054 |} .093 | .03674 || .146 | .07103 
.041 | .01093 |} .094 | .03732 || .147 | .O7174 
.042 | .01183 |} .095 } .038791 || .148 | .07245 
.043 | .01173 || .096 | .03850 |} .149 | .07316 
.044 | .01214 || .097 | .03909 |} .15 07387 
.045 | .01255 || .098 | .03968 |} .151 | .07459 
-046 | .01297 |} .099 | .04028 |) .152 | .07531 
.047 | .01339 {| .1 .04087 |} .153 | .07603 
.048 | .01382 |} .101 | .04148 || .154 | .07675 
.049 | .01425 || .102 | .04208 || .155 | .07747 
-05 | .01468 |} .103 | .04269 || .156 | .07819 
-051 | .01512 |} .104 | .04830 || .157 | .07892 
.052 | .01556 || .105 | .04391 .158 | 07965 
.053 | .01601 |! .106 | .04452 || .159 | .08038 


-165 | .08480 |} .218 | .12646 
.166 | .08554 || .219 | .12729 
.167 | .08629 |} .22 | .12811 
-168 | .08794 |} .221 | .12894 
-169 | .O8779 || .222 | .12977 
ole .08854 |} .223 | .13060 
171 | .08929 || .224 | .18144 
-172 | .09004 || .225 | .18227 
.173 | .09080 |} .226 | .133811 
174 | .09155 || .227 | .18395 
-175 | .09231 |} .228 | .18478 
-176 | .09807 |} .229 | .18562 
177 | .09384 || .23 | .138646 
.178 | .09460 |} .2381 | .13731 
179 |} .09587 || .282 | .13815 
18 .09613 |} .283 | .13900 
-181 | .09690 || .284 | .13984 
.182 | .09767 |} .285 | .14068 
.183 | .09845 |} .286 | .14154 
-184 | .09922-|| .287 | .142389 
.185 | .10000 |} .288 | .14324 
-186 | .10077 || .239 | .14409 
.187 | .10155 |} .24 | .14494 
.188 | .10283 || .241 | .14580 
-189 | .103812 || .242 | .14666 
19 -10390 || .243 ) .14751 
.191 | .10469 || .244 } .14837 
.192 | .10547 |] .245 | .14923 
-193 | .10626 || .246 | .15009 
194 | .10705 || .247 | .15095 
.195 | .10784 |} .248 | .15182 
-196 | .10864 || .249] .15268 
197 | .10943 || .25 | .15355 
.198 | .11023 || .251 | .15441 
.199 | .11102 || .252 | .15528 
2 -11182 |] .258 | .15615 
-201 | .11262 || .254 | .15702 
-202 | .11848 |} .255 | .15789 
-203 | .11423 || .256 | .15876 
.204 | 11504 |} .257 | .15964 
.205 | .11584 |} .258 | .16051 
-206 | .11665 || .259 | .16139 
.207 | .11746 |] .26 . 16226 
.208 | .11827 || .261 | .16314 
.209 } .11908 || .262 | .16402 
a1 .11990 |} .263 | .16490 
.211 | .12071 || .264 | .16578 
.212 | .12153 || .265 | .16666 

















AREAS OF THE SEGMENTS OF A CIRCLE. 








“309 | 120645 || .356 
"31. | ‘20738 {| 1357 
811 | “20380 || [358 
312. | [29023 |} 1359 











Rise 





30024 


80122 
80220 
80819 
80417 
80516 
80614 
80712 
80811 
80910 
31008 
81107 
381205 
31304 
.31403 
.31502 
.31600 
.81699 
31798 
.31897 
.81996 
32095 
82194 
82293 
82392 
32491 
32590 
82689 
32788 
82837 
82987 
33086 
83185 
83284 
33384 
383483 
03082 
.33682 
83781 
-33880 
.33980 
84079 
.84179 


84278 
34378 
34477 
84577 





454 


5 


TY, 


Area. 





For rules for finding the area of a segment see Mensuration, page 59. 


118 


g 
S 
5 


| | 
Cae Nee 
WDD & Dew 


MATHEMATICAL TABLES, 


SPHERES, 


(Some errors of 1 in the last figure only. From TRAUTWINE.) 


Sur- 
face. 





.00307 
01227 
02761 
.04909 
.G7670 
.11045 
. 15033 
. 19685 
24851 
80680 
.87123 
44179 
.51848 
.60132 
. 69028 
18540 
- 99403 
2272 
4849 
7671 
0739 
4053 
7611 
.1416 
.5466 
.9761 
.4301 
9088 
.4119 
. 9396 
.4919 
.0686 
. 6699 
2957 
.9461 
.6211 
10.321 
11.044 
11.793 
12.566 





© WO FFD OTIS BH CO CH COW WW 





131.919 





Vol- 
ume. 


.00002 


.00013 
00048 
.00102 
.00200 
.00345 
00548 
00818 
-01165 
.01598 
02127 
.02761 
.03511 











. Sur- Vol- 5 
Diam. fice itn? Diam. 
14 | 33.183 | 17.974 | 9 3 
5-16 34.472 | 19.031 J 10, a 
34 | 35.784 | 20.1 14 
7-46 | Briize | 211263 4 
14 | 38.484 | 22.449 82 
9-16 | 39.872 | 23.674 12 
5g | 41.288 | 24.942 63 
11-16 | 42.719 | 26.254 yy 
34 slit) ee 7 
13-16 45.664 | 29-016 J 11 ig 
2% | 47.173 | 30.466 V4 
15-16 | 48.708 | 31.965 Vy 
4. 50.265 | 33.510 82 
1g | 53.456 | 36.751 14 
14 | 56.745 | 40.195 4 
84 | 60.133 | 43.847 54 
ig | 63.617 | 47.713 v4 
6% | 67.201 | 51.801 f 12 
34 | 70.883 | 56.116 rv) 
% | 74.663 | 60.663 
5. 78.540 | 65.450 87 
1% | 82.516 | 70.482 | 13 
14 | 86.591 | 75.767 V4 
84 | 90.763 | 81.308 94 
44 | 95.033 | 87.113 87 
s° l1os.s7 | 99-541 | 
$4 |103.87 rv 
£4 |108.44 | 106.18 4 
6 ~ 1713.10, 413.10 3; 
¥% [117.87 | 120.31 | 15 
14 1122.72 | 127.88 4 
3g 127.08 | 139.60 16 
i |132.7 43.7 
64 |137.89 | 152.25 ff 16 es 
84 143.14 | 161.03 4 
% |148.49 | 170.14 6 
7. ~ |153.94 | 179.59 84 
1g |159.49 | 189.39 | 17 
14 1165.13 | 199.53 vy 
8% |170.87 | 210.03 Ve 
44 |176.71 | 220.89 $4 
6% [182.66 | 232.13 f 18 
$4 1188.69 | 243.73 4 
6% |194.83 | 255.72 14 
8. © |201.06 | 268.08 5; 
14 |207.39 | 280.85 || 19 
14 |213.82 | 294.01 4 
84 |220.36 | 307.58 re 
44 [226.98 | 321.56 8; 
64 |233.71 | 335.95 ff 20. % 
$4 240.53 | 350.77 rv 
% |247.45 | 360.02 16 
9. © (254.47 | 381.70 Ey) 
14 1261.59 | 397.83 ] 21 
14 |268.81 | 414.41 V4 
84 |270.12 | 431.44 16 
14 1283.53 | 448.92 34 
6% 1291.04 | 466.87 | 22 
34 |298.65 | 485.31 V4 

















Sur- 
face. 








Vol- 
ume. 





504.21 
523.60 
543.48 
563.86 
584.74 
606.13 

28.04 
650.46 
673.42 
696.91 
720.95 
745.51 
770.64 
796.33 
822.58 
849.40 

76.79 
904.78 
962. fi2 
1022. 
1085 
1150. 
1218. 
1288. 
1361 
1436 
1515. 
1596. 
1680. 
1767. 


> Ht G0 3-9 00S a4 69 CD Ht CD 29 GY © CO OD 2 


Diam, 





22 


23. 


24. 


25. 


26. 


27. 


29. 


31. 


32. 


33. 


34. 








Sur- 
face. 








SPHERES. 


SPHERES—(Continued.) 





Vol- ‘ 
nie Diam. 
5964.1 | 40 1 
6165.2 4 41. 
6370.6 v3 
6580.6 | 42. 
6795.2 \“ 
014.3 § 43. 
7238 2 v3 
406.7 4 44. 
7700.4 i“ 
7938.3 | 45. a 
181, 
8429.2 1 46.” 
8682.0 v4 
8930.9 | 47. ‘ 
9202. 
9470.8 | 48. 
9744.0 V4 
10022 9 49. 
10306 v4 
10595 | 50. 
10889 “4 
11189 | 51. 
11494 \ 
11805 4 52. 
12121 V4 
12443 | 53. 
1277 V3 
13103 ft 54. 
13442 “ 
18187 J 55. 
14137 
14494 ft 56. . 
14856 é 
15224 57. i: 
15599 
15979 | 58. ~~ 
16366 vy 
16758 | 59. 
17157 i 
17563 | 60. 
17974 v4 
18392 4 61. 
18817 “4 
19248 | 62. 
19685 1“ 
20129 | 63. 
20580 V4 
21037 | 64. 
21501 “ 
22449 | 65. Vz 
93425 6 
24429 | 66. 
25461 
26522 | 67. f 
27612 é 
erat J 68. 7 
2988 é 
31059 Ff 69. - 
3207 ! 
33510 | 70. °° 





Sur- 
face. 


5153. 
5281. 
5410 
5541 
5674 
5808 
5944. 
6082. 
6221. 
6361. 
6503. 
6647. 
6792. 
6939. 
7088. 
7235. 
7389. 
7543. 
7697. 
7854 
8011. 
Site 
8382. 


2D WWODWO WWW DORVHOWWOORMORIWHE IHN 


153894 


Vol- 
ume 


34783 
36087 
37423 
38792 
40194 
41630 
43099 
44602 
46141 
47718 
49321 
50965 
52645 
54362 
56115 
7906 
59734 
61601 
63506 
65450 
67483 
69456 
71519 
78622 
75767 
77952 
80178 
82448 
84760 
7114 
89511 
919538 
94438 
96967 
99541 
102161 
104826 
107536 
110294 
113098 
115949 
118847 
121794 
124789 
127882 
130925 
134067 
137259 
140501 
143794 
147138 
150533 
153980 
157480 
161082 
164637 
168295 
172007 
15774 


179595 


Sur- 
face. 


15615 
15837 
16061 
16286 
16513 
16742 
16972 
17204 
17437 
17672 
17908 
18146 
18386 
18626 
18869 
19114 
19360 
19607 
19856 
20106 
20358 
20612 
20867 
21124 
21382 
21642 
21904 
22167 
22432 
22698 
22966 
23235 
23506 
23779 
24053 
24828 
24606 
24885 
25165 
25447 
25730 
26016 
26302 
26590 
26880 
27172 
27464 
27759 
28055 
28353 
28652 
28953 
29255 
29559 
29865 
380172 
30481 
30791 
31103 
31416 








119 


Vol- 
ume. 





183471 
187402 
191389 
1954383 
199532 
203689 
2079038 
212175 
216505 
220894 
225341 
229848 
234414 
239042 
243728 
248475 
253284 
258155 
263088 
268083 
273141 
278263 
283447 
288696 
294010 
299388 
304831 
310340 
815915 
221556 
327264 
333039 
238882 
844792 
35077 

356819 
362935 
369122 
3753878 
881704 
888102 
394570 
401109 
407721 
414405 
421161 
427991 
434894 
441871 
448920 
456047 
463248 
470524 
477874 
485302 
492808 
500388 
508047 
515785 
523598 





120 MATHEMATICAL TABLES. 


CONTENTS IN CUBIC FEET AND WU. S. GALLONS OF 
PIPES AND CYLINDERS OF VARIOUS DIAMETERS 
AND ONE FOOT IN LENGTH. 


1 gallon = 231 cubic inches. 1 cubic foot = 7.4805 gallons. 

















For 1 Footin For 1 Foot in For 1 Foot in 
£ Length. & Length. = Length. 
ae 3 ee a ee 
og Q y =e es ~ S 5 
3.4 |Cubic Ft.| Gyo | SS [Cubic Fs.| Gas | 82 |cubic Ft) U.S: 
5 % |also Areal 7531” fe also Area} 7937" a also Area O31” 
ome ed 7 Sa _ ot j 
5 in Sq. Ft.| af tn. 5 in Sq. Ft. Cu. In. | B in Sq. Ft. a ia 

14 .0003 .0025 634 2485 1.859 19 1.969 14.7 
5-16 -0005 .004 7 2673 1,999 1914 2.074 15.51 
38 .0008 .0057 714 2867 2.145 R0 2,182 16.32 
7-16 001 .0078 The .8068 2.295 f 20% 2.292 17.15 
oa 0014 .0102 134 8276 2.45 21 2.405 17.99 
9-16 0017 .0129 8 3491 2.611 21hy 2.521 18.86 
5g 0021 .0159 814 3712 2.007 22 2.640 19.75 
11-16 -0026 .0193 844 3941 2.948 2216 2.761 20.66 
34 -003 1 .0230 834 4176 3,125 23 2.885 21.58 
13-16 .0036 .0269 9 4418 3.305 2314 3.012 22,53 
% 0042 .0312 914 -4667 3.491 24 3.142 23.50 
15-16 -0048 .0359 944 4922 3.682 25 3,409 25.50 
1 -0055 .0408 934 5185 3.879 26 3.687 27.58 
1144 .0085 .0638 § 10 5454 4.08 27 3.976 29.74 
1% -0123 .0918 # 1014 5780 4.286 28 4.276 31.99 
134 .0167 .1249 # 1016 .6013 4,498 29 4.587 34.31 
R .0218 .1632 1034 .6303 4.715 30 4,909 36.72 
214 027 .2066 11 .66 4.937 31 5.241 39.21 
eho 0341 2550 114 .6903 5,164 32 5.585 .| 41.78 
234 .0412 .8085 § 114% 7213 5.396 33 5.940 44.43 
3 0491 8672 § 11384 7580 5.633 34 6.305 47.16 
344 0576 .4309 12 7854 5.875 35 6.€81 49.98. 
544 .0668 .4998 12144 8522 | 6.37 36 7.069 52.88 
334 .0767 5738 5) 9218 6.895 37 7.467 55.86 
4 087 .6528 § 1844 .994 7.436 38 7.87 58.92 
414 0985 .7369 § 14 1.069 7.997 39 8.296 62.06 
444 1104 .8263 ff 1444 | 1147 8.578 40 8.727 65.28 
434 1231 .9206 15 1.227 9.180 41 9.168 68.58 
5 1364 1.020 1514 1.310 9,801 42 9,621 71.97 
514 1503 1.125 16:3 1.396 10.44 43 10.085 75.44 
516 .1650 1.234 1646 1.485 ins 44 10.559 78.99 
534 1803 1.349 17 1.57¢ 11.7 45 11.045 82.62 
6 .1963 1.469 17% 1.67 12.49 46 11.541 86.33 
614 .2131 1.594 18 1.768 13.22 47 12.048 90.13 
644 2304 1.724 1844 1.867 13.96 48 12.566 94.00 
——e———— A CALA 


To find the capacity of pipes greater than the largest given in the table, 
look in the table for a pipe of one half the given size, and multiply its capac- 
ity by 4; or one of one third its size, and multiply its capacity by 9, etc. 

To find the weight of water in any of the given sizes multiply the capacity 
in cubic feet by 62144 or the gallons by 84, or, if a closer approximation is 
peeve’ by the weight of a cubic foot of water at the actual temperature in 
the pipe. 

Cen the dimensions of a cylinder in inches, to find its capacity in U. S. 
gallons: Square the diameter, multiply by the length and by .0034, If d = 


2x 785 
GE ee SX) _ tonsa Te 'D and Lede in 


diameter, 1 = length, gallons = 23] 


feet, gallons = 5.875D°L. 


CAPACITY OF CYLINDRICAL VESSELS, 


121 


CYLINDRICAL VESSELS, TANKS, CISTERNS, ETC. 
Diameter in Feet and Inches, Area’ in Square Feet, and 


COON ONOUOUOT ON SUA DAD RR RR DID RR 0D 09 09 WU WWI CW WH WNWNWNWWWNWNWWWNWHHHe eee 


pt ee 


ORWWH RPOUDMSIOQTRWWOHF KHPOUDNIATIR WMH 


— het 


— et 


NAIATRWWRH RFPODOWRAURWWMRF HPOODBNSH 


et ee 


U. S&S. Gallons Capacity for One Foot in Depth, 


1 gallon = 231 cubic inches = = 0.13368 cubic feet. 





Gals. 


Diam. 


5 8 


eet 


ek, 
ar 
ORW OMW CMW OMWDW OMW OND OMI OMWD OMWD ODD OMWDW ONW HOw 


pa 
[ee] 
woocy 


1 cubie foot 


2S SS Se ee ee 





7.4805 
Area. | Gals. 
1 foot 
Sq. ft depth 
DA pep 188.66 
25.97 194.25 
26.73 199.92 
27.49 205.67 
28.27 ey ih lia | 
30.68 229.50 
33.18 248,23 
35.7 267.69 
38.48 287.88 
41,2 308.81 
44.18 330.48 
47.17 352.88 
50.27 76.01 
53.46 399.88 
56.75 424.48 
60.138 449.82 
63.62 475.89 
67.20 502.7 
70.88 5380.24 
74.66 558.51 
78.54 587.52 
82.52 617.26 
86.59 647.74 
90.76 678.95 
95.03 710.90 
99.40 743.58 
103.87 776.99 
108.43 811.14 
113.10 846.03 
117.86 881.65 
12272 918.00 
127.68 955.09 
132.73 992.91 
137.89 | 1081.5 
143.14 | 1070.8 
148.49 | 1110.8 
153.94 1151.5 
159.48 | 1193.0 
165.13.) 1285.3 
170.87 | 1278.2 
176.71 | 1821.9 
182.65 | 1366.4 
188.69 | 1411.5 
194.83 | 1457.4 
201.06 | 1504.1 
207%.09)| 1514 
213.82 | 1599.5 
220.35 | 1648.4 
226.98 | 1697.9 
233.71 1748.2 
240.53 | 1799.38 
247.45 | 1851.1 
254.47 | 1903.6 
261.59 | 1956.8 
268.80 | 2010.8 
276.12 | 2065.5 





Diam. 


82 


OM ONW OMW OMD BOW OOW OMDM OPW OMWD OMW ORW OMWD OMW Otte 





Area. 


Sq. ft. 


283.53 
291.04 
298.65 
806.35 
814.16 
822.06 
330.06 
338.16 
346.36 
354.66 
363,05 
371,54 
380.138 
888.82 
397.61 
406.49 
415.48 
424.56 
433.74 
443.01 
452.39 
461.86 
471.44 
481.11 
490.87 
500.74 
510.71 
520.77 
5380.93 
541.19 
551.55 
562.00 
572.56 
583.21 
593.96 
604.81 
615.75 
626.80 
637.94 
649.18 
660.52 

71.96 
683.49 
695.13 
706.86 
718.69 
730.62 
742.64 
754.77 
766.99 
779.31 
791.73 
804. 25 
816.86 
829.58 
842.89 


Gals. 


1 foot 


depth. 
2120.9 
RVT1 
2224.0 
2291.7 
2350.1 
2409.2 
2469.1 
2529.6 
2591.0 
2653.0 
2715.8 
2779.3 
2843.6 
2908.6 
2974.3 
3040.8 
3108.0 
3175.9 
8244.6 
3314.0 
3884.1 
3455.0 
3526.6 
3598.9 
8672.0 
8745.8 
8820.3 
3895.6 
8971.6 
4048.4 
4125.9 
4204.1 
4283.0 
4362.7 
4443.1 
4524.3 
4606.2 
4688.8 
4772.1 
4856.2 
4941.0 
5026.6 
5112.9 
5199.9 
5287.7 
5876.2 
5465.4 
5555.4 
5646.1 
5737.5 
5829.7 
5922.6 © 
6016.2 
6110.6 


6205.7 


6301.5 


122 MATHEMATICAL TABLES. 


GALLONS AND CUBIC FEET. 


United States Gallons in a given Number of Cubic Feet. 


1 cubic foot = 7.480519 U. S. gallons; 1 gallon = 231 cu. in. = .13368056 cu. ft. 


Cubic Ft. Gallons. Cubic Ft. Gallons. Cubic Ft. Gallons, 











0.7 50 374.0 8,000 59,844. 


0.1 4.3 
02 1.50 60 448.8 9.000 67,324.7 
0.3 224 70 523.6 10,000 74,805 2 
0.4 2.99 80 598.4 20,000 149.610.4 
0.5 3.74 90 673.2 30,000 224.415.6 
0.6 4.49 100 748.0 40,000 299,220.8 
0.7 5.24 200 1,496.1 50,000 374'025.9 
0.8 5.98 300 2244.2 60,000 448°831.1 
0.9 6.73 400 2'992.2 70,000 5231636.3 
1 7.48 500 3,740.3 80,000 598,441.5 
2 14,96 600 4,488.3 90,000 673,246.7 
3 22.44 700 5,236.4 100,000 748,051.9 
4 29.92 800 5,984.4 200,000 | 1,496,103.8 
5 37.40 900 6,732.5 300,000 | 21244.155.7 
6 44,88 1,000 7,480.5 400,000 | 2.992/207.6 
7 52.36 2,000 14,961.0 500,000 | 3,740.259.5 
8 59.84 3,000 22'441.6 600,000 | 4.488.311.4 
9 67.32 4,000 29/9221 700,000 | 5,236,363 3 

10 74.80 5,000 37,402.6 800,000 | 5,984.415.2 

20 149.6 6,000 44,883.1 900,000 | 6,732,467.1 

30 224.4 7,000 52,363.6 1,000,000 | %,480,519.0 

40 299.2 








Cubie Feet in a given Number of Gallons. 
oe oY Wee. 


Gallons. Cubic Ft. Gallons. Cubic Ft. Gallons. Cubic Ft. 








.134 1,000 133.681 1,000,000 133,680.6 


1 
2 267 2,000 267.361 2,000,000 267.361.1 
3 401 3,000 401.042 3,000,000 401,041.7 
4 1535 4.000 534.722 4,000,000 534.722.2 
5 668 5,000 668.403 5,000,000 668, 402.8 
6 .802 6,000 802.083 6,000,000 802,083 3 
ra 936 7,000 935.764 7,000,000 935,763.9 
8 1.069 8,000 1,069.444 | 8,000,000 | 1,069.444.4 
9 1.203 9,000 1.203.125 9,000,000 |  1,203)125.0 
10 1.337 10,000 1.336.806 [| 10,000,000 | 1,336,805.6 





——————————————————— a 


NUMBER OF SQUARE FEET IN PLATTS. 123 


NUMBER OF SQUARE FEET IN PLATES 3 TO 32 
FEET LONG, AND 1 INCH WIDE. 


For other widths, multiply by the width in inches. 1 sq. in. = .00694 sq. ft. 


























“Segue Ins. | Square A ade Ins. | Square Neate Ins. | Square 
ame g. Long.} Feet. in e. Long.| Feet. Lon g. Long.| Feet. 
Cie0 36 153 7.10 94 .6528 12.8 152 1.056 

1 37 . 2569 11 95 .6597 9 153 1.063 
2 38 . 2639 8. 0 96 .6667 10 154 1.069 
3 39 -2708 1 97 .6736 11 155 1.076 
4 40 e248 2 98 .6806 13. 0 156 1.083 
5 41 .2847 3 99 . 6875 1 157 1.09 
6 42 -2917 4 100 .6944 2 158 1.097 
q 43 .2986 5 101 . 7014 3 159 1.104 
8 44 . 8056 6 102 - 7083 4 160 1.114 
9 45 .8125 of 103 . 71538 5 161 1.118 
10 46 .3194 8 104 (222 6 162 1.125 
11 47 .3264 9 105 7292 7 163 1.132 
4.50 48 . 3333 10 106 . 7361 8 164 1.139 
1 49 . 3403 11 107 7431 9 165 1.146 
2 50 8472 9. 0 108 shes) 10 166 1.153 
3 DI 3042 1 109 . 7569 11 167 1.159 
4 2 .3611 2 110 . 76389 14, 0 168 1.167 
a Da .38681 3 111 .7708 1 169 1.174 
6 54 .375 4 112 sft 2 170 1.181 
. es 55 .8819 5 113 7847 3 171 1.188 
8 56 . 3889 6 114 C917 4 igs 1.194 - 
9 aye . 8958 e 115 . 7986 5) 173 1.201 
10 58 -4028 8 116 . 8056 6 174 1.208 
11 59 -4097 9 117 ~8125 {i 175 1.215 
5, 0 60 -4167 10 118 .8194 8 176 1.222 
1 61 .4236 ala 119 .8264 9 Ie 1,229 
2 62 .4306 10. 0 120 .8333 10 178 1.236 
3 63 -4375 1 121 8403 11 17 1.243 
4 64 .4444 2 122 8472 15. 0 180 1.25 
5 65 .4514 3 123 .8542 1 181 eo 
6 66 .4583 4 124 . 8611 2 182 1.264 
ff 7 . 4653 5 125 .8681 3 183 eM 
8 68 4722 6 126 87 4 184 1.278 
9 69 .4792 7 127 .8819 5 185 1.285 
10 7 .4861 8 128 . 8889 6 186 1.292 
11 71 .4931 9 129 . 8958 ii 187 1.299 
6. 0 vip a 10 130 . 9028 8 188 1.306 
1 Ve 5069 11 131 .9097 9 189 1.313 
2 74. .51389 11. 0 182 .9167 10 190 1.319 
3 fi .5208 1 133 . 9236 11 191 1.326 
4 q Oe i 2 134 . 9306 16. 0 192 1.333 
5 77 .53847 3 135 - 9375 1 193 1.34 
6 7 .0417 4 136 .9444 2 194 1.347 
ff 79 .5486 5 137 9514 3 195 1.354 
8 80 .5556 6 138 . 9583 4 196 1 361 
9 81 -5625 7 139 . 9653 5 197 1.368 
10 82 . 5694 8 140 .9722 6 198 iL Bir 
ari 83 .5764 9 141 . 9792 of 199 1.382 
Gand) 84 58384 10 142 . 9861 8 200 1.389 
1 85 .5905 11 143 -9931 9 201 1.396 
2 86 TOOTS 12.0 144 1.000 10 202 1.408 
3 87 . 6042 if 145 1.007 11 203 1.41 
4 88 .6111 2 146 1.014 17.0 204 1.417 
5 89 .6181 3 147 1.021 1 205 1.424 
6 90 S020) 4 148 1.02 2 206 1.481 
q 91 .6319 5 149 1.035 3 207 1.488 
8 92 . 6389 6 150 1.042 4 208 1.444 
9 93 .6458 q 151 1.049 5 209 “1.451 





124 MATHEMATICAL TABLES. 


SQUARE FEET IN PLATES—(Continued.) 


























a Hh Ins. | Square ae Ins. | Square Apes Ins. | Square 
Long. Long.| Feet. Long. Long.| Feet. Long. Long.| Feet. 
17. 6 210 1.458 peas ta) 269 1.868 Oe 828 2.278 
fy 211 1.465 6 70 1.875 5 829 2.285 
8 212 1.472 7 271 1,882 6 830 2.292 
9 213 1.47 8 272 1.889 v6 3831 2.299 
10 214 1.486 9 273 1.896 8 832 2.306 
11 215 1.493 10 274 1.903 9 8383 2.313 
18. 0 216 1.5 il 275 1.91 10 834 2.319 
1 217 1.507 28. 0 276 1.917 11 835 2.326 
2 218 1.514 1 277 1,924 28. 0 836 2.333 
5 219 1,521 2 78 1.931 1 837 2.84 
4 220 £.528 3 279 1.9388 2 838 2.847 
5 221 1.585 4 280 1.944 3 839 2.854 
6 222 2.542 5 281 1.951 4 3840 2.361 
v4 223 1.549 6 282 1.958 5 841 2.368 
8 224 1.556 vd 283 1.965 6 842 2.805 
9 225 1.563 8 284 1.972 343 2.382 
0 226 1.569 9 285 1.979 8 3844 2.389 
11 227 1.576 10 286 1.986 9 345 2.396 
19. 0 228 1.583 +4 287 1.993 10 346 27403 
1 229 1.59 24,0 288 24 11 347 2.41 
2 230 1.597 1 289 2.007 29. 0 348 2.417 
3 231 1.604 2 290 2.014 a4 349 2.424 
4 232 1.611 3 291 2.021 2 850 2.421 
5 233 1.618 4 292 2.028 3 351 2.438 
6 234 1.625 5 293 2.035 4 352 2.444 
7 235 1.682 6 294 | 2,042 15) 353 2.451 
8 236 1.639 " 295 2.049 6 854 2.458 
9 237 1.645 8 296 2.056 v4 355 2.465 
10 238 1.6538 9 297 2.063 8 356 2.472 
1} 239 1.659 10 298 2.069 9 3857 2.479 
20. 0 240 1.667 st 299 2.076 10 858 2.486 
1 241 1.674 25.0 300 2.088 hl 859 2.493 
2 249 1.681 1 301 2.09 30. 0 3860 2.5 
3 243 1.688 2 3802 2.097 1 861 - 21507 
4 244 1.694 3 3803 2.104 2 362 2.514 
5 245 1.701 4 3804 2.11 3 363 2.521 
6 246 1.708 5 805 2.118 4 364 2.528 
q 247 £715 6 306 2.125 5 365 24Do0) 
8 248 1.722 Ye 307 2.1382 6 366 2.542 
9 249 1.729 red 308 2.139 i 367 2.549 
10 250 1.736 9 3809 2.146 8 368 2.556 
11 Ase) 1.743 10 310 2.1538 9 369 2.563 
91.0 252 Dear 11 311 2.16 10 370 2.569 
] 253 R757 26. 0 812 2,167 11 371 2.576 
2 254 1.764 1 313 2.174 $1. 0 3872 2.5838 
3 255 eed 2 314 2.181 1 373 2.59 
4 256 1.778 3 315 2.188 2 374 2.597 
5 257 1.785 4 316 2.194 3 375 2.604 
6 258 1.792 5 ol? 2.201 4 376 2.611 
i 259 1.799 6 318 2.208 5 SK 2.618 
8 260 1.806 i 319 Q1915 6 38% 2.625 
9 261 1.813 8 820 2.222 q 379 2t6o20. 
10 262 1.819 9 821 2.229 8 3880 2.639 
11 268 1.826 10 822 2.236 9 381 2.646 
22.0 264 1.883 11 823, 2.243 10 382 2 6538 
1 265 1.84 27.0 3824 2,25 11 383 2.66 
9 266 1.847 1 825 2,257 32. 0 384 2.667 
3 267 1.854 2 326 2.264 1 385 2.674 
4 268 1.861 3 327 Tf 2 386 2.681 





CAPNOITY OF RECTANGULAR TANKS. 124 
f 


CAPACITIES OF RECTANGULAR TANKS IN U. S&S 
GALLONS, FOR EACH FOOT IN DEPTH. 


1 cubic foot = 7.4805 U. S. gallons. 








Length of Tank. 
Width 


of 
Tank. | feet. |ft. in.| feet.|ft. in.| feet. \ft. in.| feet. |ft. in.| feet. |ft. in.| feet, 
2:2 61 8 |8 6| 4 |4 6| 5&5 |5 6} 6 |6 6] 7 


| | ef | ff | | | | ————_ 


=p 

















t. i 

2 29,92 | 37,40 | 44.88] 52.36 | 59.84] 67.32] 74.81) 82.29] 89.77) 97.25/104.7: 

ame Ol sachs: «> 46.75 | 56.10] 65.45 | 74.80] 84.16) 93.51)102.86)112.21)121.56)13 081 
antes Ul ape es ie tee 2 67.32) 78,54 | 89.77)100.99/112.21)123,43/184.65/145.87/157.09 
SRC Gat trace Olea sta ell aie tes 91.64 |104.73}117.82) 130.91)144.00|157.09)170.18) 183.27 
4 seer eelecceoe|-covee|seee ee | 119.69)184, 65) 149, 61)164.57)179.53)194.49) 209.45 
See ek Rees ae see celeceree| sce ee|scoee 1151.48] 168.31 |185.14/201.97/218.80| 235.69 
Set nes he Maek plain epee] sees rile pe sailit= sleep 187.01 )205.71)224.41)243.11}261.82 
ieee Mh asarted~aeeeal te cpintl tetnel a: Gi calictese ciel ee ew «- |226,28) 246,86 |267.43/ 288.00 
ee EE crarcin tty ite | seretenl taxtins | kon top teis ee 65 iadraos| Poo ce 269.30/291.74/314.18 
OPO ostase | cfericcein iteicses|igereers=\| ae eve sl ae cwced pisces s| sacrteteh steres's 316.05| 340.36 








Length of Tank. 





























Width 

fo) 

Tank. | ft. in.| feet. |ft. in.| feet. ift. in.| feet. |ft. in.| feet. |ft. in.| feet. 

ChB 8 18 6| 9 |9 6] 10 |10 6] 11 |11 6] 12 

tte ins 

2 112.21 | 119.69} 127.17] 184.65) 142.13} 149.61] 157.09) 164.57] 172.05) 179.53 
2 6 | 140.26 | 149.61) 158.96] 168.31] 177.66] 187.01} 196.36) 205.71) 215.06] 224.41 
3 168.81 | 179.58} 190.75) 202.97) 213.19] 224.41] 235.63) 246.86] 258.07) 269.30 
3... 6 196.36 | 209.45) 222.54) 235.63) 248.73] 261.82] 274.90) 288.00} 801.09] 314.18 
4 224.41 | 239.37) 254,34] 269.30] 284.26) 299.22) 314.18) 329.14] 344.10] 359.06 
4 6 | 252.47 | 269.30) 286.13) 302.96) 319.79) 336.62) 353.45) 370.28) 887.11] 403.94 
5 280.52 | 299.22) 317.92} 336.62] 355.32] 374.03} 392.72] 411.43] 430.13) 448.83 
5 6 | 308.57 | 829.14) 349.71] 370.28) 390.85) 411.43] 432.00] 452.57] 473.14] 493.71 
6 336.62 | 359.06] 881.50) 403.94) 426.39] 448.83] 471.27) 493.71] 516.15] 538.59 
6 6 | 364.67 | 388.98) 418.30) 437.60) 461.92] 486.23] 510.54] 534.85) 559.16] 583.47 
v 892.72 | 418.91| 445.09} 471.27) 497.45] 523.64! 549.81) 575.99] 602.18] 628.36 
7 6 | 420.78 | 448.63) 476.88) 504.93) 532.98] 561.04] 589.08] 617.14] 645.19 673.24 
BLD Lis caplesees 478.75] 508.67) 538.59) 568.51] 598.44] 628.36] 658.28) 688.20) 718.12 
SM OIL ore. ccelamons --| 540.46] 572.25) 604.05] 635.84!) 667 63) 699.42) 731.21] 763.00 
9 sake erp o gtliaieest ars uastiaters «-.| 605.92) 639,58) 673.25) 706.90} 740.56) 774.23] 807.83 
BEE sels cis om\lsicicwst oni] oleic bese lee tan Oo wald eal OOD (AOel Gin? ol.al | Sd vend epreadit 
TIMER icc ars.c luctoecselic ¢abiente oe ene Bo Pas Sere 748.05] 785.45) 822.86] 860.26] 897.66 
TOMBE RaY oct sews Ic coereneinie cei oet Leen eine lice co ..| 824.73) 864.00) 903.26} 942.56 
11 alsia eo: || «ee s100s leapascte iteimel teinetics| ores cteal abies tes |) DUD. 14) 940.20 ooueas 
DEB aio eyes 4)|\ 0.4 00 eee. pe tices amiblereh el itainuies ol ial 8 eel abs alk owl os,saa HOO O holsencs 
12 eweeeeetsene ee e eee eee e e | e if 1077.2 


- 


126 MATHEMATICAL TABLES, 


NUMBER OF BARRELS (31 1-2 GALLONS) IN 
CISTERNS AND TANKS, 





1 Barrel = 3144 gallons = eee 4.21094 cubic feet. Reciprocal = .237477, 
‘ 
Depth Diameter in Feet. 
in ge a Ee Se ee ee se ee 
Meet, Heo ig ig | '8 We'd fowl al. | 184 |eia) ore 





1 4.663] 6.714] 9.189/11.937/15.108/18.652| 22.569] 26.859] 31.522/36 557 
5 23.3 } 33.6 | 45.7 | 59. 75.5 | 93.3 | 112.8 | 184.3 | 157.6 | 182.8 
6 28.0 | 40.3 | 54. 71 90.6 {111.9 | 185.4 | 161.2 | 189.1 | 219.3 
ff 
8 





8 
82.6 | 47.0 | 64.0 | 83.6 |105.8 |1380.6 | 158.0 | 188.0 | 220.7 | 255.9 
120.9 [149.2 | 180.6 | 214.9 | 252.2 | 292.5 


136.0 |167.9 ,; 208.1 | 241.7 | 283.7 | 329.0 
151.1 |186.5 | 225.7 | 268.6 | 315.2 | 365.6 





gabe uraer ey. 




















" 166.2 |205.2 | 248.38 | 295.4 | 346.7 | 402.1 
56.0 | 80.6 |109.7 |143.2 |181.3 [223.8 | 270.8 | 322.3 | 378.8 | 438.7 
60.6 | 87.3 1118.8 1155.2 1196.4 |242'5 | 298.4 | 349.2 | 409.8 | 475.2 
14 | 65.3 | 94.0 [127.9 [167.1 1211.5 1261.1 | 316.0 | 376.0 | 441.3 | 511.8 
15 | 69.9 |100.7 137.1 [179.1 |226.6 |289.8 | 338.5 | 402.9 | 472.8 | 548.4 
16 | 74.6 |107.4 1146.2 191.0 [241.7 |298.4 | 361.1 | 429.7 | 504.4 | 584.9 
17 79.3 |114.1 [155.4 |202.9 1256.8 |817.1 | 388.7 | 456.6 | 535.9 | 621.5 
18 | 83.9 |120.9 |164.5 [214.9 |271.9 1395.7 | 406.2 | 483.5 | 567.4 | 658.0 
19 | 88.6 [197.6 |173.6 |226.8 |287.1 1354.4 | 428.8 | 510.3 | 598.9 | 694.6 
20 | 93.3 |134.3 |182/8 1238.7 |302/2 [373.0 | 451.4 | 537.2 | 630.4 | 731.1 
| 
Depth Diameter in Feet. 
in 
Feet. | 45 16 17 18 19 20 | 21 29 
1 41.966, 47.748] 53.903] 60.431 67.332! 74.606] 82.258] 90.273 
5 209.8 938.7 269.5 302.2 336.7 Stora!) AIies 451.4 
6 251.8 | 286.5 | 323.4| 362.6 | 404.0] 447.6 | 4938.5 | 541.6 
° 293-8 | 334.2 | 377.3| 4230] 471.3] 522.2] 575.8 | 631.9 
8 335.7 | 382.0 | 431.2 | 483.4 | 538.7 | 596.8| 658.0 | 722.2 
9 vv.7 | 429.7 | 49511 548.9! 606.0! 671.5| 740.3 | 812.5 
10 419.7 | 477.5 | 539.0| 604.3| 673.31 746.1] 822.5 | 902.7 








573.0 | 646.8 | 725.2] 808.0 | 895.3] 987.0 | 1083.3 
620.7 | 700.7 | 785.6] 875.3 | 969.9 | 1069.38 | 1173.5 


668.5 | 754.6 | 846.0] 942.6 | 1044.5 | 1151.5 | 1263.8 
716.2 | 808.5 | 906.5 | 1010.0 | 1119.1 | 1233.8 | 1354.1 
: 764.0 | 862.4 | 966.9 } 1077.3 | 1193.7 | 1816.0 | 1444.4 
17 713.4 | 811.7 | 916.4 | 1027.3 | 1144.6 | 1268.3 | 1398.3 | 1534.5 
18 755.4 | 859.5 | 970.3 | 1087.8 | 1212.0 | 1342.9 | 1480.6 | 1624.9 


19 797.4 | 907.2 | 1024.2 | 1148.2 | 1279.3 | 1417.5 | 1562.8 | 1715.2 
20 839.3 | 955.0 | 1078.1 | 1208.6 | 1346.6 | 1492.1 | 1645.1 | 1805.5 


TR a RR ET ESE SN A ARES SR | ee 


8 
8 
4 
11 461.6 525.2 | 592.9 | 664.7] 740.7 | 820.7} 904.8 993.0 
6 
5 
5 
5 


LOGARITHMS. 12? 


NUMBER OF BARRELS (31 1-2 GALLONS) IN 
CISTERNS AND TANKS.—Continued. 








Diameter in Feet. 





ee | fl ef | | LL | | 


1 98.666] 107.432) 116.571] 126.083] 135.968) 146.226] 157.858] 167.863 
5 493.3 | 537.2 | 582.9] 630.4 0 i ley a I bo 839.3 
6 592.0 | 644.6 | 699.4 | 756.5 | 815.8] 877.4 | 941.1 | 1007.2 
7 690.7 | 752.0] 816.0 | 882.6] 951.8 | 1023.6 | 1098.0 | 1175.0 
8 789.3 | 859.5 | 9382.6 | 1008.7 | 1087.7 | 1169.8 | 1254.9 | 1342.9 


9 888.0 | 966.9 | 1049.1 | 1134.7 | 1223.7 | 1316.0 | 1411.7 | 1510.8 
10 986.7 | 1074.3 | 1165.7 | 1260.8 | 1359.7 | 1462.2 | 1568.6 | 1678.6 
11 1085.3 | 1181.8 | 1282.3 | 1886.9 | 1495.6 | 1608.5 | 1725.4 | 1846.5 
IZ 1184.0 | 1289.2 | 1398.8 | 1513.0 | 1631.6 | 1754.7 | 1882.3 | 2014.4 
13 1282.7 | 1896.6 | 1515.4 | 1639.1 | 1767.6 | 1900.9 | 2039.2 | 2182.2 


14 1381.3 | 1504 0 | 1632.0 | 1765.2 | 1903.6 | 2047.2 | 2196.0 | 2350.1 
15 1480.0 | 1611.5 | 1748.6 | 1891.2 | 2039.5 | 2193.4 | 2352.9 | 2517.9 
16 1578.7 | 1718.9 | 1865.1 | 2017.3 | 2175.5 | 2339.6 | 2509.7 | 2685.8 
17 1677.3 | 1826.3 | 1981.7 | 2143.4 | 2311.5 | 2485.8 | 2666.6 | 2853.7 
18 1776.0 | 1988.8 | 2098.3 | 2269.5 | 2447.4 | 2632.0 | 2823.4 | 3021.5 


19 1874.7 | 2041.2 | 2214.8 | 2895.6 | 2583.4 | 2778.3 | 2980.3 | 3189.4 
20 1973.3 | 2148.6 | 2821.4 | 2521.7 | 2719.4 | 2924.5 | 3137.2 | 3357.3 





LOGARITHMS. 


Logarithms (abbreviation log).—The log of a number is the exponent 
of the power to which it is necessary to raise a fixed number to produce the 
given number. The fixed number is called the base. Thus if the base is 10, 
the log of 1000 is 3, for 103 = 1000. There are two systems of logs in general 
use, the common, in which the base is 10, and the Naperian, or hyperbolic, 
in which the base is 2.718281828 .... The Naperian base is commonly dee 


noted by e, as in the equation e¥ = a, in which y is the Nap. log of a. 

In any system of logs, the log of 1 is 0; the log of the base, taken in that 
system, is 1. In any system the base of which is greater than 1, the logs of 
all numbers greater than 1 are positive and the logs of all numbers less than 
1 are negative. 

The modulus of any system is equal to the reciprocal of the Naperian log 
of the base of that system. The modulus of the Naperian system is 1, that 
of the common system is .4342945. 

The log of a number in any system equals the modulus of that system X 
the Naperian log of the number. 

The hyperbolic or Naperian log of any number equals the common log 
X 2.3025851. 

Every log consists of two parts, an entire part called the characteristic, or 
index, and the decimal part, or mantissa. The mantissa only is given in the 
usual tables of common logs, with the @ecimal point omitted. The charac- 
teristic is found by a simple rule, viz., it is one less than the number of 
figures to the left of the decimal point in the number whose log is to be 
found. Thus the characteristic of numbers from 1 to 9.99 + is 0, from 10 to 
99.99 -+ is 1, from 100 to 999 +-is 2, from .1 to .99 + is — 1, from .01 to .099 -4- 
is — 2, ete. Thus ' 


log of 2000 is 3.30103; logoff .2is — 1.301033 
© 200 2.301038; ~~ 02 + — 2.301033 
seme oOlUa. (ee 66 002 “* — 3.301083 
66 66 2 66 0.30103; 6 66 -0002 “ 4.30103, 


128 MATHEMATICAL TABLES, 


The minus sign is frequently written above the characteristic thus: 
log .002 = 3.30103. The characteristic only is negative, the decimal part, or 
mantissa, being always positive. 

When a log consists of a negative index and a positive mantissa, it is usual 
to write the negative sign over the index, or else to add 10 to the index, and 
to indicate the subtraction of 10 from the resulting logarithm, 

Thus log .2 = 7.30103, and this may be written 9.30103 — 10. 

In tables of logarithmic sines, etc., the — 10 is generally omitted, as being 
understood. 

Rules for use of the table of Logarithms.—To find the 
log of any whole number.—For 1 to 100 inclusive the log is given 
complete in the small table on page 129. 

For 100 to 999 inclusive the decimal part of the log is given ppppeitg the 
given number in the column headed 0 in the table (including the two figures 
to the left, making six figures). Prefix the characteristic, or index, 2. 

For 1000 to 9999 inclusive: The last four figures of the log are found 
opposite the first three figures of the given number and in the vertical 
column headed with the fourth figure of the given number ; prefix the two 
figures under column 0, and the index, which is 3, 

For numbers over 10,000 having five or more digits: Find the decimal part 
of the log for the first four digits as above, multiply the difference figure 
in the last column by the remaining digit or digits, and divide by 10 if there 
be only one digit more, by 100 if there be two more, and so on; add the 
qnctient to the log of the first four digits and prefix the index, which is 4 
if there are five digits, 5if there are six digits, and soon. The table of pro- 
portional parts may be used, as shown below. 

To find the log of a decimal fraction or of a whole 
number and a decimal.—First find the log of the quantity as if there 
were no decimal point, then prefix the index according to rule ; the index ig 
one less than the number of figures to the left of the decimal point. 

Required log of 3.141593. 


% log of 3.141 = 0.497068, Diff. = 138 
From proportional parts ee = — 690 
6e oe 6s pee, 09 = 1242 
oy nee e 003 = 041 


log 3.141593  0.4971498 


To find the number corresponding to a given log.—Find 
in the table the log nearest to the decimal part of the given log and take the 
first four digits of the required number from the column N and the top or 
foot of the column containing the log which is the next less than the given ~ 
log. To find the 5th and 6th digits subtract the log in the table from the 
given log, multiply the difference by 100, and divide by the figure in the 
Diff. column opposite the log ; annex the quotient to the four digits already 
found, and place the decimal point according to the rule; the number ef 
figures to the left ‘of the decimal point is one greater than the index, 


Find number corresponding to the log.......... . 0.497150 
Next lowest log in table corresponds to 3141...... .497068 


Diff. = 82 
Tabular diff. = 138; 82 -+- 1388 = .59 + 


The index being 0, the number is therefore 8.14159 +. 

To multiply two numbers by the use of logarithms,-~ 
Bud together the logs of the two numbers, and find the number whose log 
is the sum. 

To divide two numbers,—Subtract the log of the divisor from 
the log of the dividend, and find the number whose log is the difference. 

To raise 2 number to any given power.—Multiply the log of 
bi eee by the exponent of the power, and find the number whose log igs 
the product. 

To find any root of a given number,.—Divide the log of the 
number by the index of the root. The quotient is the log of the root. 

To find the reciprocal of a number.-—Subtract the decimal 
part of the log of the number from 0, add 1 to the index and change the sign 
of the index, The result is the log of the reciprocal, 


ya 


LOGARITHMS, 129 


Required the reciprocal of 3.141593. 


Log of 3.141593, as found above.......... ee er eT TTL -. 0.4971498 
Subtract decimal part from 0 gives..............2.-.0 +0058 . 0.5028502 
Add 1 to the index, and changing sign of the index gives.. 1.5028502 


which is the log of 0.31881. 

To find the fourth term ofa proportion by logarithms. 
—Add the logarithms of the second and third terms, and from their sum 
subtract the logarithm of the first term. 

When one logarithm is to be subtracted from another, it may be more 
convenient to convert the subtraction into an addition, which may be done 
by first subtracting the given logarithm from 10, adding the difference tc the 
other logarithm, and afterwards rejecting the 10. 

The difference between a given logarithm and 10 is called its arithmetical 
complement, or cologarithm. 

To subtract one logarithm from another is the same as to add its comple- 
ment and then reject 10 from the result. Fora —b=10—b+a4— 10. 

To work a proportion, then, by logarithms, add the complement of the 
logarithm of the first term to the logarithms of the second and third terms. 
The characteristic must afterwards be diminished by 10. 

Example in logarithms with a negative index.—Solve by 


( 2.45 
logarithms ( nai) , which means divide 526 by 1011 and raise the quotient 


to the 2.45 power. 

log 526 = 2.720986 

log 1011 = 3.004751 
log of quotient = — 1.716235 
Multiply by 2.45 
— 2.581175 

— 2.8 64940 

— 1.43 2470 


— 1.80 477575 = .20178, Ans, 
In multiplying — 1.7 by 5, we say: 5 x 7 = 35, 3 to carry; 5 x —1=—5 less 


+8 carried = — 2. In adding —-2+8-+3-+1 carried from previouscolumn, 
we say: 1+3-+8 = 12, minus2 = 10, set down 0 and carry 1;1+4-2=32 


LOGARITHMS OF NUMBERS FROM 1 To 100. 








A 
cg! 
5 
w 
vA 


Log. N. Log. N. Log. N. Log. 


0.000000 || 21 | 1.822219 || 41 | 1.612784 |; 61 | 1.785830 || 81 | 1.908485 
0.301080 |} 22 | 1.342423 || 42 | 1.628249 |) 62 | 1.792392 || 82 | 1.913814 
0.477121 || 23 | 1.361728 || 43 | 1.683468 || 63 | 1.799341 || 83 | 1.919078 
0.602060 |} 24 | 1.880211 || 44 | 1.643453 || 64 | 1.806180 || 84 | 1.924279 
1.397940 |} 45 | 1.658213 || 65 | 1.812918 || 85 | 1.929419 


0.778151 || 26 | 1.414973 || 46 | 1.662758 || 66 | 1.819544 || 86 | 1.934498 
0.845098 || 27 | 1.431364 || 47 | 1.672098 || 67 | 1.826075 || 87 | 1.939519 
0.903090 || 28 | 1.447158 || 48 | 1.681241 || 68 | 1.832509 || 88 | 1.944483 
0.954243 || 29 | 1.462398 || 49 | 1.690196 || 69 | 1.838849 |} 89 | 1.949390 
1.000000 || 80 | 1.477121 || 50 | 1.698970 || 70 | 1.845098 || 90 | 1.954243 


11} 1.041393 || 31 | 1.491862 || 51 | 1.707570 || 71 | 1.851258 || 91 | 1.959041 
12] 1.079181 || 32 | 1.505150 || 52 | 1.716003 || 72 | 1.857332 || 92 | 1.968788 
13 | 1.118943 ||} 33 | 1.518514 || 53 | 1.724276 || 73 | 1.863323 || 93 | 1.968483 
14 | 1.146128 || 34 | 1.581479 || 54 | 1.782894 || 74 | 1.869232 || 94 | 1.978128 
15 | 1.176091 || 85 | 1.544068 || 55 | 1.740363 || 75 | 1.875061 || 95 } 1.977724 


16 | 1.204120 || 36 | 1.456308 || 56 | 1.748188 || 76 | 1.880814 |; 96 | 1.982271 
17 | 1.230449 || 387 | 1.568202 || 57 | 1.755875 || 77 | 1.886491 || 97 | 1.986772 
18 | 1.255273 || 38 | 1.579784 || 58 | 1.763428 || 78 | 1.892095 |) 98 | 1.991226 
19 | 1.278754 || 39 | 1.591065 || 59 | 1.770852 || 79 | 1.897627 || 99 | 1.995635 
20 | 1.301080 || 40 | 1.602060 || 60 | 1.778151 || 80 | 1.903090 ||100 | 2.000000 











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SOON OVP COM | 
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ive) 
vo} 
ss 
oO 
rw) 
Or 


























130 LOGARITHMS OF NUMBERS, 





























































































































[No. 109 L. 040, 
Diff. 
100 | 000000 | 0434 | 0868 | 1801 | 1734 || 2166 | 2598 | 3029 | 3461 | 3891 432 
1 4321 | 4751 | 5181 | 5609 | 6088 || 6466 | 6894 | 7321 | 7748 | 8174 423 
2 8600 | 9026 | 9451 | 9876 ae 
Bel ee 28 0300 0724 | 1147 | 1570 | 1993 | 2415 424 
8 | 012887 | 3259-} 3680 | 4100 | 4521 4940 | 5860 | 577 6197 | 6616 420 
4 7033 | 7451 | 7868 | 8284 | 8700 || 9116 | 95382 | 9947 
ao -| 0861 | 077! 416 
5 | 021189 | 1603 | 2016 | 2428 | 2841 8252 | 3664 | 4075 | 4486 | 4896 412 
6 5806 | 5715 | 6125 | 6588 | 6942 || 7350 | 7757 | 8164 | 857 8978 408 
7 9384 | 9789 ——- —_ |—_ —_ 
ees 0195 | 0600 | 1004 || 1408 | 1812 | 2216 | 2619 | 3021 404 
8 | 033424 | 8826 | 4227 | 4628 | 5029 || 5430 | 5880 | 6230 | 6629 | 7028 400 
9 7426 | 7825 | 8228 | 8620 | 9017 || 9414 | 9811 |——— = 
04 0207 | 0602 | 0998 397 
PROPORTIONAL PARTS. 
Diff 1 2 3 4 5 6 v4 8 9 
434 43.4 86.8 130.2 173.6 217.0 260.4 393.8 847.2 | 390.6 
433 43.3 86.6 129.9 173.2 216.5 259.8 3803.1 3846.4 | 389.7 
432 43.2 86:4 129.6 172.8 216.0 259.2 802.4 345.6 | 388.8 
431 43.1 86.2 129.3 172.4 215 6D 258.6 301.7 344.8 |} 387.9 
430 43.0 86.0 129.0 172.0 215.0 258.0 301.0 344.0 | 387.0 
429 42.9 85.8 128.7 171.6 214.5 257.4 300.3 343.2 | 386.1 
428 42.6 85.6 128.4 sa Beg 914.0 256.8 299.6 342.4 | 385.2 
427 42.7 85.4 128.1 170.8 2138.5 256.2 298.9 341.6 | 384.38 
426 42.6 85.2 127.8 170.4 213.0 255.6 298.2 3840.8 | 383.4 
425 42.5 85.0 12725 170.0 QI255 255.0 297.5 340.0 | 382.5 
424 42.4 84.8 ee 169.6 212.0 954.4 296 .8 839.2 | 381.6 
423 42.3 84.6 126.9 169.2 21125 253.8 296.1 338.4 | 880.7 
422 42.2 84.4 126.6 168.8 211.0 253.2 295.4 337.6 | 879.8 
421 42.1 84.2 126.3 168.4 210.5 95256 294.7 836.8 | 378.9 
420 42.0 84.0 126.0 168.0 210.0 252.0 294.0 336.0 | 378.0 
419 41.9 83.8 125.7 167.6 209.5 251.4 93.3 3S avira | 
418 41.8 83.6 125.4 167.2 209.0 250.8 92.6 $34.4 | 376.2 
417 41.7 83.4 125.1 166.8 208.5 850.2 291.9 833.6 | 375.3 
416 41.6 83.2 124.8 166.4 208.0 249.6 291.2 332.8 | 374.4 
415 41.5 83.0 124.5 166.0 207.5 249.0 290.5 832.0 | 373.5 
414 41.4 82.8 124.2 165.6 207.0 248 4 289.8 Soleel|ote.o 
413 41.3 82.6 123.9 165.2 206.5 247.8 289.1 $8054. s871¢ 


412 | 41.2 | 82.4 | 123.6] 164.8] 206.0] 247.2] 288.4] 329.6 | 370.8 

















LOGARITHMS OF NUMBERS. 151 


No. 110 L. 041.] [No. 119 L. 078. | 


ny 








| P-) 
(—J 
ry 
b+) 
oo 
be 
ou 


6 7 8 9 | Diff. 









































110 | 041393 | 1787 | 2182 | 2576 | 2969 || 8862 | 3755 | 4148 | 4540 | 4982 | 393 
1 5823 | 5714 | 6105 | 6495 | 6885 || 7275 | 7664 | 8053 | 8442 | 8830 | 890 
2 9218 | 9606 | 9993 — ——_ |—_——- 

————_ ||| _ 0880 | 0766 |} 1153 | 1538 | 1924 | 2309 | 2694 | 386 
3 | 053078 | 3463 | 3846 | 4230 | 4613 |} 4996 | 5378 | 5760 | 6142 | 6524 | 383 
es 6905 | 7286 | 7666 | 8046 | 8426 |) 8805 | 9185 | 9563 | 9942 aur Rees 
5 | 060698 | 1075 | 1452 | 1829 | 2206 |} 2582 | 2958 | 3333 | 8709 | 4088 | 376 
6 4458 | 4832 | 5206 | 5580 | 5953 || 6326 | 6699 | 7071 | 7443 | 7815 | 373 
7 8186 | 8557 | 8928 | 9298 | 9668 SeeSes 

—_-———_ |__| |———_ || 0038 | 0407 | 0776 | 1145 | 1514 | 370 
8 | 071882 | 2250 | 2617 | 2985 | 3352 || 8718 | 4085 | 4451 | 4816 | 5182 | 366 
9 5547 | 5912 | 6276 |} 6640 | 7004 || 7368 | 7731 | 8094 | 8457 | 8819 | 363 





PROPORTIONAL PARTS, 


Go 2 Go G2 O29 OO oiee 


2 GO GO CO GO GO GO ¢ . . . . . . . . . 
DMDOOHWOOR TO 


AF AJ aS aS HFA FQ QT II-III NAVI VII 


OT OT OT OU OT 3 Od G3 G3 NNN AEN OH GO OO 





0 
8 
6 
4 
2 
0 

8 
6 
4 
2 
8 
8 
6 
4 
2 
0 
8 
16 
4 
R 
0 
8 
6 
4 
2 
0 
8 
6 
4 

2 
0 
8 
6 
4 
2 
0 
8 
6 
4 
2 


RR) Sa eee ee 
PRR SRUSS SISSSRARRRA 





132 LOGARITHMS OF NUMBERS. 





No. 120 L. 079.] [No. 134 L. 180. 
3 | 6 2 8 | 9 | Diff. 








a rf | ) 


120 | 079181 | 9543 | 9904 | G566 | 0626 || ooB7 | 1347 | 1707 | e067 | 2426 | 860 


1 | 082785 | 3144 | 3503 | 3861 | 4219 || 4576 | 4934 | 5291 | 5647 | 6004 
2 6360 | 6716 | 7071 | 7426 | 7781 || 8186 | 8490 | 8845 | 9198 | 9552 
3 9905 |——— 
————| 0258 | 0611} 0963 | 1315 || 1667 | 2018 | 2370 | 2721 | 307 352 
4 | 093422 | 3772 | 4122 ' 4471 | 4820 |! 5169 | 5518 | 5866 | 6215 | 6562 349 
5 6910 | 7257 | 7604 | 7951 | 8298 || 8644 | 8990 | 9335 | 9681 |—-— 
6 
7 
8 
9 
0 









































100371 | 0715 | 1059 | 1408 | 1747 || 2091 | 2434 | 2777 | 8119 | 3462 343 
3804 | 4146 | 4487 | 4828 | 5169 || 5510 | 5851 | 6191 | 6531 | 6871 341 
7210 | 7549 | 7888 | 8227 | 8565 ||} 8903 | 9241 | 9579 | 9916 |-—— 


























110590 | 0926 | 1263 | 1599 1934 2270 | 2605 | 2940 | 8275 | 3609 335 
3943 | 4277 | 4611 | 4944 | 5278 || 5611 | 5943 | 6276 | 6608 | 6940 333 





7271 | 7603 | 7934 | 8265 | 8595 || 8926 | 9256 | 9586 | 9915 


1560 | 1888 |) 2216 | 2544 | 2871 | 8198 | 3525 328 
4830 | 5156 || 5451 | 5806 | 6131 | 6456 | 6781 325 























1 

2 | 120574 | 0903 | 1231 
3 8852 | 4178 | 4504 
| 



































7105 | 7429 | 77538 | 8076 | 8399 || 8722 | 9045 | 9368 | 9690 : 
13 | 0012 323 
PROPORTIONAL PARTS. 

Diff 1 2 3 4 5 6 7 8 9 
355 35.5 71.0 106.5 142.0 177.5 213 0 248.5 284.0 | 319.5 
354 85.4 70.8 106.2 141.6 177.0 212.4 247.8 283.2 | 318.6 
3853 85.3 70.6 105.9 141.2 176.5 211.8 PAG td 282.4 | 317.7 
352 35.2 70.4 105.6 140.8 176.0 211.2 246.4 281.6 | 316.8 
851 85.1 70.2 105.3 140.4 175.5 210.6 245.7 280.8 | 315.9 
350 35.0 70.0 105.0 140.0 175.0 210.0 245.0 280.0 } 315.0 
349 34.9 69.8 104.7 189.6 174.5 209.4 244.3 279.2 | 314.1 
348 34.8 69.6 104.4 189.2 | %174.0 208.8 243.6 278.4 | 3138.2 
347 34.7 69.4 104.1 138.8 173.5 208.2 242.9 277.6 | 312.3 
346 34.6 69.2 103.8 138.4 173.0 207.6 242.2 276.8 | 311.4 
845 84.5 69.0 103.5 138.0 172.5 207.0 241.5 276.0 | 310.5 
344 34.4 68.8 103.2 137.6 172.0 206.4 240.8 275.2 | 309.6 
343 34.3 68.6 102.9 1I3t.2 ib 205.8 240.1 274.4 | 308.7 
342 34.2 68.4 102.6 136.8 171.0 205.2 239.4 273.6 | 307.8 
341 34.1 68.2 102.3 136.4 170.5 204.6 238.7 272.8 | 306.9 
340 384.0 68.0 102.0 136.0 170.0 204.0 238.0 272.0 | 306.0 
339 33.9 67.8 101.7 185.6 169.5 208 .4 20.3 271.2 | 305.1 
338 33.8 67.6 101.4 185.2 169.0 202.8 236.6 270.4 | 3804.2 
337 33. 67 101.1 134.8 168.5 202.2 235.9 269.6 | 303.3 
836 33.6 67.2 100.8 184.4 168.0 201.6 235.2 268.8 | 302.4 
335 83.5 67.0 100.5 134.0 167.5 201.0 234.5 268.0 | 801.5 
334 33.4 66.8 100.2 133.6 167.0 200.4 233.8 267.2 | 300.6 
333 33.3 66.6 99.9 13322 166.5 199.8 233.1 266.4 | 299.7 
332 33.2 66.4 99.6 132.8 166.0 199.2 232.4 265.6 | 298.8 
331 30.1 66 2 99.3 182.4 165.5 198.6 231.7) 264.8 | 297.9 
330 33.0 66.0 99.0 182.0 165.0 198.0 231.0 264.0 | 297.0 
829 32.9 65.8 98.7 131.6 164.5 197.4 230.3 2638.2 | 296.1 
328 32.8 65.6 98.4 131-2 164.0 196.8 229.6 262.4 | 295.2 
827 32.7 65.4 98.1 130.8 163.5 196.2 228.9 261.6 | 294.3 
826 32.6 65.2 97.8 180.4 163.0 195.6 228.2} 260.8 | 293.4 
325 82.5 65.0 97.5 180.0 162.5 195.0 227 5 260.0 | 292.5 
324 32.4 64.8 97.2 129.6 162.0 194.4 226.8 259.2 | 291.6 
323 32.3 64.6 96.9 129.2 161.5 193.8 226.1 258.4 | 290.7 
322 382.2 64.4 96.6 |. 128.8 | 161.0 193.2 225.4 257.6 | 289.8 








LOGARITHMS OF NUMBERS. 133 











































































































No. 135 L. 130.] [No. 149 L. 175. 
N. 0 1 2 8 4 6 | 6 q 8 9 | Diff. 
135 | 130384 | 0655 | 0977 | 1298 | 1619 || 1939 | 2260 | 2580 | 2900 | 3219 | 321 
6\ 3539 | 3858 | 4177 | 4496 | 4814 || 5138 | 5451 | 5769 | 6086 | 6403 | 318 
® | Great | 7087 | 7308 ré71 | 7987 || 8303 | 8618 | 9934 | 9249 | 9564 | 316 
8 | 9879 bel aa prsecS Creed BIST: 
__ | 0194 | 0508 | 0822 | 1136 || 1450 | 1763 | 2076 | 2389 | 2702 | 314 
9 | 143015 | 3327 | 3639 | 3951 | 4263 || 4574 | 4885 | 5196 | 5507 | 5818 | 311 
140! 6128 | 6488 | 6748 | 7058 | 7367 || vev6 | 7985 | 8294 | 8603 | 8911 | 309 
1| 9219 | 9527 | 9835 Tee wes ae 
poe 0142 | 0449 || 0756 | 1063 | 1370 | 1676 | 1982 | 307 
2 | 152288 | 2594 | 2900 | 3205 | 3510 || 3815 | 4120 | 4424 | 4728 | 5032 | 305 
3 | 5336 | 5640 | 5943 | 6246 | 6549 || 6852 | 7154 | 7457 | 7759 | 8061 | 308 
4| 8362 | 8664 | 8965 | 9266 | 9567 || 9868 || Sede 
LBs Se pat Ne Bask 2 ADA 0168 | 0469 | 0769 | 1068 | 301 
5 | 161368 | 1667 | 1967 | 2266 | 2564 || 2863 | 8161 | 3460 | 3758 | 4055 | 299 
6| 4353 | 4650 | 4947 | 5244 | 5541 || 5888 | 6134 | 6430 | 6726 | 7022) 297 
7 | 17 | 7613 | 7908 | 8203 | 8497 || 8792 | 9086 | 9380 | 9674 | 9968] 295 
8 | 170262 | 0555 | 0848 | 1141 | 1434 || 1726 | 2019 | 2311 | 2603 | 2805 | 993 
9| 3186 | 3478 | 8769 | 4060 | 4351 || 4641 | 4932 | 5222 | 5512 | 5802 | 201 
PROPORTIONAL PARTS. 
Diff.) 1 | 2 3 4 5 6 M7 8 9 
321 | 32.1 | 64.2 | 96.3 | 128.4| 160.5| 192.6| 224.7 | 256.8 | 288.9 
320 | 32.0] 64.0 | 96.0 | 128.0] 160.0| 192.0] 224.0 | 256.0 | 288/0 
319 |31.9| 63.8 | 95.7 | 127.6] 159.5| 191.4 | 293.3 | 255.2 | 287/1 
318 |31.8| 63.6 | 95.4 | 127.2] 159.0| 190.8| 292.6| 254.4 | 286.2 
3i7 | 31.7] 63.4 | 95.1 | 126.8] 158.5| 190.2| 221.9 | 253.6 | 285.3 
316 | 31.6) 63.2 | 94.8 | 126.4] 158.0] 189.6 | 221.2! 252.8 | 284\4 
3i5 |31.5| 68.0 | 94.5 | 196.0] 457.5| 189.0 | 220.5 | 252/0 | 2838/5 
314 | 31.4| 62:8 | 94.2 | 125.6| 157.0| 188.4] 219.8| 251.2 | 292.6 
313 | 31.3 | 62.6 | 93.9 | 125.2] 156.5 | 187.8| 219.1 | 250.4 | 281.7 
312 | 31.2] 62.4 | 93.6 | 124.8| 156.0| 187.2 | 218.4 | 249.6 | 280.8 
311 |31.1| 62.2 | 98.3 | 124.4] 155.5] 186.6| 217.7] 248.8 | 279.9 
310 | 31.0! 62.0 | 98.0 | 124.01 155.0| 186.0] 217.0 | 248.0 | 279'0 








805 | 80.5] 61.0 91.5 122.0 | 152.5 | 1838.0 | 218.5 | 244.0 | 274.5 
304 | 30.4 | 60.8 91.2 121.6 | 152.0 | 182.4 | 212.8 | 248.2 | 273.6 
303 | 80.3 | 60.6 90.9 121.2} 151.5 | 181.8 |. 212.1 | 242.4 | 272.7 
302 | 80.2 | 60.4 90.6 120.8 | 151.0 | 181.2) 211.4 | 241.6 | 271.8 
301 | 30.1 | 60.2 90.3 120.4 | 150.5 180.6 | 210.7 | 240.8 | 270.9 
300 | 30.0 | 60.0 90.0 120.0 | 150.0; 180.0 | 210.0 | 240.0 | 270.0 
299 | 29.9 | 59.8 89.7 119.6 | 149.5 | 179.4 | 209.3} 2389.2 | 269.1 
298 | 29.8 | 59.6 89.4 119.2 | 149.0} 178.8 | 208.6 | 288.4 | 268.2 
297 | 29.7 | 59.4 89.1 118.8 | 148.5 | 178.2 | 207.9 | 287.6 | 267.3 
296 | 29.6 | 59.2 88.8 118.4 | 148.0 | 177.6 | 207.2 | 286.8 | 266.4 
295 | 29.5 59.0 88.5 118.0 | 147.5) 177.0 | 206.5 | 2386.0 | 265.5 
294 | 29.4, 58.8 88.2 117.6 | 147.0 | 176.4 | 205.8 | 285.2 | 264.6 
293 | 29.3 | 58.6 87.9 117.2 | 146.5 | 175.8 | 205.1 | 284.4 | 263.7 
292 | 29.2 | 58.4 87.6 116.8 | 146.0 | 175.2] 204.4 | 283.6 | 262.8 
291 | 29.1] 58.2 87.3 116.4 | 145.5) 174.6 | 2038.7 | 282.8 | 261.9 
290 | 29.0) 58.0 87.6 116.0 | 145.0 | 174.0] 208.0 | 282.0 | 261.0 
289 | 28.9] 57.8 86.7 115.6 | 144.5 |} 178.4 | 202.38 | 281.2 | 260.1 
288 | 28.8 | 57.6 86.4 115.2 | 144.0 | 172.8 | 201.6 | 280.4 | 259.2 
287 | 28.7 | 57.4 86.1 114.8 | 148.5 | °172.2 | 200.9 | 229.6 | 258.3 
286 | 28.6 | 57.2 85.8 114.4 | 148.0] 171.61 200.2 | 228.8 | 257.4 


134 LOGARITHMS OF NUMBERS. 























































































































| No. 150 L. 176.] [No. 169 L. 230, | 
N. 0 1 | 2 3 | 4 | 5 6 | a 8 9 | Diff. | 
150 76091 | 63881 | 6670 | 6959 | 7248 {| 7586 | 7825 | 8113 | 8401 | 8689 289 
1 8977 | 9264 | 9552 | 98389 |——— ee irae 
Eee, 0126 || 0413 | 0699 | 0986 | 1272 | 1558 287 
2 | 181844 | 2129 | 2415 | 2700 | 2985 || 8270 | 3555 | 38889 | 4123 | 4407 285 
3| 4691 | 4975 | 5259 | 5542 | 5825 || 6108 | 6391 | 6674 | 6956 | 7239 | 283 
4 7521 | 7803 | 8084 | 83866 | 8647 || 8928 | 9209 | 9490 | 9771 
5 | 190332 | 0612 | 0892 | 1171 | 1451 1730 | 2010 
6 3125 | 3403 | 8681 | 8959 | 4237 || 4514 792 
fe 5900 | 6176 | 6453 | 6729 | 7005 || 7281 | 7556 
8 8657 | 8982 | 9206 | 9481 | 9755 ||—_]—}|—_ |__| ____ 
ee la —. 0029 | 038038 
9 | 201897 | 1670 | 1943 | 2216 | 2488 || 2761 | 8083 
160 4120 | 4391 | 4663 | 4934 | 5204 || 5475 | 5746 
1 6826 | 7096 | 7365 | 7634 | 7904 || 81738 | 8441 
2 9515 | 9783 aa | <_< |—____|____ 
—__—_—_ |__| 0051 | 0319 | 0586 || 0853 | 1121 
8 | 212188 | 2454 | 2720 | 2986 | 8252 || 3518 | 3783 
4 4844 | 5109 | 5873 | 5638 | 5902 || 6166 | 6480 
5 7484 | 7747 | 8010 | 8278 | 8536 || 8798 | 9060 
6 | 220108 | 0370 | 0681 | 0892 | 1153 || 1414 | 1675 
q 2716 | 2976 | 82386 | 3496 | 8755 || 4015 | 4274 
8 5309 | 5568 | 5826 | 6084 | 6342 || 6600 | 6858 
9 pg 8144 | 8400 | 8657 | 8913 || 9170 | 9426 
PROPORTIONAL PARTS. 
Diff 1 2 8 4 5 6 
285 28.5 57.0 85.5 114.0 142.5 171.0 
28.4 56.8 85.2 113.6 142.0 170.4 
283 28.3 56.6 84.9 113.2 141.5 169.8 
282 28 .2 56.4 84.6 112.8 141.0 169.2 
281 28.1 56.2 84.3 112 4 140.5 168.6 
28.0} 56.0 84.0 112.0 140.0 168.0 
279 27.9 55.8 83.7 111.6 189.5 167.4 
27 27.8 55.6 83.4 111.2 139.0 166.8 
Q77 Qi o6a OO se 83.1 110.8 188.5 166.2 
276 27.6 Hayes 82.8 110.4 188.0 165.6 
27 27.5 55.0 82.5 110.0 187.5 165.0 
274 27.4 54.8 S2.8) 109.6 137.0 164.4 
273 27.3 54.6 81.9 109.2 136.5 163.8 
Q72 Paes Ps 54.4 81.6 108.8 1386.0 163.2 
271 ha | 54.2 81.3 108.4 135.5 162.6 
270 27.0 54.0 81.0 108.0 1385.0 162.0 
269 26.9 53.8 80.7 107.6 1384.5 161.4 
268 26.8 53.6 80.4 107.2 134.0 160.8 
267 26.7 53.4 80.1 106.8 1383.5 160.2 
266 26.6 53.2 79.8 106.4 1383.0 159.6 
265 26.5 53.0 "9.5 106.0 182.5 159.0 
264 26.4 52.8 79.2 105.6 182.0 158.4 
263 26.3 52.6 78.9 105.2 181.5 157.8 
262 26.2 52.4 78.6 104.8 131.0 1D vee 
261 26.1 5252 78.3 104.4 130.5 156.6 
260 26.0 52.0 %8.0 104.0 130.0 156.0 
259 25.9 51.8 V7.0 103.6 129.5 155.4 
258 25.8 51.6 7.4 103.2 129.0 154.8 
257 25.7 51.4 Tico 102.8 128.5 154.2 
256 235.6 5p ay 2 76.8 102.4 128.0 153.6 
255 2565 51.0 76.5 102.0 IZA 153.0 








LOGARITHMS OF NUMBERS, 12 





No. 170 L. 230.] 







































é ‘ 4 ( 
1|~ 2996 | 3250 | 3504 | 3757 | 4011 || 4264 | 4517 | 4770 | 5023 | 5276 | 253 
2] 5528 | 5781 | 6033 | 6285 | 6537 || 6789 | 7041 | 7292 | 7544 | 7795 | 252 
3| 8046 | 8297 | 8548 | 8799 | 9049 || 9299 | 9550 | 9800 | —_|___ 
PST ed RR, Mena | AS LOANED 0050 | 0300 | 250 
4 | 240549 | 0799 | 1048 | 1297 | 1546 || 1795 | 2044 | 2203 | 2541 | 2790] 249 
5 | 3038 | 3286 | 3534 | 8782 | 4030 || 4277 | 4525 | 4772 | 5019 | 5266 | 248 
6| 5513.) 5759 | 6006 | 6252 | 6499 || 6745 | 6991 | 7237 | 7482 | 7728 | 246 
7| 7973 | 8219 | 8464 | 8709 | 8954 |) 9198 | 9443 | 9687 | 9932 7 
a a | O16 Lad 
g | 250420 | 0664 | 0908 | 1151 | 1395 || 1638 | 1881 | 2125 | 2368 | 2610 | 243 
9 | 2853 | 3096 | 3338 | 3580 | 3822 || 4064 | 4306 | 4548 | 4790 | 5031 | 242 
180] 5273 | 5514 | 5755 | 5996 | 6237 || 6477 | 6718 | 6958 | 7198 | 7439} 241 
1| 7679 | 7918 | 8158 | 8398 | 8637 || 8877 | 9116 | 9355 | 9594 | 9833 | 239 
3 | 260071 | 0310 | 0548 | 0787 | 1025 || 1263 | 1501 | 1739 | 1976 | 2214 | 238 
3| 2451 | 2688 | 2925 | 3162 | 3399 || 3636 | 3873 | 4109 | 4346 | 4582 | 237 
4] 4818 | 5054 | 5290 | 5525 | 5761 || 5996 | 6232 | 6467 | 6702 | 6937 | 235 
5| 172 | 7406 | 7641 | 7875 | 8110 || 8844 | 8578 | 8812 | 9046 | 9279 | 284 
6} 9513 | 9746 | 9980 | —— | eaten era ens ei alle Bil 
——|——_| 0218 | 0446 |] 0679 | 0912 | 1144 | 1377 | 1609 | 233 
7 | 271842 | 2074 | 2806 | 2538 | 2770 || 3001 | 3233 | 3464 | 3696 | 3927 | 282 
8 | 4158 | 4389 | 4620 | 4850 | 5081 || 5311 | 5542 | 5772 | 6002 | 6232 | 230 
9| 6462 | 6692 | 6921 | 7151 | 7380 || 7609 | 7838 | 8067 | 8296 | 8525 | 229 








PROPORTIONAL Parts, 





























Diff.| 1 2 3 4 5 6 7 8 | 9 
25 | 25.5] 61.0 | 76.5 | 102.0] 127.5] 153.0] 178.5 | 204.0 | 229.5 
254 | 25.4] 50:8 | 7%. 2 152:4 | 17:8 | 203:2 | 228°6 
253 | 25.8| 50.6 | %5.9 | 101-2] 126.5 | 151.8] 177.1 | 202.4 | 227-7 
252 | 25.2] 50.4 | 75.6 | 100.8] 126.0] 151.2] 176.4] 201.6 | 226.8 
251 | 25.1} 50:2 | 75.3 | 100.4] 125.5] 150.6] 175.7 | 200.8 | 225.9 
250 | 250] 50.0 | %.0 | 100.0] 125.0] 150.0] 175.0 | 200.0 | 225.0 
a9 | 24.9] 49.8 | 74.7 | 99.6 | 124.5] 149.4] 174.3] 199.2 | 204.1 
248 | 24.8| 49.6 | 74.4 | 99.2] 124.0] 148.8] 173.6] 198.4 | 223.2 
47 | 24.7] 49.4 | 74.1 | 98.8] 123.5] 148.2] 172.9] 197.6 | 222.3 
246 | 24.6] 49.2 | 73.8 | 98.4] 123.0] 147.6) 172.2 | 196.8 | 221.4 
245 | 24.5] 49.0 | 73.5 | 98.0] 122.5] 147.0] 171.5) 196.0 | 220.5 
24 | 24.4] 48.8 | 73.2 7.6] 122.0] 146.4] 170.8] 195.2 | 219.6 
243 | 24.3] 48.6 | 72.9 V2] 121.5 | 145.8) 170.1] 194.4 | 218.7 
249 | 24:2] 48.4 | 72.6 | 96.8 121.0] 145.2] 169.4] 193.6 | 217.8 
241 | 24.1] 48.2 | 72.3 | 96.4] 120.5] 144.6] 168.7 | 192.8 | 216.9 
240 | 24.0] 48.0 | 72.0 | 96.0] 120.0] 144.0] 168.0 | 192.0 | 216.0 
939 | 23.9| 47.8 | 71.7 | 95.6] 119.5] 143.4] 167.3] 191.2 | 215.1 
238 | 23.8] 47.6 | 71.4 | 95.2] 119.0] 142.8] 166.6 | 190.4 | 214.2 
237 | 93.7] 47.4 | T11 | 94:8] 118.5] 142.2] 165.9] 189.6 | 213.3 
236 | 23.6| 47.2 | 70.8 | 94.4] 118.0] 141.6| 165.2] 188.8 | 212.4 
235 | 23.5) 47.0 | 70.5 | 94.0) 117.5] 141.0| 164.5 | 188.0 | 211.5 
234 123.4] 46.8 | 70.2 | 93.6] 117.0] 140.4] 163.8] 187.2 | 210.6 
933 | 93.3| 46.6 | 69.9 | 93.2| 116.5] 139.8] 163.1 | 186.4 | 209.7 
232 | 23.2] 46.4 | 69.6 | 92.8| 116.0] 139.2] 162.4 | 185.6 | 208.8 
931 | 93.1| 46.2 | 69.3 | 92.4| 115.5] 138.6 | 161.7] 184.8 | 207.9 
230 | 23.0] 46.0 | 69.0 | 92.0} 115.0} 138.0] 161.0] 184.0 | 207.0 
229 | 22.9] 45.8 | 68.7 | 91.6| 114.5 | 187.4] 160.3) 183.2 | 206.1 
228 122.8] 45.6 | 684 | 91.2] 114:0| 136.8| 159.6 | 182.4 | 205.2 
22.7 68.1 | 90.8 | 113.5 | 136.2) 158.9 | 181.6 | 204.8 
22.6 ! 





136 LOGARITHMS OF NUMBERS, 


No. 190 L. 278.] \ [No. 214 L. 332. 





a mn | | me | a | ee OO | OO 


3 


——— | | | 


——_— | | | ———— | — | — —_ ] —__ 


COONS RPwwoe 


SS es 


2 
S 





311754 
3867 
5970 
8063 


820146 


2219 
4282 
6336 
8380 


tw) 
eS 
ey WHR O DO OND RPwWDeH 











—_|-——_ 203 


830414 | 0617 | 0819 | 1022 | 1225 202 


PROPORTIONAL PARTS. 


| | | | | | 


22 
8 RERRBBEN 


I DOOHW WP OT 


DP AArDOAAO2OWAID 
Or QUOT DI DP INI AE 
Re BRIO 09M OF 





SSSEEEES SESHSSSSS SSREERES 
PODOWRAD OCWRADOWR ADGWRANO 


182.7 
181.8 


No. 215 L. 832.] 











LOGARITHMS OF NUMBERS. 























137 






































[No. 239 L. 380. 
N. 0 1 2 4 4 5 6 vj 8 9 | Diff. 
215 | 382488 | 2640 | 2842 8246 || 3447 | 3649 | 3850 | 4051 | 4253 202 
6 4454 | 4655 | 4856 | 5057 | 5257 || 5458 | 5658 | 5859 | 6059 | 6260 201 | 
i 6460 | 6660 | 6860 | '7060 | 7260 || 7459 | 7659 | 7858 | 8058 | 8257 200 
8 8456 | 8656 | 8855 | 9054 | 9253 |) 9451 | 9650 | 9849 ——_ 
ma | | ——-— 0047 | 0246 199 
9 | 340444 | 0642 ; 0841 | 1039 | 1287 || 14385 | 1682 | 1880 | 2028 | 2225 198 
220 2423 | 2620 | 2817 | 8014 | 8212 || 3409 | 3606 | 3802 | 3999 | 4196 197 
1 4892 | 4589 | 4785 | 4981 | 517’ 53874 | 5570 | 5766 | 5962 | 6157 196 
2 6353 | 6549 | 6744 | 6939 | 7185 || 73830 | 7525 | 7720 | 7915 | 8110 195 
3 8305 | 8500 | 8694 | 8889 | 90838 || 9278 | 9472 | 9666 | 9860 ar ' +S, 
a a eS Se See se 5. 
41 350248 | 0442 | 0686 | 0829 | 1023 || 1216 | 1410 | 1603 | 1796 | 1989 193 
5 21838 | 23875 | 2568 | 2761 | 2954 || 3147 | 3889 | 3532 | 3724 | 3916 193 
6 4108 | 4801 | 4498 | 4685 } 4876 |} 5068 | 5260 | 5452 | 5643 | 5834 192 
v6 6026 | 6217 | 6408 | 6599 | 6790 |} 6981 | 7172 | 7363 | 7554 | 7744 191 
8 ae 8125 | 8816 | 8506 | 8696 || 8886 | 9076 | 9266 | 9456 | 9646 190 | 
9 SM Ss a oR SS i (ES 
0025 | 0215 | 0404 | 0593 || 0788 | 0972 | 1161 | 1850 | 15389 189 
| 230 | 861728 | 1917 | 2105 | 2294 | 2482 || 267 2859 | 3048] 3286 | 3424 188 | 
: a 8612 | 8800 | 3988 7 4176 | 4363 |; 4551 | 4739 | 4926 | 5113 | 53801 188 
2 5675 | 5862 | 6049 | 6236 || 6423 | 6610 | 6796 | 6983 | 7169 187 
3 7356 | 7542 | 7729 | 7915 } 8101 || 8287 | 8473 | 8659 | 8845 | 90380 186 
4 9216 f 9401 | 9587 | 977: 9958 ——— | ———_|—_— | ——___|—__. 
—_— —— 0148 | 0828 | 0513 | 0698 | 08838 185 
5 | 871068 | 1253 | 1487 | 1622 | 1806 || 1991 | 2175 | 2360 | 2544 | 2728 184 
6. 2912 | 8096 | 3280 | 8464 | 3647 || 8881 | 4015 | 4198 | 43882 | 4565 184 
tf 4748 | 4932 | 5115 | 5298 | 5481 || 5664 | 5846 | 6029 | 6212 | 6394 183 
8 6577 | 6759 | 6942 | 7124 | 7306 || 7488 | '7670 | 7852 | 8034 | 8216 182 
9 8398 | 8580 | 8761 | 8943 | 9124 || 9806 | 9487 | 9668 | 9849 
38 0080 | 181 
PROPORTIONAL PARTS. 
Diff 1 2 3 4 5 6 v4 8 9 
202 } 20.2) 40.4 60.6 80.8 101.0 121.2 141.4 161.6 | 181.8 
201 20.1 40.2 60.3 80.4 100.5 120.6 140.7 160.8 | 180.9 
200 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 | 180.0 
199 19.9 89.8 59.7 79.6 99.5 119.4 139.3 159.2 | 179.1 
198 19.8 89.6 59.4 79.2 99.0 118.8 138.6 158.4 | 178.2 
197 197. 89.4 59.1 78.8 98.5 118.2 137.9 157.6 | 177.3 
196 19.6 89.2 58.8 78.4 98.0 117.6 137.2 156.8 | 176.4 
195 19.5 39.0 58.5 78.0 97.5 117.0 1386.5 156.0 | 175.5 
194 19.4 38.8 58.2 SUG 97.0 116.4 135.8 155.2 | 174.6 
193 | 19.3] 38.6 57.9 72 96.5 | 115.8} 185.1 | 154.4 | 173.7 
192 19.2 88.4 57.6 76.8 96.0 115.2 184.4 158.6 | 172.8 
191 19.1 38.2 57.3 76.4 95.5 114.6 (BS er¢ 152.8 | 171.9 
190 19.0 38.0 57.0 76.0 95.0 114.0 133.0 152.0 | 171.0 
189 18.9 37.8 56.7 75.6 94.5 113.4 182.3 151.2) goed 
188 18.8 37.6 56.4 75.2 94.0 112.8 131.6 150.4 | 169.2 
187 18.7} 374 56.1 94.8 93.5 T1I2ES 130.9 149.6 | 168.3 
186 18.6 37.2 55.8 94.4 93.0 111.6 130.2 148.8 | 167.4 
185 | 18.5 | 37.0 55.5 74.0 92.5] 111.0} 129:5 | 148.0 | 166.5 
184 18.4 36.8 55.2 73.6 92.0 110.4 128.8 147.2 | 165.6 
183 |18.3| 36.6 54.9 43.2 91.5) 109.8 | 128.1 | 146.4 | 164.7 
182 18.2 36.4 54.6 72.8 91.0 109.2 127.4 145.6 | 163.8 
181 .| 18.1 36.2 54.3 72.4 90.5 108.6 126.7 144.8 | 162.9 
180 18.0] 36.0 54.0 72.0 90.0 108.0 126.0 144.0 } 162.0 
179 17.9 35.8 53.7 71.6 89.5 107.4 125.3 143.2 | 161.1 


138 LOGARITHMS OF NUMBERS, 





No, 240 L. 380.] [No. 269 L. 431. 











OU 0 te 
= 
Oo 
2 
6 8) 
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er) 
use 
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Ps 
Ne} 
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er 
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7940 | 8114 | 8287 | 8461 | 8634 |! 8808 | 8981 | 9154 | 9328 | 9501 | 173 
9674 | 9847 


401401 | 1573 | 1745 | 1917 | 2089 || 2261 | 2433 | 2605 | 2777 | 2949 72 
3121 | 8292 | 3464 | 3635 |.38807 || 38978 | 4149 | 43820 | 4492 | 4663 | 171 
4834 | 5005 | 5176 | 5346 | 5517 || 5688 | 5858 | 6029 | 6199 | 6370] 171 
6540 | 6710 | 6881 | 7051 | 7221 || 7391 | 7561 | 7731 | 7901 | 8070} 170 
mi 8410 | 8579 | 8749 | 8918 || 9087 | 9257 | 9426 | 9595 | 9764 | 169 
9 Ue 

————| 0102 | 0271 | 0440 | 0609 || O77’? | 0946 | 1114 | 1283 | 1451 | 169 

411620 | 1788 | 1956 | 2124 | 2293 || 2461 | 2629 | 2796 | 2964 | 31382 | 168 

8300 | 3467 | 3635 | 3803 | 397 41387 | 4305 | 4472 | 4639 | 4806 | 167 


4973 | 5140 | 5307 | 5474 | 5641 || 5808 | 5974 | 6141 | 6308 | 6474 | 167 
6641 | 6807 | 6973 | 71389 | 7306 || 7472 | 7638 | 7804 | 7970 | 8135 | 166 
8301 | 8467 | 8633 |. 8798 | 8964 || 9129 | 9295 | 9460 | 9625 | 9791 | 165 


————-| 0121 | 0286 | 0451 | 0616 || 0781. | 0945 | 1110 | 1275 | 1439 | 165 
421604 | 1768 | 1983 | 2097 | 2261 || 2426 | 2590 | 2754 | 2918 | 3082} 164 
8246 | 3410 | 3574 | 38737 | 8901 || 4065 | 4228 | 4892 | 4555 | 4718 | 164 
4882 | 5045 | 5208 | 5871 | 5534 || 5697 | 5860 | 6023 | 6186 | 6349 | 163 
6511 | 6674 | 6836 | 6999 | 7161 |) 7324 | 7486 | 7648 | 7811 | 7978} 162 
8135 | 8297 | 8459 | 8621 | 87838 || 8944 | 9106 | 9268 | 9429 | 9591 | 162 


rie) 
OV 


OCOANATR WHHS OM VOorhwwo KO COIS 
























































ri) 
S 















































9752 | 9914 |——~ he festa 
43 0075 | 0236 | 0398 || 0559 | 0720 | O881 | 1042 | 1208 161 
PROPORTIONAL PARTS, 
Diff 1 2 3 4 5 6 fe 8 9 
178 17.8 35.6 53.4 (lee 89.0 106.8 124.6 142.4 | 160.2 
iver Lit 35.4 Doel 70.8 88.5 106.2 123.9 141.6 | 159.38 
176 17.6 35.2 52.8 70.4 88.0 105.6 123.2 140.8 | 158.4 
Love) Lt 35.0 S2u5 70.0 87.5 105.0 122.5 140.0 | 157.5 
174 17.4} 34.8 §2.2 69.6 87.0 104.4 121.8 189.2 | 156.6 
173 17.3 34.6 51.9 69.2 86.5 103.8 4 i | 138.45) 155.7 
172 AW 4 34.4 51.6 68.8 86.0 103.2 120.4 187.6 | 154.8 
171 17.1 34.2 51.3 68.4 85.5 102.6 119.7 1386.8 | 153.9 
170 17.0 34.0 51.0 68.0 85.0 102.0 119.0 136.0 | 153.0 
169 16.9 33.8 50.7 67.6 84.5 101.4 118.35} 135.2) ). 152.1 
168 16.8 83.6 50.4 67.2 84.0 100.8 117.6 1384.4 | 151.2 | 
16.7 33.4 50.1 66.8 83.5 100.2| 116.9 1383.6 | 150.3 
16.6 33.2 49.8 66.4. 83.0 99.6 116.2 182.8 | 149.4 
16.5 33.0 49.5 66.0 82.5 99.0 115.5 182 148.5 
16.4 32.8 49.2 65.6 82.0 98.4 114.8 1381.2 | 147.6 
16.3 82.6 48.9 65.2 81.5 97.8 114.1 130.4 | 146.7 
16.2 32.4 48.5 64.8 81.0 97.2 113.4 129.6 | 145.8 
16.1 382.2 48.3 64.4 80.5 96.6 112.7 128.8 } 144.9 








No. 270 L. 431.] 





LOGARITHMS OF NUMBERS. 


[No. 299 L. 476. 


139 












































































































270 | 481364 | 1525 | 1685 
1 | 2969 | 3130 | 8290 | 3450 | 3610 || 3770 | 8930 | 4090 | 4249 | 4409 | 160 
2} 4569 | 4729 4 4888 | 5048 | 5207 || 5367 | 5526 | 5685 | 5844 | 6004 | 159 
3| 6163 | 6322 | 6481 | 6640 | 6799 || 6957 | 7116 | T275 | 7433 | 7592] 159 
4| 751 | 7909 | 8067 | 8226 | 8384 || 8542 | 8701 | 8859 | 9017 | 9175 | 158 
5 | 9333 | 9491 | 9648 | 9806 | 9964 |!——_|_____ |-____|_ 
ae ee —|| 0122 | 0279 | 0437 | 0594 | 0752 | 158 
6 | 440909 | 1066 | 1224 | 1381 | 1538 || 1695 | 1852 | 2009 | 2166 | 2383 | 157 
7 | 2480 | 2637 | 2793 | 2950 | 3106 || 8263 | 3419 | 3576 | 3732 | 3889] 157 
8} 4045 | 4201 | 4357 | 4513 | 4669 || 4825 | 4981 | 5137 | 5293 | 5449] 156 
9| 5604 | 5760 | 5915 | 6071 | 6226 || 6382 | 6537 | 6692 | 6848 | 7003 | 155 
280 | 7158 | 7313 | 7468 | 7623 | 7778 || 7933 } 8088 | S242 | 8397 | 8552 | 155 
1| 8706 | 8861 | 9015 | 9170 | 9324 || 9478 ( 9633 | 9787 | 9941 
——|—_ — — 0095 | 154 
2 | 450249 | 0403 | 0557 | O711 | 0865 || 1018 | 1172 | 1326 | 1479 | 1633 | 154 
3| 1786 | 1940 | 2093 | 2247 | 2400 || 2553 | 2706 | 2859 | 3012 | 3165 | 153 
4| 3318 | 3471 | 3624 | 3777 | 3930 || 4082 | 4235 | 4387 | 4540 | 4692 | 153 
5} 4845 | 4997 | 5150 | 5302 | 5454 || 5606 | 5758 | 5910 | 6062 | 6214] 152 
6} 6366 | 6518 | 6670 | 6821 | 6973 || 7125 | 7276 | 7428 | 7579 | 7731 | 152 
7 | 7882 | 8033 | 8184 | 8336 | 8487 || 8638 | 8789 | 8940 | 9091 | 9242 | 151 
S| | 9392 1.9543 | 9604 | 9845 | 9995 |} —— | 
—_—_|—___|—___;___|—__| 0146 | 0296 | 0447 | 0597 | 0748 | 151 
9 | 460898 | 1048 | 1198 | 1348 | 1499 || 1649 | 1799 | 1948 | 2098 | 2248 | 150 
290 | 2398 | 2548 | 2697 | 2847 | 2997 || 8146 | 8296 | 3445 | 3594 | 8744 | 150 
1} 3893 | 4042 | 4191 | 4340 | 4490 | 4639 | 4788 | 4936 | 5085 | 5234 | 149 
2| 5383 | 5582 | 5680 | 5829 | 5977 || 6126 | 6274 | 6423 | 6571 | 6719 | 149 
3| 6868 | 7016 | 7164 | 7312 | 7460 |) 7608 | 7756 | '7904 | 8052 | 8200] 148 
4| 8347 | 8495 | 8643 | 8790 | 8938 || 9085 | 9233 | 9380 | 9527 | 9675 | 148 
5 | 9822 | 9969 j—— a 
———| 0116 | 0263 | 0410 | 0557 | 0704 | 0851 | 0998 | 1145 | 147 
6 | 471292 | 1438 | 1585 | 1732 | 1878 | 2025 | 2171 | 2318 | 2464 | 2610 | 146 
7 | 2756 | 2903 | 3049 | 3195 | 3341 || 3487 | 3033 | 38779 | 3925 | 4071 | 146 
8 | 4216 | 4362 | 4508 | 4653 | 4799 || 4944 | 5090 | 5235 | 6381 | 5526 | 146 
9 | 5671 | 5816 | 5962 | 6107 | 6252 || 6397 | 642 | 6687 | 6832 | 6976 | 145 
| ! 
PROPORTIONAL PARTS. 
Die (met 2 3 4 5 6 7 8 9 
161 | 16.1] 32.2 | 48.3 | 64.4 | 80.5 | 96.6 | 112.7 | 128.8 | 144.9 
160 | 16.0] 32.0 | 48.0 | 64.0 | 80.0 | 96.0 | 112.0] 128.0] 144.0 
159 |15.9| 31.8 | 47.7 | 68.6 | 79.5 | 95.4 | 111.3]. 127.2 | 143.1 
158 | 15.8| 31.6 | 47.4 | 638.2 | 79.0 | 94.8 | 110.6] 126.4 | 142.2 
157 |15.7| 81.4 | 47.1 | 62.8 | 78,5) | 94.2 |. 109.9] 125.6) 141.3 
156 | 15.6| 31.2 | 46.8 | 62.4 | 78.0 | 93.6 | 109.2] 124.8 | 140.4 
155 | 15.5] 31.0 | 46.5 | 62.0 | 77.5 | 93.0 | 108.5| 124.0] 139.5 
154 | 15.4] 30.8 | 46.2 | 61.6 | %7.0 | 92.4 | 107.8] 123.2 | 138.6 
153° | 15.3| 30.6 | 45.9 | 61.2 | 76.5 | 91.8 | 107.1 | 122.4 | 187.7 
152 |15.2| 30.4 | 45.6 | 60.8 | 76.0 | 91.2 } 106.4] 121.6] 136.8 
151 | 15.1 | 80.2 | 45.3. | 60.4. | 75.5 |. 90.6 | 105.7 | 120-8 | 185.9 
45.0 | 60.0 | %5.0 | 90.0 | 105.0] 120.0 | 135.0 
44.7 | 596 } 74.5 | 89.4 | 104.3) 119.2 | 184.1 
44.4 | 59.2 | 74.0 | 88.8 | 103.6] 118.4 | 183.2 
44.1 | 58.8 | 73.5 | 88.2 | 102.9] 117.6 | 132.3 
43.8 | 58.4 | %3.0 | 87.6 | 102.2| 116.8} 131.4 
43.5 | 58.0 | 72.5 | 87.0 | 101.5] 116.0] 130.5 
43.2 | 57.6 | 72.0 | 86.4 | 100.8} 115.2] 129.6 
42.9 | 57.2 | 71.5 | 85.8 | 100.1] 114.4 | 128.7 
42.6 | 56.8 | 71.0 | 852 | 99.4] 118.6 | 127.8 
42.8 | 56.4 | 70.5 | 84.6 98 1 | 112.8 | 126.9 
42.0 | 56.0 | 70.0 | 81.0 98.0 126.0 





co 


© =F Od. OT 9 aS 


oo 
hare 


HD OTH C2 0 


2 


7 
8 
9 
0 
1 
2 
3 
L 
5 
6 
7 
8 


oo 
(Su) 


Oo BIOowhwo HMO © 


7266 
8711 


491362 


2760 
4155 
5544 
6930 
8311 
9687 


501059 


530200 | 0328 


LOGARITHMS OF NUMBERS, 
(No. 339 L. 531. 


7 8 


411 | 7555 | 7700 || 7844 | 7989 | 8133 | 8278 
8855 | 8999 | 9143 || 9287 | 9431 | 9575 | 9719 
0294 | 0438 0725 | 0869 | 1012 

1729 





9802 
rt 
0456 | 0584 | 0712 || 0840 | o968 | 1096 | 1228 | 1351 


PROPORTIONAL PARTS, 


Sonne 


SSPSSSSSSSERE 
HS RIOWHrONWOIOH PY 
Oror v 
SHASSSSSS REA 
DWOAOCKDNDWAOCKLOANMWO 
a2 +2 
JSNFSSSSLLSSS 
0 DO RO DW WR OW DH Pre 
eo OOO 

SESLLLSSESESS 
COWOWR KH OOTW ODO 


— 
——= 
_ 


101.6 | 114.3 





BS LOGARITHMS OF NUMBERS. 141 





























1 
2 
3 
4 
5 
6 
7 
8 
9 
350 
1 
2 
3 
4 
5 
6 
@ 
8 
9 
360 
1 7507 | 7627 | 7748 | 7868 | 7988 || 8108 | 8228 | 8349 | 8469 | 8589 | 120 
2 8709 | 8829 | 8948 | 9068 | 9188 || 9308 | 9428 | 9548 | 9667 | 9787 | 120 
3 9900 | ———_ __—_— |__| | I 
0026 | 0146 | 0265 | 0385 || 0504 | 0624 | 0743 | 0863 | 0982} 119 
4 | 561101 | 1221 | 1340 | 1459 | 157 1698 | 1817 | 1936 | 2055 | 2174 | 119 
5 2293 | 2412 | 2531 | 2650 | 2769 || 2887 | 3006 | 3125 | 8244 | 3362] 119 
6 8481 | 3600 | 3718 | 3837 | 3955 || 4074 | 4192 | 4311 | 4429 | 4548 | 119 
7 4666 | 4784 | 4903 | 5021 | 51389 || 5257 | 53876 | 5494 | 5612 | 5730] 118 
8 5848 | 5966 | 6084 | 6202 | 6320 || 6437 | 6555 | 6673 | 6791 | 6909 | 118 
9 7026 | 7144 | 7262 | 7379 | 7497 || 7614 | 77 (849 | 7967 | 8084} 118 
370 8202 | 8319 | 8436 | 8554 | 8671 || 8788 | 8905 | 9023 | 9140 | 9257 | 117 
1 9374 | 9491 | 9608 | 9725 | 9842 || 9959 /———;__-|_-_—_ 
ee eee eee ee ee 0076 | 0193 | 0309 | 0426 | 117 
2 | 570543 | 0660 | 0776 | 0893 | 1010 || 1126 | 1243 | 1359 | 1476 | 1592 | 117 
3 1709 | 1825 | 1942 | 2058 | 2174 || 2291 | 2407 | 2523 | 2639 | 2755 | 116 
4 2872 | 2988 | 3104 | 3220 | 3336 || 3452 | 3568 | 3684 | 3800 | 3915 | 116 
5 4031 | 4147 | 4263 | 4879 | 4494 || 4610 | 4726 | 4841 | 4957 | 5072 | 116 
6 5188 | 5303 | 5419 | 5534 | 5650 || 5765 | 5880 | 5996 | 6111 | 6226] 115 
7 6341 | 6457 | 6572 | 6687 | 6802 || 6917 | 7082 | 7147 | 7262 | W377 1] 115 
8 7492 | 7607 | 7722 | 7836 | 7951 || 8066 | 8181 } 8295 | 8410 | 8525} 115 
9 8639 | 8754 | 8868 | 8983 | 9097 |) 9212 | 9326 | 9441 | 9555 | 9669 | 114 








a | | | ce fl ee 









25.6 38.4 51.2 64.0 76.8 89.6 | 102.4 | 115.2 
25.4 38.1 50.8 63.5 76.2 88.9 | 101.6 | 114.3 
25.2 37.8 50.4 63.0 75.6 88.2 | 100.8 | 113.4 
25.0 37.5. 50.0 62.5 75.0 87.5 | 100.0 | 112.5 
24.8 37.2: 49.6 62.0 74.4 86.8 99.2 | 111.6 
24.6 36.9 49.2 61.5 73.8 86.1 98.4 | 110.7 
24.4 36.6. 48.8 61.0 (3.2 85.4 97.6 | 109.8 
24.2 36.3. 48.4 60.5 72.6 $4.7 96.8 | 108.9 
24.0 36.0 48.0 60.0 72.0 84.0 96.0 | 108.0 
23.8 85.7 47.6 59.5 71.4 83.3 95.2 | 107.1 








142 LOGARITHMS OF NUMBERS. 










No. 880. L. 579.] [No. 414 L. 617. 








WeeOn eal al dival te, 


| rns | saceees | pommmncsee | ee | ee | | ee | ee | a | a 









































































880 | 579784 | 9898 |"oo19 | o126 0241 | 0355 | 0469 | 0583 | 0697 | 0811 | 114 

1 | 580925 | 1039 | 1153 | 1267 | 1381 || 1495 | 1608 | 1722 | 1886 | 1950 

2} 2063 | 2177 | 2291 | 2404 | 2518 || 2631 | 2745 | 2858 | 2972 | 8085 

31 3199 | 3312 | 3426 | 3589 | 3652 || 3765 | 3879 | 3992 | 4105 | 4218 

41 4331 | 4444 | 4557 | 4670 | 4783 || 4896 | 5009 | 5122 | 5235 | 5348 | 118 

5 | 5461 | 5574 | 5686 | 5799 | 5912 || 6024 | 6187 | 6250 | 6362 | 6475 

6 | 6587 | 6700 | 6812 | 6925 } '7037 || 7149 | 7262 | 7374 | 7486 | "7599 

7| 7711 | 7823 | 79385 | 8047 | 8160 || 8272 8496 | 8608 | 8720 | 112 

8 8832 8944 | 9056 | 9167 | 9279 || 9391 | 9503 | 9615 | 9726 | 9838 

9{| 9950 |_—— tA sl Bh ey WA aS 2 

0061 | 0173 | 0284 | 0396 |) 0507 | 0619 | 0730 | 0842 | 0953 

390 | 591065 | 1176 | 1287 | 1399 | 1510 || 1621 | 1732 | 1843 | 1955 | 2066 
2177 | 2288 | 2399 | 2510 | 2621 || 2732 | 2843 | 2954 | 3064 | 3175 | 111 

21 3286 | 3397 | 3508 | 3618 | 3729 || 3840 | 3950 | 4061 | 4171 | 4282 

3| 4398 | 4503 | 4614 | 4724 | 4884 || 4945 | 5055 | 5165 | 5276 | 5386 

41 5496 | 5606 | 5717 | 5827 | 5937 || 6047 | 6157 | 6267 | 6377 | 6487 

5 | 6597 | evo7 | 6817 | 6927 | 7037 || 7246 | 7256 | 7366 | 7476 | 7586} 110 

G6} 7695 | 7805 | 7914 | S024 | 8134 || 8243 | 8353 | 8462 | 8572 | 8681 

71 8791 | 8900 | 9009 | 9119 | 9228 || 93837 | 9446 | 9556 | 9665 | 977 

8 9883 | 9992 |———|-_-—|——_— -———|—_——-}_ 109 

px ———| 0104 | 0210 | 0319 || 0428 | 0537 | 0646 | 0755 | 0864 

9 | 600973 | 4082 ) 1191 | 1299 | 1408 || 1517 | 1625 | 1734 | 1843 | 1951 

400 | 2060} 2169 | 2277 | 2386 | 2494 || 2603 | 2711 | 2819 | 2998 | 3036 

1| 3144 | 3253 | 3361-| 8469 | 3577 |) 3686 | 3794 | 3902 | 4010 | 4118} 40g 

21 4226 | 4334 | 4442 | 4550 | 4658 || 4766 | 4874 | 4982 | 5089 | 5197 

31 5305 | 5413 | 5521 | 5628 | 5736 || 5844 | 5951 | 6059 | 6166 | 6274 

41 6381 | 6489 | 6596 | 6704 | 6811 |] 6919 | 7026 | 7133 | 7241 | 7348 

5| 7455 | 7562 | 7669 | 7777 | 7884 || 7991.( 8098 | 8205 | 8312 | 8419 | 407 

61 8526 | 8633 | 8740 | 8847 | 8954 || 9061 | 9167 | 9274 | 9381 | 9488 

71 9594 | 9701 | 9808 | 9914 CER MRL A Ae 

———|—__ |__| 0021 || 0128 | 0234 | 0341 | 0447 | 0554 

8 | 610660 | 0767 ; 0873 { 0979 | 1086 || 1192 | 1298 | 1405 | 1511 | 1617 

9 1829 | 1936 | 2042 | 2148 |} 2254 | 2360 | 2466 | 2572 | 2678 | 496 

410} 2784 | 2890 | 2996 | 3102 | 3207 || 8813 | 8419 | 3525 | 3630 | 2736 

1| 3842 | 3947 | 4053 | 4159 | 4264 || 4370 | 4475 | 4581 | 4686 | 4792 

21 4897 | 5003 | 5108 | 5213 | 5319 |] 5424 | 5529 | 5634 | 5740 | 6845 

3] 59501 6055 | 6160 | 6265 | 6370 || 6476 | 6581 | 6686 | 6790 | 6895 | 105 

4} 7000} 7105 | 7210 | 7315 | 7420 734 | 7839 | 7943 

PROPORTIONAL PARTS, 

Diff.| 1) 2 3 4 | 5 6 7 8 9 
11.8] 23.6 | 35.4 | 47.2 | 59.0 | 70.8 | 82.6 | 94.4 [ 106.2 
11.7] 28.4 | 85.1 | 46.8 | 58.5 | 70.2 | 81.9 | 98.6 | 105.3 
11.6 | 23.2 | 84.8 | 46.4 | 58.0 | 69.6 | 81.2 | 92.8 | 104.4 
11.5] 23.0 | 34.5 | 46.0 | 57.5 | 69.0 | 80.5 | 92.0 | 103.5 
11.4] 228 | 84.2 | 45.6 | 57.0 | 68.4 | 79.8 | 91.2 | 102.6 
11.8} 22.6 | 38.9 | 45.2 | 56.5 | 67.8 | 79.1 | 90.4 |-101.7 
11.2] 22.4 | 83.6 | 44.8 | 56.0 | 67.2 | %8.4 | 89.6 | 100.8 
11.1| 22.2 | $8.8 | 44.4 | 55.5 | 66.6 | v7.7 | 88.8 | 99.9 
11.0] 22.0 | 38.0 | 44.0 | 55.0 | 66.0 | 77.0 | 88.0 | 99.0 
10.9! 21.8 | 82.7 | 48.6 | 54.5 | 65.4 | 76.8 | 87.2 | 98.1 
10.8] 21.6 | 82.4 | 43.2 | 54.0 | 64.8 | 75.6 | 86.4 | 97.2 
10.7| 21.4 | 32.4 | 42.8 | 53.5 | 64.2 | 74.9 | 85.6 | 96.3 
10.6} 21.2 31.8 42.4 | 58.0 | 63.6 | 74.2 | 84.8 | 95.4 
10.5} 21.0 | 81.! 42.0 | 52.5 | 63.0 | 93.5 | 84.0 | 94.5 

20.8 | 31.2 | 41.6 | 52.0 | 62.4 | 72.8 } 83.2 | 93.6 


No, 415 L. 618.] 


LOGARITHMS OF NUMBERS. 148 





415 | 618048 | 8153 | 8257 | 8362 | 8466 || 8571 | 8676 | 8780 | 8884 | 8989 | 105 





620186 | 0240 
1176 | 1280 
2214 | 2318 


8249 | 3353 
4282 | 4385 
5312 | 5415 
6340 | 6443 
7366 | 7468 
8889 | 8491 
9410 } 9512 


Koake Camrst 





ROWE OD OO Hr 
5 
~~ 
ww 
Or 
Ou 
ie) 


Se ee Re ee eee 


iS 


OO MOOR MWH OS OOF SBOP wwreoe womrsk on 
jor) 
OU 
(=) 
ivy) 
S 
oe) 
S 
He 
S 
Or 


i 
t 


660865 | 0960 
1813 | 1907 

















2002 | 2096 4 2191 || 2286 | 2380 | 2475 | 2569 | 2663 


9093 | 9198 | 9302 | 9406 | 9511 || 9615 | 9719 | 9824 | 9928 }——— 


Bleor wy CM 
0344 | 0448 | 0552 || 0656 | 0760 | 0864 | 0968 | 1072 | 104 
1384 | 1488 | 1592 || 1695 | 1799 | 1903 | 2007 | 2110 
2421 | 2525 | 2628 || 2732 } 2835.| 2939 | 3042 | 3146 


8456 | 3559 | 8663 || 3766 | 3869 | 3973 | 4076 | 41°79 i 
4488 | 4591 |°4695 || 4798 | 4901 | 5004 | 5107 | 5210 | 103 | 
5518 | 5621 | 5724 || 5827 | 5929 | 6082 | 6135 | 6238 

6546 | 6648 | 6751 || 6853 | 6956 | 7058 | 7161 | 7263 

(O71 | 7673 | T77TS || 7878 { 7980 | 8082 | 8185 | 8287 

8593 | 8695 | 8797 || 8900 | 9002 | 9104 | 9206 | 9308 | 102 
9613 | 9715 | 9817 || 9919 |——— 
——— || ———| 0021 | 0128 | 0224 | 0326 
0631 | 0733 | 0835 |} 0936 | 1038 | 1189 | 1241 | 1342 
1647 | 1748 | 1849 |) 1951 | 2052 | 2153 | 2255 | 2356 
2660 | 2761 | 2862 || 2963 | 3064 |} 3165 | 8266 | 3367 


3670 | 8771 | 8872 || 8973 | 4074 | 4175 | 4276 | 4876 | 101 





























2662 | 2761 | 2860 || 2959 | 3058 | 3156 | 8255 | 8854 99 







6600 | 6698 | 6796 || 6894 | 6992 | 7089 | 7187 | 7285 98 














1472 | 1569 1666 |} 1762 | 1859 | 1956 | 2053 | 2150 97 





5331 | 5427 | 5523 || 5619 | 5715 | 5810 | 5906 | 6002 96 








0106 | 0201 {| 0296 }| 0891 | 0486 | 0581 | 0676 | 9771 95 
1055 | 1150 | 1245 || 1839 | 1434 | 1529 | 1623 | 1718 

















PROPORTIONAL PARTS, 


3 4 5 ne 8 | 9 





we Or Or Or Or OT Or 
BOSrr WM 
WOWtIOowon 





144° LOGARITHMS OF NUMBERS. 























\ q | 
No. 460 L. 662.] [No. 499 L. 698. 
N| 0 4g is 4 5 6.1 2 8 | 9 | Dift. | 
460 | 662758 | 2852 | 2947 | 3041 | 3135 || 3230 | 3824 | 3418 | 3512 | 3607 
3701 | 3795 | 3889 | 3983 | 4078 || 4172 } 4266 | 4360 | 4454 | 4548 
2| 4642 | 4736 | 4830 | 4924 | 5018 || 5112 | 5206 | 5299 | 5393 | 5487 | 94 
3| 5581 | 5675 | 5769 | 5862 | 5956 || 6050 | 6143 | 6237 | 6331 | 6424 
4| 6518 | 6612 | 6705 | 6799 | 6892 || 6986 | 7079 | 7173 | 7266 | 7360 
5 | 7453 | 7546 | 7640 | 7733 | 7826 || 7920 | 8013 | 8106 | 8199 | 8293 
6 | 8386 | 8479 | 8572 | 8665 | 8759 || 8852 | 8945 | 9038 | 9131 | 9224 
x | 9317 | 9410 | 9503 | 9596 | 9689 |) 9782 | 9875 | 9967 |——|—_—_ 
en Fors ard Fc nk Povo | ana, Dect al Pence YP Rie 
g | 670246 | 0339 | 0431 | 0524 | 0617 || 0710 | 0802 | 0895 | 0988 | 1080 
9| 1173 | 1265 | 1358 | 1451 | 1543 || 1636 | 1728 | 1821 | 1913 | 2005 
470 | 2098 | 2190 | 2283 | 2375 | 2467 || 2560 | 2652 | B744 | 2836 | 2929 
1} 3021 | 3113 | 3205 | 3297 | 3390 || 3482 | 3574 | 3666 | 3758 | 3850 
2| 3942 | 4034 | 4126 | 4218 | 4310 || 4402 | 4494 | 4586 | 4677 | 4769 | 92 
3| 4861 | 4953 | 5045 | 5137 | 5228 || 5320 | 5412 | 5503 | 5595 | 5687 
4| 5778 | 5870 | 5962 | 6033 | 6145 || 6236 | 6328 | 6419 | 6511 | 6602 
5 | 6694 | 6785 | 6876 | 6968 | 7059 || 7151 | 7242 | 7338 | 7424 | 7516 
6| 7607 | 7698 | 7789 | 7881 | 7972 || 8063 | 8154 | 8245 | 8336 | 8427 
7 | 8518 | 8609 | 8700 | 8791 | 8882 || 8973 | 9064 | 9155 | 9246 | 9337] 91 
8 | 9428 | 9519 | 9610 | 9700 | 9791 || 9882 | 9973 ean Si Sea 
pg itt ee ge Ll anne ted | aegis 
9 | 680336 | 0426 | 0517 | 0607 | 0698 || 0789 | 0879 | O970 | 1060 | 1151 























480 1241 | 1332 | 1422 | 1513 | 1603 || 1693 | 1784 | 1874 | 1964 
1 2145 | 2235 | 2826 | 2416 | 2506 ||} 2596 | 2686 | 2777 | 2867 | 2957 
2 8047 | 8137 | 3227 | 3317 | 38407 || 8497 | 3587 | 38677 | 3767 | 3857 90 
3 8947 | 4037 | 4127 | 4217 | 4807 |) 43896 } 4486 | 4576 | 4666 | 4756 
4 4845 | 49385 | 5025 | 5114 | 5204 || 5294 | 5383 | 5473 | 5563 | 5652 
5 5742 | 5831 | 5921 | 6010 | 6100 |} 6189 | 6279 | 63868 | 6458 | 6547 
6 6636 | 6726 | 6815 | 6904 | 6994 || 7083 | 7172 | 7261 | 73851 | 7440 
ff 7529 | 7618 | 7707 | 7796 | 7886 ||} 7975 | 8064 | 8153 | 8242 | 8331 89 
8 8420 | 8509 | 8598 | 8687 | 8776 || 8865 | 8953 | 9042 | 9131 | 9220 
9 9309 | 9398 | 9486 | 9575 | 9664 || 9753 | 9841 | 9930 |__| 

————— | |__| |__| —_|—_—_ 0019 | 0107 

490 | 690196 | 0285 | 0373 | 0462 | 0550 || 0639 | 0728 | 0816 | 0905 | 0993 
1 1081 | 1170 | 1258 | 1847 | 1435 || 1524 | 1612 | 1700 | 1789 | 1877 
2 1965 | 2053 | 2142 | 2230 | 2818 |; 2406 | 2494 | 2583 | 2671 | 2759 
3 2847 | 2935 | 3023 | 3111 | 8199 || 8287 | 3375 | 3463 | 3551 | 3639 88 
4 38727 | 3815 | 3903 | 3991 | 407 4166 | 4254 | 4342 | 4430 | 4517 
5 4605 | 4693 | 4781 | 4868 | 4956 || 5044 | 5131 | 5219 | 5307 | 5394 
6 5482 | 55€9 | 5657 744 | 5882 |} 5919 | 6007 | 6094 | 6182 | 6269 
vg 6356 | 6444 | 6531 | 6618 | 6706 || 6793 | 6880 | 6968 | ‘7055 | 7142 
8 7229 | 7317 | 7404 | 7491 | 7578 || 7665 | 7752.) 7839 | 7926 | 8014 8 
9 8100 | 8188 | 8275 | €362 | 8449 || 8535 | 8622 | 8709 | 8796 | 8883 7 

PROPORTIONAL PARTS, 

Diff 1 2 38 4 5 6 fe 8 9 
98 9.8 19.6 29.4 39.2 49.0 58.8 68.6 78.4 88.2 
9% 9,7 19.4 29.1 38.8 48.5 58.2 67.9 07.6 87.2 
96 9.6 19.2 {| 28.8 88.4 48.0 57.6 67.2 76.8 86.4 
95 9.5 | 19.0 28.5 38.0 47.5 57.0 66.5 %6.0 85.5 
94 | 9.4 18.8 28.2 387.6 47.0 56.4 65.8 70.2 84.6 
93 9.3 |. 18.6 27.9 37.2 46.5 55.8 65.1 74.4 83.7 
92 9.2] 18.4 27.6 36.8 46.0 55.2 64.4 73.6 82.8 
91 9.1 18.2 27.3 386.4 45.5 54.6 63.7 72.8 81.9 
90 9,0 18.0 27.0 36.0 45.0 54.0 63.0 72.0 81.0 
89 8.9 | 17.8 26.7 35.6 44.5 53.4 62.3 412 80.1 
88 8.8} 17.6 26.4 30.2 44.0 52.8 61.6 70.4 79.2 
87 83% 17.4 26.1 34.8 43.5 52.2 60.9 69.6 78.3 
86 8.6) aeiniee 25.8 34.4 43.0 51.6 60.2 68.8 77.4 

eee aie eee 


LOGARITHMS OF NUMBERS, 145° 






No. 500 L. 698.] [No, 544 L. 736, 



















0 1 2 3 


4 





500 | 698970 | 9057 | 9144 | 9231 | 9317 || 9404 | 9491 | 9578 | 9664 | 9751 
1 9838 | 9924 
——|——— 0011 | 0098 | 0184 || 0271 | 0858 | 0444 | 0531 | 0617 
2 | 700704 | O790 | O877 | 0963 | 1050 || 1186 | 1222 | 1809 | 1395 | 1482 
3 1568 | 1654 | 1741 | 1827 | 1913 || 1999 | 2086 | 2172 |} 2258 | 2344 
ot 2431 | 2517 | 2603 | 2689 | 2775 || 2861 | 2947 | 3033 | 3119 | 38205 
5 8291 | 383877 | 3463 | 38549 | 3635 || 8721 | 8807 | 3893 | 3979 | 4065 86 
6 4151 | 42386 | 4822 | 4408 | 4494 || 4579 | 4665 | 4751 | 4837 | 4922 
i 5008 | 5094 | 5179 | 5265 | 5350 || 5486 | 5522 | 5607 | 5693 | 5778 
: 5864 | 5949 | 6035 | 6120 | 6266 || 6291 | 6376 | 6462 | 6547 | 6632 
0 
1 
2 
3 
4 











6718 | 6803 | 6888 | 6974 | 7059 || 7144 | 7229 | 7315 | 7400 | 7485 


7570 | 7655 | 7740 | 7826 | 7911 || 7996 |} 8081 | 8166 | 8251 | 8336 85 
8421 | 8506 | 8591 | 8676 | 8761 || 8846 | 8931 | 9015 | 9100 | 9185 
































3456 | 8538 | 3620 | 3702 | 8784 || 3866 | 3948 } 4080 | 4112 | 4194 82 





730782 | 0863 0944 | 1024 | 1105 || 1186 | 1266 | 1347 | 1428 | 1508 
1589 | 1669 | 1750 | 1880 | 1911 || 1991 | 2072 | 2152 | 2238 | 2318 


2394 | 2474 | 2555 | 2685 | 2715 || 2796 | 2876 | 2956 | 3037 | 3117 





1 
2 
3 
5 
6 9165 | 9246 | 93827 | 9408 | 9489 || 9570 | 9651 | 9732 | 9813 | 9893 81 
vs 
8 
9 
0 


1 8197 | 3278 | 3358 | 3438 | 3518 || 3598 | 3679 | 3759 | 3839 | 3919 
2 3999 | 4079 | 4160 | 4240 | 4820 || 4400 | 4480 | 4560 | 4640 | 4720 80 
3 4800 | 4880 | 4960 | 5040 | 5120 || 5200 | 5279 | 5359 | 5489 | 5519 
4 5599 | 5679 | 5759 | 5838 | 5918 || 5998 | 6078 | 6157 | 6287 | 6317 





146 LOGARITHMS Of NUMBERS, 













No. 545 L. 736.] LNo. 584 L. 767, 





0 ) Wee wane s | 6 |7| 8 | 9 |p. 


N. 

545 736897 | 6476 | 6556 | 6635 | 6715 || 6795 | 6874 | 6954 | 7034 | 7118 
"7 

8 

9 








ae ——— 
oo 


7193 | 7272 | 7352 | 7431 | 7511 || 7590 | 7670 | 7749 | 7829 | 7908 
7987 | 8067 | 8146 | 8225 | 8305 || 83884 | 8463 | 8543 | 8622 | 8701 
8781 | 8860 | 8939 | 9018 | 9097 || 9177 | 9256 | 9385 | 9414 | 9493 
9572 | 9651 | 9731 | 9810 | 9889 |; 9968 }———-|———_ 
——| 0047 | 0126 | 0205 | 0284 79 


740363 | 0442 | 0521 | 0600 | 0678 || O757 | 0836 | 0915 | 0994 | 1073 























5075 | 5153 | 52381 | 5809 | 53887 |) 5465 | 5543 | 5621 | 5699 | 5777 78 





























2048 | 2125 | 2202 | 2279 | 2256 || 2493 | 2509} 2586 | 2663 | e740 | *% 





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5 
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6636 | 6712 | 6788 | 6864 | 6940 || 7016 | 7092 | 7168 | 7244 | 7320 76 




















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5669 | 5743 | 5818 | 5892 | 5966 || 6041 | 6115 | 6190+ 6264 | 6338 
6413 | 6487 | 6562 | 6636 | 6710 || 6785 | 6859 | 6933 | 7007 | 7082 





1 
2 
3 
4 
5 
6 
é 
9 2679 | 2754 | 2829 | 2904 | 2978 || 8053 | 3128 | 8203 | 3278 | 38353 
580 
1 
2 
3 
4 











PROPORTIONAL PARTS, 








Diff 1 2 3 4 5 6 us 8 9 
83 8.3 | 16.6 24.9 83.2 41.5 49.8 58.1 66.4 74.7 
82 8.2 | 16.4 24.6 382.8 41.0 49.2 57.4 65.6 73.8 
81 Sell. 24.3 382.4 40.5 48.6 56.7 64.8 (2.9 
80 8.0} 16.0 24.0 82.0 40.0 48.0 56.0 64.0 72.0 
79 1.97) 15.8 23.7 31.6 389.5 47.4 55.8 63.2 71.1 

78 t 23.4 : 46.8 54.6 62.4 70.2 
ae 23.1 ; 46.2 53.9 61.6 69.3 
7.6 22.8 : 45.6 53.2 60.8 68.4 
7.5 22.5 F 45.0 52.5 60.0 67.5 
7.4 22.2 : 44,4 51.8 59.2 66.6 








LOGARITEMS OF NUMBERS. 147 





No. 585 L. 767.] 


N. 0 1 2 8 4 5 6 7 8 9 | Diff. 




























































































585 | 767156 | 7230 | 73804 | 7379 | 7453 || 7527 | 7601 | 7675 | 7749 | 7823 
6 7898 | 7972 | 8046 | 8120 | 8194 || 8268 | 8342 | 8416 | 8490 | 8564 %4 
, 8638 | 8712 | 8786 | 8860 | 8934 || 9008 | 9082 | 9156 | 9280 | 9303 
8 9377 | 9451 | 9525 | 9599 | 9673 || $746 | 9820 | 9894 | 9968 
=e Le Laos | et bee 0042 
9 | 770115 | 0189 | 0263 | 0336 | 0410 || 0484 | 0557 | 0631 | O05 | 077 
590 0852 | 0926 | 0999 | 1073 | 1146 || 1220 | 1293 | 1867 | 1440 | 1514 
1 1587 | 1661 | 1734 | 1808 | 1881 || 1955 | 2028 | 2102 | 2175 | 2248 
2 2329 | 2305 | 2468 | 2542 | 2615 || 2688 | 276% | 2835 | 2908 | 2081 
3 3055 | 3128 | 3201 | 3274 | 3348 || 3421 | 3494 | 3567 | 3640 | 3713 
4 8786 | 3860 | 3933 | 4006 | 4079 || 4152 | 4225 | 4298 | 4371 "3 
5 4517 | 4590 | 4663 | 4736 | 4809 || 4882 | 4955 | 5028 | 5100 | 5173 
6 5246 | 5319 | 5392 | 5465 | 5538 || 5610 | 5683 | 5756 | 5829 | 5902 
7 5974 | 6047 | 6120 | 6193 | 6265 || 6388 | 6411 | 6483 | 6556 | 6629 
8 6701 | 6774 | 6846 | 6919 | 6992 || 7064 | 7137 | 7209 | 7282 | 7354 
9 7427 | 7499 | 7572 | 7644 | 7717 || 7789 | 7862 | 7934 | 8006 | 8079 
600 8151 | 8224 | 8296 | 8368 | 8441 || 8513 | 8585 | 8658 | 8730 | 8802 
1 8874 | 8947 | 9019 | 9091 | 9163 || 9236 | 9308 | 9380 | 9452 | 9524 
2 9596 | 9669 | 9741 | 9813 | 9885 || 9957 Liab 8 all 
pn 2 eA Siem ll RE AREY ak = I 0029 | 0101 | 0173 | 0245 "2 
3 | 780317 | 0889 | 0461 | 0533 | 0605 || 0677 | 0749 | 0821 | 0893 | 0965 
4 1037 | 1109 | 1181 | 1253 | 1324 || 1896 | 1468 | 1540 | 1612 | 1684 
5 1755 | 1827 | 1899 | 1971 | 2042 || 2114 | 2186 | 2258 | 2329 | 2401 
6 2473 | 2544 | 2616 | 2688 | 2759 || 2831 | 2902 | 2974 | 3046 | 3117 
y 3189 | 3260 | 3332 | 3403 | 3475 || 3546 | 3618 | 3689 | 3761 | 3832 
8 3904 | 3975 | 4046 | 4118 | 4189 || 4261 | 4332 | 4408 | 4475 | 4546 
9 4617 | 4689 | 4760 | 4831 | 4902 || 4974 | 5045 | 5116 | 5187 | 5259 
610 5330 | 5401 | 5472 | 5543 | 5615 || 5686 | 5757 | 5828 | 5899 | 5970 
1 6041 | 6112 | 6183 | 6254 | 6325 || 6396 | 6467 | 6538 | 6609 | 6680 | 71 
21 8751 | 6822 | 6893 | 6964 | 7035 || 7106 | 7177 | 7248 | 7319 | 7390 
3 7460 | 7531 | 7602 | 7673 | 77 7815 | 7885 | 7956 | 8027 | 8098 
4 8168 | 8239 | 8310 | 8381 | 8451 || 8522 | 8593 | 8663 | 8734 | 8804 
5 8875 | 8946 | 9016 | 9087 | 9157 || 9228 | 9299 | 9369 | 9440 | 9510 
6 9581 | 9651 | 9722 | 9792 | 9863 || 9933 ts DESEIE o SRitay eca t 
ee ee 1 0004 10074 10144 |. 0215 
7 | 790285 | 0356 | 0426 | 0496 | 0567 || 0637 | 0707 | 0778 | 0848 | 0918 
8 0988 | 1059 | 1129 | 1199 | 1269 || 1340 | 1410 | 1480 | 1550 | 1620 
9 1691 | 1761 | 1831 | 1901 | 1971 || 2041 | 2111 | 2181 | 2252 | 2322 
620 2392 | 2462 | 2532 | 2602 | 2672 || 2742 | 2812 | 2882 | 2952 | 3022 70 
1 3092 | 3162 | 3231 | 3301 | 3371 || 3441 | 3511 | 3581 | 3651 | 3721 
2 3790 | 3860 | 3930 | 4000 | 4070 || 4139 | 4209 | 4279 | 4349 | 4418 
3 4488 | 4558 | 4627 | 4697 | 4767 || 4836 | 4906 | 4976 | 5045 | 5115 
4 5185 | 5254 | 5324 | 5393 | 5463 || 5532 | 5602 | 5672 ) 5741 | 5811 
5 5880 | 5949 | 6019 | 6088 | 6158 || 6227 | 6297 | 6366 | 6436 | 6505 
6 6574 | 6644 | 6713 | 6782 | 6852 || 6921 | 6990 | ‘7060 | 7129 | 7198 
7268 | 7337 | 7406 | 7475 | 7545 || 7614 | 7683 | 7752 , 7821 | 7890 
8 7960 | 8029 | 8098 | 8167 | 8236 || 8305 | 8374 | 8443 | 8513 | 8582 
9 8651 | 8720 | 8789 | 8858 | 8927 || 8996 | 9065 | 9134 | 9203 | 927 69 
PROPORTIONAL PARTS. 
Vif. 1 2 3 4 5 6 y3 8 9 
" 7.5.1 15.0 22.5 30.0 87.5 45.0 52.5 60.0 67.5 
74 7.41 14.8 22.2 29 .6 37.0 44.4 51.8 59.2 66.6 
73 7.3) 14.6 21.9 99 .2 36.5 43.8 51.1 58.4 65.7 
72 7.2| 14.4 21.6 28.8 36.0 43.2 50.4 57.6 64.8 
71 @7\ 14.2 21.3 28.4 35.5 42.6 49.7 56.8 63.9 
70 7.0| 14.0 21.0 28.0 35.0 42.0 49.0 56.0 63.0 
69 6.9 | 13.8 20.7 27.6 34.5 41.4 48.3 55.2 62.1 





148 LOGARITHMS OF NUMBERS, 


No. 680 L. 799.] [No. 674 L. 829, | 























630 | 799341 | 9409 | 9478 | 9547 | 9616 || 9685 | 9754 | 9823 | 9892 | 9961 
1 | 800029 | 0098 | 0167 | 0236 | 0305 || 0873 0511 | 0580 | 0648 
2 O717 | 0786 | 0854 | 0928 | 0992 || 1061 | 1129 | 1198 | 1266 | 1335 
3 1404 | 1472 | 1541 | 1609 | 1678 || 1747 | 1815 | 1884 | 1952 | 2021 
4 2089 | 2158 | 2226 | 2295 |} 2363 || 2432 | 2500 | 2568 | 2637 | 2705 
5 2774 | 2842 | 2910 | 2979 | 8047 || 3116 | 3184 | 38252 | 3321 | 3389 
6 3457 | 3525 | 3594 | 3662 | 3730 || 3798 | 3867 | 3935 | 4003 } 4071 
vi 4139 | 4208 | 4276 | 4344 | 4412 || 4480 | 4548 | 4616 | 4685 | 4753 
8 4821 | 4889 | 4957 | 5025 | 5093 || 5161 | 5229 | 5297 | 5365 | 54383 68 
9 5501 | 5569 | 5637 | 5705 | 5773 || 5841 | 5908 | 5976 | 6044 | 6112 

640 | 806180 | 6248 | 6316 | 6884 | 6451 || 6519 | 6587 | 6655 | 6723 | 6790 
1 6858 | 6926 | 6994 | 7061 | 7129 || 7197 | 7264 | 7332 | 7400 | 7467 
2 75385 | 7603 | 7670 | 7738 | 7806 || 7873 | 7941 | 8008 | 8076 | 8143 
3 8211 | 8279 | 8346 | 8414 | 8481 || 8549 | 8616 | 8684 | 8751 | 8818 
4 8886 | 8953 | 9021 | 9088 | 9156 || 9223 | 9290 | 9858 | 9425 | 9492 
5 9560 | 9627 | 9694 | 9762 | 9829 |} 9896 | 9964 — 

——_|—— |-——_— |__| |_—_| | 0031 | 0098 | 0165 
6 | 810233 | 0300 | 0367 | 0434 | 0501 || 0569 | 0636 | 0703 | 0770 | 0887 
i 04 | 0971 | 1039 | 1106 | 1173 || 1240 | 1807 | 1874 | 1441 | 1508 6% 
8 1575 | 1642 | 1709 | 1776 | 1843 || 1910 } 1977 | 2044 | 2111 | 2178 
9 2245 | 2312 | 2379 2512 || 2579 | 2646 | 2718 | 2780 | 2847 

650 2918 | 2980 | 3047 | 3114 | 3181 || 3247 | 3314 | 3381 | 3448 | 3514 
1 8581 | 3648 | 3714 | 3781 | 3848 || 3914 | 3981 | 4048 | 4114 | 4181 
2 4248 | 4314 | 4381 | 4447 | 4514 || 4581 | 4647 | 4714 | 4780 | 4847 
3 4913 | 4980 | 5046 | 5118 | 5179 || 5246 | 5312 | 5878 5511 
4 5578 | 5644 | 5711 | 5777 | 5848 || 5910 | 5976 | 6042 | 6109 | 6175 
5 6241 | 6308 | 6374 | 6440 | 6506 || 6573 | 6639 | 6705 | 6771 | 6838 
6 6904 | 6970 | 7036 | 7102 | 7169 || 7235 | 7301 | 7367 | 7433 | 7499 
x 7565 | 7631 | 7698 | 7764 | 7830 || 7896 | 7962 | 8028 | 8094 | 8160 
8 8226 | 8292 | 8358 | 8424 | 8490 || 8556 | 8622 | 8688 | 8754 } 8820 66 
9 8885 | 8951 | 9017 | 9083 | 9149 || 9215 | 9281 | 9346 | 9412 } 9478 


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1 
2 
3 
4 
5 
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8 4776 | 4841 | 4906 | 4971 | 5036 || 5101 | 5166 | 5231 | 5296 | 5361 
9 
70 
1 
2 
3 
4 





LOGARITHMS OF NUMBERS. £49 


No. 675 L, 829.) ‘{No. 719 L, 857. | 























6 Pe ggg a OES a Mae Rea a A Be 
0011 | 0075 | 0189 | 0204 || 0268 | 0382 | 0396 | 0460 | 0525 
% | 830589 | 0653 | 0717 | 0781 | 0845 || 0909 | 0973 | 1087 | 1102 | 1166 
8 1230 | 1294 | 1358 | 1422 | 1486 || 1550 | 1614 | 1678 | 1742 | 1806 | 64 
9] 1870 | 1984 | 1998 | 2062 | 2126 || 2189 | 2253 | 2317 | 2381 | 2445 
680 | 2509 | 2573 | 2637 | 2700 | 2764 || 2828 | 2892 | 2956 | 3020 | 3083 
1 3147 | 3211 | 3275 | 3388 | 3402 || 3466 | 3530 } 3593 | 3657 | 3721 
2) 8784 | 3848 | 3912 | 3975 | 4039 || 4103 | 4166 | 4230 | 4294 | 4357 
3| 4421 | 4484 | 4548 | 4611 | 4675 || 4739 | 4802 | 4866 | 4929 | 4993 
4] 5056 | 5120 | 5183 | 5247 | 5310 || 5373 | 5437 | 5500 | 5564 | 5627 
5 | 5691 | 5754 | 581% | 5881 | 5944 |] 6007 | 6071 | 6134 | 6197 | 6261 
6 | 6324 | 6387 | 6451 | 6514 | 6577 || 6641 | 6704 { 6767 | 6830 | 6894 
7 | 6957 | 7020 | 7083 | 7146 | 7210 || 7273 | 7336 | 7399 | 7462 | 7525 
8} 7588 | 7652 | 7715 | 7778 | 7841 |! 7904 | 7967 | 8030 | 8093 | 8156 
9| 8219 | 8282 | 8345 | 8408 | 8471 |] 8534 | 8597 | 8660 | 8723 | 8786 | 63 
690 | 8849 | 8912 | 8975 | 9038 | 9101 |] 9164 | 9227 | 9289 | 9352 | 9415 
1 9478 | 9541 | 9604 | 9667 | 9729 || 9792 | 9855 | 9918 } 9981 an 
2 | 840106 | 0169 | 0232 | 0294 | 0357 || 0420 | 0482 | 0545 | 0608 | 0671 
3| 0733 | 0796 | 0859 | 0921 | 0984 || 1046 | 1109 | 1172 | 1234 | 1297 
4} 1359 | 1422 | 1485 | 1547 | 1610 || 1672 | 1735 | 1797 | 1860 | 1922 
5 1985 | 2047 | 2110 | 2172 | 2285 || 2297 | 2360 | 2422 | 2484 | 2547 
6} 2609 | 2672 | 2734 | 2796 | 2859 || 2921 | 2988 | 3046 | 3108 | 3170 
7% | - 3233 | 3295 | 3357 | 3420 | 3482 || 3544 | 3606 | 3669 | 3731 | 3793 
81 38855 | 3918 | 3980 | 4042 | 4104 || 4166 | 4229 | 4291 | 4353 | 4415 
9] 4477 | 4539 | 4601 , 4664 | 4726 || 4788 | 4850 } 4912 | 4974 | 5036 
700 | 5098 | 5160-| 5222 | 5284 | 5346 |} 5408 } 5470 | 5532 | 5594 | 5656] 62 
1 5718 | 5780 | 5842 | 5904 | 5966 || 6028 | 6090 | 6151 | 6213 | 6275 
2] 6337 | 6399 | 6461 | 6523 | 6585 || 6646 | 6708 | 6770 | 6832 | 6894 
8] 6955 | 7017 | 7079 | 7141 | 7202 || 7264 | 7326 | 7388 | 7449 | V511 
4) 573 | 7634 | 7696 | 7758 | 7819 || 7881 | 7943 | 8004 | 8066 | 8128 
5 | 8189 | 8251 | 8312 | 8374 | 8435 || 8497 | 8559 | 8620 | 8682 | 8743 
6 | 8805 | 8866 | 8928 | 8989 | 9051 || 9112 | 9174 | 9235 | 9297 | 9358 
7% | 9419 | 9481 | 9542 | 9604 | 9665 |] 9726 | 9788 | 9849 | 9911 | 9972 
8 | 850033 | 0095 | 0156 | 0217 | 0279 || 0840 | 0401 | 0462 | 0524 | 0585 
9 | 0646 | 0707 | 0769 | 0830 | 0891 |} 0952 | 1014 | 1075 | 1136 | 1197 
710 1258 | 1820 |} 1381 | 1442 | 1503 || 1564 | 1625 | 1686 | 1747 | 1809 
1 1870 | 1931 | 1992 | 2053 | 2114 || 2175 | 2286 | 2207 | 2358 | 2419 
2] 2480 | 2541 | 2802 | 2663 | 2724 || 2785 | 2846 | 2907 | 2968 | 3029 61 
3} 3090 | 3150 | 3211 | 3272 | 3883 || 3894 | 3455 | 3516 | 3577 | 3687 
4] 8698 | 3759 | 3820 } 3881 | 3941 |] 4002 | 4063 | 4124 | 4185 | 4245 
5 | 4806 | 4367 | 4428 | 4488 | 4549 || 4610 | 4670 | 4731 | 4792 | 4852 
6| 4913 | 4974 | 5034 | 5095 | 5156 || 5216 | 5277 | 5887 | 5398 | 5459 
7 | 5519 | 5580 | 5640 | 5701 | 5761 || 5822 | 5882 | 5943 | 6003 | 6064 
8 6124 | 6185 | 6245 | 6806 | 6366 || 6427 | 6487 | 6548 | 6608 | 6668 
9 | 6729 | 6789 | 6850 | 6910 | 6970 || 70381 | 7091 | 7152 | 7212 | 7272 
PROPORTIONAL PARTS. 
Dif. ti 1 2 3 4 5 6 v 8 9 
65 | 6.5 | 13.0 19.5 | 26.0 | 82.5 | 39.0 | 45.5 58.5 
64 6.4] 12.8 19.2 | 25.6. | 32.0 | 88.4 | 44.8 57.6 
638 | 6.3] 12.6 18.9 | 25.2 31.5 87.8 | 44.1 56.7 
62 | 6.2] 12.4 18.6 | 24.8 31.0 7.2 | 43.4 55.8 
61 6.1] 12.2 18.3 | 24.4 30.5 | 86.6 | 42.7 54.9 
60 | 6.0| 12.0 18.0 | 24.0 | 30.0 | 36.0 | 42.0 54.0 








150 LOGARITHMS OF NUMBERS. | 





No. 720 L. 857.] [No. 764 L. 883. 





ee | me me | a fm | ff | | | a | | 


9138 | 9198 } 9258 | 9318 } $27 9439 } 9499 | 9559 | 9619 | 9679 60 
9739 | 9799 | 9859 | 9918 | 2978 |}——|———_; ——__ | —___|___. 


2 
3 
4 
5 | 860338 | 0398 | 0458 | 0518 | 0578 || 0637 | 0697 | 0757 | 0817 | 0877 
6 
8 





0937 | 0996 | 1056 | 1116 | 1176 || 1236 | 1295 | 1855 | 1415 | 1475 
7 1534 | 1594 | 1654 | 1714 | 177 1833 | 1893 | 1952 | 2012 | 2072 
2131 | 2191 | 2251 | 2310 | 2870 || 24380 | 2489 | 2549 | 2608 | 2668 
9 2728 | 2787 | 2847 | 2906 | 2966 || 38025 | 3085 | 3144 | 38204 | 3263 
0 


3323 | 3382 | 3442 | 3501 | 3561 || 38620 | 3680 | 3739 | 8799 | 3858 


9818 | 9877. | 9985 | 9994 |——}| ———_| ——__| ____]_—__—__| __ 
































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16. 





LOGARITAMS OF NUMBERS. 


No. 765 L. 882] 


—_ | ———— | | | | 









































765 | 883661 | 3718 | 3775 | 3882 | 3888 || 3945 | 4002 | 4059 
6 4229 | 4285 | 4842 | 4399 | 4455 || 4512 | 4569 | 4625 
f¢ 4795 | 4852 | 4909 | 4965 | 5022 || 5078 | 5135 | 5192 
8 5361 | 5418 | 5474 | 5581 | 5587 || 5644 | 5700 | 5757 
9 5926 | 5983 | 6039 | 6096 | 6152 ||} 6209 | 6265 | 6821 
770 6491 | 6547 | 6604 | 6660 | 6716 || 6773 | 6829 | 6885 
1 7054 | 7111 | 7167 | 7223 | 7280 || 7336 | '7892 | 7449 
2 W617 | 7674 | 7730 | 7786 | 7842 || 7898 | 7955 | 8011 
3 8179 | 8236 | 8292 | 8348 | 8404 || 8460 | 8516 | 857 
4 8741 | 8797 | 8858 | 8909 | 8965 || 902 907 9134 
5 9302 | 9358 | 9414 | 947 9526 || 9582 | 9638 | 9694 
6 9862 | 9918 | 997: | | | ——_—__ | —_ 
0030.) 0086 || 0141 | 0197 | 02538 
7 ) 890421 | 0477 | 0533 | 0589 | 0645 || 0700 | 0756 | 0812 
8 0980 | 1035 | 1091 | 1147 | 1203 || 1259 | 1314 | 1370 
9: 15387 | 15938 | 1649 | 1705 | 1760 || 1816 | 1872 | 1928 
780 2095 | 2150 | 2206 | 2262 | 2317 || 2878 | 2429 | 2484 
1 2651 | 2707 | 2762 | 2818 | 287 2929 | 2985 | 3040 
2 8207 | 3262 | 3318 | 337 8429 || 8484 | 3540 | 3595 
3 3762 | 3817 | 3873 | 3928 | 3984 || 4039 | 4094 | 4150 
4 4316 | 4871 | 4427 | 4482 | 4588 || 4593 | 4648 | 4704 
5 4870 | 4925 | 4980 | 5036 | 5091 5146 | 5201 | 5257 
6 5423 | 5478 | 55383 | 5588 | 5644 || 5699 | 5754 | 5809 
v4 5975 | 6030 | 6085 | 6140 | 6195 || 6251 | 6806 | 6861 
8 6526 | 6581 | 6686 | 6692 | 6747 || 6802 | 6857 | 6912 
9 COL aloe LCL Ste | cae (297 || 73852 | 7407 | 7462 
790 "627 | 7682 | 7737 | 7792 | 7847 || 7902 | 7957 | 8012 
1 8176 | 8231 | 8286 | 8341 | 8396 |} 8451 | 8506 | 8561 
2 87 8780 | 8835 | 8890 | 8944 || 8999 | 9054 | 9109 
3 9273 | 9328 | 9383 | 94387 | 9492 || 9547 | 9602 | 9656 
4 9821 | 9875 | 9580 | 9985 ee 
———| 0039 || 0094 | 0149 | 0203 
5 | 9003867 | 0422 76 | 0531 | 0586 || 0640 | 0695 | 0749 
6 0913 | 0968 | 1022 | 1077 | 1131 1186 | 1240 | 1295 
2 1458 | 1513 | 1567 | 1622 | 1676 |) 1781 | 1785 | 1840 
8 2003 | 2057 | 2112 | 2166 | 2221 || 227 2829 | 2384 
9 2547 | 2601 | 2655 | 2710 | 2764 || 2818 | 2873 | 2927 
S00 3090 | 3144 | 3199 | 8253 | 3307 || 3361 | 3416 | 3470 
1 8633 | 8687 | 3741 | 3795 | 3849 |} 3904 | 3958 | 4012 
2 4174 | 4229 | 4283 | 4337 | 4891 || 4445 | 4499 | 4553 
3 4716 | 4770 | 4824 | 4878 | 4932 || 4986} 5040 | 5094 
4 5256 | 5310 | 5364 | 5418 | 5472 || 5526 | 5580 | 5634 
5 5796 | 5850 | 5904 | 5958 | 6012 || 6066 | 6119 | 6173 
6 6335 | 63889 | 6443 | 6497 | 6551 6604 | 6658 | 6712 
uf 6874 | 6927 | 6981 | '7085 | 7089 || 7143 | 7196 | 7250 
8 7411 | 7465 | 7519 | 7573 | 7626 || 7680 | 7734 | 7787 
9 7949 | 8002 | 8056 | 8110 | 8163 || 8217 | 8270 
PROPORTIONAL PARTS. 
Diff. 1 2 3 4 5 6 G 8 9 
57 11.4 17.1 22.8 84.2 39.9 45.6 51.3 


5 

0 33.6 39.2 44.8 50.4 
5 383.0 38.5 44.0 49.5 
0 82.4 37.8 43.2 









TOR LOGARITHM2 OF NUMBERS, 





















































No. 840 L. 908.] [No. 854 L. 931. 
N.| 0 LC SM, Beak 4 Bi 6) PS is We 9, ie 
810 | 908485 | 8539 | 8592 | 8646 | 8699 |) 8753 | 8807 | 8860 | 8014 | 8967 
1 9021 | 9074 | 9128 | 9181 | 9235 || 9289 | 9342 | 9396 | 9449 | 9503 
2 9556 | 9610 | 9663 | 9716 } 9770 || 9823 | 9877 | 9930 | 9984 roe 
3 | 910091 | 0144 | 0197 | 0251 | 0804 || 0858 | 0411 | 0464 | 0518 | 0571 
4 | 0624 | 0678 | 0731 | 0784 | 0838 || 0891 | 0944 | 0998 | 1051 | 1104 
5 1158 | 1211 | 1264 | 1817 | 1371 || 1424 | 1477 | 1580 | 1584 | 1687 
6 1690 | 1743 | 1797 | 1850 | 1908 || 1956 | 2009 | 2063 | 2116 | 2169 
7 2222 | 2275 | 2828 | 2381 | 2485 || 2488 | 2541 | 2594 | 2647 | 2700 
8 2753 | 2806 | 2859 | 29138 | 2966 || 3019 | 307 3125 | 3178 | 3231 
9 8284 | 3337 | 3390 | 3443 | 3496 || 3549 | 3602 | 3655 | 37 3761 53 
820 | . 3814 | 3867 | 3920 | 3973 | 4026 || 4079 | 4132 | 4184 | 4287 | 4290 
1 4343 | 4396 | 4449 | 4502 | 4555 |; 4608 | 4660 | 4713 ! 4766 | 4819 
2 4872 | 4925 | 4977 | 5030 | 5083 || 5136 | 5189 | 5241 | 5294 | 5347 
3 5400 | 5453 | 5505 | 5558 | 5611 || 5664 | 5716 | 5769 | 5822 | 5875 
4| 5927 | 5980 | 6033 | 6085 | 6138 || 6191 | 6243 | 6296 | 6349 | 6401 
5 6454 | 6507 | 6559 | 6612 | 6664 || 6717 | 6770 | 6822 | 6875 | 6927 
6 6980 | 7033 | ‘7085 |} 7188 | 7190 || 7243 | 7295 | 73848 | '7400 | 7453 
v4 7506 | 7558 | 7611 | 7663 | 7716 || 7768 | 7820 | 787 7925 | 7978 
8 | 8030 | 8083 | 8135 | 8188 | 8240 || 8293 | 8345 | 8397 | 8450 | 8502 
9 | 8555 | 8607 | 8659 | 8712 | 8764 || 8816 | 8a69 | sozt | 8973 | 9026 
830 | 9078 | 9130 | 9188 | 9235 | 9287 || 9340 | 9392 | 9444 | 9496 | 9549 
1 9601 | 9653 | 9706 | 9758 | 9810 || 9862 | 9914 | 9967 |———_|_—_ 
| |_| ——_ | ——_ | | —__—__ |__| —_ 0019 | 0071 
2 | 920123 | 0176 | 0228 | 0280 | 0382 |} 0884 | 0486 | 0489 | 0541 | 0598 
3 0645 | 0697 | 0749 | 0801 | 0853 || 0906 | 0958 | 1010 | 1062 | 1114 59 
4 1166 | 1218 | 1270 | 1822 | 1374 || 1426 | 1478 | 1530 | 1582 | 1624 
5 | 1686 | 1738 | 1790 | 1842 | 1894 || 1946 | 1998 | 2050 | 2102 | 2154 
6 2206 | 2258 | 23810 | 2862 | 2414 || 2466 | 2518 | 257 2622 | 2674 
ai 2725 | 2777 | 2829 | 2881 | 2933 || 2985 | 3037 | 3089 | 3140 | 3192 
8 8244 | 3296 | 3348 | 3399 | 3451 || 3503 | 3555 | 3607 | 3658 | 3710 
9 8762 | 8814 | 38865 | 3917 | 38969 || 4024 | 4072 | 4124 | 4176 
840! 4279 | 4331 | 4388 4486 || 4538 | 4589 | 4641 | 4698 | 4744 
al 4796 | 4848 | 4899 } 4951 | 5003 || 5054 | 5106 | 5157 | 5209 | 5261 
2 5312 | 5364 | 5415 | 5467 | 5518 ||} 5570 | 5621 | 5673 | 5725 | 5776 
3} 5828 | 5879 | 5931 | 5982 | 6034 || 6085 | 6137 | 6188 | 6240 | 6291 
4| 6342 | 6394 | 6445 | 6497 | 6548 || 6600 | 6651 | 6702 | 6754 | 6805 
D 6857 | 6908 | 6959 | 7011 | 7062 || 7114 | 7165 | 7216 | 7268 | 7319 
6 7370 | 7422 | 7473 | 7524 | 757 7627 | 7678 | 7730 | 7781 | 78382 
vg 7883 | '7935 | 7986 | 8037 | 8088 || 8140 | 8191 | 8242 | 8293 | 83845 
8 | 98396 | 8447 | 8498 | 8549 | 8601 || S652 | 8703 | 8754 | 8805 | 8857 
9 | 8908 | 8959 | 9010 | 9061 | 9112 |] 9163 | 9215 | 9266 | 9317 | 9368 
850 | 9419 | 9470 | S521 | 9572 | 9628 || 9674 | 9725 | 9776 | 9827 | 9879] 
1 9930 | 9981. |——]|- —— | ——_- | ——— | ——_ | ——_ |__| 
———| 0032 | 0083 | 0134 {| 0185 | 0236 | 0287 | 0388 | 0389 
2 | 980440 } 0491 | 0542 | 0592 | 0643 || 0694 | 0745 | 0796 | 0847 | 0898 
3 0949 | 1000 } 1051 | 1102 } 1153 || 1204 | 1254 | 1305 | 1356 | 1407 
4 1458 | 1509 | 1560 | 1610 | 1661 || 1712 | 1763 | 1814 | 1865 | 1915 





LOGARITHMS OF NUMBERS. 1538 


No. 855 L. 931.] , [No. 899 L. 954, | 





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1 
2 
3 
4 
5 
6 
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8 
9 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
0 
1 
2 
3 
z 
5 
6 
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8 
9 





154 LOGARITHMS OF NUMBERS, 





[No. 944 L. 975, 





me a ee a ee ae 





















1 

2 

3 

= 

5 

6 

it 

8 

9 

0 

1 

2 NORTE OR a a PR CS A TS Nr A ea 

3 

4 

5 

6 

8 

9 8316 | 3863 | 3410 | 3457 | 3504 || 3552 | 3599 | 3646 | 38693 | 3741 
920 8788 | 3835 | 38882 | 3929 | 3977 || 4024 | 4071 | 4118 | 4165 | 4212 

1 4260 | 4807 | 4354 | 4401 | 4448 || 4495 | 4542 | 4590 | 4637 | 4684 

2 4731 | 4778 | 4825 | 4872 | 4919 || 4966 | 5013 | 5061 | 5108 | 5155 

3 5202 | 5249 | 5296 | 5843 | 5890 || 54387 | 5484 | 5531 | 5578 | 5625 

4 5672 | 5719 | 5766 | 5813 | 5860 || 5907 | 5954 | 6001 | 6048 | 6095 47 

5 6142 | 6189 | 6236 | 6283 | 6329 || 6376 | 6423 | 6470 | 6517 | 6564 

6 6611 | 6658 | 6705 | 6752 | 6799 || 6845 | 6892 | 6939 | 6986 | 7033 

7 7080 | 7127 | 7173 | 7220 | 7267 || 73814 | 73861 | 7408 | 7454 | 7501 

8 7548 | 7595 | 7642 | 7688 | 7735 || 7782 | 7829 | 7875 | 7922 | 7969 

9 8016 | 8062 | 8109 | 8156 | 8203 || 8249 | 8296 8290 | 8436 
ae 8483 | 8530 | 8576 | 8623 | 8670 || 8716 | 8763 | 8810 | 8856 | 8903 

2 

3 ESE TEE ES, (NEE ae) POR ES RT EU ace MO 

4 

5 

6 

7 

8 

9 
940 

1 

2 

38 

4 





PROPORTIONAL PARTS, 










4 5 


a | cr |e | | 


47 4.7 9.4 14.1 18.8 23.5 28.2 82.9 37.6 42.3 
4.6 9.2 13.8 18.4 23.0 27.6 32.2 36.8 41.4 















LOGARITHMS OF NUMBERS. 155 





No. 945 L. 975.] . [No. 989 L. 995. 





3 4 5 6 7 8 9 | Diff. 





— 









































7 | 6350 | 6396 | 6442 | 6488 | 6523 || 6579 | 6625 | 6671 | 6717 | 6763 
6808 | 6854 | 6900 | 6946 | 6992 || 7037 | 7083 | 7129 | 7175 | 7220 
9| 7266 | 7312 | 7358 | 7403 | 7449 || 7495 | Yo41 | 7586 | 7632 | 7678 
950 | "724 | 7769 | 7815 | 7861 | 7906 || 7952 | 7998 | 8043 | 8089 | 8135 
1] 8181 | 8226 | 8272 | $317 | 8363 || 8409 | 8454 | 8500 | 8546 | 8591 
2| 8637 | 8683 | 8728 | 8774 | 8819 || 8865 | 8911 | 8956 | 9002 | 9047 
3 | 9093 | 9138 | 9184 | 9230 | 9275 || 9321 | 9366 | 9412 | 9457 | 9503 
4| 9548 | 9594 | 9639 | 9685 | 9730 || 9776 | 9821 | 9867 } 9912 | 9958 
5 | 980003 | 0049 | 0094 | 0140 | 0185 || 0231 | 0276 | 0322 | 0367 | 0412 
6 | 0458 | 0503 | 0549 | 0594 | 0640 |] 0685 | 0730 | 0776 | 0821 | 0867 
7 | 0912 | 0957 | 1003 | 1048 | 1093 || 1139 | 1184 | 1229 | 1275 | 132 
8| 1366 | 1411 | 1456 | 1501 | 1547 || 1502 | 1637 | 1683 | 1728 | 1773 
9 | 1819 | 1864 | 1909 | 1954 | 2000 || 2045 | 2090 | 2135 | 2181 | 2226 
960 | 2271 | 2816 | 2362 | 2407 | 2452 |] 2497 | 2548 | 2588 | 2683 | 2678 
1] 2728 | 2769 | 2814 | 2859 | 2904 || 2949 | 2994 | 3040 | 8085 | 3130 
2| 8175 | 3220 | 8265 | 8310 | 3356 || 3401 | 8446 | 8491 | 3536 | 3581 
3} 3626 | 3671 | 38716 | 8762 | 8807 || 3852 | 8897 | 3942 | 8987 | 4032 
4] 4077 | 4122 | 4167 | 4212 | 4257 || 4302 | 4347 | 4392 | 4437 | 4482] |. 
5| 4527 | 4572 | 4617 | 4662 | 4707 || 4752 | 4797 | 4842 | 4887 | 4932) 4 
6 | 4977 | 5022 | 5067 | 5112 | 5157 || 5202 | 5247 | 5292 | 5337 | 5382 
7 | 5426 | 5471 | 5516 | 5561 | 5606 || 5651 | 5696 | 5741 | 5786 | 5830 
8| 5875 | 5920 | 5965 | 6010 | 6055 || 6100 | 6144 | 6189 | 6234 | 6279 
9 | 6324 | 6369 | 6413 | 6458 | 6503 || 6548 | 6593 | 6637 | 6682 | 6727 
970 | 6772 | 6817 | 6861 | 6906 | 6951 |] 6996 | 7040 | 7085 | 7180 } 7175 
1| 7219 | 7264 | 7309 | 7353 | 7398 || 7443 | 7488 | 7582 | 7577 | 7622 
2! 7666 | 7711 | 7756 | 7800 | 7845 || 7800 | 7934 | 7979 | Soz4 | 8068 
3| 8113 | 8157 | 8202 | 8247 | S201 || 8336 | 8361 | 8425 | 8470 | 8514 
4| 8559 | 8604 | 8648 | 8693 | 8737 || 8782 | 8826 | S871 | 8916 | 8960 
5 | 9005 | 9049 | 9094 | 9138 | 9183 || 9227 | 9272 | 9316 | 9361 | 9405 
6 | 9450 | 9494 | 9539 | 9583 | 9628 || 9672 | 9717 | 9761 | 9806 | 9850 
7 | 9895 | 9939 | 9983 —_|—__ |__ |__| 
0028 | 0072 || 0117 | O161 | 0206 | 0250 | 0294 
8 | 990339 | 0383 | 0428 | 0472 | 0516 || 0561 | 0605 | 0650 | 0694 | 0738 
9) 0783 | 0827 | 0871 | 0916 | 0960 |} 1004 | 1049 | 1098 | 1137 | 1182 
980} 1286 | 1270 | 1315 | 1359 | 1403 || 1448 | 1492 |. 1586 | 1580 | 1625 
1| 1669 | 1713 | 1758 | 1802 | 1846 |} 1890 | 1935 | 1979 | 2023 | 2067 
2| 2111 | 2156 | 2200 | 2244 | 2288 || 2333 | 2877 | 2401 | 2465 | 2509 
3] 2554 | 2598 | 2642 | 2686 | 2730 || 2774 | 2819 | 2863 | 2907 | 2951 
4| 2995 | 3039 | 8083 | 3127 | 8172 || 8216 | 8260 | 8304 | 3348 | 3392 
5 | 8436 | 3480 | 3524 | 8568 | 3613 || 3657 | 8701 | 3745 | 8789 | 3833 
6 | 3877 | 3021 | 3965 | 4009 | 4053 || 4097 | 4141 | 4185 | 4229 | 4273 
7| 4317 | 4361 | 4405 | 4449 | 4493 || 4537 | 4581 | 4625 | 4669 | 4713 | 44 
8| 4757 | 4801 | 4845 | 4889 | 4933 || 4977 | 5021 | 5065 | 5108 | 5152 
9 | 5196 | 5240 | 5264 | 5328 | 5372 || 5416 | 5460 | Saud | 5547 | 5591 








Diff 1 2 38 4 5 6 7 8 9 
46 4.6 9.2 13.8 18.4 23.0 27.6 82.2 36.8 41.4 
45 4.5 9.0 13.5 18.0 22.5 27.0 81.5 |! 36:0. 40.5 
os 4.4 8.8 13.2 17.6 22.0 26.4 30.8 35.2 39.6 
43 4.3 8.6 12.9 17.2 21.5 25.8 30.1 34.4 38.7 
ne PS SE RE ED 


156 MATHEMATICAL TABLES. 


No, 900 L. 995.] _ TNo. 999 1, 909 








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HYPERBOLIC LOGARITHMS. 


















































No. | Log. No. | Log. No. | Log. No. | Log. No. | Log. 
1.01 .0099 || 1.45 | .3716 || 1.89 | .6366 || 2.83 | .8458 |; 2.77 | 1.0188 
1.02 .0198 || 1.46 .3784 || 1.90 .6419 || 2.34 .8502 |] 2.7 1.0225 
1.03 .0296 || 1.47 .8853 || 1.91 .6471 || 2.35 .8544 || 2.79 | 1.0260 
1.04 .0392 |} 1.48 .38920 || 1.92 .6523 || 2.36 .8587 || 2.80 | 1.0296 
1.05 .0488 || 1.49 -3988 || 1.93 6575 || 2.37 .8629 || 2.81 | 1.03382 
1.06 | .0583 || 1.50 | .4055 || 1.94 | .6627 || 2.388 | .867 2.82 | 1.0367 
1.07 0677 || 1.51 -4121 || 1.95 667 2.39 .8713 || 2.83 | 1.0403 
1.08 077 1.52 -4187 || 1.96 .6729 || 2.40 8755 || 2.84 | 1.0488 
1.09 | .0862 || 1.53 | .4253 || 1.97 | .6780 || 2.41 8796 || 2.85 | 1.0478 
1.10 .0958 || 1.54 -4318 || 1.98 .6831 || 2.42 8838 || 2.86 | 1.0508 
1.11 -1044 || 1.55 .4883 || 1.99 .6881 || 2.43 8879 || 2.87 | 1.0543 
1.12 -1183 || 1.56 -4447 || 2.00 .6931 || 2.44 8920 || 2.88 | 1.0578 
1.13 1222 || 1.57 4511 || 2.01 .6981 |} 2.45 8961 |} 2.89 | 1.0613 
1.14 -1310 || 1.58 4574 || 2.02 .70381 || 2.46 -9002 || 2.90 | 1.0647 
1.15 .1398 || 1.59 -4637 || 2.08 -7080 || 2.47 -9042 |] 2.91 | 1.0682 
1.16 .1484 || 1.60 -4700 || 2.04 -7129 || 2.48 .9083 || 2.92 } 1.0716 
along .1570 || 1.61 -4762 || 2.05 Hi ( 2.49 -9123 || 2.93 | 1.0750 
¢ 18 -1655 || 1.62 -4824 || 2.06 (227% || 2.50 9163 || 2.94 | 1.0784 
7.19 -1740 || 1.63 -4886 || 2.07 724 2.51 9203 || 2.95 | 1.0818 
1.20} .1828 || 1.64] .4947 || 2.08 | .7824 || 2.52 9243 || 2.96 | 1.0852 
1.21 -1906 || 1.65 -5008 || 2.09 7372 || 2.58 9282 || 2.97 } 1.0886 
dee -1988 || 1.66 .5068 || 2.10 -7419 || 2.54 9822 |) 2.98 | 1.0919 
1.23 2207 1.67 -5128 || 2.11 7467 || 2.55 9361 |) 2.99 | 1.0953 
1.24 -2151 || 1.68 .6188 || 2.12 7514 || 2.56 9400 ||} 8.00 | 1.0986 
1.2 .2231 |} 1.69 -6247 || 2.18 7561 || 2.57 9439 || 3.01 | 1.1019 
1.26 -2311 |} 1.70 -5806 || 2.14 7608 || 2.58 9478 |) 8.02 | 1.1053 
1.27 .2390 || 1.71 .53865 || 2.15 7655 || 2.59 9517 || 3.03 | 1.1086 
1.28 -2469 }| 1.72 6423 || 2.15 7701 || 2.60 9555 || 8.04 | 1.1119 
1.29 .2546 |] 1.73 -5481 || 2.17 |. .7747 || 2.61 9594 || 3.05 | 1.1151 
1.30 -2624 |} 1.74 .55389 || 2.18 7793 || 2.62 9632 |/ 3.06 } 1.1184 
1.31 -2700 || 1.7 -5596 || 2.19 - 7839 || 2.63 9670 |} 8.07 | 1.1217 
1.32 ~2et0 |) 1.76 -5653 || 2.20 7885 |} 2.64 9708 || 3.08 | 1.1249 
1.33 -2852 |) 1.77 -5710 || 2.21 7930 || 2.65 9746 || 8.09 | 1.1282 
1.34 2927 || 1.78 -5766 || 2.22 V975 || 2.66 9783 |) 8.10 | 1.1314 
1.35 -8001 |{ 1.79 -5822 |} 2.238 8620 || 2.67 9821 || 3.11 | 1.1846 
1.36 -3075 |) 1.80 587 2.24 8065 || 2.68 9858 || 3.12 | 1.1878 
1.37 .3148 || 1.81 -5933 ]) 2.25 8109 || 2.69 .9895 || 38.18 | 1.1410 
1,38 .38221 || 1.82 .5988 || 2.26 8154 || 2.7 9933 |; 5.14 | 1.1442 
1.39 .8293 || 1.83 -6043 || 2.27 8198 || 2.71 9969 |} 3.15 | 1.1474 
1.40 .3365 || 1.84 -6098 || 2.28 8242 || 2.72 | 1.0006 || 38 16 | 1.1506 
1.41 -38436 || 1.85 -6152 || 2.29 8286 || 2.73 | 1.0043 || 3.17 | 1.15387 
1.42 | .8507 || 1.86 {| .6206 || 2.30 | .8329 || 2.74 | 1.0080 || 3.18 | 1.1569 
1.43 3077 || 1.87 -6259 |) 2.31 -8372 || 2.75 | 1.0116 || 3.19 | 1.1600 
1.44 | .3646 || 1.88 | .6313 || 2.82 | .8416 || 2.76 | 1.0152 || 8.20 | 1.1632 


HYPERBOLIC LOGARITHMS. 15? 






































No, | Log No. | Log. || No. | Log No. | Log. No. | Log. 
8.21 | 1.1663 || 3.87 | 1.3533 || 4.53 | 1.5107 || 5.19 | 1.6467 || 5.85 | 1.7664 
8.22 | 1.1694 || 3.88 | 1.8558 || 4.54 | 1.5129 |} 5.20 | 1.6487 || 5.86 | 1.7681 
3.23 } 1.1725 || 3.89 | 1.8584 || 4.55 | 1.5151 || 5.21 | 1.6506 || 6.87 | 1.7699 
3.24 |} 1.1756 || 3.90 | 1.3610 || 4.56 | 1.5178 || 5.22 | 1.6525 || 5.88 | 1.7716 
3.25 | 1.1787 || 3.91 | 1.8635 || 4.57 | 1.8195 || 5.28 | 1.6544 || 5.89 | 1.7733 
38.26 | 1.1817 || 8.92 | 1.8661 || 4.58 | 1.5217 |) 5.24 | 1.6563 || 5.90 | 1.7750 
3.27 | 1.1848 || 3.93 | 1.3686 || 4.59 | 1.5289 || 5.25 | 1.6582 || 5.91 | 1.7766 
3.28 | 1.1878 || 3.94 | 1.3712 || 4.60 | 1.5261 || 5.26 | 1.6601 || 5.92 | 1.7783 
8.29 | 1.1909 || 3.95 | 1.3787 || 4.61 | 1.5282 || 5.27 | 1.6620 || 5.93 | 1.7800 
8.30 | 1.1939 || 3.96 | 1.38762 || 4.62 | 1.5304 || 5.28 | 1.6639 || 5.94 | 1.7817 
8.31 | 1.1969 || 3.97 | 1.8788 || 4.63 | 1.5326 || 5.29 | 1.6658 || 5.95 | 1.7834 
3.82 | 1.1999 || 3.98 | 1.3813 || 4.64 | 1.5347 |; 5.80 | 1.6677 || 5.96 | 1.7851 
3.33 | 1.2080 || 3.99 | 1.8838 |} 4.65 | 1.5369 || 5.31 | 1.6696 || 5.97 | 1.7867 
3.34 | 1.2060 |} 4.00 | 1.3868 |} 4.66 | 1.5390 || 5.32 | 1.6715 || 5.98 | 1.7884 
8.35 | 1.2090 |} 4.01 | 1.3888 || 4.67 | 1.5412 || 5.33 | 1.6734 || 5.99 | 1.7901 
8.36 | 1.2119 || 4.02 | 1.3913 |) 4.68 | 1.5433 || 5.34 | 1.6752 || 6.00 | 1.7918 
8.37 | 1.2149 || 4.03 | 1.8938 |} 4.69 | 1.5454 || 5.35 | 1.6771 || 6.01 | 1.7934 
8.38 | 1.2179 || 4.04 | 1.3962 || 4.70 | 1.5476 || 5.86 | 1.6790 |] 6.02 | 1.7951 
8.39 | 1.2208 || 4.05 | 1.3987 || 4.71 | 1.5497 || 5.387 | 1.6808 || 6.03 | 1.7967 
8.40 | 1.2288 || 4.06 | 1.4012 || 4.72 | 1.5518 || 5.38 | 1.6827 || 6.04 | 1.7984 
8.41 | 1.2267 || 4.07 | 1.4036 || 4.73 | 1.5539 || 5.89 | 1.6845 || 6.05 | 1.8001 
3.42 | 1.2296 || 4.08 | 1.4061 || 4.74 | 1.5560 || 5.40 | 1.6864 || 6.06 | 1.8017 
3.43 | 1.2326 || 4.09 | 1.4085 |] 4.75 | 1.5581 || 5.41 | 1.6882 || 6.07 | 1.8034 
8.44 | 1.2355 || 4.10 | 1.4110 |} 4.76 | 1.5602 || 5.42 | 1.6901 || 6.08 | 1.8050 
3.45 | 1.2384 || 4.11 | 1.4134 || 4.77 | 1.5623 |] 5.43 | 1.6919 || 6.09 | 1.8066 
8.46 | 1.2413 || 4.12 | 1.4159 || 4.78 | 1.5644 || 5.44 | 1.6938 || 6.10 | 1.8083 
8 47 | 1.2442 || 4.13 | 1.4183 || 4.79 | 1.5665 || 5.45 | 1.6956 || 6.11 | 1.8099 
8.48 | 1.2470 || 4.14 | 1.4207 || 4.80 | 1.5686 || 5.46 | 1.6974 || 6.12 | 1.8116 
8.49 | 1.2499 || 4.15 | 1.4231 || 4.81 } 1.5707 || 5.47 | 1.6993 || 6.13 | 1.8132 
3.50 | 1.2528 || 4.16 | 1.4255 || 4.82 | 1.5728 || 5.48 | 1.7011 || 6.14 | 1.8148 
8.51 | 1.2556 || 4.17 | 1.4279 || 4.83 | 1.5748 || 5.49 | 1.7029 || 6.15 | 1.8165 
3.52 | 1.2585 || 4.18 | 1.4303 || 4.84 | 1.5769 || 5.50 | 1.7047 || 6.16 | 1.8181 
8.53 | 1.2613 || 4.19 | 1.4327 || 4.85 | 1.5790 || 5.51 | 1.7066 || 6.17 | 1.8197 
8.54 | 1.2641 || 4.20 | 1.4351 || 4.86 | 1.5810 || 5.52 | 1.7084 || 6.18 | 1.8213 
3.55 | 1.2669 || 4.21 | 1.4375 || 4.87 | 1.5831 || 5.53 | 1.7102 || 6.19 | 1.8229 
8.56 | 1.2698 || 4.22 | 1.4898 || 4.88 | 1.5851 || 5.54 | 1.7120 || 6.20 | 1.8245 
8,57 | 1.2726 || 4.28 | 1.4422 || 4.89 | 1.5872 || 5.55 | 1.7138 |] 6.21 | 1.8262 
8.58 | 1.2754 || 4.24 | 1.4446 || 4.90 | 1.5892 |] 5.56 | 1.7156 || 6.22 | 1.8278 
8.59 | 1.2782 || 4.25 | 1.4469 || 4.91 | 1.5918 |} 5.57 | 1.7174 || 6.238 | 1.8294 
3.60 | 1.2809 || 4.26 | 1.4493 || 4.92 | 1.5933 || 5.58 | 1.7192 || 6.24 | 1.8310 
8.61 | 1.2837 |] 4.27 | 1.4516 || 4.93 | 1.5953 || 5.59 | 1.7210 || 6.25 | 1.83826 
8.62 | 1.2865 || 4.28 | 1.4540 || 4.94 | 1.5974 |] 5.60 | 1.7228 || 6.26 | 1.8342 
8.63 | 1.2892 || 4.29 | 1.4563 || 4.95 | 1.5994 |) 5.61 | 1.7246 || 6.27 | 1.8358 
8.64 | 1.2920 || 4.80 | 1.4586 || 4.96 | 1.6014 || 5.62 | 1.7263 || 6.28 | 1.8374 
3.65 | 1.2947 || 4.81 | 1.4609 || 4.97 | 1.6084 || 5.63 | 1.7281 || 6.29 | 1.8390 
83.66 } 1.2975 || 4.382 | 1.4633 || 4.98 | 1.6054 || 5.64 | 1.7299 || 6.30 | 1.8405 
3.67 | 1.3002 || 4.383 | 1.4656 || 4.99 | 1.6074 || 5.65 | 1.7317 || 6.31 | 1.8421 
3.68 | 1.3029 || 4.34 | 1.4679 || 5.00 | 1.6094 || 5.66 | 1.7334 |] 6.82 | 1.8437 
8.69 | 1.3056 || 4.35 | 1.4702 || 5.01 | 1.6114 || 5.67 | 1.7852 || 6.33 | 1.8453 
3.70 | 1.3083 || 4.36 | 1.4725 || 5.02 | 1.6134 || 5.68 | 1.7370 || 6.34 | 1.8469 
8.971 | 1.2110 || 4.87 | 1.4748 |] 5.03 | 1.6154 || 5.69 | 1.7887 || 6.385 | 1.8485 
3.72 | 1.38137 || 4.388 | 1.477 5.04 | 1.6174 || 5.70 | 1.7405 || 6.36 | 1.8500 
3.73 | 1.3164 || 4.89 | 1.4793 |} 5.05 | 1.6194 || 5.71 | 1.7422 || 6.387 | 1.8516 
8.74 | 1.3191 || 4.40 | 1.4816 || 5.06 | 1.6214 || 5.72 | 1.7440 |] 6.38 | 1.8532 
8.%5 | 1.3218 || 4.41 | 1.4839 || 5.07 | 1.6233 || 5.73 | 1.7457 || 6.39 | 1.8547 
8.%6 | 1.3244 || 4.42 | 1.4861 5.08 | 1.6253 || 5.74 | 1.7475 || 6.40 | 1.8568 
3.77 | 1.3271 || 4.48 | 1.4884 || 5.09 | 1.6278 |] 5.75 | 1.7492 || 6.41 | 1.8579 
8.78 | 1.3297 || 4.44 | 1.4907 || 5.10 | 1.6292 || 5.76 | 1.7509 |} 6.42 | 1.8594 
8.79 | 1.3324 || 4.45 | 1.4929 |} 5.11 | 1.6312 || 5.77 | 1.7527 || 6.43 | 1.8610 
3.80 | 1.3350 || 4.46 | 1.4951 5.12 | 1.6332 || 5.78 | 1.7544 || 6.44 | 1.8625 
3,81 | 1.3376 || 4.47 | 1.4974 |] 5.13 | 1.6351 || 5.79 | 1.7561 || 6.45 | 1.8641 
8,82 | 1.3403 |] 4.48 | 1.4996 |) 5.14 | 1.6371 || 5.80 | 1.757 6.46 | 1.8656 
3.83 | 1.3429 || 4.49 | 1.5019 |] 5.15 | 1.6390 || 5.81 | 1.7596 || 6.47 | 1.8672 
8.84 | 1.3455 |] 4.50 | 1.5041 |] 5.16 | 1.6409 |] 5.82 | 1.7613 || 6.48 | 1.8687 
8.85 | 1.8481 |} 4.51 | 1.5063 || 5.17 | 1.642 5.83 | 1.7630 |} 6.49 | 1.8703 
3.86 | 1.8507 H! 4.52 | 1.5085 1 5.18 | 1.6448 || 5.84 | 1.7647 Il 6.50 | 1.8718 
rE I nn nn ey 











6.60 
7.25 





6.61 
6.62 8901 2 
6.63 8916 2 
6.64 8931 2 
6.65 8946 2 
6.66 8961 3 
6.67 8976 3 
6.68 8991 3 
6.69 9006 3 
6.7 9021 3 
6.71 9036 3 
6.72 9051 3 
6.73 9066 3 
6.74 9081 3 
6.75 9095 3 
6.7 4 
6.7 9125 4 
6.78 9140 4 
6. f 4 
6. 4 
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; 4 
6.83 9213 4 
6.84 9228 4 
6.85 9242 4 
6.86 9257 5 
6.87 9272 5 
6.88 9286 5 
6.89 9301 5 
6.90 9315 5 
6.91 9330 5 
5 
5 
5 
5 
6 
6 
6 
6 


AD AD AEE TT AD A Fy Fag a ad TE a Td TI I I ISN NNN NN NSN NNN NNN NNNNN 
DIDMNH WW KH OSHRIOAL DOM DODIAMA OW OSDRIBAL OWE SSHIOMARWURSSHIS 


OF AF ADAYA B AT ag AF AF QATAINIAIAIAMAABWAAH 
BF AIRIMNVIRNWININAAAWOD 


mem irtoet ODOODOSDOCOONMOMDMONOOONO 


lor Bor) 
=) 
He OF DRO OHO D2 DOE WW HOO MIDUPWEH SLES 
gee a ae an NS ae epee lS th NSS Ne aedeagal radia a eee oleae 
$i. tie Bait Peace Criene wince) 8 A Wipiel ond pies aes 
a _— 
Om vr -— 
Om ot o 





MATHEMATICAL TABLES. 








Peek fk fk fk peek peek peek fh fk fod feeh peed feed feed Red fel beak fed bad Pat Pd bed Ped Pd 
a Le Pe ee ee oe an PC Ar pe kr ee fe rem re Dec ny 
ile) 
ical 
ris) 
iS 











J 
les) 
So 


81 


07 


Se et et OO 
oR Wor OoOd 


-16 


0 00 Gd GO Ce 00 G0 CO 0 00 G0 GO 00 60 60.40.20 G0 60 GO-GO. G0 5H 60.4.0 49 CD GO .G0.00 GO CO GO. GO DO GH GO 00 00 GO FAFA IAFF I I II III II 
rie RPE Sa SAS rice tb oleae a gah Be ee A Eee Be ont Ge ait Sa SHEE Ea Te ae oaboan 
ERNYOCeSRBRWTOODS 


Ara oOrn 








WOBDOOODOOOODOOOOOODOOO OOOO DOO OOOO OOOO OO OOOO OOO O WO 0 0 G 00 GH 6 60 0 GO G0 Go G9 0 G G0 G0 G0 
SDHARWSDHOARNVODSRVY ODDS WODALOODOEN SHAT ODSRNWODSRNDSDAENSDARWSOWDAKRWOCHSD 


$B SLD DD DBI ITI DDD DD ONO OWT TUB Be iB BB 09 09 09 G9 C9 29 09 WW WS ES AAD ODD OOOO DBO POO MOOS RE eSSS 





SW 0 ~ 
= 
(or) 
Ll 
o 


@W WW 





























ol 


. 





10 


11 


NATURAL TRIGONOMETRICAL FUNCTIONS. 


159 


NATURAL TRIGONOMETRICAL FUNCTIONS. 


M, } Sine, 





.00000 
00436 
00873 
.01309 
.01745 
.02181 
30 | .02618 
03054 
-03490 
15 |.03926 
30 | .04362 
04798 
05234 
-05669 





-06105 
.06540 
.06976 
07411 
.07846 
-08281 
-08716 
.09150 
-09585 
-10019 
-10453 
- 10887 
.11320 
011754 
.12187 
» 12620 
- 13053 
-13485 
-13917 
.14849 
14781 
slb2t2 
- 15643 
-16074 
- 16505 
- 16935 
17865 
.17794 
- 18224 
. 18652 
-19081 
-19509 
.19937 
. 20364 
. 20791 
-21218 
.21644 
.22070 
-22495 
.22920 
23345 








—_— 


Cosine,| Ver. Sin. 






































Co-Vers.| Cosec, | Tang, | Cotan. | Secant. 
1.0000 Infinite |.00000|Infinite | 1.0000 
.99564/229.18 |.00436/229.18 ; 1.0000 
-99127/114.59 {.00873/114.59 1.0000 
.98691} 76.897 |.01309| 76.390 | 1.0001 
.98255) 57.299 {.01745) 57.290 | 1.0001 
.97819} 45.840 1.02182) 45.829 | 1.0002 
.97382| 38.202 |.02618] 38.188 | 1.0003 
.96946] 82.746 |.03055} 32.730 | 1.0005 
.96510} 28.654 |.03492} 28.636 | 1.0006 
-96074| 25.471 |.03929} 25.452 | 1.0008 
.95633] 22.926 |.04366} 22.904 | 1.0009 
.95202] 20.843 |.04803] 20.819 | 1.0011 
. 94766] 19.107 1.05241] 19.081 | 1.0014 
.94331| 17.639 }.05678} 17.611 | 1.0016 
.93895| 16.380 }.06116) 16.350 | 1.0019 
.93460] 15.290 |.06554| 15.257 | 1.0021 
.93024| 14.336 |.06993] 14.301 | 1.0024 
.92589| 13.494 |.07431) 13.457 | 1.0028 
-92154) 12.745 |.07870) 12.706 | 1.0031 
91719} 12.076 |.08309) 12.035 | 1.0034 
91284) 11.474 |.08749] 11.430 | 1.0038 
-90850} 10.929 |.09189) 10.883 | 1.0042 
-90415) 10.433 |.09629) 10.3885 | 1.0046 
-89981} 9.9812}-10069| 9.9310) 1.0051 
.89547) 9.5668).10510) 9.5144) 1.0055 
-891138; 9.1855}.10952; 9.1309] 1.0060 
.88680} 8.8337|.11393| 8.7769) 1.0065 
-88246) 8.5079|.11836} 8.4490) 1.0070 
-87813) 8.2055].12278} 8.1443) 1.0075 
.87380} 7.9240).12722|} 7.8606) 1.0081 
-86947| 7.6613]|.13165| 7.5958) 1.0086 
.86515| 7.4156}.12609} 7.3479) 1.0092 
.86083) 7.1853)-.14054) 7.1154) 1.0098 
-85651| 6.9690).14499} 6.8969) 1.0105 
.85219] 6.7655)-14945) 6.6912) 1.0111 
.84788} 6.5736;-15391| 6.4971; 1.0118 
.84357| 6.3924|-15838) 6.3138) 1.0125 
.83926| 6.2211}-16286] 6.1402) 1.0132 
-83495| 6.0589|.16734) 5.9758] 1.0139 
.83065| 5.9049]}-17183) 5.8197) 1.0147 
.82635| 5.7588)-17633} 5.6713) 1.0154 
.82206| 5.6198}-18083) 5.5301] 1.0162 
8177 5.4874|.18534| 5.3955) 1.0170 
.81348] 5.3612}.18986) 5.2672] 1.0179 
.80919| 5.2408].19488) 5.1446) 1.0187 
.80491). 5.1258}-19891) 5.0273] 1.0196 
.80063} 5.0158}-20345) 4.9152) 1.0205 
-79636| 4.9106)-20800} 4.8077) 1.0214 
- 79209} 4.8097).21256| 4.7046) 1.0223 
-78782| 4.7180}-21712} 4.6057) 1.0283 
. 78356] 4.6202)-22169) 4.5107) 1.0243 
-77930| 4.5311)-22628) 4.4194) 1.0253 
«77505, 4.4454|-238087) 4.3315} 1.0263 
-77080| 4.3630) -23547| 4.2468) 1.0273 
-76655| 4.2837)-24008| 4.1653) 1.0284 
-76231| 4.2072|-24470) 4.0867) 1.0295 
»75808] 4.1336).24933) 4.0108] 1.0306 
.75385| 4.0025).253897| 3.9375) 1.0317 
- 74962) 3.9939] .25862) 3.8667) 1.0329 
-74540| 3.9277) .26328) 3.7983) 1.0341 
-74118) 3.8637) .26795| 3.7320) 1.0353 
Secant. | Cotan.| Tang, Cosec. 





Ver, Sir, 





.00000 


.00001 
.00004 
.00009 
-00015 
.00024 
.00054 
00047 
-00061 
00077 
00095 
-00115 
001387 
.00161 
.00187 
00214 
00244 
00275 
-00308 
.00343 
00381 
.00420 
00460 
00503 
.00548 
-00594 
.00643 
.00693 
00745 
.00800 
00856 
.00913 
00973 
.01035 
.01098 
01164 
01231 
-013800 
.01371 
-01444 
-01519 
-01596 
-01675 
-O1755 
01887 
-01921 
-02008 
02095 
-02185 
02277 
.02370 
-02466 
.02563 
02662 
02768 
.02866 
02970 
03077 
.03185 
03295 











.03407 
Co -Vers. 





Cosine. 





1.0000 
-99999 
-99996 
-99991 
-99985 
-99976 
99966 
99953 
.99939 
299923 
-99905 
99885 
.99863 
-99839 
-99813 
99786 
- 99756 
99725 
-99692 
- 99656 
99619 
-99580 
99540 
99497 
-99452 
99406 
-993857 
98307 
99255 
-99200 
99144 
-99086 
-99027 
98965 
98902 
98836 
- 98769 
- 98700 
-98629 
- 98556 
98481 
98404 
98325 
98245 
- 98163. 
98079 
-97992 
97905 
97815 
97723 
-97630 
97534 
97437 
97338 
97237 
97134 
-97030 
- 96923 
96815 
95705 
- 96593 








Sine, © 








89 


88 


87 


86 


85 


84 


83 


82° 


81 


80 


79 


78 


a7 


76 


75 


° 





From 75° to 90° read from bottom of table upwards, 


> | 


160 4 MATHEMATICAL TABLES, 





ne ee 


© | M. } Sine, | Co-Vers.| Cosec, Tang, | Cotan. | Secant, |Ver. Sin.| Cosine. 





—_————. |§ ——— ————— | | | ————___ _] —__} —__ 


15 | 6 |.25882) .74118} 3.8637|.26795| 3.7320) 1 
15 |.26303) .78697) 3.8018].27262] 3.6680] 1 
80 |.26724| .78276) 9 3.7420).27732| 3.6059) 1 
45 |.27144| .72856}] 3.6840].28203) 3.5457) 1 
16} 0 |.27564| .'72436) 38.6280}.28674] 38.4874) 1 
15 |.27983| .72017} 3.5736).29147) 3.4808) 1 
80 |.28402] .71598) 3.5209|.29621| 3.3759) 1 
45 |.28820| .71180] 38.4699].80096; 3.3226) 1 
17 | O |.29287) .70763) 3.4203).80573}) 3.2709} 1 
15 |.29654] .70846) 8.3722}.81051} 3.2205) 1 
‘80 |.30070| .69929) 3.8255).31530) 3.1716) 1 
45 |.80486| .69514) 3.2801/.82010) 3.1240) 1 
18 | 0 |.80902| .69098] 3.2361].82492! 3.0777) 1 
15 |.81816} .68684) 3.1982).32975) 3.0326) 1 
30 |.81730} .68270) 3.1515).38459) 2.9887) 1 
45 |.82144| .67856] 3.1110|.33945) 2.9459) 1 
19 | O |.82557| .67443) 3.0715).34433] 2.9042) 1 
15 |.32969| .67031} 3.0331|.34921) 2.8636) 1 
30 |.33381| .66619] 2.9957).35412} 2.8239) 1 
45 |.33792) .66208) 2.9593].85904| 2.7852) 1 
20} 0 |.34202| .65798) 2.9238].86397} 2.7475) 3 
15 |.34612) .65388) 2.8892).36892} 2.7106) 1 
30 |.85021| .64979] 2.8554|.37388] 2.6746) 1 
45 |.85429| .64571] 2.8225).37887) 2.6395) 1 
21) O |.35887} .64163) 2.7904).88386) 2.6051} 1 
15 |.86244| .63756} 2.7591|.88888) 2.5715) 1 
30 |.36650] .68350} 2.7285).39391] 2.5886) 1 
45 |.387056| .62944] 2.6986].39896] 2.5065) 1. . “ 
22) O |.387461) .62539] 2.6695).40403) 2.4751) 1.0785] -07282| .92718] 68 | 0 
15 |.87865| .62135] 2.6410}.40911] 2.4443) 1. 07 
30 | .388268] .617382] 2.6131).41421| 2.4142) 1.0824] .07612) .92388 30 
1 
1 
1 
1 
1 
1 
if 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 





:0457| .04370| .956301 73 | 0 
0515] 04804 "95106| 72} 0 
'0576| .05448] .94552| 71] 0 


'0642| .06031| .93969| 70} 0 





0711] .06642| .93358] 69| 0 


45 |.88671) .613829] 2.5859).41933} 2.3847 
23] O |.389073} .60927| 2.5593).42447| 2.3559 
15 |.89474] .60526) 2.5333].42963) 2.327 
80 |.39875| 60125) 2.5078}.48481} 2.2998 
45 |.40275} .59725) 2.4829].44001} 2 2727 
24} 0 |.40674| .59326) 2.4586}.44523) 2.2460 
15 |.41072| .58928] 2.4348).45047) 2.2199 
30 |.41469) .58531] 2.4114).45573) 2.1943 
45 | 41866] .58134) 2.3886].46101| 2.1692 
25 | O |.42262] .57738) 2.8662).46631| 2.1445 
15 |.42657) .57343] 2.38443).47163] 2.1203 
80 |.43051} .56949) 2.3228).47697| 2.0965 
45 |.43445) .56555) + 2.3018].48234) 2.0732 
26) 0 |.43837) .56163) 2.2812].48773} 2.0503 
15 |.44229) .55771| + 2.2610}.49314} 2.027 
80 |.44620) .55380| 2.2412).49858] 2.0057 
45 |.45010) .54990| 2.2217).50404) 1. 
271 0 |.45399} .54601} 2.2027).50952) 1 
15 |.45787) .54213; 2.1840).51503) 1 
30 |.46175| .58825] 2.1657).52057) 1 
45 |.46561} .538439) 2.1477).52612] 1 
28} 0 |.46947) .58053) 2.13800):53171] 1 
15 |.47332) .52668) 2.1127).53782] 1.8611 
1 
1 
1 
1 
1 
1 
1 


"0864| .07950| .92050/ 67} 0 
0946 -08645| .91355| 66] 0 
:1034] .09369| .90631] 65 | 0 


-1126} .10121) .89679] 64 | 0 
-1150} .10313] .89687 45 
1174] .10507} .89493 386 
-1198} .107'02] .89298 15 
-1223} .10899] .89101} 63 | 0 
-1248] .11098} .88902 45 
.1274] .11299] .88701 30 
.1800} .11501} .88499 15 
-1826] .11705) .88295} 62 | 0 
-1852] 11911] .88089 45 

80 |.47716) .52284) 2.0957) .54295 

45 |.48099} .51901} 2.0790] .54862 
29} O |.48481) .51519} 2.0627) .55431 


Cosine.| Ver. Sin.| Secant. | Cotan,| Tang. Cosec. | Co-Vers,{ Sine. o |} M, 


Frem 60° to 75° read from bottom of table upwards, 


NATURAL TRIGONOMETRICAL FUNCTIONS. 























161 





© | M.} Sine. | Co-Vers.} Cosec. | Tang. | Cotan, | Secant. |Ver. Sin.| Cosine, 

80; 0 |.50000} .50000) 2.0000].57735) 1.7320) 1. 1547! .13397] .86603} 60] 0 
15 50377} .49623} 1.9850).58318} 1.7147) 1.1576) .13616} .86384 45 

80 |.50754| .49246) 1.9703).58904; 1.6977) 1.1606] .13837| .86163 380 

45 |.5112 48871} 1.9558).59494; 1.6808) 1.1636] .14059} .85941 15 

31 | 0 |.51504| .48496} 1.9416}.60086) 1.6643) 1.1666] .14283) .85717| 59 | O 
15 |.51877| .48123) 1.9276).60681) 1.6479) 1.1697] .14509) .85491 45 

80 |.52250) .47750} 1.9189).61280}; 1.6319} 1.1728) .14736} .85264 30 

45 |.52621|) .4737 1.9004} .61882; 1.6160} 1.1760) .14965) .85035 15 

32} O }.52992} .47008} 1.8871}.62487) 1.6003) 1.1792} .15195) .84805| 58 | 0 
15 }.53361|} .46639; 1.8740).638095; 1.5849) 1.1824] .15427) .84573 45 

30 |.538730} .46270} 1.8612!.63707| 1.5697) 1.1857) .15661| .84339 80 

45 |.54097| .45903) 1.8485|.64322) 1.5547) 1.1890} .15896| .84104 15 

$8 | O |.54464] .455386} 1.8361).64941| 1.5399) 1 1924] .16133] .838867| 57 | 0 
15 !'.54829) .45171| 1.8238) .65563|} 1.5253] 1.1958] .16371) .83629 45 

80 |.55194) .44806} 1.8118).66188] 1.5108) 1.1992] .16611] .83389 30 

45 |.55557| .44443} 1.7999).66818} 1.4966} 1.2027) .16853] .83147 15 

84) 0 |.55919} .44081} 1.7883).67451; 1.4826) 1.2062} .17096] .82904|) 56] 0 
15 |.56280} .438720| 1.7768) .68087; 1.4687) 1.2098} .17341) .82659 45 

80 }:56641| .43359) 1.7655}.68728) 1.4550) 1.2184) .17587) .82413 30 

45 ;.57000) .48000) 1.7544).69872) 1.4415) 1.2171) .17835) .82165 15 

85 | 0 §.57358| .42642] 1.'7434).70021} 1.4281} 1.2208} .18085} .61915) 55 | 0 
15 (.57715| .42285} 9 1.'7827|.70673} 1.4150) 1.2245] .18336] .81664 45 

80 |.58070} .41930] 1.'7220).71329} 1.4019) 1.2283) .18588) .81412 30 

45 |.58425; .41575] 1.7116).71990| 1.3891) 1.2322] .18843) .81157 15 

36 .58779| .41221| 1.'7013).72654| 1.3764) 1.2361] .19098] .80902] 54) 0 
15 |.59131] .40869} 1.6912).73323) 1.38638) 1.2400] .19356] .80644 45 

80 |.59482) .40518) 1.6812).73996| 1.38514) 1.2440} .19614! .80386 30 

45 |.59832} .40168} 1.6713).74673) 1.3392) 1.2480) .19875} .80125 15 

87 | 0 |.60181) .89819] 1.6616].75355} 1.3270) 1.2521] .20136] .79864| 53 | 0 
K45 |.60529} .89471} 1.6521|.76042} 1.3151) 1.2563] .20400] .79600 45 

30 |.60876| .39124) 1.6427).76733} 1.3082] 1.2605) .20665] .79335 30 

45 |.61222| .388778] 1.6334].77428) 1.2915] 1.2647] .20981| .79069 15 

88| 0 |.61566} .38434] 1.6243].78129) 1.2799] 1.2690} .21199] .78801) 52 | 0 
15 |.61909} .38091] 1.6153).78834) 1.2685) 1.2784] .21468] .78532 45 
80 |.62251) .37749| 1.6064|.79543) 1.2572) 1.2778) .21-739) . 78261 as 

45 |.6259 37408} 1.5976].80258) 1.2460} 1.2822} .22012] .77988 15 

$9 | 0 |.62932| .37068) 1.5890}.8097 1.2349] 1.2868] .22285] .77715| 51 | 0 
15 |.63271| .86729) 1.5805}.81703) 1.2239) 1.2913) .22561) .77439 45 

30 |.63608} .386392} 1.5721) .82434) 1.2131) 1.2960} .22838)] .77162 30 

45 |,.63944| .86056} 1.5639).83169} 1.2024) 1.3007) .23116) .76884 15 

40} 0 }.6427 35721) 1.5557).83910] 1.1918) 1.3054] .23396] .76604| 50 | 0 
15 |.64612) .385388} 1.5477|.84656) 1.1812) 1.8102] .28677) .76323 45 

80 |.64945| .35055} 1.5398).85408} 1.1708) 1.3151} .28959) .76041 30 

45 |.65276| .34724| 1.53820).86165) 1.1606] 1.3200] .24244] .75756 15 

41 | 0 |.65606} .34394| 1.5242).86929} 1.1504] 1.8250} .24529) .75471/ 49 | 0 
15 |.65935| .34065| 1.5166).87698) 1.1403) 1.3801] .24816] .75184 45 

30 |.66262} .338738] 1.5092).88472} 1.13803] 1.3352} .25104] .74896 30 

45 |.66588) .83412} 1.5018).89253) 1.1204] 1.3404} .25394] .74606 15 

42 | 0 |.66913] .33087| 1.4945|.90040| 1.1106] 1.3456] .25686] .74314] 48] 0 
15 |.67237| .382763| 1.4873].90834; 1.1009] 1.3509] .25978} .74022 45 

80 |.67559} .82441| 1.4802].91633} 1.0913} 1.8563} .26272) .73728 30 

45 |.67880) .382120| 1.4732}.92439] 1.0818) 1.3618] .26568] .73432 15 

43 | 0 |.68200| .81800] 1.4663].93251} 1.0724] 1.8673] .26865] .73135| 47] 0 
15 |.68518} .381482} 1.4595).94071); 1.0630) 1.3729) .27163] .72837 45 

80 |.68885) .81165} 1.4527).94896) 1.0538) 1.8786] .27463) .725387 80 

45 |.69151| .30849] 1.4461].95729) 1.0446} 1.3843) .27764) .7223 15 

44} 0 |.69466| .30534| 1.4396|.96569} 1.0355] 1.3902] .28066] .71934| 46} 0 
57/6977 30221] 1.4331|.97416} 1.0265} 1.3961] .28370] .71630) _ } 45 

80 |.70091) .29909] 1.4267).98270| 1.0176] 1.4020] .28675) .71325 30 

45 |.70401| .29599} 1.4204).99131} 1.0088) 1.4081} .28981) .71019 15 

45 | 0 |.70711| .29289) 1.4142|1.0000} 1.0000) 1.4142] .29289] .70711] 45] 0 
Cosine.|Ver, Sin.| Secant, | Cotan,| Tang, Cosec. | Co-Vers.| Sine, oO] Me 


From 45° to 60° read from bottom of table upwards, 


28 pry eet 


162 





Deg. 


bot 
So CONQO PWM OS | 


MATHEMATICAL TABLES, 


LOGARITHMIC SINES, ETC. 


Sine. Cosec. 


Infinite. 
11.75814 
11.45718 
11.28120 
11.15642 


11.0597 

10.98077 
10.91411 
10.85644 
10.80567 


10.76033 
10.71940 
10.68212 
10.64791 
10.61632 


10.58700 
10.55966 
10.53406 
10.5102 
10.48736 


_9.58405/10.46595 
9.55433/10.44567 
9.57358)10. 42642 
9.59188/10.40812 


In.Neg. 
8.24186 
8.54282 
8.71880 
8.84358 


8.94030 
9.01928 
9.08589 
9.14356 
9.19433 


9.23967 
9.28060 
9.31788 
9.35209 
9.38368 


9.41300 
9.44034 
9.46594 
9.48998 
9.51264 





| 9.60931|10.39069 


9.62595) 10.37405 
9.64184)10.35816 
9.65705} 10.34295 
9.67161 |10.32839 
9.68557 }10.31443 


§.69897'|10 30103 
9.71184}10.28816 
9 .72421}10.27579 
9.73611|10.26389 
9.74756)10.25244 


9.75859|10.24141 
9.76922)10. 28078 
9.77946) 10.22054 
9 .'78934|10. 21066 
9.79887|10. 20113 


9.80807/1C. 19193 
9.81694) 10.18396 
9.82551/10.17449 
9. 83278) 10. 16622 
9.84177)\10. 15823 


9.84949/10. 15052 


Cosine. | Secant. 


Versin. |Tangent. 


In. Neg. |In. Neg. 
6.18271; 8.24192 
6.78474| 8.54308 
7.138687) 8.71940 
7.88667] 8.84464 


7.58039} 8.94195 
7.73863] 9.02162 
7.87238) 9.08914 
7.98820} 9.14780 
8.09032) 9.19971 


8.18162) 9.24632 
8.26418) 9.28865 


Cotan., 





Infinite. 
11.75808 
11. 45692 
11.28060 
11°155386 


11.05805 
10.97838 
10.91086 
10. 85220 
10.80029 


10.753868 
10.71135 


10.00000 


Covers. | Secant. 


9.99235 
9.98457 
9.97665 


10.00007 
10.00026 
10.00060 
9.96860 |10.00106 


9.96040 |10.00166 
9.95205 |10.00239 
9.94356 |10.00325 
9.93492 |10.00425 
9.92612|10.00588 


9.91717 |10.00665 
9.90805 |10.00805 





Cosine. 


10.00000|}10.00000 


9.99993 
9.99974 
9.99940 
9.99894 


9.99834 
9.99761 


9.99673} 


9.99575 
9.99462 


9.99335 
9.99195 








8.33950 
8.40875 
8.47282 


8.53243 
8.58814 
8.64043 
8.68969 
8.73625 


8.78037 
8.82230 
8.86223 
8.90034 
8.93679 


8.97170 
9.00521 
9.03740 
9.068388 
9.09823 


9.12702 
9.15483 
9.18171 
9.20771 
9.23290 


9.25781 
9.28099 
9.30398 
9.32631 
9.34802 


9.36913 
9.38968 
9.40969 
9.42918 
9.44818 


9.82747 
9.36386 
9.389677 


9.42805 


10.67258 
10.63664 
10.60323 


10.57195 
9.45750 110.54250 
9.48534 |10.51466 
9.51178 |10.48822 
9.58697 |10. 46303 


9.56107 |10.43&93 
9.58418 | 10. 41582 
9.60641 |10.89359 
9.62785 |10.37215 
9.64858 |10.35142 


9.66867 |10.331383 
9.68818 ]10.31182 
9.70717 10. 29283 
9.72567 |10.27433 
9.74875 |10. 25625 


9.76144 |10. 23856 
9.77877 |10. 22123 
9.79579 |10.20421 
9.81252|10.18748 
9.82899 |10.17101 


9.84523 |10. 15477 
9.86126 | 10.13874 
9.87711 |10.12289 
9.89281 }10.10719 
9.90887 |19.09163 


9.92381 |10.07°619 
9.93916 /10.06084 
9.95444 |10.04556 
9.96966 |10.03034 
9.98484 |10.015i16 


9.46671) 10.00000/10.00000 


2S 5 Cee I ESE) ERB S| (Ce Ee Cee ee aS Sy Pe ee ay) Se, | See eee 


Covers. 


9.89877 
9.88933 
9.87971 


9.86992 ]10.01506 


9.85996 
9.84981 
9.83947 


9.82894 |10.02433 


9.81821 
9.80729 
9.79615 
9.78481 
9.77325 


9.7614€ 
9.74945 
9.73720 
9.72471 
9.71197 


9.69897 
9.68571 
9.67217 
9.65836 
9.64425 


9.62984 
9.61512 
9.60008 
9.58471 
9.56900 


9.55293 
9.53648 
9.51966 
9.50243 
9.48479 


9.46871 |10.15052 


Cotan, |Tangent.| Versin. 


9.99040 
9.98872 
9.98690 


9.98494 
9.98284 
9.98060 
9.97821 
9.97567 


9.97299 
9.97015 
9.96717 
9.96403 
9.96073 


9.95728 
9.95366 
9.94988 
9.94593 
9.94182 


9.93753 
9.93807 
9.92842 
9.92359 
9.91857 


9.91336 
9.90796 
9.90235 
9.89653 
9.89050 


9.88425 
9.8777 

9.87107 
9.86413 
9.85693 


9.84949 


10.00960 
10.01128 
10.01310 


10.01716 
10.01940 
10.02179 


10.02701 
10.02985 
10.03283 
10.03597 
10.03927 


10.04272 
10.04634 
10.05012 
10.05407 
10.05818 


10.06247 
10 .06693 
10.07158 
10.07641 
10.08143 


10. 08664 
10.09204 
10.09765 
10,10347 
10.10950 


10.115%5 
10. 12222 
10. 12893 
10.13587 
10.143807 


Cosec. Sine. 














From 45° to 90° read from bottom of table upwards, 


SPECIFIC GRAVITY. 163 


MATERIALS. 
THE CHEMICAL ELEMENTS. 


The Common Elements (42). 








&3 83 22783 28 
A’s Name. Eg Name. bo a Name 00 
ibs Pas ee Poe pied 
Ow On <E Isa <5 
Al | Aluminum F | Fluorine 19. Pd | Palladium {106. 

Sb | Antimony Au | Gold — 197.2 {| P| Phosphorus] 81. 

As | Arsenic H | Hydrogen 1.01f Pt | Platinum 194.9 
Ba | Barium I Todine 126.8 | K | Potassium | 39.1 
Bi | Bismuth Ir _ | Iridium 193.1 § Si | Silicon 28.4 
B Boron Fe | Iron 56. Ag } Silver 107.9 
Br | Bromine Pb | Lead 206.9 f Na | Sodium 23. 

Cd | Cadmium Li | Lithium 7.039 Sr | Strontium 7.6 
Ca | Calcium Mg| Magnesium | 24.349 S Sulphur 32.1 
C Carbon Mn| Manganese | 55. Sn | Tin 119. 

Cl Chlorine Hg | Mercury 200. Ti | Titanium 48.1 
Cr | Chromiusn Ni | Nickel 58.7 # W | Tungsten  |184.8 
Co | Cobalt : N | Nitrogen 14. | Va | Vanadium } 51.4 
Cu | Copper 63.6 # O Oxygen 16. Zn | Zine 65.4 





The atomic weights of many ot the elements vary in the decimal place as 
given by different authorities. The above are the most recent values re< 
ferred to O = 16 and H = 1.008. When H is taken as 1, O = 15.879, and the 
other figures are diminished proportionately. (See Jour. Am. Chem. Soc., 
March, 1896.) 


Whe Rare Hlements (27). 


Beryllium, Be. Glucinum, G. Rubidium, Rb. Thallium, Tl. 
Ceesium, Cs. Indium, In. Ruthenium, Ru. Thorium, Th. 
Cerium, Ce. Lanthanum, La. Samarium, Sm. Uranium, U. 
Didymium, D. Molybdenum, Mo. Scandium, Se. Ytterbium, Yr. 
Erbium, E. Niobium, Nb. Selenium, Se. Yttrium, Y. 
Gallium, Ga. Osmium, Os. Tantalum, Ta. Zirconium, Zr, 
Germanium, Ge. Rhodium, R. Tellurium, Te. 


SPECIFIC GRAVITY. 


The specific gravity of a substance is its weight as compared with the 
weight of an equal bulk of pure water. 

To find the specific gravity of a substance, 

W = weight of body in air; w = weight of body submerged in water. 





Specific gravity Wow 

If the substance be lighter than the water, sink it by means of a heavier 
substance, and deduct the weight of the heavier substance. 

Specific-gravity determinations are usually referred to the standard of the 
weight of water at 62° F., 62.355 lbs. per cubic foot. Some experimenters 
have used 60° F. as the standard, and others 32° and 39.1° F. There is no 
general agreement. 

Given sp. gr. referred to water at 39.1° F., to reduce it to the standard of 
62° F. multiply it by 1.00112. 

Given sp. gr. referred to water at 62° F., to find weight per cubic foot mul. 
tiply by 62.355. Given weight per cubic foot, to find sp. gr. multiply by 
0.016037. Given sp. gr., to find weight per cubic inch multiply by .036085. 


164 | MATERIALS. 


Weight and Specific Gravity of Metals. 





Specific Gravity. Agile SoG |Weight Weight 
Range accord- ay PP ; per per 


ing to Heettie oe Cubic | Cubic 





. several Foot, | Inch, 
Authorities. Siete of! ‘Ibs.’ | lbs. 
Aluminum........ ete ott tle 2.50: to +2.71 2.67 166.5 .0963 
AMCEIMODVs 1.5% 0s ee cae ae wee 6.66 to 6.86 6.76 421.6 .2439 
Oe) Bb ee ae ying 9.74 to 9.90 9.82 612.4 63044 
rass: Copper inc? 
GIL AY bev OP aR pak & Uw) S40 | ess | “30a 
iY . [ 8.36 521.3 | .3017 
50 oe? 8.20 511.4 -2959 
u Copper, 95 to A 
Bronze } mp? ent 8.52 to 8.96 8.853 552. | .3195. 
Cadmmungdcdice tay s.+ ek 8.6 to“ 8:7 8.65 539. .3121 
Oalekumriesitasicke.) ss hes 1.58 
OPPORIUM ws'5/eh sls esp) lees 5.0 
Cobalt... .cssieicas bos cape Si54 to 8.6 
Golds DULCE wae dss os =e: 19.245 to 19.361 19.258 1200.9 6949 
TIPDOL each. foe sin sieteisis e pitee .69 to 8.92 8.853 552 3195 
Tridium emitted eixer 22.38 to 23. 1396 807 
Tron Cashes: gece wed ieee 6.85 to 7.48 fe ?4 be) 450 2604 
haitie WW LOUGHE cul etoe ss ce: 1.4 40°99 7.70 480 2779 
TGA ES <5 uci seeng ae ae 11.07 to 11.44 11.38 709.7 .4106 
Manganese Nata eniees Os deb’: 48 to 8. 8. 499. . 2887 
Magnesium.......2..- 08 1.69 to 1.75 ae 7 109. .0641 
32°] 13.60 to 13.62 13.62 849.3 .4915 
Mercury). %..4 site 60° 13.58 , 18.58 846.8 -4900 
212% 13.37) to. 13738 13.38 834.4 .4828 
INTORBD te Os cee coe Ae tkey 1eCags 8.279 to 8.93 8.8 548.7 AB 
Platinum tee ese ot 20.33 to 22.07 21.5 1347.0 7758 
Potassium. Ppt oa eA ng ty 0.865 
Srbver Jp. 0os sea% sie wadten. 10.474 to 10.511 10.505 655.1 3791 
Sogdian). .2 Asse eS 0.97 
Steele gee. 525 Neeeaae hake 7.69* to 7.932t 7.854 485.6 2834 
OU YAs trae Meee eat. a tcetetity eee bts SOL MLO pple 5409 4.350 458.3 2652 
PUIGATIIUNG 2,05 «ic us acic section 5.3 
Tungsten. ....... SEA)’. Als to 17.6 


ZADCUR EAT 25) 9h 5. dieie SUSE 6.86 to 7.20 7.00 436.5 1.2526 


* Hard and burned. 

+ Very pure and soft. The sp. gr. decreases as the carbon is increased. 

In the first column of figures the lowest are usually those of cast metals, 
which are more or less porous; the highest are of metals finely rolled or 
drawn into wire. 


Specific Gravity of Liquids at 60° F. 


Acid, Muriaticwes occ. ed. e. 1.200 Oil, ORVOcannses sincaavcns 92 
SE, CUNT IE ee LS A Ue Paine. 2, oy ecco ees 97 
Se (SUlpNUriGaern. oR . 1.849) §* Petroleuny.: 3.3.2.5. -78 to .88 
Alcohol; pure?y.ciseeeess sc. fee. 004 PE AR OL. A ANS A ee ae a" OR 
S95? (9B per eent “i ee » £816) **° Purpentine, 0205.2 87 
WY BO SS een, Broce ci PG WOd | -iceo on WUELLO Ne arama eect 92 
Ammonia;27.9 pereent... ©... sol 4-“Tamt ye iW tae be ties ors ceweenne 
Bromine: 218): .c cst eeeeieiec< DoW) || | NINCLAL «cinicle siete eile ete 1.08 
Carbon disulphide ............ 1.26, | Water... 2< 009 43h0n aenees 
Hiner, Sulphuric. s., weecetie. «i> ryt Sea, -o0 5 stnsaracid sees 1.026 to 1.03 
Oil, Linseed... nic jen cae ee sie 94 


Compression of The following Fluids under a Pressure of 
15 lbs. per Square Ench,. 


Water....... a fo a ore toreene .00004663 | Ether.........2..2.. 00006158 
Alcohol,....... ++... .0000216 | Mercury..........+/.00000265 


SPECIFIC GRAVITY. 165 


The Hydrometer. 


The hydrumeter is an instrument for determining the density of liquids. 
It is usually made of glass, and consists of three parts: (1) the upper part, 
a graduated stem or fine tube of uniform diameter; (2) a bulb, or enlarge- 
ment of the tube, containing air; and (3) a small bulb at the bottom, con- 
taining shot or mercury which causes the instrument to float in a vertical 
position. The graduations are figures representin> either specific gravities, 
or the numbers of an arbitrary scale, as in Baumé’s, Twaddell’s, Beck’s, 
and other hydrometers. 

There is a tendency to discard all hydrometers with arbitrary scales and 
to use only those which read in terms of the specific gravity directly. 








Liquids { Liquids Liquids | Liquids qm .; Liquids | Liquids 





wm 
3 | Heavier | Lighter § $ < Heavier | Lighter | $ r= Heavier | Lighter 
=| than than {5 5] than than §%5| than than 
© 2| Water, | Water, § 2 a Water, | Water, #2 s| Water, | Water, 
AM! sp.gr. | sp.gr. JA sp.gr. | sp.gr. $F! sp. er. | sp. gr. 
0 5 Ua Uae ee Cee 19 1.143 . 942 38 1.333 .839 
1 1.007 20 1.1p2 . 936 39 1.3845 834 
2 5 ns Pi es wee, 21 1.160 . 930 40 1.357 .830 
3 1.020 Ate, ee 22 1.169 924 41 1.369 825 
4 LEO Sten lielostiaveia se 23 1.178 918 42 1.382 -820 
5 AO QIE EE aie alew oc te 24 1.188 913 44 1.407 Sit 
6 BOA wars otle.3% 25 1.197 907 46 1.434 808 
7 pO ih a, eae 26 1.206 .901 48 1.462 «(94 
8 pls COU AN 5 20's tess oe ata 27 1.216 -896 50 1.490 (85 
Paes D 1 bl Oats ee) a ee 28 1.226 .890 52 1.520 ues 
10 1.070 1.000 29 1.236 .885 54 1.551 . 768 
11 1.078 993 30 1.246 .880 56 1.583 . 760 
12 1.086 986 31 1.256 874 58 1.617 . 753 
13 1,094 980 32 1.267 . 869 60 1.652 «745 
14 1.101 97: 33 eee .864 65 1.747 aiatsteretaiete 
15 1.109 967 34 1,288 . 859 70 F854) les areas 
16 1.118 960 35 1.299 854 "5 L974 hee iearad se 
17 1.126 954 36 1.310 .849 %6 23000! hae ceisshiees 
18 1.134 948 37 1.322 844 





























Weight 
er 

Specific Gravity. Specific Gravity, Cubic 

Foot, 
lbs, 

A Avge 

Alder........ 0.56 to 0.80 Hornbeam, 76 76) 47 
Applexiacsecs 73 to .79 Juniper...... -56 56] 35 
ASHics sja:taeieaus .60to .84 arch nes .56 .56| 35 
Bamboo...... .31 to .40 Lignum vitee| .65 to 1.83 1.00} 62 
Beech........ -62 to .85 Ihindentse:. <4 -604 37 
BiIpGie wav. -56 to .74 OCUSE, 555% ¢: 728 46 
Oats 31s 'e ele .91 to 1.38 Mahogany .56to 1.06 .81] 51 
Cedar hn); .<4 49 to 75 Maple..... MenlieDn bOe eto 68] 42 
Cherry, .<..-- 61 to .72 Mulberry .. 56 to 73| 46 
Chestnut ....| .46to .66 Oak, Live.. .96 to 1.26 1.11} 69 
Oto based tas 4 “White .69 to .86 77| 48 
Cypress...... 41 to .66 ‘¢ Red ETS tol e75 74) 46 
Dogwood....} .76 Pine, White..] .85 to .55 45) 28 
Hbony-....... 1.13 to 1.33 **  Yellow.| .46to ,7 61] 38 
Elm..... Reeth DOD LOmete Roplara i: 88 to .58 ~ .48) 3¢ 
in ep ecies i, 48 to .70 SPLUCE wy es -e -40to .50 .45) 28 
Gumpieee. ss: 84 to 1.00 Sycamore....| .59to .62 .60) 37 
Hackmatack | .59 Teak -66 to. 9B self on 
Hemlock . 86 to .41 Wialnuti,. «2: 50to .67 58] 36 
Hickory...... .69to .94 Willow....... 49to .59 .54) 34 


Hollyzecin:: 76 





166 MATERIALS, 


Weight and Specific Gravity of Stones, Brick, 
Cement, ete. 








Pounds per Specific 
Cubic Foot. Gravity. 
Asphaloum 2205.5 Wet ces suis etiaetelee 87 1.39 
BriGk ss SOLted brs &. Woe ve cletec eet ectres 100 1.6 
ee OOUTTNOMM eer cs stan to rece ete oe 112 1.79 
SS ere ara. tare FT Pear oe ae 125 2.0 
see ey POSSEO ML SER ee Seed nieces SS tea wet 135 2.16 
SOUMEEIHULT Qe at ata ctecikts Fat c. cbeites aan 140 to 150 2.24 to 2.4 
Brickwork i in MtOrtars.S..%. caeceees te 100 ity 
SS GOMECME: aetiewe hao welve ports 112 1.79 
Cement, Rosendale, loose......... B Nese 60 -96 
ce Portland, SMbMol, cciemase cen ce 78 1.25 
Clayeniree Sethu csvset Some o 5d 86Un Go Ja. goae 120 to 150 1.92 to 2.4 
Concrete ..... Reeve facistalsentelo s tale sie wine teen 120 to 140 1.92 to 2.24 
Harth, loose... =.-\:'..% Sele eeehae Gs aacitete sa alee 72 to 80 1.15 to 1.28 
SoH TATAIUCU ss 5 erste tee cte.c mele ale § wicletes' ate 90 to 110 1.44 to 1.76 
HENCE. are reictstote e stvieclera Wile Me. cis sates etiels 250 4. 
GIDSSiR cals neeectesc estes thees LE a 156 to 172 2.5 to 2.74 
© FLING. 00.60 eee ecceeccccceeescecace 180 to 196 2.88 to 3.14 
Gece t t-te: et tieer Bene edt steveasl? § 160to 170 2.56 to 2.72 
Gravel...... eiate iG sictclslegtetwich wale eee BBoce 100 to 120 1.6 to 1.92 
Gypsum........ AAP iti 00d 5 canna Goes 130 to 150 2.08 to 2.4 
Hornblende............ A. AR lok ees 4 sepa 200 to 220 8.2. to 3.52 
Lime, -quick;-in bulk... f.. 002s 3. ccbe ce 50 to 55 r.8 to .88 
PTMESECON CG sec Seok cig caidie ee tolee scutes ae 70 to 200 2.72 103.2 
Magnesia, Carbonate..........-sssseec0- 150 2.4 
IMATOTO' Sb eaaes, Lee cltace em kacabicae 160 to 180 2.56 to 2.88 
Masonry, dry. rubble: gas. tee es eee 140 to 160 2.24 to 2.56 
dressed:, j. U3. 22 AAS err 140 to 180 2.24 to 2.88 
VIOPHATEY Ces het tee Gates tie lasicse Bic Pees ahs, Sy 90 to 100 1.44 to 1.6 
TBC LEY. talalevs Si aicats es! Ea aa ate cro ace ethic. Meiae 72 1.15 
PIASTCTHOL PALIS Soc. sleds Gels ca esclecbees 74to 80 1.18 to 1.28 
QUATLZ. Ue aicssi0is' = icae ace sitet eames 165 2.64 
DAN Giecte < Ccbiare eee ee etd catheter tose 90 to 110 1.44 to 1.76 
Sandstone... «Jy <iucees Vetere PAeaes soos 140 to 150 2.24 to 2.4 
SAO eysiise vwievwuieertel son) < oS ESS Re 170 to 180 2.72 to 2.88 
PRONG TAVALTLOUS «c's oc oinis lee aie etelols eleitvere eh cites 135 to 200 2.16 to 3.4 
PUD Meistele cain c's sas islscaie bese tic'> arb clerereieic s sais 170 to 200 2.72 to 3.4 
UY UVES, SSRs ck Ais A ge a a 110 to 120 1.76 to 1.92 
SOSBPSEONC...6..500csccsswlewese AeebEe aati e 166 to 175 2.65 to 2.8 





Specific Gravity and Weight of Gases at Atmospheric 
Pressure and 32° F. 


(For other temperatures and pressures see pp. 459, 479.) 




















Density, Pes Grammes]| Lbs. per |Cubic Ft. 

PANTS alle = 1. |per Litre.| Cu. Ft. | per Lb. 
PO Nin IR” bap RR Se a gmecaeters. 2. 1.0000 14.444 1.2931 - 080723 12.388 
OXY SORT O sine ae volcan ihe 1.1052 15.963 1.4291 08921 11.209 
Hydrogen, Hale. pees 0.0692 1.000 0.0895 .00559 178.931 
Nitrogen, Ns... se ae 0.9701 14.012 1:2544 .07831 Met a, 
Car bon monoxide, CO...| 0.9671 13.968 1.2505 07807 12.810 
Carbon dioxide, CO, ec 1.5197 21.950 1.9650 12267 8.152 
Methane, marsh-gas, CH,| 0.5530 7.987 0.7150 04464 22.429 
Hutylene; CoU4g+ «em 6 ee 0.9674 13.973 1.2510 .07809 12.805 
Acetylene, CaHg......... 0.8982 12.973 1.1614 07251 13.792 
AWMODIA, NIELS. <sictepeie« ots 0.5889 8.506 0.7615 .04754 21.036 
Water vapor, H.O....... 0.6218 8.981 0.8041 05020 19,922 





PROPERTIES OF THE USEFUL METALS. 167 


PROPERTIES OF THE USEFUL METALS, 


Aluminum, Al.—Atomic weight 27.1. Specific gravity 2.6 to 2.7. 
The lightest of all the useful metals except magnesium. A soft, ductile, 
malleable metal, of a white color, approaching silver, but with a bluish cast. 
Very non-corrosive. Tenacity about one third that of wrought-iron. Tor- 
merly a rare metal, but since 1890 its production and use have greatly in- 
creased on account of the discovery of cheap processes for reducing it from 
the ore. Melts at about 1160° F. For further description. see Aluminum, 
under Strength of Materials. 

Antimony (Stibium), Sb.—At. wt. 120.4. Sp. gr. 6.7 to 6.8. A brittle 
metal of a bluish-white color and highly crystalline or laminated structure. 
Melts at 842° F. Heated in the open air it burns with a bluish-white flame. 
Its chief use is for the manufacture of certain alloys, as type-metal (anti 
mony 1, lead 4), britannia (antimony 1, tin 9), and various anti-friction 
metals (see Alloys). Cubical expansion by heat from &° to 212° F., 0.0070, 
Specific heat .050. : . 

Bismuth, Bi.— At. wt. 208.1. Bismuthis of a peculiar light reddish 
color, highly crystalline, and so brittle that it can readily be pulverized. I€ 
melts at 510° F., and boils at about 2300° F. Sp. gr. 9.823 at 54° F., and 
10.055 just above the melting-point. Specific heat about .0301 at ordinary 
temperatures. Coefficient of cubical expansion from 32° to 212°, 0.0040. Con- 
ductivity for heat about 1/56 and for electricity only about 1/80 of that of 
silver. Its tensile strength is about 6400 lbs. per square inch. Bismuth ex- 
pands in cooling, and Tribe has shown that this expansion does not take 
place until after solidification. Bismuth is the most diamagnetic element 
known, a sphere of it being repelled by a magnet. 

Cadmium, Cd.—At. wt. 112. Sp. gr.8.6to8.7. A bluish-white metal, 
lustrous, with ‘a fibrous fracture. Melts below 500° F. and volatilizes at 
about 680° F. It is used as an ingredient in some fusible alloys with lead, 
tin, and bismuth. Cubical expansion from 32° to 212° F., 0.0094. 

Copper, Cu.—At. wt. 63.2. Sp. gr. 8.81 to 8.95. Fuses at about 1920° 
F. Distinguished from all other metals by its reddish color. Very ductile 
and malleable, and its tenacity is next to iron. Tensile strength 20,000 to 
30,000 lbs: per square inch. Heat conductivity 73.6% of that of silver, and su- 
perior to that of other metals. Electric conductivity equal to that of gold 
and silver. Expansion by heat from 32° to 212° F., 0.0051 of its volume. 
Specific heat .098. (See Copper under Strength of Materials; also Alloys.) 

Goid (Aurum), Aw.—At. wt. 197.2. Sp. gr., when pure and pressed in a 
die, 19.34. Melts at about 1915° F. The most malleable and ductile of all 
metals. One ounce Troy may be beaten so as to cover 160 sq. ft. of surface. 
The average thickness of gold-leaf is 1/282000 of an inch, or 100 sq. ft. per 
ounce. One grain may be drawn into a wire 500 ft, in length. The ductil- 
ity is destroyed by the presence of 1/2000 part of lead, bismuth, or antimony. 
Gold is hardened by the addition of silver or of copper. In U.S. gold coin 
there are 90 parts gold and 10 parts of alloy, which is chiefly copper with a 
little silver. By jewelers the fineness of gold is expressed in carats, pure 
gold being 24 carats, three fourths fine 18 carats, ete. 

Kridiuma.—tIridium is one of the rarer metals. It has a white lustre, re- 
seibling that of steel; its hardness is about equal to that of the ruby; in 
the cold it is quite brittle, but at a white heat it is somewhat malleable. It 
is one of the Meaviest of metals, having a specific gravity Of v.38. It is ex- 
tremely infusible and almost absolutely inoxidizable. 

For uses of iridium, methods of manufacturing it, etc., see paper by W. D. 
Dudley on the “ Iridium Industry,” Trans, A. I. M. E. 1884. 

iron (Ferrum), He.—At. wt. 56. Sp. gr.: Cast, 6.85 to 7.48; Wrought, 
7.4to 7.9. Pure iron is extremely infusible, its melting point being above 
3000° F' , but its fusibility increases with the addition of carbon, cast iron fus- 
ing about 2500° F. Conductivity for heat 11.9, and for electricity 12 to 14.8, 
silver being 100. Expansion in bulk by heat: cast iron .0033, and wrought iron 
0035, from 32° to 212° F. Specific heat: cast iron .1298, wrought iron .1138, 
steel .1165. Cast iron exposed to continued heat becomes permanently ex- 
panded 114 to 3 per cent of its length. Grate-bars should therefore be 
allowed about 4 per Coney: (For other properties see Iron and Steel 
under Strength of Materials.) ; 

Lead Fe eaaiunay Pb.—At. wt. 206.9. Sp. gr. 11.07 to 11.44 by different 
authorities. Melts at about 625° F., softens and becomes pasty at about 
617° F. If broken by a sudden blow when just below the melting-point it is 
quite brittle and the fracture appears crystalline. Lead is very malleable 


168 MATERIALS. 


and ductile, but its tenacity is such that it can be drawn into wire with great 
difficulty. Tensile strength, 1600 to 2400 lbs. per square inch. Its elasticity is 
very low, and the metal flows under very slight strain. Lead dissolves to 
some extent in pure water, but water containing carbonates or sulphates 
forms over it a film of insoluble salt which prevents further action. 

Magnesium, Mig.—At. wt. 24. Sp. gr. 1.69 to 1.75. Silver-white, 
brilliant, malleable, and ductile. It is one of the lightest of metals, weighing 
only about two thirds as much as aluminum. In the form of filings, wire, 
or thin ribbons it is highly combustible, burning with a light of dazzling 
brilliancy, useful for signal-lights and for flash-lights for photographers. It 
is nearly non-corrosive, a thin film of carbonate of magnesia forming on ex- 
posure to damp air, which protects it from further corrosion. It may be 
alloyed with aluminum, 5 per cent Mg added to Al giving about as much in- 
crease of strength and hardness as 10 per cent of copper. Cubical expansion 
by heat 0.0083, from 32° to 212° F, Melts at 1200° F. Specific heat .25, 

Manganese, Min.—At. wt. 55. Sp. gr. 7to 8. The pure metal is not 
used in the arts, but alloys of manganese and iron, called spiegeleisen when 
containing below 25 per cent of manganese, and ferro-manganese when con- 
taining from 25 to 90 per cent, are used in the manuf -cture of steel. Metallic 
manganese, when alloyed with iron, oxidizes rapidly in the air, and its fune: 
tion in steel manufacture is to remove the oxygen from the bath of steel 
whether it exists as oxide of iron or as occluded gas. 

Miereury (Hydrargyrum), HMig.—At. wt. 199.8. A silver-white metal, 
liquid at temperatures above—38¥° F’., and boils at 680° F, Unchangeable as 
gold, silver, and platinum in the atmosphere at ordinary temperatures, but 
oxidizes to the red oxide when near its boiling-point. Sp. gr.: when liquid 
13.58 to 13.59, when frozen 14.4 to 14.5. Easily tarnished by sulphur fumes, 
also by dust, from which it may be freed by straining through a cloth. No 
metal except iron or platinum should be allowed to touch mercury. The 
smallest portions of tin, lead, zinc, and even copper to a less extent, cause it. 
to tarnish and lose its perfect liquidity. Coefficient of cubical expansion 
from 32° to 212° F. .0182; per deg. .000101. 

Nickel, Ni.—At. wt. 58.3. Sp. gr. 8.27 to 8.93. <A silvery-white metal 
with a strong lustre, not tarnishing on exposure to the air. Ductile, hard, 
and as tenacious asiron. It is attracted to the magnet and may be made 
magnetic like iron. Nickel is very difficult of fusion, melting at about 
3000° F. Chiefly used in alloys with copper, as german-silver, nickel-silver, 
etc., and recently in the manufacture of steel to increase its hardness and 
strength, also for nickel-plating. Cubical expansion from 82° to 212° F., 
0.0088. Specific heat .109. 

Platinum, Pt.—At. wt. 195. A whitish steel-gray metal, malleable, 
very ductile, and as unalterable by ordinary agencies as gold. When fused 
and refined it is as soft-as copper. Sp. gr. 21.15. It is fusible only by the 
oxyhydrogen blowpipe or in strong electric currents. When combined with 
iridium it forms an alloy of great hardness, which has been used for gun- 
vents and for standard weights and measures. The most important uses of. 
platinum in the arts are for vessels for chemical laboratories and manufac- 
tories, and for the connecting wires in incandescent electric lamps. Cubical 
expansion from 32° to 212° F., 0.0027, less than that of any other metal ex- 
cept the rare metals, and almost the same as glass. 

Silver (Argentum), Ag@.—At. wt. 107.7. Sp. gr. 10.1 to 11.1, according to 
condition and purity. lt is the whitest of the metals, very malleable and 
ductile, and in hardness intermediate between gold and copper. Melts at 
‘about 1750° F.. Specific heat .056. Cubical expansion from 32° to 212° F., 
0.0058. As a conductor of electricity it is equal to copper. As a conductor 
of heat it is superior to all other metals. 

Tin (Stannum) Sn.—At. wt. 118. Sp. gr. 7.298. White, lustrous, soft, 
malleable, of little strength, tenacity about 3500 lbs. per square inch. Fuses 
at 442° F. Not sensibly volatile when melted at ordinary heats. Heat con- 
ductivity 14.5, electric conductivity 12.4; silver being 100 in each ease. 
Expansion of volume by heat .0069 from 32° to 212° F. Specific heat .055. Its 
chief uses are for coating of sheet-iron (called tin plate) and for making 
alloys with copper and other metals. 

Zine, Zn.—At. wt. 65. Sp. gr. 7.14. Melts at 780° F. Volatilizes and 
burns in the air when melted, with bluish-white fumes of zine oxide. It is 
ductile and malleable, but toa much less extent than copper, and its tenacity, 
about 5000 to 6000 Ibs. per square inch, is about one tenth that of wrought 
iron. It is practically non-corrosive in the atmosphere, a thin film of car- 
bonate of zinc forming upon it. Cubical expansion between 82° and 212° F. 


MEASURES AND WEIGHTS OF VARIOUS MATERIALS. 169 


0.0088. Specific heat .096. Electric conductivity 29, heat conductivity 36, 
silver being 100. Its principal uses are for coating iron surfaces, called 
“ galvanizing,’’ and for making brass and other alloys. 
Table Showing the Order of 
Malleability. Ductility. Tenacity. Unfusibility. 


Gold Platinum Tron Platinum 
Silver Silver Copper Iron 
Aluminum Tron Aluminum Copper 
Copper, Copper Platinum Gold 

Tin Gold Silver Silver 
Lead Aluminum Zine Aluminum 
Zine Zine Gold Zine 
Platinum Tin Tin Lead 

Tron Lead Lead Tin 


WEIGHT OF RODS, BARS, PLATES, TUBES, AND 
SPHERES OF DIFFERENT MATERIALS, 


Notation: b = breadth, ¢ = thickness, s = side of square, d = external 
diameter, d, = internal diaineter, all in inches. 

Sectional areas: of square bars =: s?; of flat bars = bt; of round rods => 
.7854d2; of tubes = .7854(d2 — d,?2) = 3.1416(dt — 1%). 

Volume of 1 foot in length: of square bars = 1¥s?; of flat bars = 12b¢; of 
round bars = 9.4248d?; of tubes = 9.4248(d? — d,?) = 37.699(dt — t?), in cu. in. 

Weight per foot length = volume x weight per cubic inch of the material. 
Weight of a sphere = diam.? ¥ .5236 X weight per cubie inch. 























e 2) DQ py o oO | %& Lo} Cy 
Be 1 2 , ha a e!e_ 
#13 soa) 38 Er 3 me B32 3 
e )° iss sou} BSeg]°o BH | ssa 
Bis S43] DHS BaD | A ~ | Bad = 
na Pg [ROS weal Bes | Oe ES | a 
Material. Mia | Pe he OR ode See | el Oe oR 
S Pa logo peg] +e | oT 235 pad 2h 
BG |Sis |SS2] Got] dey | aq io | ayh | ao, 
8 los |S23| f28| ses | os Be a wea | wag 
S48) COD] PQQ] CA oeil omg Opnrs 
a |— |e E E BT |e = = 
Cast iron, 25:3"... 7.218/450. | 87.5] 31452) 381gbt| .2604)15-16|2.454d2| .1363d® 
Wrought Iron..... 7.7% (480. } 40. 814s2| 8lgbt}| 2779/1. 2.618d?| .1455d®’ 
SUCOl sce ee svetieets 7 .854/489.6] 40.8/38.4s2 13.4b¢ |.2833/1.02 12.670d?|.1484ds 


Copper & Bronze ; 
(copper and tit 8.855/552. | 46. |3.833s2/3.833b7].3195)1.15 |3.011d?!.1673ds 





Brass | 5 Copper... g 3931523.2| 43.6)3.633s|3.633b2|.3029| 1.09 |2. 854d) 1586 
Toad # oh ot es 11.38 1709.6} 59.1/4.9352 |4.930¢ |.4106'1.48 [3.870021 215043 
Aluminum ........ 267 1166.5} 13.911.16s? |1.16bt |.0963(0.347/0.908d2|_0504a 
Glass .ig ee eect 2'62 1163.4] 13.611.13s2 |1.130¢ |.094510.34 |0.891d21.0495a8 
Pine Wood, dry ...| 0.481| 30,0] 2.5/0.218? |0.21¢ |.0174/1-16 |0.184d2| 009148 


Weight per cylindrical in., 1 in. long, = coefficient of d? in ninth col. +12. 

For tubes use the coefficient of d? in ninth column, as for rods, and 
multiply it into (d?—d,;?); or multiply it by 4(dt—i?). 

For holiow spheres use the coefficient of d? in thelast column and 
multiply it into (d?—d;?). 

For hexagons multiply the weight of square bars by 0.866 (short 
diam. of hexagon=side of square). Wor octagons multiply by 0.8284. 


MEASURES AND WEIGHTS OF VARIOUS 
MATERIALS (APPROXIMATE). 


Brickw ork.— Brickwork is estimated by the thousand, and for various 
thicknesses of wall runs as follows: : 
we wall, or 4 brick in thickness, it bricks per superficial feet. 


47 66 66 66 9 66 oe 66 98 ee 66 6 ad 
21144 “cc 6 “ee 2144 66 66 66 35 66 66 oe oe ~ 


An ordinary brick measures about 814 x 4 x 2 inches, which is equal 
cubic inches, or 26.2 bricks to a cubic foot, The average weight is 14 ibe 


170 MATERIALS. 


Fuel.—A bushel of bituminous coal weighs 76 pounds and contains 2668 
cubic inches = 1.554 cubic feet. 29.47 bushels = 1 gross ton, 

A bushel of coke weighs 46 Ibs. (85 to 42 Ibs.). 

One acre of bituminous coal contains 1600 tons of 2240 Ibs. per foot of 
thickness of coal worked. 15 to 25 per cent must be deducted for waste in 
mining. 


41 to 45 cubic feet bituminous coal when broken down...... = 1 ton, 2240 Ibs. 
34to41 ‘ ‘* anthracite, prepared for market......... = 1 ton, 2240 lbs. 
123 Pe sSivot Charcoaliyasa4s\t.ce cee «sie eteies er Sts, aie Sie ae = 1 ton, 2240 Ibs. 
10.9.° of OS Feild T GOK Cass ee heels's erebre che Carer tease Setaks simian = i ton, 2240 Ibs. 
d cubic foot of anthracite coal (see also page 625).....00.006 = 55 to 66 lbs. 
SCSI UMITNOUSS, eeiyecaviae cle scl maleic: Mlanieincie tleicie'e = 50 to 55 lbs. 
i es $f; Cum berland: Coal is.) atoteecierclsonis oSainetiacewice ne = 53 Ibs. 
che SCP CanneleCOak: ca dodies sil tos ciuesalidtias spine cieelass = 50.3 lbs. 
Lous *¢ charcoal (hardwood)... Bfe class olcielota ers oncrols eels are ‘ste sibie's == 10.0 IDS; 
Lead es be (PIMC) ee Tae ae vic eechera stems o1G eralatatete Cae Pe ates = 18 lbs. 


pin 
A bushel of charcoal.—In 1881 the American Charcoal- Iron Work- 
ers’ Association adopted for use in its official publications for the standard 
bushel of charcoal 2748 cubic inches, or 20 pounds. A ton of charcoal is to 
be taken at 2000 pounds. This figure of 20 pounds to the bushel was taken 
as a fair average of different bushels used throughout the country, and it 
has since been established by law in some States. 


Ores, Earths, etc. 


13 cubic feet of ordinary gold or silver ore, in mine...... = 1 ton = 2000 ibs. 
20 gee, st Ra DEOKeEN¢QUAT UZ ns crates ealaeiiete ce acai atee = 1 ton = 2000 lbs. 
38 feetrohoravelin Dames wees cerca ces cites cs cleme Ro lere cacti cepa = 1 ton; 
7 cubic fectefigravyel When Ory. vss. desis osc as saci cies vceis seats seek = 1 ton. 
25 SSiehe TSAIIGY <2) syatre ie cake sa biaiale mie salle S eters aise ele istaicitie 7s 5 et Sre be =" 1iton 
Ise ws SOME AC ALICIA IC emis bic. istetcle cre b ctareigiclsttole:aiw\tiai eid siete sree ieletat =), tons 
a an Set rabies CW HEN CIV. 5 Sh apace stot ac ete ccise’e ale tisaip slot steerer ae avO TS 
Liiemes Ro Hens S* TCL ey Vl stewie ts Ghia Pals widicveele eae e eee s adteilol oes cd terns ator = ton. 
Cement.—English Portland, sp. gr. 1.25 to 1.51, per bbl.... 400 to 430 lbs. 
Rosendale, U.S., a struck bushel ............... 62 to 70 lbs. 
Maime.—A struck bushel. S99 cb. ood s hoc cee ee eae 72 to 75 lbs. 
Grain.—A struck bushel of wheat = 60 lbs.: ; of corn = 56 Ibs.; of oats = 
30 lbs. 


Salt.—A struck bushel of salt, coarse, Syracuse, N. Y. = 56 lbs.; Tark’s 
Island = 76 to 80 lbs, 
Weight of Earth Willing. 
(From Howe’s “ Retaining Walls.’’) 
Average weigh? in 
lbs. per cubic foot. 


Earth, common loamy lOOSe ya cetees aueee cece Say ee roy ale) 

SOMUss ra KEINE eo eee ane aes APE dane $2 to 92 

Ss ey ss rammed moderately......... 90 to 109 

GEA EC] boc ias cove ec dace tec: caren cen ene eee se ,eee.e 90 to 106 

SHI GLan cee cipro nivale oro aeletemecce caseemue septnerc cee 90 to a 
Soft flowing mud), «22 fiaaaen ent oe ee 104 to 12 

Sand, perfectly wet.. otis NAW steress MeePet ceases Siz rate ees 
COMMERCIAI i Pee OF IRON BARS, 

Fiats. 








Width. Thickness. Width. Thickness. Width. |} Thickness. 





34 7 to 5; 1% © 14 to 144 4 14 to2 
% 1g to 2 4g to 134 416 144 to 2 
1 1Z to e168 214 14 to 134 5 44 to 2 
4 to 1 284 44 tol 514 44 to2 
14 toi 246 3/16 to 134 6 4 to2 
13 4 to 14% 256 Y%tolk 644 44 to 2 
1 1g to 114 234 4tolg 4 to 2 
1 14 to 114 144 to 2 vers 144 to2 


4A 
184 B/16 to 146 34 14 to 2 
{ 








WEIGHTS OF WROUGHT IRON BARS. 171 


‘ ee 14 to 13g inches, advancing by 16ths, and 13g to 5 inches by 
th 
a Squares: : 5/16 to 114 inches, advancing by i6ths, and 114 to 3 inches by 


Halt rounds: 7/16, 14, 5, 11/16, 34, 1, V6, 1A, 114, 134, 2 inches, 

Hexagons: 3 to 1% inches, advaneing b y8 

Ovals: 1g x 4, % x 5/16, 34 x 34, % X< 7/16 aN 
a ovals 214 x 44, 56 x 5/32, 34 X 8/16, % X 7/82, 114 x 14, 194 x 56, 

xX % Inc 

Round-edge flats: 114 x 14, 184 x 54, 1% « 5 inch. 

Bands: % to 114 inches, advancing by 8ths, 7 to 16 B. W. gauge. 

1144 to 5 inches, advancing by 4ths, 7 to 16 gauge up to 3 Hichics. 4 to 14 
gauge, 3144 to5 inches. 


WEIGHTS OF SQUARE AND ROUND BARS OF 
WROUGHT IRON IN POUNDS PER LINEAL FOOT. 


Iron weighing 480 lbs. per cubic foot. For steel add 2 per cent. 





























Stel) va be 5 a 2 ) a a 
eeS|/sAS [sas || gSP1 SAS [eas || vss ieAs iems 
SES(o25 lscg .|| og | aSS.. lune || 208 ees jeve 
seliag les al SSeS | esha Sam oll ogo les™ wig c= op 
See | wstsg/wesOs|| $55 | weg fwsos sea |woeodasog 
sa48|2358 (S86$\ e468 | S865 (2 26S8|| 548 SSSS 2253 
ce oa > = rae pe = Ss i} eles te U2 = 
0 11/16 24.08 18.91 34 96.30 75.64 
1/16 | .018 .010 3, | 25.21 | 19.80 || 7716 77.40 
053 -041 13/16 26.37 20.71 4 100.8 79.19 
3/16 117 .092 % OMS S: 21.64 9/16 | 103.1 81.00 
V4 208 164 || 15716 | 28.76 | 22.59 105.5 | 82.83 
5/16 326 256 30.00 23.56 || 11/16 | 107.8 84.69 
% 469 368 1/16 31.26 24.55 4, 110.2 86.56 
T/16 638 501 1 82.55 25.57 || 18/16 | 112.6 88.45 
6 833 654 3/16 03.87 26.60 % 115.1 90.36 
9716 | 1.055 82 V4 35.21 | 27.65 || 15716 | 117.5 | 92.29 
1.302 1.023 5/16 36.58 28.73 120.0 94.25 
11/16 TSG e237 3% 37.97 29.82 4% 12501 98.22 
187 1.473 7/16 89.39 80.94 14 130.2 102.3 
13/16 | 2.201 | 1.728 Z 40.83 | 32.07 || 3g | 135.5 | 106.4 
q 2.502 2.004 9/16 42.30 383.23 4% 140.8 110.6 
15/16 2.930 2.301 5% 43.80 84.40 % 146.3 114.9 
3.300 2.618 11/16 45.33 35.60 34 151.9 119.3 
1/16 3.763 2.955 46.88 86.82 % 157.6 123.7 
V4 4.219 | 3.313 || 13/16 | 48.45 | 38.05 |/7 163.3 | 128.3 
3/16 4.701 3.692 y 50.05 89.31 73 169.2 oes 
1% | 5.208 | 4.091 || 15/16 | 51.68 | 40.59 || 4% | 175.2 | 137.6 
5/16 5.742 4.510 Bo.oe 41.89 36 181.3 142.4 
3% 6.302 | 4.950 || 1/16 | 55.01 |. 43.21 |] 44 | 187.5 | 147.3 
7/16 6.888 5.410 (4 56.72 44.55 5g 193.8 152.2 
% 7.500 5.890 3/16 58.45 45.91 34 200.2 157.2 
9/16 8.138 6.392 4 60.21 47.29 % 206.7 162.4 
54 8.802 6.913 5/16 61.99 48.69 ||8 213.3 167.6 
11/16 9.492 7.455 3% 63.80 50.11 yy 226.9 178.2 
34 10.21 8.018 7/16 65.64 51755 % 240.8 189.2 
13/16 | 10.95 8.601 , 67.50 53.01 34 25062 200.4 
LEZ 9.204 9/16 69.39 54.50 ||9 270.0 212.1 
15/16 | 12.51 9.828 54 71.30 56.00 4 285.2 224.0 
13.33 10.47 11/16 43.24 Dinos 14 300.8 236.3 
1/16 | 14.18 WA 4. 95.21 59.07 34 316.9 248.9 
15.05 11.82 18/16 77.20 60.63 1/10 333.3 261.8 
3/16 | 15.95. | 12.53 % | v9.22 | 62.22 || 34 | 250.2 | 275.1 
4, 16.88 13.25 15/16 81.26 63.82 as 3867.5 288.6 
5/16 } 17.83 14.0 83.33 65.45 34 385.2 3802.5 
6 18.80 1477 1/16 85.43 67.10 |/11 403.3 316.58 
7/16 | 19.80 15.55 87.55 68.7 1% 421.9 331.3 
20.83 | 16.36 3/ie | 89.70 | 70.45 4 | 440.8 | 346.2 
9/16 | 21.89 1%, 1 91.88 42.16 460.2 861.4 


é 19." 8% 
56 | 22.97 | 18.04 5/16 | 94.08 | 73.89 |/12 480. | 877. 


MATERIALS. 


172 








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173 


WEIGHTS OF FLAT WROUGHT IRON. 


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174 | MATERIALS. 


WEIGHT OF IRON AND STEEL SHEETS, 
Weights per Square Foot. 
for weights by Decimal Gauge, see page 32.) 


Thickness by American (Brown and 











Thickness by Birmingham Gauge. Sharpe’s) Gauge. 
Thick- Thick- 
No. of | nessin | Iron. | Steel. J No-of | nessin | Iron. | Steel. 
Gauge. | Inches. Gauge. | Inches. 
0000 454 18.16 | 18.52 0000 46 18.40 18.77 
000 425 17.00 | 17.384 000 4096 16.38 16.71 
00 038 15.20 | 15,50 00 3648 14.59 14.88 
0 34 13.60 | 138.87 0 3249 13.00 18.26 
1 * 3 12.00 | 12.24 1 2893 iT BY 11.80 
2 284 11.36 | 11.59 2 2576 10.30 10.51 
3 259 10.386 | 10.57 3 2294 9.18 9.36 
4 238 9.52 9.71 4 2043 8.17 8.34 
5 22 8.80 8.98 5 1819 7.28 7.42 
6 203 8.12 8.28 6 1620 6.48 6.61 
7 18 7.20 7.34 7 1443 5.77 5.89 
8 165 6.60 6.73 8 1285 5.14 5.24 
9 148 5.92 6.04 9: 1144 4.58 4.67 
10 134 5.36 5.47 10 1019 4.08 4.16 
11 12 4.80 4.90 11 0907 3.63 3.7 
12 109 4.36 4.45 12 0808 3.23 3.30 
13 095 3.80 3.88 13 0720 2.88 2.94 
14 083 3.32 8.39 14 0641 2.56 2.62 
15 072 2.88 2.94 15 057 2.28 2.33 
16 065 2.60 2.65 16 0508 2.03 2.07 
17 058 2.32 2.3% 17 .0453 1.81 1.85 
18 049 1.96 2.00 18 0403 1.61 1.64 
19 042 1.68 1.71 19 0359 1.44 1.46 
20 035 1.40 1.48 20 0320 1.28 1.31 
21 032 1.28 1.31 21 0285 1.14 1.16 
22 028 1.12 1.14 22 .0253 1.01 1.03 
23 025 1.00 1.02 23 0226 . 904 2922 
24 022 88 898 24 0201 804 .820 
25 02 .80 816 25 0179 716 730 
26 .018 7. 734 26 0159 636 649 
27 016 64 653 27 0142 568 579 
28 014 56 571 28 012 504 514 
29 013 52 530 29 6113 452 461 
30 012 48 .490 30 0100 400 408 
31 01 40 408 31 0089 356 363 
32 009 36 367 382 0080 320 326 
33 008 32 326 33 0071 284 290 
34 007 28 286 34 0063 252 257 
85 005 20 204 35 0056 224 228 
Tron. Steel. 
Specific gravity.... ....cecsesee- 7.0 7.854 
Weight per cubic foot.......... « ~ 480: 489.6 
oe Ce ADCH. ovina oss : 2078 2833 


As there are many gauges in use differing from each other, and even the 
thicknesses of a certain specified gauge, asthe Birmingham, are not assumed 
the same by all manufacturers, orders for sheets and wires should always 
state the weight per square foot, or the thickness in thousandths of an inch, 


“195 


WEIGHT OF PLATE IRON. 





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98°19 | S99 | 90S | OO'Sr | ge°6e | Gy'Ee 
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176 MATERIALS. 


WEIGHTS OF STEEL BLOOMS. 
Soft steel. 1 cubic inch = 0.284 1b. 1 cubic foot = 490.75 lbs. 





Lengths, 





Sizes. j 
1” 6” 497 187’ 94” 80/" 36” 42" 48/7 47’ 60/7 66/" 





mw ee | — fe | | | | | ee 


12” x 4’ | 18.63) 82 | 164 | 245 | 327 | 409 | 491 | 573 | 654 | 736 | 818 | 900 
11 x6 | 18.75) 113 | 225 | 338 | 450 | 563 | 675 | 788 | 900 /1013 11125 |1238 
5. 843 | 937 |1031 
12.50} 75 | 150 | 225 | 300 | 875 | 450 | 525 | 600 | 675 | 750 | 825 


19.88} 120 | 239 | 358 | 477 | 596 | 715 | 835 | 955 |1074 1193 |1312 
17.04} 102 | 204 | 307 | 409 | 511 | 613 | 716 | 818 | 920 [1022 /1125 
14.20) 85 | 170 | 256 | 341 | 426 | 511 | 596 | 682 | 767 | 852 | 937 
11.36] 68 | 136 | 205 | 273 | 341 | 409 | 477 | 546 | 614 | 682 | 750 

8.52} 51 | 102 | 153 | 204 | 255 | 806 | 358 | 409 | 460 | 511 | 562 


17.89} 107 | 215 | 822 | 430 | 587 | 644 | 751 | 859 | 966 |1073 |1181 
15.34] 92 | 184 | 276 | 368 | 460 | 552 | 644 | 736 | 828 | 920 /1012 
12.78) 77 | 153 | 230 | 307 | 883 | 460 | 537 | 614 | 690 | 767 | 844 
10.22) 61 | 123 | 184 | 245 | 307 | 868 | 429 | 490 | 552 | 613 | 674 


18.18} 109 | 218 | 327 | 436 | 545 | 655 | 764 | 873 | 982 |1091 |1200 
15.9 | 95 | 191 | 286 | 3882 | 477 | 572 | 668 | 763 | 859 | 954 |1049 


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SIZES AND WEIGHTS OF STRUCTURAL SHAPES. 177 
SIZES AND WEIGHTS OF STRUCTURAL SHAPES. 


Minimum, Maximum, and Intermediate Weights and 
Dimensions of Carnegie Steel I-Beams, 








Web § Sec- |Depth Weight 














Sec- |Depth| Weight Web 

tion | of per eee Thick- § tion] of per qanee Thick- 
Index;Beam.| Foot. ‘| ness. {Index|Beam.| Foot, ‘| ness. 
ins lbs ins ins, ins lbs ins ins 

Bi 24 100 7.25 75 B19 6 025 8.58 0.48 
" * 95 7.19 0.69 «4 is 14.7 8.45 0.35 
&s ec 90 G13 0.63 *§ ss 12.25 | 3.40 0.23 
fi ss 85 7.07 0.57 B21 5 14.75 3.29 0.50 
bs Ss 80 7.00 0.50 “ 2 12.25 8.15 0.36 
B38 20 fh 6.40 0.65 $s 9.75 8.00 0.21 
es fe q 6.33 0.58 B23 4 10.5 2.88 0.41 
2 os 65 6.25 0.50 0 Fe 9.5 2.81 0.34 
B80 18 7 6.26 0.72 6% af 8.5 2.73 0.26 
2 y 65 6.18 0.64 a ¥f T*D 2.66 0.19 
$e ee 60 6.10 0.56 B77 3 75 2.52 0.36 
tf be 55 6.00 0.46 t, oe 6.5 2.42 0.26 
B7 15 55 5.75 0.66 cs Be 5.5 2.33 0.17 
Ss « 50 5.65 0.56 B2 20 100 7 28 0.88 
st a 45 3) (0}9) 0.46 es rs 95 21 0.81 
ab oe 42 5.50 0.41 s PS 90 7.14 0.74 
B9 12 35 5.09 0.44 s§ de 85 7.06 0.66 
$ oe 31.5 5.00 0.35 _ rs 80 7.00 0.60 
Bit 10 40 5.10 0.75 B4 15 100 6.77 1.18 
6 $e 35 4,95 0.60 a ee 95 6.68 1.09 
id $s 30 4.81 0.46 s we 90 6.58 0.99 
Sh 20 4.66 0.31 ae vs 85 6.48 0.89 
B13 9 35 4.77 02728 $s cs 80 6.40 0.81 
a a 30 4.61 0.57 B5 15 G5 6.29 0.88 
ss ee 25 4.45 0.41 fs me 70 6.19 0.78 
8 ve 21 4.33 -0.29 < ee 65 6.10 0.69 
B15 8 25.5 4.27 0.54 t As 60 6.00 0.59 
ee eS 23 4.18 0 45 B8 12 55 5.61 0.82 
ty aa 20.5 4.09 0.36 He vr 50 / 5.49 0.70 
te be 18 4.00 0 27 se P 45 D.on 0.58 
B17 a 20 3.87 0.46 +f . 40 5.25 0.46 
“s ‘ ws ty ee Sections B2, B4, B5, and B8 are 


**special’* beams, the others are 
“ standard.” 





Sectional area = weight in lbs. per ft. + 3.4, or 0.2941. 
Weight in lbs. per foot = sectional area x 3.4. 


Maximum and Minimum Weights and Dimensions of 
Carnegie Steel Deck Beams, 


Weight per |p ‘ Web Increase of 

Saseion Depth | “Foot, Ibs, |/l@2ee Width.) wa ioiness, Web and 
Index. | Beam, |————————_ |] —— > | +. | Flange per 
inches. lb. increase 


Min. | Max.| Min. | Max.| Min. | Max. of Weight. 




















B100 10 27.23 | 35.7 5.25. | 5.60 -38 63 .029 
B101 9 26.00 | 30.00 | 4.91] 5.07 44 57 -033 
B102 8 20.15 | 24.48 | 5.00] 5.16 31 47 037 
B103 7 18.11 | 28.46 | 4.87 | 5.10 381 54 042 
B105 6 15.30 | 18.86 | 4.38 | 4.53] .28 43 049° 





a a ER RR I A RT 
> 


178 MATERIALS, 


Minimum, Maximum, and Intermediate Weights and 
Dimensions of Carnegie Standard Channels, 

















& mc ae 4 4 at aye “4 
‘ota Sil nae At: oe Sa] -s!| oie a oy as euls @ 
o obg ees | ost |S .0f ge o'8 8 | eC eal eee ae 
Oh 1S Pel es) eon | APSE le eer ol ea | a 
BO NSE). Moo pes? | 2og | So) sage oo PEs a2 oe 
gz DORM! Pay |} S&S Ofe ee DOH ofa, | Sea Os 
n |A = & = ee = = 
yi 15 55 3.82 0.82 C5 8 16.25 2.44 0.40 
4G 50 3.72 0.72 ee * IY i 2.30 0.31 
“e id 45 3.62 0.62 = re 11-25 2.26 0.22 
* He 40 8.52 0.52 C6 7 19.75 nol 0.63 
“ Hy 85 3.43 0.4 Hk S Taso 2.41 0.53 
*s ‘ 33 3.40 0.40 oa st 14.75 2.30 0.42 
C2 12 40 3.42 0.7 de ae 12.25 2-20 0.32 
4 i 85 3.30 0.64 oS, ‘f 9.75 2.09 0.21 
be 7 5 3. iG 0.51 C7 6 15.50 2.28 0 56 
% a" 25 8.05 0.389 ie - 13 eG 0.44 
“ i 20.5 2.94 0.28 es sf 10.50 2.04 0.32 
C3 10 35 3.18 0.82 se s 1492 0.20 
r re 30 2.04 0.68 C8 5 11.50 2.04 0.48 
oS - 25 2.89 0.53 ee S 9 1.89 0.33 
*s Me 20 2.74 0.38 $3 - 6.50 75 0.19 
*S MY 15 2.60 0.24 C9 4 liao 10 0.33 
C4 9 25 2.82 0.62 af “3 6.25 1.65 0.25 
ae. rf 20 2.65 0.45 hy ry 5.25 1.58 0.18 
BY Es 15 2.49 0.29 C72 3 6 1.60 0.36 
* 4 1Sae0 2.43 0.23 ee . 5 1.50 0.26 
C5 8 2125 2.62 0.58 cs . 4 1.41 0.17 
“i ve Koh fi 2.00 0.49 


Weights and Dimensions of Carnegie Steel Z-Bars. 

















= Size. F Size. 

aie oO ® mn ASNS, iM oo wn Rs) 
Seca eG eirel ut ft anoles PISS tesa ge ieee Laie 
5 ol eo A ya) Peott ee te = S of © 

© 6 = eS ® om § of = S 3 ® cm 
om sO & = p= te) SS eae 

(op) al Fy = ee op) ial fy Ee - 
Zim 368:13 162 \'6 15.6) Z6 , 3% |85/16|51/16| 26.0 
eee ig 1-8 9/16 |.6 1/16 | 188 6. 8 Neisi6 |S 86 sents means 
« bw 3ii56 1603601 QO INT ag o 103 1/716 8.2 
32 ieO/168) 3. 16. |. 6 oo Dt ) Big 12g ledteig | | 108 
s 6 | 49/16|61/16125.4, “ 3g °°) 3 3/16;| 4 te) 12 4 
“ 111/16 |38 5 16 % | 28.09 zs | vie |81/16| 4 13.8 
Z3 34 3.4% 6 29.3 ie 4% 38 4% 4 1/16 parc: 
ifs 13/16 38 9/16 | 6 1/16 | 32.0 st 9/16 38/16|4 1,9 
“ mails 5416 1% | 34:64 Z9 56 131/16 | 4 18.9 
74 | 5/16 |8 4 | 5 1.68 “ | 11716 |3 % | 41/16] 20.9 
os 34 3 5/16 1-5 1/16 | 13.9 ff 34 8 3/16|4 22.9 
ot 1 776 beeen ls 32 116.40 710) big ota 67 
Z5 w% 13 4 (15 17.81 “| 5/16 |2 3% 131/16) 84 
a 9/16 3 5/16 | 5 1/16 | 20.2 Zi1 36 2 11/16) 3 9.7 
. % 3 8% 5 lg 22.6 3 7/16 2 9% 8 1/16 11.4 
76 | 11/16 |3 4 15 23.70 Zi2| % 1211/16 3 12.5 
9/16 2 % 3 1/16 14.2 





5 


SIZES AND WEIGHTS OF STRUCTURAL SHAPES. 179 


Pencoyd Steel Angles, 
EVEN LEGS. 





Approximate Weight in Pounds per Foot for Various 
Thicknesses in Inches. 

















Size in 
- Inches. 
14 |8/16] 14 |5/16] 94 17/16] 44 |9/16) 54 N11/16) 94 |18/16| 76 |15/16) 4 
.125|.1875]} .25|.3125| .375) .4875 6625) .625] .6875|] .75 | .8125| .875| .9375) 1.00 
8x8 26 .4/29.8)33.2] 86.6/39.0) 42.4/45.8] 49.3/52.8 
6x6 14.8)17.8/19.7/22.0/24.4] 26.5/28.8] 31.0/38.4] 35.9 
5 x5 12.3)14.3/16.3/18.2/20.1] 22.0/23.8] 25.6127.4) 29.4 
4 x4 8.2) 9.8]/11.3]12.8/14.5/15.8) 17.2)18.6 
316 x 314 7.1] 8.5) 9 8[11.1/12.4/13.7 
oe xo 4.9) 6.1] 7.2) 8.3!) 9.4110.4/11.5 
234 x 234 4.5| 5.5] 6.6| 7.7| 8.6 
26 x 216 3.1/4.1| 5.0] 5.9] 6.9] 7.8 
914 x24| | 2.7/3.6] 4.5] 5.4 
x2 2.5/3.2] 4.0] 4.8 
134x134} | 2.1/2.8] 3.5] 4.1 
11% x 114/1.2| 1.8]2.4) 2.9) 3.5 
134 x 114|1.0] 1.5]2.0 
ex TOS) 12h s5 








UNEVEN LEGS. 





Approximate Weight in Pounds per Foot for Various 
Thicknesses in Inches. 





























Size in eres he EWC ES Oi ae 2 Gk DA LU 
Inches. | | |. /16\ 14 |5/16| 36 |7/16| 34 |9/16| 56 |11/16| 34 |13/16| 76 |15/16| 1 
% 1875 35 -3125 35 |. .4375)| .50 |.5625 “5 -6875 5 -8125 “815 -9375| 1.00 
8 x6 23 .0/25.8]/28.7| 81.7|33.8] 36.6]39.5] 42.5/45.6 
7 x3 17.0/19.0]21.0] 23.0/24.8] 26.7/28.6] 30.5)/32.5 
616x4~ 12.9]15.0]17.0|19.0/21.2| 23.4/25.6] 27.8]29.8) 31.9 
6° x4 12.2114.3]16.3/18.1/20.1] 22.0/28.8] 25.6/27.4] 29.4 
6 x3% 11.6]13.6]15.5/17.1/19.0| 20.8/22.6| 24.5/26.5] 28.6 
56 x 314 11.0/12.8]14.6|16.2)17.9 
oa 11.0}12.8]14.6|16.2]17.9] 19.6/21.3 
5 x3 8.7 |10.3]/12.0/13.6|15.2|16.8] 18.4|20.0 
6g 8.2 | 9.7/11.2]12.8]14.2/15.7] 17.2/18.7 
416 x3 7.7 | 9.1]10.5/11.9|13.3] 14.7] 16.0/17.4 
4° x3 7.7 | 9.1]10.5/11.9]13.3/14.7| 16.0/17.4 
ees: 7.1 | 8.5} 9.8]11.1/12.4]13.8 
314 x3 (6-6 | 7-8] 9.1/10.3/11.6)12.9 
314 x 2% 4.2/6.1 | 7.2] 8.3] 9.4 
314 x2 4,715.5 | 6.6 
3° x2% 4.5/5.5 | 6.6] 7.7] 8.7 
B x2 4.1/5.0 | 5.9] 6.9] 7.9 
QW x2 2.713.54.5 | 5.4] 6.2] 7.0 
214 x 114 2.3/3.913.7 | 4.4 
2 x1% 2.1|2.9/3.6 | 4.3 
2 xil4 1.9/2.6/3.3 | 3.9 











ANGLE-COVERS. 


Ped 3/16 14 5/16 36 7/16 \% 9/16 | 56° 











3 x3 9:3 |-- 10.4 fb ficb 


234 x 234 
214 


180 


MATERIALS. 


SQUARE-ROOT ANGLES. 





Approximate Weight in Pounds 
per Foot for Various Thicknesses 





Approximate Weight in 
Pounds per Foot for 
Various Thicknesses 





























Size in in Inches. Size in cate 
titer i in Inches, 
14 |5/16} 36 17/16) 1% [9/16 | 1g | 3/16 | 14 | 5/16} 8% 
.25 |.3125].870!.4375| .50 1.5625) .625 . 125). 1875] .25 | .8125} 375 
4 x4 9.8} 11.4] 13.0} 14.6116.292 x2 3.8 | 4.1 | 4.9 
34% x34 1 EB oo 99} 11.4 134 x 134 2.9 | 8.6 | 4.4 
3 Ka Ae a OG let Pi ote Bat FOs4 14x1% 1.80/2.4 | 8.0 
234 x 234) 4.5) 5.6 | 6.7} 7.8) 8.9 14x14 1.53)/2.04] 2.55 
216 x 216| 4.1] 5.1 | 6.1] 7.1) 8.2 1. x 0,82} 1.16)1.58 
214 x 214| 8.6] 4.5 | 5.4 
Pencoyd Tees, 
Section Size Weight Section Size Weight 
Number. in Inches. per Foot. § Number. in Inches. | per Foot. 
EVEN TEES. UNEVEN TEES. 
440T 4 x4 10.9 | 
441T 4 x4 13.7 437 4x8 9.0 
335T 3146 x 314 70 44T Amo 10.2 
336T 344 x 84% 9.0 45T 4 x44 13.5 
33TT 34 x 3144 11.0 38T 3144x3 7.0 
330T 8x8 6.5 89T 3144 x3 8.5 
331T 3..x8 7.7 80T 38 x1l\% 4.0 
225T 214 x 24 5.0 31T 8 x24 5.0 
226T 214 x2 5.8 82T 8 x2k% 6.0 
Dp ad by 216 x 2 6.6 S37 8 x24 7.0 
2227 214 x 214 4.0 34T 8 x24 8.0 
223T 214 x 244 4.0 35T 3 x34 8.3 
220T x2 8.5 36T 38 x34 9.5 
117T 134 x 134 2.4 28T 234 x 134 ' 6.6 
115T 114x114 2.0 20T 4x2 79 
112T 14x14 1,5 25T 216 x 114 8.3 
110T xit 1.0 26T 216 x 234 Bat 
QT 216x3 6.0 
24T 2144x 9/16 2.2 
‘UNEVEN TEES. 20T 2) x) 9/16 2.0 
Pde 2° x1, 1/16 2.0 
21T 2 x 2.5 
64T 6x4 ite e! 23T 2 xl 3.0 
65T 6x 514 39.0 17E 134 x1 1/16 1.9 
538T 5x34 17.0 18T 134 x 114 8.5 
54T 5x4 VMESyest3) 16? 1x 15/16 1.4 
42T 4x2 6.5 12T 144 x 15/16 1.2 
Pencoyd Miscellaneous Shapes, 
Section : pe Weight per Foot 
Namber: Section. Size in Inches. ic Poundg: 
217M Heavy rails. 6 50.0 
210M Floor-bars. | 3 1/16x4x3 1/16x14 tol] * 7.1 to 14.8 
260M es Me 26 x 6 x 214 x14 to % 9.8 to 14.7 


eR RR SEE RR I TSP Rr RAT 


SIZES AND WEIGHTS OF ROOFING MATERIALS, 181 


SIZES AND WEIGHTS OF ROOFING MATERIALS, 
Corrugated Iron. (The Cincinnati Corrugating Co.) 
SCHEDULE OF WEIGHTS. 


Weight 


g |Thickness in Weight per | "j09'sq. Ng Weight in oz, 


. ‘ Weight per 4 
m8 /decimal parts 100 sq. ft. : per sq. ft. 
b 3 of an inch. oie. ooiaeta Corrugated Co1 puea ted Flat, Galvane 

to) Flat. 9 ‘|and Painted. Galvanized: ized. 
No. 28 015625 6214 lbs. 70 lbs, 86 lbs 1214 oz. 
No. 26 01875 is) “ 8 99 *“* 1444 '° 
No. 24 025 100 fs Hitt sé 127 SF 1814 ‘ 
No. 22 .03125 125 nS 138 * 154 eis 2214 ‘ 
No. 20 0875 150. 165 182 * 2615 ** 
No. 18 05 200 #8 220 236) rt 3414 ** 
No. 16 0625 250 * O75 ft 201) 4216 ‘ 


The above table is on the basis of sheets rolled according to the U. 8. 
Standard Sheet-metal Gauge of 1893 (see page 31). It is also on the basis of 
246 x %& in. corrugations. 

To estimate the weight per 100 sq. ft. on the roof when lapped one corru- 
gation at sides and 4 in. at ends, add approximately 1214% to the weights per 
100 sq. ft., respectively, given above. 

Corrugations 244 in. wide by 14 or 5 in. deep are recognized generally as 
the standard size for both roofing and siding; sheets are manufactured 
usually in lengths 6, 7, 8, 9, and 10 ft., and have a width of 26% or 26 in. out- 
side width—ten corrugations,—and will cover 2 ft. when lapped one corruga- 
tion at sides. 

Ordinary corrugated sheets should have a lap of 144 or 2 corrugations side- 
lap for roofing in order to secure water-tight side seams; if the roof is 
rather steep 14 corrugations will answer. 

Some manufacturers make a special high-edge corrugation on sides of 
sheets (The Cincinnati Corrugating Co.), and thereby are enabled to secure 
a water-proof side-lap with one corrugation only, thus saving from 6% to 12% 
of material to cover a given area. 

The usual width of flat sheets used for making the above corrugated 
material is 2814 inches. 

No. 28 gauge corrugated iron is generally used for applying to wooden 
buildings; but for applying to iron framework No. 24 gauge or heavier 
should be adopted. 

Few manufacturers are prepared to corrugate heavier than No. 20 gauge, 
but some have facilities for corrugating as heavy as No. 12 gauge. 

Ten feet is the limit in length of corrugated sheets. 

Galvanizing sheet iron adds about 214 oz, to its weight per square foot. 


Corrugated Arches, 


For corrugated curved sheets for floor and ceiling construction in fire- 
proof buildings, No. 16, 18, or 20 gauge iron is commonly used, and sheets 
ae & be curved from 4 to 10in. rise—the higher the rise the stronger the 
arch, 

By a series of tests it has been demonstrated that corrugated arches give 
the most satisfactory results with a base length not exceeding 6 ft., and & 
ft. or even less is preferable where great strength is required. 

These corrugated arches are usually made with 24 x 5 in. corrugations, 
and in same width of sheet as above mentioned. 


Terra=Cotta. 


Porous terra-cotta roofing 3” thick weighs 16 Ibs. per square foot and 2” 
thick, 12 lbs. per square foot. : : : 
Ceiling made of the same material 2” thick weighs 11 lbs, per square foot. 


Tiles. 


Flat tiles 614” x 1014” x 56” weigh from 1480 to 1850 lbs. per square of 
roof (100 square feet), the Jap being one-half the length of the tile. 

Tiles with grooves and fillets weigh from 740 to 925 Ibs, per square of roof, 

Pan-tiles 1444’ X 1044’’ laid 10” to the weather weigh 850 lbs. per square, 


182 MATERIALS. 


Tin Plate—Tinned Sheet Steel. 


The usual sizes for roofing tin are 14” * 20” and 20’ x 28/7.. Without 
allowance for lap or waste, tin roofing weighs from 50 to 62 lbs. per square 

Tin on the roof weighs from 62 to 75 lbs. per square. 

Roofing plates or terne plates (steel plates coated with an alloy of tin 
and lead) are made only in IC and IX thicknesses (29 and 27 Birmingham 
gauge). ‘‘Coke” and *‘charcoal”’ tin plates, old names used when iron 
made with coke and charcoal was used for the tinned plate, are still used in 
the trade, although steel plates have been substituted for iron: a coke plate 
now commonly meaning one made of Bessemer steel, and a charcoal plate 
one of open-hearth steel. The thickness of the tin coating on the plates 
varies with different “ brands.”’ 

For valuable information on Tin Roofing, see circu!ars of Merchant & Co., 
Philadelphia. : 

The thickness and weight of tin plates were formerly designated in the 
trade, both in the United States and England, by letters, such as I.C., D.C., 
I.X., D.X., ete. A new system was introduced in the United States in 1898, 
known as the ‘‘ American base-box system.’’ The base-box is a package 
containing 32,000 square inches of plate. The actual boxes used in the trade 
contain 60, 120, or 240 sheets, according to’the size. The number of square 
inches in any given box divided by 32,000 is known as the *‘ box ratio.” This 
ratio multiplied by the weight or price of the base-box gives the weight or 
price of the given box. Thus the ratio of a box of 120 sheets 14 < 20 in. is 
33,600 -+- 32,000 = 1.05, and the price at $3.00 base is $3.00 x 1.05 = $3.15. The 
following tables are furnished by the American Tin Plate Co., Chicago, Hl. 


Comparison of Gauges and Weights of Tin Plates, 
(Based on U.S. Standard Sheet-metal Gauge.) 








AMERICAN BASE-BOX. ENGLISH BASE-BOX. 
(32,000 sq. in.) (81,360 sq. in.) 

Weight. Gauge. Gauge. Weight. 

DOO Saee as sas ve talnine a tiee s No. 38.00 | No. 88.00........... 54.44 lbs. 

Ge: Saha: ve sowie Ria avahics ia: a BOwas Pw OMe ieens ener 57.84 ‘ 

Doeiyies ecg. Coabrd ceacy cid ad “* 35.64 J nj Oc OD esckerert Matctomts 61:24.5* 

Ee ASE ore aia ee aes Le cyte’ besos 1.34202 Sere UOnad be iteersete 68.05 ‘* 

TOseeMetet es Sede a5 sterile avec s © 34.20 **. DAS OD cote bianeis eet (4c85 ee 

BO) Fane ryan’ ghuesdaniegel bores ‘* 33.48 DY BOD pei tole = Sohail 80.00 ‘* 

BO ee ites 20 aja's x's sised oth ch aisers i Pair +6 82,00 Le fe see 8500 Ff 

DO Metrayecin d «tale stantopre oe Meats ip ori: £ © PORICT. Reg detasns a Gs 90.00 ‘* 

DOS MME: a ciesiy sro o SOR Sa ee Os BS SSB L yO4 oh catagels oss <2 95.00 ‘* 

MOVES Meee se <0 ose bghels dea s 30.81) © 30.65 . 100.00 *§ I.C.L. 
SEE es cere aETORE Rear © 30.08 §e S02 OBicres torte ete 108.00 ‘“* LC, 
DSU ee eR che siocegs “tis =z the © “6 28.64 Taha Oehts Rese peehte 126.00 *“* IX.L. 
MARR EINERE co 5. tisio.= die cou ohe one ie SieoD ey eoOU ia bekdersb she 136.00 °*, IX. 
TG Meester som ia ners orsigery. atten Sr ¢ 26.48 Son emer ee 15%.00; (oie D 2 Xe 
NB Olmert as fs ss cé ea aes aa ago POAC a5 cele ee 178.00 ** 1.3X. 
POO Maemo hates cid gee ontace cis yore «* 24.80 Sipe hs OSs crt Bs « ats «acs 199.00 “* I.4X. 
OU Mamet ere) fs, 0 2 os ioe eee BO Fede Song Laine atte a eee 220 00 Tox 
Pe US oe ok aac a ananey eee WSBT DOR ee arene = 241.00 ‘** I.6X. 
OO Ote mentee tee eet Le) me 2o70 pum OD POE dc sctett eae 262000 gee Lah Ne 
QU es Sete senten Sues aides bee ts Bh SMR 1SUON a oo citar a | COO e CU mame Les 
140 goer Vee iensiae Seeucbactiis/Fiee ee -) Se eae haa Ok ayetart oft ote be 139,.00:5* D.C. 
180) ie cee tits ae ee a eee AE Sas) NEGO O SAY came rte 180.00 “ D.X. 
220 iy tte: oe cet in es rs.se- 01% rebeeae OS oh aoe eat oie tA aE ee 211400555, .D.2X- 
210 ies cu taramedantejae ca ape = fs ede OU iieeee akon aon heater oe 242.00 ‘* D. 3X, 
280 ‘* Pe a bela Oe “orate SOU ax. estate Sass 273.00 ** D. 4x. 

American Packages Tin Plate. 

Inches Sheets 7 Inches Sheets 

Wide. | Leng. per Box Wide. doris hs per Box 
9 to 16%% Square. 240 #12 ‘* 1234/1714 and longer. 120 

7 “ 25% Square. 120 413 ‘* 1334/To 16 in. long, incl.| 240 
-26 ** 30 Square. 60 13 to 1334|1644 and longer. 120 
9 “ 1034 All lengths. 240 Wi4 “ 1434)To 15 in. long, incl. 240 
11 ‘* 1134;To 18 in. long, incl.| 240 914 ‘° 1434/1514 and longer. 120 
11 ‘* 1134 1814 and longer. 120 #15 ‘* 2534) All lengths. 120 


12 * 1234._To 17 in. long, incl. 240 §26 ‘ 30 |Alllengths. 60 
Small sizes of light base weights will be packed in double boxes. 








SIZES AND WEIGHTS OF ROOFING MATERIALS 183 


Slate. 


Number and.superficial area of slate required for one square of roof. 
(1 square = 100 square feet.) 





Dimensions} Number | Superficial |Dimensions| Number | Superficial 


in per Area in in per Area in 
Inches. Square. Sq. Ft. Inches. Square. Sq. Ft. 

6x12 533 267 12x 18 160 240 

7x12 CU oe NAB nde eee 10 x 20 169 2385 

8x12 AOQ Fr os Borersrdsts e201 5.2 11 x 20 154 

9x12 355 SE. 12x20 141 

7x14 37 254 14 x 20 121 

8x14 Pe en ecleay Latte cote cate 16 x 20 137 

9x14 2) | ae lee SaaS MRE CEC 12x 22 126 281 
10x14 QOUM RU ORR RIE. 14x 22 108 

8x 16 277 246 12x 24 114 228 

9x 16 AGT Sener s,. Sennen td 14x 24 98 
10x 16 POSES CHE eee ee 16 x 24 86 

9x18 213 240 14 x 26 89 225 
10x18 LSS SM EES fete fee tes 16 x 26 if 





As slate is usually laid, the number of square feet of roof covered by one 
slate can be obtained from the following formula : 


width x (length — 3 inches) 
288 
Apes of slate of various lengths and thicknesses required for one square 
of roof: 





= the number of square feet of roof covered. 





Weight in Pounds per Square for the Thickness. 








Inches. yr 3-16” ys 36/7 yy" 56! 34! 1” 





12 483 724 967 1450 1936 2419 2902 3872 
14 460 688 920 1379 1842 2301 2760 3683 
16 445 667 890 1336 1784 2229 2670 3567 
18 434 650 869 1303 1740 2174 2607 3480 
20 425 637 851 1276 1704 2129 2553 3408 
22 418 626 836 1254 1675 2093 2508 3350 
24 412 617 825 1238 1653 2066 2478 3306 
26 407 610 815 1222 .| . 163) 2039, 2445 3263 


poner Je eee 
The weights given above are based on the number of slate required for one 
square of roof, taking the weight of a cubic foot of slate at 175 pounds. 





Pine Shingles. 


Baber and weight of pine shingles required to cover one square of 
roof: 





Number of | Number of | Weight in 
Inches Shingles | Pounds of 





Fxposed tojper Square| Shingle on Remarks. 
Weather. | of Roof. |One-square 
of Roofs. 

4 900 216 The number of shingles per square is 
416 800 192 for common gable-roofs. For hip. - 
5 720 173 roofs add five per cent. to these figures. 
514 655 157 The weights per square are based on 

6 


600 144 the number per square. 





184 


MATERIALS. 


Skylight Glass. 


The weights of various sizes and thicknesses of fluted or rough plate-glass 


required for one square of roof. 


Dimensions in Thickness in 


Inches. Inches. in Square Feet. Square of Roof. 
12x 48 3-16 3.997 250 
15 x 60 V4 6.246 350 
20 x 100 36 13.880 500 
94 x 156 94 101.768 700 


Area 


Weight in Lbs. per 





In the above table no allowance is made for lap. 


If ordinary window-glass is used, single thick glass (about 1-16”) will weigh 
about, 82 lbs. per square, and double thick glass (about 14’) will weigh about 
164 lbs. per square, no allowance being made for lap. A box of ordinary 
window-glass contains as nearly 50 square feet as the size of the panes will 
admit of. Panes of any size are made to order by the manufacturers, but a 
great variety of sizes are usually kept in stock, ranging from 6x8 inches to 
36 x 60 inches. 


APPROXIMATE WEIGHTS OF VARIOUS ROOK 
COVERINGS. 


For preliminary estimates the weights of various roof coverings may be 
taken as tabulated below (a square of roof = 10 ft. square = 100 sq. ft.): 


Weight in Lbs. pe 

Name. Batiere of Rock, : 
Cast-iron plates (36 thick) ......ceeccecceee 1500 
Coppers 220) taza. wigs tee oe D emsidalde aclad asics . 80- 125 
Felt and asphalt............. AY caine gislein cans ett 100 
Keltiand Pavel ices ccleue ces ocdeees snnebeones 800-1000 
Bron; (COPRUSATCHIAL. cco ae code on dane oh cette 100- 375 
lron, galvanized, flat.) 3... cidsceccese}aseee 100- 350 
Lathiand plaster... o-11-+..cciedees-se ee -.ee. 900-1000 
Sheathing, pine, 1’ thick yellow, northern.. 300 
‘ eee ‘*  southern.. 400 
Spruce sm Vithiclkew. Gat, sie, ossotiec ete 200 
Sheathing, chestnut or maple, 1” thick...... 400 
i ash, hickory, or oak, 1” thick.... 500 
Sheet iron (1-16/A thick). iio .05. 305.6.5. 008 300 
“bd $ i | aid lathsnee. s+. eee 500 
Shingles: ping. . {25.. 5... PSL dei. .0 200 
Slates (14” thick)......... Fick oA eee 900 
Skylights (glass 3-16’ to 16” thick).......... 250- 700 
Sheet lead...... PPE oe tes ese non ee ce tees 500- 800 
PREEROCTE OOF 205 £2, FORMA See FaESES heer tees 650 
PRISM. tin o's ¢ o's 6c big Ae te sigh eee Maen cee 70- 125 
OR DAG! 0.4 0ctccae toate tat sens 1500-2000 
“* — (grooves and fillets)..............00.8- 00-1000 
LARS cee GeO Rt obamiorcnin. do. conicado boc na: 1006 
part TTIOTTAL,., <ccctecdete es ome ryiee 2000-3000 
Critics cities es ccenees ceo deer tam eeeoe eevee ore 100- 200 


Approximate Loads per Square Foot for Roofs of Spans 
under 75 Feet, Including Weight of Truss, 
(Carnegie Steel Co.) 


Roof covered with corrugated sheets, unboarded......... 8 lbs. 
Roof covered with corrugated sheets, on boards...... cele OE 
Roof covered with slate, on laths..................--. meas. do ** 
same,.on DOnTds.t4 im, LHIGK,22c.,. ..,.ccocce teen anne 16459 
Roof covered with ahinetes. On yaths. . 2 254. eee ee 10m 
Add to above if plastered below rafters.... .............. 10 
Snow, light, weighs per cubic foot......... ...,....6-- 5to 12 * 


For spans over 75 feet add 4 lbs. to the above loads per square foot. 
It is customary to add 30 lbs. per square foot to the above for snow and 
wind when separate calculations are not made, 


WEIGHT OF CAST-IRON PIPES OR COLUMNS. 185 


WEIGHT OF CAST-IRON PIPES OR COLUMNS. 
In Lbs. per Lineal Foot, 


Cast iron = 450 lbs. per cubic foot. 
































Thick. ‘ Thick. é Thick. A 

Bore. | of een Bore. of ares Bore. of oe a 
| Metal, |P : Metal. |P : Metal, (PCF + 00% 

Ins. Ins, Lbs. Ins. Ins, Lbs. Ins. Ins. Lbs. 

3 36 12.4 10 34 7.2 22 34 167.5 

4 2 1014 8 54.0 % 196.5 

5g 221.2 5g 68 2 23 34 174.9 

3% 36 14.3 34 82.8 % 205.1 

% 19.6 11 44 56.5 1 235.6 

54 25.0 54 1.3 24 34 182.2 

4 36 16.1 34 86.5 % 213.7% 

% 22.1 114% 4 58.9 1 245.4 

5g 28.4 BE |:)CCO74.4 25 34 189.6 

446 3% 17.9 34 90.2 % 992. 3 

fe 24.5 12 % 61.3 1 255.3 

DE 31.5 56 Nino 26 34 197.0 

5 BE 19.8 34 93.9 % 230.9 

pg 27.0 1214 16 63.8 1 265.1 

bg 34.4 i 80.5 27 34 204.3 

5% Be 21.6 34 97.6 KR 239.4 

6 29.4 13 4% 66.3 1 74.9 

bg 37.6 D6 83.6 28 34 PHD 

6 Be 23.5 34 101.2 % 248.1 

2 31.8 14 4% (ee 1 284.7 

4 40.7 5g 89.7 29 34 219.1 

64% Bg 25.3 34 108.6 % 256.6 

6 34.4 15 54 95.9 1 294.5 

d6 43.7 4 116.0 30 % 265.2 

q 36 2741 % 186.4 1 304.3 

% 36.8 16 56 102.0 14 343.7 

5g 46.8 A, 123.3 31 % 273.5 

76 36 29.0 % 145.0 1 314.2 

4% 89.3 17 28 108.2 1% 354.8 

54 49.9 34 130.7 82 % 282.4 

8 34 80.8 y 153.6 1 324.0 

14 41.7 18 5% 114.3 14 365.8 

5g 52.9 34 138.1 33 % 291.0 

84 4 44.2 % 162.1 1 333.8 

56 56.0 19 5% 120.4 1% 376.9 

34 68.1 34 145.4 34 % 299.6 

9 My 46.6 % 170.7 1 343.7 

5g 59.1 20 54 126.6 14% 388.0 

34 41.8 34 152.8 35 % 808.1 

944 % 49.1 % 179.3 1 353.4 

% 62.1 21 5g 132 37, 114 399.0 

34 75.5 34 160.1 26 % 316.6 

10 1% 51.5 % 187.9 a 363.1 

5g 65.2 22 %B 138.8 1144 410.0 





The weight of the two flanges may be reckoned = weight of one foot. 


186 MATERIALS. 


WEIGHTS vF CASES TS Cire TEs TO LAY 12 FEET 


Weights are Gross Weights, including Hub. 
(Calculated by F. H. Lewis.) 


Thickness. Inside Diameter. 





Inches. a ae 4" | 6” |. 8 | 10 | 12” | 14” | 467 | 18% | 2p 





es | ff | | | Oe | ne 


36 
13-32 2 40625 228 | 331 435 
7-16 4375 247 | 3858} 47 581 692 | 804 
15-32 4687 266 | 3886 | 505 | 624 | 744] 863 
5 286 | 414} 541 668 | 795 22 | 1050} 1177 



































P31 209 804 400 | 
16 
17-32 .53125 306 442 Dit 712 846 988 | 1118 | 1253 
9-16 5625 327 470 613 756 899 | 1043 | 1186 | 1829 
19-32 59875 |..2 22.19 498 649 801 951 | 1108 | 1254 | 1405 
625 686 845 | 1003 | 1163 | 1322 | 1481 | 1640 
11--16 687 935 | 1110 | 1285 | 1460 | 1635 | 1810 
4, AS et ean eee Ale. Fee na Al Poe tei 1026 | 1216 | 1408 | 1598 | 1789 | 1980 
13-16 8125 1324. | 1531 | 1738 _| 1945 } 2152 
vy Tope ill ogee: eos oe 1432 | 1656 | 1879 | 2101 | 2824 
15-16 GBT ym BH tucrede ads feet tte tp se oUt veri es ceat | oppelaetea 1783 | 2021 | 2259 | 2498 
1 Tey ie Ey Id GAY sci Meo ctae [Vege lou tee |B ees 1909 | 2163 | 2418 | 2672 
1144 Pe 2bgete || bez cpehcoesl Wet lage lines ce RGIS ates Sl rele sete eee eee emer 2738 | 8024 
1% ROB Re CR Aar. ais he owle ods (PERE ete ail clothe tol 'Pe'ern 4 o.legee ae cot eeeeraers 8062 | 3380 
13¢ Wael el ho ete ee ceed | 8389 | 3739 
Thickness. Inside Diameter. 
Equiv. Or " my) " 20/7 ” ov ” ” 
Inches. ah ieiae QQ | 247 | Qi 30” | 33” | 86” | 42” | 487 | 60 
625 1799 
11-:6 6875 1985 | 2160 | 2422 
4 Pah) 2171 | 2362 | 2648 | 2984 | 3221 | 3507 
13-16 8125 2359 | 2565 | 287 38156 | 3496 | 8806 | 4426 
% 875 2547 769 | 3103 | 8437 | 8771 | 4105 | 4773 | 5442 
15-16 9375 2737 | 2975 | 3332 | 8690 | 4048 | 4406 | 5122 | 5839 
1 aR 2927 | 3180 | 3562 | 3942 | 4325 | 4708 | 5472 | 6236 
1% 1/125 3310 | 8598 | 4027 } 4456 | 4886 | 5316 | 6176 | 7034 
144 1.25 3698 | 4016 | 4492 | 4970 | 5447 | 5924 | 6880 | 7833 Q745 
13 Pe DOM Bs ek eects 4439 | 4964 | 5491 | 6015 | 6540 | 7591 | 8640 | 10740 
1% leo 5439 | 6012 | 6584 | 7158 | 8303 | 9447 | 11738 
15g ROO eee bce ks bee (pure ol See Sc 6539 | 7159 | 7782 | 9022 |10260 | 12744 
134 OME [ER icurs. |) ato ovadlsttRe cal lcteee 7737 | 8405 | 9742 |11076 | 18750 
1% WB Rous). SE Sea A Pes De EE oe a gt 10468 {11898 , 14762 
2 CREM eRe | hs ase cdl ve 7s are ll 2a los ativan hepa seb esos haomene sate ve 11197 [12725 | 1577 
214 DME atin A Iccdce W wlcll' » etre: -c:| Gin wkehevel ll igyenoretel ueaMerene | aeemenenes 14885 | 17821 
ot SA MNMM | VA crt 5m |hsdhese. vote! oletocd vera'|ic avelhes & | antrcvatohenl) ate) avail cae tetereieil| Ree ete = 19880 
234 LA. |) i i Pee perieykawetpawe om or fs 21956 





Weicht of Underground Pipes (Adopted by the Natl. Fire Pro- 
tectiou Assoc , May 23, 19U5). Weights not to be less than those specified 
where the normal pressures do not exceed 125 lbs. Where the normal pres- 
sures are in excess of 125 Ibs., heavier piping should be used. Weights given 
include sockets. Pipe to be made in accordance with the essential features 
of the standard specifications for cast-iron water-pipe of the New England 
Water Works Assoe., 1902. 


Pipe, inches: .....0.ee. 4 6 8 10 12° 14 16 
Weight per foot- pound 19 32 48 67 Teese toe 


CAST-IRON PIPE FITTINGS. 187 


CAST-IRON PIPE FITTINGS, 
Approximate Weight.’ 
(Addyston Pipe and Steel Co., Cincinnati, Ohio.) 
Size in. Weignit 


sizein |Weightg Sizein |Weight § Sizein | Weight 
Inches. jin Lbs. § 


Inches. |in Lbs. Inches. | in Lbs. § Inches, |in Lbs. 




















CROSSES. TEES. SLEEVES. REDUCERS. 
2 40 8x4 220 2 10 8x 3 116 
3 110 8x3 920 3 25 10x8 212 

3x2 90 10 390 4 45 10x 6 170 
4 120 108 330 6 65 10x4 160 
4x3 114 10x6 370 8 80 12x10 320 
4x2 90 104 350 10 140 12x8 250 
6 200 10x3 310 12 190 12x6 250 
6x4 160 12 600 14 208 12x 4 250 
6x3 160 1210 555 16 350 14x12 475 
8 325 12x8 515 18 375 14x10 440 
8x6 280 12x6 550 20 500 14x8 390 

8x4 265 124 525 24 710 14x6 285 

8x3 205 14x 12 650 30 965 16x12 475 
10 : 7S 14x 10 650 36 1200 d 6 x 10 435 
10x § {5 14x8 SMG eran eeege peeve x1 9 
10x6 450 14x6 545 | _90° ELBOWS. J 50x14 BuB 
10x 4 390 14 x4 525 2 14 20x 12 540 
10x38 350 14x3 490 3 34 20x 8 400 
12 740 16 790 4 55 24 x 20 990 
12x 10 650 16x14 850 6 120 380 x 24 1305 
1x8 620 16 x 12 850 8 150 30x 18 1355 
tose ‘ eM 16x10 850 aw oe 36 x 30 1730 
12 x 525 16x8 U5 37 OES 7 eee y4 
12x3 495 16x6 680 14 450 eae Be 
14x 10 "50 16x4 655 16 660 F- os 
14x8 685 18 1235 18 850 6x4 | 95 
1ix6 570 20 1475 20 5300 6x3 70 
16 1100 20x 16 1115 4 2 prpre 
16x 14 ae 20x12 | 1025 30 3000 i 2 sane iT 
16 x 1 20 x 10 1090 B47 qp4n0 RENDS_ 2 
toaieinl nti daaleben ee Oo | 3ordse BENDS. | 6 leaion 
16x 8 825 20 x 6 875 3 30 PLUGS 
16x6 700 90x 4 845 a TOs 9h ates 
16x 4 650 20x10 | 1465 6 95 2 3 
18 1560 24 2000 8 150 3 10 
20 1790 24% 12 4425 10 200 4 10 
20 x 12 1370 94x8 1375 12 290 6 15 
20x 10 1225 24 x6 1450 16 510 8 30 
20x8 1000 30 3025 18 580 10 46 
20 x 6 1000 30 x 24 9640 20 780 12 66 
204 1000 30 x 20 2900 24 1425 14 90 
24 2400 30x 12 2035 30 2000 i. on 
24 x 20 2020 30 x 10 2050 “1/16 or 22149 : 

24 x 6 1340 ff 30x6 1825 "4 sodas) 20 150 
30 x 20 2635 36 5140 aes Ss tok Nek ae 24 185 
30x12 | 2250 36x30 | 4200 6 UM at iar ain epee Lt Ate 
BOx8 | 1995_ ff 36x12 | 4050 a Meh CAPS. 
5 205 n2 
ee 45° BRANCH 12 260 3 20 

2 28 PIPES. 16 450 4 oo 

3 BOB wD a saalt ye ee a 24 1289 6 60 

3x2 “6 f 3B 90 30 2000 Re oh 

4 100 4 (abel tapeeaaprems ae ames 

4x3 90 ne 205 Ao ed 12 120 
4x2 87 6x6~x 145 xo 2 
6 150 330 ree 42 | DRIP BOXES 
6x4 145 8x6 330 4x2 40 4 295 
6x3 145 24 2765 6x4 95 6 330 
6x2 7 $24x24x20] 2145 6x3 " 8 375 
8 300 30 4170 8x6 126 10 15 
8x6 270 2 10300 8x4 116 20 1420 





188 MATERIALS, 


WEIGHTS OF CAST-IRON WATER- AND GAS-PIPE, 
(Addyston Pipe and Steel Co., Cincinnati, Ohio.) 


























&# Standard Water-pipe. Ae Standard Gas-pipe. 
oo ’ od 3 — 
NO Thick- Per A'S Thick- Per 
ma |Per Foot.! jess. | Length. “iA |Per Foot.| jess, Length. 
2 7 5/16 63 Q 6 4 48 
3 5 36 180 3 1244 5/16 150 
3 17 ey 204 
4 22 4 264 4 HTT h. 84 204 
6 33 12 396 6 3 7/16 360 
8 42 44 504 8 40 [/16 480 
a 45 4 540 
10 60 9/16 720 10 50 7/16 600 
12 %5 9/16 900 12 70 4% 840 
14 117 34 1400 14 84 9/16 1000 
16 125 34 1500 16 100 9/16 1200 
18 167 % 2000 18 134 11/16 1600 
20 200 15/16 2400 20 150 11/16 1800 
24 250 1 8000 24 184 34 2200 
30 350 . 1g 4200 30 250 34 3000 
36 475 18 5700 36 350 4 4200 
42 600 180 4200 2 417 15/16 5000 
48 Yui 1% 9300 48 542 11g 6500 
60 1830 2 15960 § 60 900 13% 10800 
72 1835 214 22020 42 250 1% 15000 





THICKNESS OF CAST-IRON WATER-PIPES. 


P. H. Baermann, in a paper read before the Engineers’ Club of Phila- 
deiphia in 1882, gave twenty different formulas for determining the thick- 
ness of cast-iron pipes under pressure, The formulas are of three classes: 

1. Depending upon the diameter only. 

2. Those depending upon the diameter and head, and which add a con- 
stant. 

8. Those depending upon the diameter and head, contain an additive or 
subtractive term depending upon the Giameter, and add a constant. 

The more modern formulas are of the third class, and are as follows: 


t = .00008hd +- .01d +- .86.......... sess. Shedd, No, 1. 
t = .00006hd + .0133d + .296.......+e006-.. Warren Foundry, No. 2. 
t = .000058hd + .0152d + .812........ 200. Francis, No. 3. 
é = .000048nd + .013d + .82........ ABSHoG: Dupuit, No. 4. 
t = .00004hd + 1 Vd + .15..........206.- BOX, No. 5. 
t = .000135hd + .4 — .0011d............... Whitman, No. 6. 
t = .00006(A +- 230)d + .333 — .0083d...... Fanning, No. 7, 
t = .00015hd +- .25 — .0052d.......... ..... Meggs, No. 8. 


In which ¢t = thickness in inches, h = head in feet, d = diameter in inches, 


Rankine, ‘Civil Engineering,” p. 721, says: ‘‘Cast-iron pipes should be 
made of a soft and tough quality of iron. Great attention should be paid 
to moulding them correctly, so that the thickness may be exactly uniform all 
round, Each pipe should be tested for air-bubbles and flaws by ringing it 
with a hammer, and for strength by exposing it to double the intended 
greatest working pressure.” The rule for computing the thickness of a pipe 


to resist a given working pressure is f = ws where r is the radius in inches, 


p the pressure in pounds per square inch, and f the tenacity of the iron per 

square inch. When f = 18000, and a factor of safety of 5 is used, the above 

expressed in terms of d and h becomes 

5d .4838h dh 
3600 ~ 16628 

“There are limitations, however, arising from difficulties in casting, and 


by the strain produced by shocks, which cause the thickness to be made 
greater than that given by the above formula,” 


t= = .00006dh 


, THICKNESS OF CAST-IRON PIPE. 189 


Whickness of Metal and Weight per Length for Different 
Sizes of Cast-iron Pipes under Various Heads of Water. 


(Warren Foundry and Machine Co.) 











50 100 150 200 250 300 

Ft, Head.) Ft. Head.| Ft. Head. | Ft. Head.| Ft. Head. | Ft. Head. 

‘ n , el Loe. MPM Ss Sin, °F No3 fe mn , q 
Sie. | G5 |e | os lee| os lsh] os ]a| 82 | ee |i] sh 
Eo| Me | Eo)hS| Bo | wel} hol hs) 2S | Fs | £o| BS 
22/24 |S [SA | SS | S4/Sa)S4| S42 | 4 [Sa] oA 

ae a sks} Ee sha ae raha Bs aS Es ahs} ae 

oH a | on om. Bo} | Et at a a 

3 144) .853] 149 862) 158) .871| 157 380 161 390} 166 
4 obl} 197] .87 204) .3885) 211) .397] 218 409 226 421) 235 
5 .o78} (254) .393]' 265 408} 275) .423} 286) .438 298 453} 3809 
6 .093] 815] .411) 330} .429) 345] .447| 361 465 377 483] 393 
8 .422]} 445) .450) 47 474) 502] .498) 529 522 557 | .546] 584 
10 .459] 600) .489) 641 519) 682! .549) 723 579 766 609} 808 
12 491) 768) .527) 826 563} 885] .599) 944] .635 1004 671} 1064 
14 .524| 952) .566} 10381 608} 1111} .650) 1191 692 127 734) 1352 
16 .557| 1152] .604) 1253 652] 1860} .'700; 1463 748 1568 796) 1673 


24 | .687| 2120) .759) 2349] .831) 2580} .903) 2811] 9% 3045 |1.047) 3279 
80 | .785| 3020) .875) 8376) .965) 3785/1.055) 4095; 1.145 | 4458 |1.285) 4822 
86 | .882) 4070) .990) 4581) 1.098) 5096)1.206; 5613) 1.314 | 6183 |1.422) 6656 
42 980] 5265)1.106] 5958) 1.232) 6657/1.358) 7360] 1.484} 8070 |1.610) 8804 
48 '1.078' 661611.222' 7521' 1.866! 8431'1.510 9340' 1.654 ' 10269 °1.798'11195 





All pipe east vertically in dry sand; the 3 to. 12 inch in lengths of 12 feet, 
all larger sizes in. lengths of 12 feet 4 inches. 


Safe Pressures and Equivalent Heads of Water for Cast 
J iron Pipe of Different Sizes and Thicknesses, 


(Calculated by F. H. Lewis, from Fanning’s Formula.) 








Size of Pipe. 





6” 8” 10” 12” 14” 16” if 18” 90” 





be | 

a 

ie) 

& 

a 
= 


nese Wes 8/8 Sus |SS | Sas | Bs Sas |S [Ss S'S hes | SS Ss S'S les Sle 
2\5 5 =) I 3 i 
BaSBiZs(S oF SSS |BS(S9|2s eo|F5 eo|Felaoleeleo\Zelao 
OS | OR) DG (ORO, | OR|Og | OR |Om Om Og |OR| Og | OR) Og | OR | og | om 
m4 | AY | mi AY | eA |p BPH |p mn |p Se wales BAY | BAY |p 
Pas. Par Shiney a a AS 
ee ff Sf | | | | | ff | | | | | | | | 
7-16 112} 258} 49) 112) 18} 42 
1-2 224) 516} 124| 250}, 74) 171], 44) 101] 24) 55 
9-16 336| 774] 199! 458] 130] 300) 89} 205) 62] 143] 42) 97 
5-8 fe cweloece 274| 631) 186] 429) 132} 304] 99) 228) 74) 170] 56] 129} 41) 95 
11-16 ° oe . 177|' 408} 137] 316) 106] 244) 84] 194| 66) 152) 51) 118 
3-4 ccclccce|- wie |cove|eowe|eces 224) 516} 174) 401) 138} 316] 112) 258} 91) 210) 74) 170 
13-16 cece] coce| coos locce| vice} ieee |. oie levee | 212) 488) 170) 392] 140) 323), 116) 267] 96) 221 
= coelso-s|oocslevcclooce cleccclee 249) 574] 202) 465] 168] 387} 141) 325] 119) 274 
15-16 cccelecce|ccceiooes|coce|sooe|cees| sees | core eoee| 234] 538] 196] 452] 166] 382) 141) 325 
1 cecclcces| cose loos leoee| coos) coos ccsclevcs(sese| 266! 612] 224| 516) 191) 440) 164) 378 
11-8 cee]: c00|sccelccee|coes| cee] coes|eece loos SUeclecsclecse|e-cs|ocve| CLOW 400 200 nan 

















190 MATERIALS, 


Safe Pressures, etc., for Cast-iron Pipe.—(Continued.} 



































Size of Pipe. 
99" 94” 9G" 380” 83” 36” 49" 48” 60” 
a SE ol tp Ray Lledo ee 
mw Jegle lesa (2918 ./2cle ec esis .jfcle jecle jecla . 
I = 5 a wolas Za\c O12 S|u3 
FEE S/25/829/25/82/28 (5/25/2512 5/89/ 45S 212 s/2 0/23/33 
BA S| | | toed I Be | POOH) Sa Se oe | Ory 
Bg ee ee eg ee imei ime ie dele 
11-16 | 40) 92] 30] 69] 19| 64 | _ ns Wis BS a Fe C8 
3-4 60| 138] 49] 113] 36] 83} 24) 55 
13-16 $0} 184] 68) 157} 53] 120] 39) 90 
7-8 101| 233} 86] 198] 69] 159] 54) 124] 42] 97) 82] 74 
15-16 | 121] 279] 105] 242| 85] 196} 69] 159] 55] 127) 44] 101 
1 142| 327] 124] 286] 102] 235] 84) 194] 69] 159] 57] 131] 38] 88] 24] 55 
11-8 182| 419] 161] 371] 135] 311] 114] 263] 96] 221} 82] 189) 59} 136) 43] 99 
1 1-4 224| 516} 199) 458] 169] 389] 144] 332] 124] 286] 107] 247] 81] 187] 62] 143] 34] 78 
13-8 |..../....| 237] 546] 202! 465] 174) 401) 151! 348] 132] 304] 103) 237] 81] 187] 491 113 
11-2 = Jiccc|.coe[ecce{ecee] 236] 544] 204] 470] 178] 410] 157) 362] 124] 286] 99] 228] 64] 147 
1 5-8 soclecse|cocelooee|sece|eeee| 234] 538] 205] 472] 182] 419] 145] 334] 118] 272) 79] 182 
1 3-4 aledeclcswefsswe| cdgeliecctllene|seneh aolrooT| 2071L477|4107|) c80), 1s6\co13 |meOd Ral 
17-8 Reilscaclocce|neee| sseclesee| aeeclicsectseaalicces| tecelscen|atoo|msornt oa leony Imag] Rane 
2 sonel'scecl case] soow| cabal vecc| sere | devcllaccatsce |occcleessl 210 |;4eeialrama0l | son poss 
2 1-8 cece eee e@eel|ceee|corel] eoseleoe eorolcoe eees|eoee @eeeleoes|eoes 193 445 139 320 
2 1-4 eoeleooe ee eecelececeiceselesoe|eeceieoe eeeeleeeeleses|eeoeiecsce 212 488 154 355 
S 1-2 eoeelecoe| cove eee cove saece(sees | coeelceeriocor| seeelooes|eaer|e80e| +00! sees 184 424 
23-4 Bis | soe ciebelicees!| (Senate cvelllsceall waeeilasee tees |cetel erecl| oeeell chen ne cel seree | mer iaTmeo 
Nors.—The absolute safe static pressure which may be 
: tahoe 2T 5 
put upon pipe is given by the formula P= D Xe in 
which formula P is the pressure per square inch; T, the 
thickness of the shell; S, the ultimate strength per square Size 
inch of the metal in tension; and D, the inside diameter of of | Lbs. 
the pipe. In the tables S is taken as 18000 pounds per Pipe. 
square inch, with a working strain of one fifth this amount 
or 3600 pounds per square inch. The formula for the ee 
‘ A fi 
absolute safe static pressure then is: P= D 4” | 6% 
re 
It is, however, usual to allow for ‘‘ water-ram” by in- g Fa 
creasing tho thickness enough to provide for 100 pounds 1) 316 
additional static pressure, and, to insure sufficient metal for 12 on6 
good casting and for wear and tear, a further increase. 14 248 
equal to .333 (1 —-). 16 226 
100 - 18 209 
The expression for the thickness then becomes: 20 196 
P-+100)D ie fag Pee 
Tie oe Seat ey 24 | 176 
7200 100 Dye 165 
and for safe working pressure 7 30 | 156 
"9200 D 33 149 
= aN r= s33(1 ea) — 100, 36 | 143 
100 42 133 
The additional section provided as above represents an 48 | 126 
increased value under static pressure for the different sizes 60 116 


of pipe as follows (see table in margin). So that to test 
the pipes up to one fifth of the ultimate strength of the 
material, the pressures in the marginal table should be 
added to the pressure-values given in the table above. 





RIVETED HYDRAULIC PIPE. 191 


RIVETED HYDRAULIC PIPE. 
(Pelton Water Wheel Co.) 
Weight per foot with safe head for various sizes of double-riveted pipe. 





























aus, : | = : 
mane) ce s Fs “ise cs ‘ 
aw 2 leg e | 3 8]. 8s lles jee pbs. uigehy Gt, 
Poles |eo | rsa!) ges | oS (Fs | 8s |aee | ges 
GH jome) Soe | ctml| see || St (ons) SES | see] Sas 
OS |ids| Sle | Ses] S30 | os | ees] Sa | tos | 29 
Baio c) Sas | Pas | Bs AS |S 3s) 52S | Tay | Meh 
SH SP) S64 | chin | 948 || SH |sPO) seq | chin | O48 
A la es tr E a |e es ss E 
3 | 18 05 810 214 18 | 12 109 295 | 2514 
4 | 18 05 607 3 ictal oh 125 337 | 29 
4 | 16 062 | 760 334 18 | 10 14 878 | 3824 
5 | 18 05 485 334 18 8 171 460 | 40 
B16 062 605 416 SO le: 36% He vGee 151 | 16 
By 14 078 757 534 20: (140 1s 1675 189 | 193% 
6 | 18 05 405 414 2 12 | .109 265 | 2714 
6 | 16 062 | 505 514 a0 ak | ie 125 304 | 3146 
RG ee! 078 630 614 OOo 10m | hd 340 | 35 
(eee 05 346 434 20 Si euibed 415 | 4514 
Rel iced 062 | 433 6 oo len 16 062 138 134 
Wh oi4 078 | 540 1 etd Cae aha ye Ian 
Be (2336 062 | 378 7 2205) 1a iat 0g 240 | 30% 
So p14 07 472 834 Q 11 125 276 | 3414 
8 | 12 109 660 12 82 21 10 14 309 | 39 
Oe! 26 062 | 336 iM 22 8 171 376 
9 | 14 078 | 420 914 24 | 14 078 158 | 2384 
an Wes 109 587 1234 24°] 12° |- 74109 220 | 32 
10 | 16 062 | 307 814 See bett 125 253 | 37 
to. 314 07 37S 1014 24°Ah 4 10 14 283 | 42 
oy exis 109 | 530 1414 24 8 171 346 | 50 
10, eit 125 607 1614 24 6 20 405 | 59 
10 | 10 14 680 1814 26 | 14 078 145 | 25 
Tis fei6 062 | 2%5 9 26 | 12 109 203 | 3544 
ty dé Of8 | 844 rf Pia Nae 125 22 3916 
11 2 109 | 480 1514 26 | 10 14 261 | 4414 
dips fal 125 | 553 lily 26 8 171 319 | 54 
11 | 10 14 617 1944 Q 6 20 373 | 64 
122 | 16 062 | 252 10 a8 | 14 078 185 | 274 
das) eid 078 | 316 1214 28.) 12 109 188 | 38 
12 | 12 109 | 442 17 Q 11 125 216 | 4214 
Tag Pe 125 | 506 1914 28 | 10 14 242 | 4716 
12; | 410 14 567 2184 28 8 171 295 | 58 
13 | 16 062 | 233 1014 28 6 20 346 | 69 
shy n14 07 201 13 30 | 12 109 76 | 39% 
13~| 12 109 | 407 18 30 | 11 125 202 | 45 
Butt 125 | 467 201% 30 | 10 14 226 | 5014 
13 | 10 14 522 23 30 iad aoe 276 | 6134 
14 | 16 062 | 216 1114 30 6 20 323 | 73 
14 | 14 07 7 14 Bo TEP t7 25 404 | 90 
14 | 12 | .109 | 2378 1914 36 | it 125 168 | 54 
14} 11 125 | 433 2017 36 | 10 14 189 | 6014 
14 | 10 14 485 25 BO ese 187 252. | 81 
15 | 16 062 | 202 1134 36 | 4 25 337 | 109 
15 | 14 078 | 252 1434 368 | 6S 312 420 | 135 
15 | 12 109 | 352 20% 40 | 10 14 170 | 67% 
15 } 11 125 | 405 2314 40 | 335 187 226 | 90 
15 | 10 14 453 26 40 | 14 25 303 | 120 
16 | 16 062 | 190 13 ADH THR, 312 78 | 150 
16 | 14 07 237 16 40 | % 37 455 | 180 
16:1 ("19 109 | 332 2014 BAS fet 14 162 | 71 
16 “(Mat 125 | 379 2416 42 | 187 216 | 9414 
16 | 10 14 425 28146 42 | % 5 289 | 126 
18 | 16 062 168 1434 2 5 312 360 | 158 





192 MATERIALS, Breet ie es 


STANDARD PIPE FLANGES. 
adopted August, 1894, at a conference of committees of the American 
Society of Mechanical Engineers, and the Master Steam and Hot Water Fit- 
ters’ Association, with representatives of leading manufacturers and users 
of pipe.—Trans. A. S. M. E., xxi. 29. (The standard dimensions given have 
not yet, 1901, been adopted by some manufacturers on account of their un- 
willingness to make a change in their patterns.) 
The list is divided into two groups; for medium and high pressures, the 
first ranging up to 75 lbs. per square inch, and the second up to 200 Ibs. 






































am.| , 2 wn ; 
=3(S/2 |§ lg} 2 | 3 | [58 
BBA band bf int % os 8 a) Rikon 
: —/2@ {5 & uf A 3 “115 gz eRe 
Q | . Ea a ry 8 @ fy S| |B |S |PAw 
® n od ies wn o a) qa 1 jes | oo =| eR 
Him 2 38 lo S12 = Mo o & O| Rien [a 
2/4 % jagiecie g CEs bo A jal $| 3|Za9 
mid dy |S 3 AS | @ lel 2ieioer 
sie wiiggigas| A | "Si 2 pote atases 
a fot 15-5|°O) a o @ . wa mu oie | OOF & 
a /eS] ieclgels] & | S| af | Og [8/4 )3/g64 
Sie) 23/2 d\5 =I sey 32'S eo jefe )e2)o5h 
2i2+ = Sssl\bsls| Ss £3 } 2a Sa Isic lolesy 
& Ba | |B? |an Ey fe eo m= 12/1 |o* 
2 } .f09 | $i 460)14 6 274 2 434] 4) 98/2 | 825 
Qe] 420 | re | 550/14 7 ii] gy Buel 4 2s)24 1050 
3°| 1443 | 3 | 690/14 "i, 34, 214 6 | 4) 54/246) 1830 
314; 1466 | 46 | 700|%4 814 ay be 7 | 4) 5gleig) 2530 
‘486 | 44 | 800|%¢ 9 a5 24 T46| 4 34/234 2100 
416) .498 | 16 | 900/16 914 13 234 734) 8| 34/3 1430 
5 .025 4 |1000\44 10 48 246 84) 8) 34/3 1630 
6 .563 | x |1060/4% 11 ] 216 914 8| 34 3 2360 
7 | 160 | 56 |1120I%6 124) ze] 284 1034 8| 34/314) 3200 
8 | .639 | 5g /1280)14 1344 4 ess 1134| 8 34/344) 4190 
9 | .678 | 44 |1310\% 15 114 3 1314|12| 34|34¢ 3610 
10 | .713 | 34 |1330/3 16 1st} 8 1414|12| %4|354 2970 
12 79 | 48 [1470/36 19 186 344 17 112) 7/334) 4280 
14 .864 | % |1600\3 21 13 3% 1834|12]1 [414] 4280 
15 .904 42 |1600/3, 2214 134 356 20 16/1 |414| 3660 
16 | .946 |1  |1600|3% 2316 1y5| 384 2144/16|1 |414| 4210 
18 | 1.02 lig 1690 is 25 13% 346 2234 |16]116/434) 4540 
20 7 1.09 14g /1780)3, 2714 132 334 25 |20)144)5 | 4490 
22 11.18 113, [1850/14 2914 133 334 2714 |20/114|514| 4320 
24 | 1.25 134 |1920/4/8134 82144 174/384 4° °|2914 2044/20]114)/514) 5180 
26 | 1.80 17 1980/14/8384 s4igl1sg 2 "(3% 41¢/3144 31394/24|114|534) 5030 
28 11.38 {13g [2040/14/86 366l1;— 23,14 4144/3344 34 (281114/6 | 5000 
30 | 1.48 {144 |2000)14'38  s8aqlile 2tgi4  434/8546 36 |28113¢/614| 4590 
36 | 1.71 |154 |1920|14|4414 4534134 284/414 474142 4234/82|184)614 5790 
2 11.87 [2 [2100/14/51 528411%% 264/414 5834/4814 4914/36) 114|714| 5700 
48 | 2.17 [244 \2130I4\5714 Bo1gle” 2814345341548 56 |44)1141734! 6090 





Notes.—Sizes up to 24 inches are designed for 200 lbs. or less. 

Sizes from 24 to 48 inches are divided into two scales, one for 200 lbs., the 
other for less. 

The sizes of bolts given are for high pressure. For medium pressures the 
diameters are 1g in. less for pipes 2 to 20 in. diameter inclusive, and 14 in. 
less for larger sizes, except 48-in. pipe, for which the size of bolt is 13 in. 

When two lines of figures occur under one heading, the single columns are 
for both medium and high pressures. Beginning with 24 inches, the left-hand 
columns are for medium and the right-hand lines are for bigh pressures. 

The sudden increase in diameters at 16 inches is due to the possible inser- 
tion of wrought-iron pipe, making with a nearly constant width of gasket a 
greater diameter desirable. 

When wrought-iron pipe is used, if thinner flanges than those given are 
sufficient, it is proposed that bosses be used to bring the nuts up to the 
standard lengths. This avoids the use of a reinforcement around the pipe. 

Figures in the 3d, 4th, 5th, and last columns refer only to pipe for high 
pressure. 

In drilling valve flanges a vertical line parallel to the spindles should be 
midway between two holes on the upper side of the flanges. 


CAST-IRON PIPE AND PIPE FLANGES, 


193 


FLANGE DIMENSIONS, ETC., FOR EXTRA HEAVY 
PIPE FIETINGS (UP TO 250 LBS, PRESSURE). — 
Adopted by a Conference of Manufacturers, June 28, 1901, 


Size of 
Pipe. 


DIMENSIONS OF PIPE 


(J. E. Codman, Engine 


Diam. of 
Flange. 


Inches. 








Diameter 
of Bolt 








Thickness | Diameter of | Number of] Size of 
of Flange. | Bolt Circle. Bolts. | Bolts. 
Inches, Inches. Inches. 
% 5 4 5 
1s. 5% 4 
114 654 8 55 
1 3-16 714 8 5g 
14 7% 8 34 
15-16 814 8 34 
134 914 8 34 
1 7-16 1054 12 % 
146 11% 12 is 
154 13 12 y 
134 14 12 % 
1% 1514 16 % 
2 1784 16 u% 
alg 20 20 % 
2 3-16 21 20 1 
2 2414 
a6 2634 24 11¢ 
252 2834 28 114 
234 3114 28 114 
FLANGES AND CAST-IRON 
PIPES, 
ers’ Club of Philadelphia, 1889.) 
wg | HG Gs 2) && | Thickness S861 S08 
22) sh 23 | 53 o of Pipe. wom | ome 
ae a 241/59 |) 8 (222 FS s8 | ada 
Sa@viipn e SO) 5° | Sa |Frac.| Dec. | SSFR | Sha 
ry AY a BO - Es 
2 614 34 4 5, 3% 80 6.96 4,41 
3 we 34 4 62 18 30 396; 11.16 5.93 
4 9 34 6 11-16 | “7-16 420 15.84 7.66 
5 934 34 6 | % 7-16 | .443| 21.00 9.63 
6 1034 94 8 34 15-32 466 26.64 11.82 
8 1314 34 8 13-16 | 4 511} 89.386 | 16.91 
10 1514 34 10 RB 9-16 557 54.00 23.00 
12 1734 % 12 15-16 | 19-32 603 70.56 30.13 
14 20 % 14 21-32 649 89.04 38.34 
16 22 % 16 1 1-16 | 11-16 695} 109.44 47.70 
18 24 % 16 144 G41] 181.76 58.23 
20 27 1 18 1 3-16 | 25-32 "87| 156.00 70.00 
22 | 2884 1 20 | 114 27-32| .833] 182.16 | 83.05 
24 31144 1 22 15-16 | % 879| 210.24 97.42 
26 3314 1 24 13g 15-16 925] 240.24 4113.18 
28 3514 1 24 1 7-16 | 31-82} .971| 272.16 130.35 
30 38 1 26 1 9-16 1.017) 306.00 149.00 
32 40 11g 28 154 1 1-16] 1.063) 341.76 169.17 
34 4214 144 30 1 11-16|114 1.109} 3879.44 19V.90 
36 45 14% 382 134 1 5-32) 1.155} 419.04 214.26 
38 47 144 82 1 18-16]1 3-16) 1.201} 460.56 239.27 
40 49 11g 34 1% 114 1.247} 504.00 266 .00 
42 5114 144 34 1 15-16/1 5-16) 1.293] 549.36 294 49 
44 5314 1144 36 2 111-32] 1.3839] 596.64 | 324.78 
46 5534 14 38 2 1-16 |132 1.885] 645.84 | 356.94 
48 58 114 4Q 214 17-16| 1.431! 696.96 | 391.00 


< D = Diameter of pipe. 
FormMvuLa.—Thickness of flange = 0.033D -++ 0.56; thickness of pipe 


All dimensions in inches, 


— 


0.023 D 4- 0.327; weight of pipe per foot = 0.24D2 + 3D; weight of flange = 


.001D3 + 0.1D2 + D 


+2; diameter of flange = 1.125)+ 4.25; diameter of 


boit circie = 1.092D -- 2.566; diameter of bolt = 0,011D -+-0,73; number of 
bolts = 0.78D -+ 2.56, 





MATERIALS. 








194 


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g 1090°69 | 00°83 | S828 |006°O JaLeol| SIZ OLI/SLOL° TL SBP GST | See" 893° bel Ap [892° FP!) GLe* | Sa PT cI 
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Cayton, EQN, TeAO!IEN) 
‘Odi POPICAA UOAT-JGSNOAM, JO SUOTSUIUIIG PlepuULis 








side 
Diam. 


ominal 


In 


N 


WROUGHT-IRON PIPE. 195 


For discussion of the Briggs Standard of Wrought-iron Pipe Dimensions, 
see Report of the Committee of the A. S. M. H. in ** Standard Pipe and Pipe 
Threads,’ 1886. Trans., Vol. VIII, p. 29. The diameter of the bottom of 


the thread is derived from the formula D — (0.05D + 1.9) x 4, in which 
7 


D= outside diameter of the tubes, and » the number of threads to the 
inch. The diameter of the top of the thread is derived from the formula 


0.8-— x 2-++ d, or 1.65 -++ d, in which d is the diameter at the bottom of the 


thread at the end of the pipe. 
The sizes for the diameters at the bottom and top of the thread at the end 
of the pipe are as follows: 





Diam. } Diam. | Diam. §{ Diam.| Diam. | Diam. 
fof Pipe,| at Bot-| at Top fof Pipe,| at Bot-| at Top 
s Nom- | tom of of Nom- | tom of of 

inal. |Thread.!/Thread.¥ inal, |Thread.|Thread. 


Diam. | Diam. ) Diam. 
of Pipe, | at Bot-| at Top 


in in. in. in in in. in in in. 
4 384 .393 246 2.620 | 2.820 8 8.334 | 8.534 
14 .433 soe 3 3.24t 38.441 9 9.327 9.527 
3g .568 .658 314 3.738 3.938 10 10.445 | 10.645 
01 .815 4 4 234 4.434 11 11.489 | 11.639 
34 911 1.025 41g 4.731 4.931 ip 12.483 | 12.633 
1 1.144 1.283 5 5.290 5.490 13 13.675 | 18.875 
1144 1 488 1.627 6 6.346 | 6 546 14 14.669 | 14.869 


Having the taper, length of full-threaded portion, and the sizes at bottom 
and top of thread at the end of the pipe, as given in the table, taps and dies 
can be made to secure these points correctly, the length of the imperfect 
threaded portions on the pipe, and the length the tap is run into the fittings 
beyond the point at which the size is as given, or, in other words, beyond 
the end of the pipe, having no effect upon the standard. The angle of the 
thread is 60°, and itis slightly rounded off at top and bottom, so that, instead 
pf its depth being U.866 its pitch, as is the case with a full V-thread, it is 
4/5 the pitch, or equal to 0.8 -- », 1 being the number of threads per inch, 

Taper of conical tube ends, 1 in 32 to axis of tube = 34 inch to the foot 
total taper. 


196 MATERIALS: 


WROUGHT-IRON WELDED TUBES, EXTRA STRONG. 
Standard Dimensions. 





Actual Out-} Thickness, | Thickness, | Actual Inside Actual Inside 

















Nominal side Extra Double Diameter, | Diameter, 
Diameter. | Diameter Strong Extra Extra Double Extra 
‘ ‘ Strong. Strong. Strong. 
Inches. Inches. Inches. Inches. Inches. Inches. 
0.405 0.100 ee ELIS ig 0.205 LNG Settee telat ere 
A 0.54 0.1238 Mate aieiatesee'stare 0.294 EEA ARE 
52 0.675 0.127 wis relaiele eters 0.421 Deictele ore ees 
vA 0:84 0.149 0.298 0.542 0.244 
34 1.05 0.157 0.314 0.'786 0.422 
1 1.315 0.182 0.264 0.951 0.587 
114 1.66 0.194 0.888 1.272 : 0.884 
1% 1.9 0.203 0.406 1.494 1.088 
2 2.375 0.221 0.442 1.983 1.491 
244 2.875 0.280 0.560 2.315 1.755 
3 3.5 0.304 0.608 2.892 2.284 
344 4.0 0.321 0.642 8.858 2.716 
4 4.5 0.341 0.682 3.818 3.186 





STANDARD SIZES, ETC., OF LAP-WELDED CHAR-~ 
COAL-IRON BOILER-TUBES, 
(National Tube Works.) 























. ‘ “12 10 ‘ o a 
& |e oS bodes Bog less | Soe] as 
S Ss eee eee Piyse Fait Bee HO 
a |A )/53|°3 a jm BE | BS 
m of |= |]—2.8 | Internal External | ‘3 n |o..9 | 6 a 
8 Bee Pas So | So A A ao ous) ors | aes 
Sahl, ie ad aa | eo rea. rea. S29 |S07 5| su¢ a8 
Ro | 5 = | aS =] mn | doRS fp aoa 
OF | aS. | aa] 2s; |. 2 ws eg SBS One 
Ro | eo | sa | Bo) HE GBS |ga0s8) a= | 5 
a | ja |S Ja | A | 5 
ey eae ill peal air aria, of eb ial ue gL eS 
in, | in..} in. | in in. | sq. in.}sq.ft.| sq. in.|sq.ft.} ft. ft. ft. lbs. 
-810} .095 | 2,545] 3.142 515] .0036 -785| .0055| 4,479 3.820 4.149 90 


1-4} 1,060] .095 | 3.330) 3.927 882] .0061 1.227) .0085) 3.604 | 3.056 3.330 1.15- 
1-2} 1.310] .095 | 4.115] 4.712] 1.348] .0094 1.767} .0123] 2.916 |, 2.547 |; 2.732 1.40 
3-4| 1,560] .095 } 4.901] 5.498 1.911} .0133 2.405} .0167) 2.448 | 2.183 | 2.316 1,65 

1.810] .095 | 5.686] 6.283} 2.573) .0179 3.142) .0218} 9.110 | 1.910 2.010 1.91 
-4) 2.060} .095 | 6.472) 7.069 3.333] .0231 3.976] 0276] 1.854 | 1.698 1.776 2.16 
-2| 2.282) .109 | 7.169] 7.854 4.090] .0284 4.909] .0341| 1.674 | 1.528 1,601 2,75 
—4| 2.532} .109 | 7.955) 8.639) 5.035) .0350 5.940) .0412} 1.508 | 1.389 1,449 3.04 

2.782) .109 | 8.740) 9.425] 6.079] .0422 7.069} .0491] 1.373 | 1.273 1.322 3.33 
-4| 3.010} .120 | 9.456]10.210 7.116] .0494/ 8.296) .0576) 1.269 | 1.175 1.222 3.96 
-2) 3.260] .120 }10.242|10,996} 8.347] .0580 9.621} .0668} 1.172 ! 1.091 1.132 4,28 
—4| 3.510} -120 }11.027) 11.781 9.676] .0672| 11.045) .0767) 1.088 { 1.019 1.054 4.60 

3.732] 184 111.724} 12.566} 10.939) 0760) 12.566] 0873) 1.024 955 990 5.47 
-2| 4.232] .134 |13.295)14.137] 14.066] .0977) 15.904] .1104) .903 849 876 6.17 

4.704] .148 |14.778]15.708] 17.379] .1207| 19.635] .1364| .812 764 788 7.58 

5.670} .165 |17.813] 18.850} 25.250} .1750) 28.274) .1963] .674 637 .656 | 10.16 

6.670] .165 |20.954]21.991} 94.942] .2427) 38.485) .2678) .573 046 .560 | 11.90 

7.670] .165 |24.096|25.133{ 46,204] .3209| 50.266} .3491] .498 ATT 488 13.65 

8.640] .180 |27.143] 28.274] 58.630] .4072] 63.617] .4418] .442 A424 433 | 16.76 
10 9.594) .203 |30.141)31.416] 72.292) .5020) 78.540) .5454) .398 382 .390 | 21.00 
11 10,560} .220 |33.175|34.558) 87.583) .6082| 95.033} .6600] .362 347 355 | 25.00 
12 11.542} .229 |36.260)37.699] 104.629) .7266] 113.098} .7854| .331 318 .325 | 28.50 
13 12,524] .238 139.345) 40.841] 123.190] .8555] 132.733] .9217| .305 294 300 | 32.06 
14 13,504] .248 [42.424 )/ 43.982] 143.224] .9946] 153.938|1.0690] .283 273 278 | 36.00 
15 14,482] .259 ]45.497|47.124} 164.721|1.1439]| 176.715|1.2272) .264 255 260 | 40.60 
16 15.458} .271 |48.563}50.266| 187.671!1.3033| 201.06211.3963] 247 2239 243 | 45.20 
17 16.432| .284 |51.623/53.407) 212.066| 1.4727) 226.981/1.5763) 232 +225 229 | 49.90 
18 17.416] .292 |54.714|56.549| 238.225|1.6543} 254.470|1.7671] .219 212 216 | 54.82 
19 18.400} .300 |57.805)59.690} 265.905) 1.8466] 283.529) 1.9690] .208 201 205 } 59.48 
20 19.360] .320 | 60,821 |62.832] 294.375]2.0443| 314.159) 2.1817] .197 191 194 | 66.77 
21 20.320| .3840 |63.837 |65.974 | 324.294} 2.2520] 346.361! 2.4053] .188 182 185 | 73.40 


DOO IV Se SHH 69 69 09 C9 ON DODD tt 











In estimating the effective steam-heating or boiler surface of tubes, the surface in 
ee with air or gases of combustion (whether internal or external to the tubes) is to , 

e taken. 

_For heating liquids by steam, superheating steam, or ‘transferring heat from one 
liquid or gas to another, the mean surface of the tubes is to be taken, 


RIVETED IRON PIPER. 197 


To find the square feet of surface, $8, in a tube of a given length, L, in feet, 
and diameter, d, in inches, mY the length in feet by the diameter in 
inches and by .2618. Or, S= 84" — 261gaL, For the diameters in the 


table below, multiply the length in feet by the figures given opposite the 
diameter. ) , 











Square Feet Square Feet - | Square Feet 
Inches, : s 
Diatietes per Foot Ga per Foot Bee per Foot 
; Length. ; Length. ' Length. 
14 .0654 214 5890 5 1.3090 
% -1809 214 .6545 6 1.5708 
34 .1963 234 C199 7 11.8326 
1 .2618 3 (854 8 ‘2.0944 
114 18272 314 ~ _. 8508 9 (2.38562 
144 8927 816 .9163 10 2.6180 
134 4581 334 .9817 11 2.8798 
Ps .5236 4 1.047 12 3.1416 


form for shipment. 








RIVETED IRON PIPE. 
(Abendroth & Root Mfg. Co.) 
Sheets punched and rolled, ready for riveting, are packed in convenient 


for punched and formed sheets. 


The following table shows the iron and rivets required 





Number Square Feet of Iron 
required to make 100 Lineal 
Feet Punched and Formed 
Sheets when put together. 


Diam- 
eter in 
Inches. 


Width of 


Lap in 
Inches. 


Square 
Feet. 


Approximate No. 
of Rivets 1 Inch 


r 100 Lineal 


apart required 
for 
Feet 


Number Square Feet of Iron 
required to make 100 Lineal 
Feet Punched and Formed 
Sheets when put together. 


Diam- 
eter in 
Inches. 


Width of 


Lap in 
Inches. 


p<. | | Se Se es ee ee pe eee Oe eee ss ee eee 





sdvsus 
zeeese 
oman oF 
RoOSHEO 
SnD FR, 
Shae epee 
¥ ae +" = 
e [a'e} 5 ; ao 
Square | BU Se 
Doct, BS aon aa 
897 2,800 
423 2,900 
452 8,000 
506 8,200 
562 8,500 
617 3,700 
670 3,900 
25 4,100 
ui 4,400 
836 4,600 
998 5,200 





WEIGHT OF ONE SQUARE FOOT OF SHEET-IRON 
FOR RIVETED PIPE. 


Thickness by the Birmingham Wire-Gatuge,. 





No. of 
Gauge. 


26 
24 
22 
20 


Thick- 
ness in | Weight 
Decimals} in lbs., 
of an Black. 
Inch. 
.018 .80 
022 1.00 
.028 1.25 
-0385 1.56 


Weight 

in lbs., 

Galvan- 
iz 






No. of 
Gauge. 


Thick- 
nessin |Weight 
Decimals | in lbs., 
of an Black. 
Inch. 
.049 1.82 
065 Pa DO a 
.083 3.12 
.109 4.37 





198 MATERIALS. 


SPIRAL RIVETED PIPE. 
(Abendroth & Root Mfg. Co.) 





Thickness. Diam- | Approximate Weight | Approximate Burst- 
eter, in lbs. per Foot in ing Pressure in lbs. 
. 2 Oo are > 

sek G.| Inches, | Inches: Length. per Square Inch, 

26 .018 38to 6 |lbs.= > 

24 .022 8to12 | ‘* =W%of diam. inins. 

22 028 3to14-) “= 4 ie ¥ 

20 .035 2 tO 240 sia) > ‘§ ‘¢ 2700 Ibs. diam. in ins, 

18 .049 2.t0 2% aloe 0 Me “¢ 13600 $$ + * a 

16 -065 6to 24 fe 8 : Set 14800588 --e2 88 ‘ss 

14 .083 810.24 agai] . see |64005¢* |S oF 

12 .109 9to 24 | **.=1.4 “a Se | S8000% "= pes N 


The above are black pipes. Galvanized weighs 10 to 30 % heavier. 
Double Galvanized Spiral Riveted Flanged Pressure Pipe, tested to 150 lbs. 
hydraulic pressure. 







































































Inside diameters, inches....| 8 | 4 10/11 12/13) 14{15|16|18]<0)22)24 
EMICKNESS way Wie Ghee aa "120 = a is 18 gis sis 16/16) 16, 14/14}14)14]14}12}12 
Nominal wt. per foot, lbs...| 244] 3 8/11/12) 14]15 20122/24]29|34140 £0 
DIMENSIONS OF SPIRAL PIPE FITTINGS. 
nikiin feito 
Inside sursidé | Number | Diameter ee Sizes of 
Diameter. SA pahe Bolt-holes. | Bolt-holes.. WA ee sth Bolts. 
Drilled. 
ins. ins. ins. ins. ins. 
3 6 4 V% 434 7/16 x 134 
4 7 8 16 5 15/16 7/16 x 134 
5 8 8 1% 6 15/16 7/16 x 184 
6 8% 8 54 1% 14 x 134 
7 10 8 % 14 x 134 
8 11 8 8 10 x2 
9 13 8 54 1114 16x2 
10 14 8 54 1244 1gx2 
11 15 12 % 1336 14x2 
12 16 12 3% 1414 1g x2 
13 17 12 d8 1514 16x 2 
14 17% 12 d8 1614 1gx2lg 
15 2 5% 17 7/16 16x26 
16 21 3/16 12 % 1914 16x26 
18 2314 16 11/16 2114 16x 2le 
20 D51¢ 16 11/16 2314 gx 
22 2814 16 34 6 5g x26 
24 30 16 34 2734 5g x 216 





SEAMLESS BRASS TUBE. IRON-PIPE SIZES. 
(For actual dimensions see tables of Wrought-iron Pipe.) 





Nominal| Weight | Nom. | Weight { Nom. | Weight {| Nom. | Weight 
Size. |per Foot.J Size. jper Foot. Size. |per Foot.§ Size. |per Foot. 


ee eee Ee te ae ——————— | 


ins lbs ins lbs. ins. lbs ins lbs 
25 34 1.25 2 4.0 4 12.70 

vA 43 1 hy Q16 5.7 41 13.90 

36 62 114 2.50 3 8.30 5 15.75 


i 90 114 3. 314 10 90 6 18.31 


[ 
} 


; 


BRASS TUBING; COILED PIPES. 199 


SEAMLESS DRAWN BRASS TUBING. 
(Randolph & Clowes, Waterbury, Conn.) 


Outside diameter 3/16 to 734 inches. Thickness of walls 8 to 25 Stubs’ 


Gauge, length 12 feet. The following are the standard sizes: 


Outside Length Stubbs’ f Outside Length Stubbs’ § Outside Length Stubbs’ 























bDiam- | or Old § Diam- or Old § Diam- or Old 
eter. Feet. Gauge. eter. * |Gauge.§ eter. Feet. Gauge 
4 12 20 134 12 14 256 12 1t 
5-16 12 19 1% 2 14 234 12 11 
3% 12 19 15g 2 13 3 12 11 
1% 12 18 134 12 13 314 12 11 
56 12 18 1 13-16} 12 13 314 12 11 
34 12 17 1% 12 12 4 10° to. 12\"eeit 
13-16 12 Li 1 15-16} 12 12 5 10 to: 12) Syl 
Y 12 17 2 12a 12 54 110 to 12} 11 
15-16 12 17 Qt 12 12 5144 |10 to 12} 11 
1 12 16 244 12 12 534 |10 to 12} 11 
ig 12 16 236 12 12 6 10 to 12} + 11 
14 12 15 216 12 11 
BENT AND COILED PIPES, 
(National Pipe Bending Co., New Haven, Conn.) 
COILS AND BENDS OF IRON AND STEEL PIPE. 
{ 
DIZEIOM PIPE se ciel ersrccs- Inches} 14} 3; W% 34) 1 | 11%4| 144) 2 24] 3 
Least outside diameter of 
CO Ue oe Bc Bice SEA eee Inches} 2 | 214] 344] 4144) 6 | 8 /}12 | 16 | 24 | 82 
tSize of pipe.:........3. Inches] 84%} 4 | 44/5 {6 |7 |8 | 9 | 10 | 12 
Least outside diameter of 
GO asta ars cissejnecicisets Inches/40 |48 |52 1/58 |66 |d0 |92 {105 {130 |156 





Lengths continuous welded up to 3-in, pipe or coupled as desired. 


COILS AND BENDS OF DRAWN BRASS AND COPPER TUBING. 
























































_ Size of tube, outside diameter.....Inches| 14} 38¢} 6) 56) -34; 1 | 114) 13% 
Least outside diameter of coil..... Inches) 2 s|olt6i2) edie) 38 | 4 | 6 le 
Size of tube, outside diameter.....Inches 1%) 15g} 134| 2 | 214) 234] 214] 234 
Least outside diameter of coil.....Inches} 8 | 9 |10 |12 |14 |16 {18 |20 

Lengths continuous brazed, soldered, or coupled as desired. 
90° BENDS. EXTRA-HEAVY WROUGHT-IRON PIPE. 
Diameter of pipe.............. Inches} 4 | 44/5 |6 |7 |8 | 9 {10 |12 
URN he ape lose cad dbocmocseaccoe Inches/22 |24 |26 {80 |86 {42 {18 |60 {72 


Centre to end.,.......6.++.---Inches|/26 /2814/81 |86 (43 [50 [57 |70 {84 


The radii given are for the centre of the pipe. ‘‘ Centre to end ” means 
the perpendicular distance from the centre of one end of the bent pipe toa 

_ plane passing across the other end. Standard iron pipes of sizes 4 to 8 in. 
are bent to radii 8 in. larger than the radii in the above table; sizes 9 to 12 in. 


to radii 12 in. larger. : 
Welded Solid Drawnsesteel Tubes, imported by P.S. Justice & 
Co., Philadelphia, are made in sizes from 14 to 414 in. external diameter, 
varying by Mths, and with thickness of walls from 1/16 to 11/16 in, The 
maximum length is 15 feet, 


200 MATERIALS. 


WEIGHY OF BRASS, COPPER, AND ZINC TUBING, 
Per Foot, 


Thickness by Brown & Sharpe’s Gauge. 











Copper, 
Brass, No. 17. Brass, No. 20. Lightning-rod Tube, 
No, 28. 
Inch. Lbs. Inch. Lbs. Inch. Lbs. 
Y% .107 2 .032 V4 .162 
5-16 P15¢ 8-16 .089 9-16 .176 
36 1185 VA .063 5 .186 
7-16 204 5-16 . 106 11-16 FOL. 
17 .266 34 .126 34 229 
9-11 pe i A me ; eo. A. a ant 
33 2 1 
; 377 9-16 "208 Zine, No. 20 
4 462 54 .220 
542 34 .252 
114 675 % £284 14 161 
144 .740 1 sot 56 185 
114 915 114 .500 4 234 
134 -.980 1% 580 % ate 
1.90 311 
214 1.506 114 380. 
3 2.188 144 452 


LEAD PIPE IN LENGTHS OF 10 FEET. 








In. 8-8 Thick. 5-16 Thick. 14 Thick. 8-16 Thick. 
Ib. OZ. lb. OZ. Ib. OZ, lb. OZ. 

21% 17 0 Tt tO): 11 0 8 0 

3 20 0 16 0 2 0 9 0 
3% 22 0 18 0 15 0 9 § 

4 25 0 21 0 16 0 12 8 
416 18 0 14 0 

5 31 0 20 0 


LEAD WASTE-PIPE. 


Us in., 2 lbs. per foot. uv} in., 4 lbs. per foot. 
“3 and 4 lbs. per foot. ee "By 6, and 8 lbs, 
3 “34 and 5 lbs. a? foot. 46 ** 6 and 8 lbs. 


5 in. 8, 10, and 12 lbs, 


LEAD AND TIN TUBING. 
¥ inch. 14 inch. 
SHEET LEAD. 
Weight per square foot, ae 3, 3 38 4, 414, 5, 6, 8, 9, 10 lbs, and upwards. 
Other weights rolled to ord¢ 


BLOCK-TIN PIPE. 


346i in, 414, 614, a : oz. per foot. 1 in., 15, and 18 oz. per foot, 
6 ** 6, 7, and 1 14“ hand 1% lbs,“ 
64 ** Sand 10 o, fey Mag “2 anbaredbs, . * 
$4‘ 10and120z. “ “ Méand3lbs, “ 


LEAD PIPE. 


LEAD AND TIN-LINED LEAD PIPE. 


(Tatham & Bros., New York.) 











g i Weight per 
2 & Foot and Rod. 
3 za 
(@) | 
3¢ in E 7 Ibs. per rod 
¢° D 10 oz. per foot 
ee (® 12 74 ee 
= B LED ee 
oe Ac 1144 79 66 
ce AA 144 sé 66 
ee AAA 134 66 ee 
7-16 in. 13 oz. ey 
Ss teers 4 
14 in EK 9 Ibs. per rod 
D 34 lb. per foot 
ee CG 1 ee oe 
“ec B 1 A 6é ac 
ee 1% ce cs 
66 A 194 6é ee 
46 AA 9 6e (a4 
ee 9 cr 73 
a6 AAA a oe 66 
5g in. E 125 5 per.rod 
a D Pee per LOOb 
66 Cc 14g (73 be 
6é B 9 46 “ce 
ce A 9 ce “ce 
ae AA 234 66 6 
“4 AAA | 314 ‘ bs 
34 in E Tn DeGeLOoOb 
ot D 14 ee be 
66 0) 1 eeé oe 
4eé B Be 66 “se 
ee A 8 66 66 
66 AA 314 66 66 


66 AAA 434 66 66 











&. 
28 
fn} o e 
oe co ay 
= BS o 
ze ro) Pa 
Tain: EK 
6 pe D 
8 66 Cc 9 
12 “6 B a 
16 se A 4 
19 ee AA 434 
27 sf AAA a 
1144 in E 2 
ee D 9 Z 
4 i Cc ve 
9 B 334 
|| A |*494 
13 ss AA 534 
ue AAA 634 
iy 1/4 in E 3 
if Y 3 
25 ip C ig 
= B 5 
‘ A 6 
9 . AA oa 
13 i AAA 9 
16 ||134 in Cc 4 
20 B 5 
22 A 6 
25 ci AA 6) 
8 }|2 in Cc 434 
10 ‘ B 6 
es uh A v4 
16 us AA 9 
20 Ny AAA  |1134 











66 


Weight per 
Foot and Rod. 





6c 
66 
66 
“6 
6é 
a6 
6b 
66 
ee 
66 
66 


Thickness in 
1-100th In. 


114 lbs. per foot | 10 
9 ee 46 ital 





(Tatham & Bros., New York.) 


Fall. | 84: inch.} Letter.|3¢ inch. |/14 inch. 5g inch.|34 inch. 


Aad aie ee: 
of Feet |. P°& 
30 ft. 15 lbs. D 10 o7 
50 ft. 25 Ibs. C 12 oz 
Vontts 38 lbs. B 1, Ib 
100 ft. 50 lbs. A 
150 ft. 75 Ibs. AA 

















34 1b. | 1 Wb. | 114 lbs. 
1° lb. | 1% Ibs.| 134 Ibs. 


114 lbs.| 2 Ibs. 244 lbs. 


114 lbs.| 134 lbs.| 214 Ibs.| 3. Ibs. 
144 Ibs.| 2 Ibs.| 234 Ibs,| 3% Ibs. 
200 ft. | 100lbs. | AAA | 134 lbs.|3 Ibs.) 3% lbs.| 434 lbs. 








Calibre and Weight per Foot. 





1 inch. 





WEIGHT OF LEAD PIPE WHICH SHOULD BE USED 
FOR A GIVEN HEAD OF WATER. 


144 in. 


.| 244 Ibs. 
.| 38 Ibs. 
.| 834 Ibs. 
.| 434 Ibs. 
s.|6 Ibs. 
.| 634 Ibs. 








Wo find the thickness of lead pipe required when the 


head of water is given. 


(Chadwick Lead Works). 


RuLe.—Multiply the head in feet by size of pipe wanted, expressed deci- 
mally, and divide by 750; the quotient will give thickness required, in one- 


hundredths of an inch, 


EXAMPLE.—Required thickness of half-inch pipe for a 


2 X 0.50 + 750 = 0,16inch. _ 


head of 25 feet. 


MATERIALS. 


202 
























































9°SI¢ | 9° EFS OT Fes “ecg: 9. O1QnD Tod qysIo\ # LET cht 666 60'S T9610" 0G: 
| Be Pa T 69'T 89°§ 06°§ 068SE0° 61 
81e°8 | 869°8 988°S 088°8 f° AYTABIS Oyfoodg ff a1 'T 8 I G9 26°F GOE0FO’ 8 
F6'T “0° 98°S 06 9 LGZCFO" aL 
cel” Chl” E820" 66c0° FFT§00" OP 81% 0€ 6 6¢ z 682 0z80S0° Of. 
TSt° Oot” 2980" GLE0° TES600° 68 PPS 69°% C86 986 890290" GE. 
VAS Ost” Ogt0* FO” 996800" SE PLS 06°3 CLIT bP Ol FS80F90" bL 
I6E° G06" 2950° 0090° ESPF00" 4g 80°¢ 96'S 18 PL G9 GT 196720° st 
1s" co" GTL0° 2910" 000¢00° 96 OFS 99°§ 89°SE 22°61 808080" or 
OFS £93" 6060" 960° F19S00° Gs 88'S IP Go" Es C6 FS 6F2060° Iv 
026° 986" vIT" 03T* F0€900° rE 98°P 69'P 69 66 &P 1s 68101" OL 
608" Teg" 4 GGT" 0802.00" && 06°F 8I'¢ bP LE F966 SPPIE” 6 
OFS" 098" TSt" I6L° 096200" es og's 68'G GG LP 86 6P 6F8e1° 8: 
688" FOP 86" TPG" 86800" Ig 89 vo'9 g¢'6g9 10°€9 or ad Z 
66P° FSP" 286° F08" SG0010° 0€ &6°9 ince 80 °S2 OF 62 GOZO” ¥ 
CSP" O1g" 698" 686" 296110" 66 6L°2 F3'8 29 ¥6 & 001 P6IST” 3 
TFG" ELg" aS a PSP" TF9SIO™ 86 FL°8 G36 BE" 6 P9er TEP06" ¥ 
809° €F9° 92° O19" C6IPIO" 46 c8'6 68 OT Gg OST 8 6ST Ch6ZS" & 
689° GL" 264" 692° PESTO" 96 €0°TT 29°11 68 681 6° 006 E9LCG" o 
992° TIS" 916" 026° 006210" Gs 88 er OLE Ch 68s § 896 08686" [ 
098° 116° col L Co T 00L0c0" ize 061 GL PL 68" LOE c’61& 98FCS*° 0 
996" 60 T PAS ae | re T 1219660" 66 19 GT 6g OT LL 086 0° GOP O8F9s" 00 
80°T cit 868 T F6'T LPESCO™ GG SLT co’ st 16° 6LP 0°80S F96OP" 008 
eS 661 L186 CVG C9F8C0" Ie 69°61 £8 0G 8a" C09 G*0P9 0009F" 0000" 
‘sq'T ‘SqT ‘SQT ‘Ssq'T “yout “Sq'T ‘SsqT ‘sq'T “SqT “youl 
‘ssvig ‘reddog ‘ssuig | ‘aaddop "SSBIg ‘reddog ‘ssuig | ‘aeddop 
‘ON WOeg | ‘osnes) a ‘ON ORY | “osnBxy 
400,44 otenbs "190,q [BouTT 000‘T JO 9ZI§ JO “ON "400, orenbs i *qa0,q [BoUrT COOL JO OZIS JO “ON 
Ja so1vig Jo yysion | Jod o1tM JO JUSIOM sod saqe[g JO JUSIOM | Jed o1lM JO IUcIOM 








(SIBINJOVJNUBUT SUIPBI] JO S91qQ¥B} W014) 
‘asneyH 8 od1B9 FW UMOIG 


"SHEVId GNV HHIM SSVHE GNV HHddOO 40 LHAVIAM 


BOLT COPPER=-SHEET AND BAR BRASS. 203 


WEIGHT OF ROUND BOLT COPPER. 











Per Foot. 

Incbes. | Pounds. Inches. Pounds. Inches. Pounds. 
34 425 1 3.02 154 7.99 
4% 756 1% 3.83 134 9.27 
54 1.18 114 4.72 1% 10.64 
34 1.70 13g 5.72 12.10 
yA 2181 1% 6.81 








WEIGHT OF SHEET AND BAR BRASS, 





Thicicness,} Sheets | Square] Round } peste pe ee Sheets | Square} Round 





Side or per Bars 1] Bars 14. Side or per | Bars 1] Bars 1 
Diam. sq.ft. |ft.long./ft.long.§ Diam. sq.ft. |ft. long.|ft.long. 
Inches. Inches 

1-16 AG .014 2.010 0) BIS1=16 46 .32 4.10 3.29 
1 5.45 056 £045 1% 49.05 4.59 3.61 
3-16 8.17 12: . 100 1 3-16 51.77 5.12 4.02 
14 10 90 227 .178 144 54.50 5.67 4.45 
5-16 13.62 855 20 1 5-16 57.22 6.26 4.91 
3% 16.35 .510 401 13g 59.95 6.86 5.39 
7-16 19.07 695 545 1 7-16 62.67 7.50 5.89 
6 21.80 907 st12 1% 65.40 8.16 6.41 
9-16 24,52 1.15 .902 1 9-16 68.12 8.86 6.95 
5 At .20 1.42 Leeglid 15g 70.85 9.59 7.53 
11-16 29.97 1.72 1.35 1 11-16 73.57 | 10.84 8.12 
34 207 2.04 1.60 13 76.30 | 11.12 8.73 
13-16 35.42 2.40 1.88 1 13-16 79.02 | 11.98 9.36 
% 38.15 2.48 2.18 % aha 12.7 10.01 
15-16 40.87 3.19 %.50 1 15-16 84.47 | 18.63 | 10.7 
43.60 3.63 2.85 87.20 |] 14.52] 11.40 








_— 


COMPOSITION OF VARIOUS GRADES OF ROLLED 
BRASS, ETC. (See also pp. 321-326.) 


ee 





Trade Name. Copper} Zinc. Tin. | Lead. | Nickel. 
Common high! orassai fice. cess 61.5 OE URE [beet raricret er [-ovey'el el css. eaten cota 
Mellow imetalls, fa a4 .<clces std cette 60 CA! OL a eal PRR Be (AE, rg 
Oatride@.Drassem sees scien eacasete 66% SAME ecole claloys'| wc’ are one [ee ates 
GOW DIASS «42.5 010000, 408 sisi sccirioc 80 ON aE ieee |\o'd4oia.c aye |e ceaemeiene 
GIOCE DASSae ress icstecsieccem siesmacee 60 CN) 2) at Ae Ea 116 ynsleseereare 
DEUUEOO oe nate ce weidaeoa ss ameciere 60 AD aren ef cotess <): 1% tO Zi aaeee 
Spring: brass. of-s to .iid. sees em eae 6634 3314 WW6 | Ai sae eee 
18 per cent German silver... ...-. 6144 PULSE “ll CPR aN encase 18 





The above table was furnished by the superintendent of a mill in Connec- 
ticut in 1894. He says: While each mill has its own proportions for various 
mixtures, depending upon the purposes for which the product is intended, 
the figures given are about the average standard. Thus, between car tridge 
brass with 3314 per cent zinc and common high brass with 38144 per cent 
zinc, there are any number of different mixtures known gener ally as ‘‘ high 
brass,”’ or specifically as *‘ spinning brass,’ ‘drawing brass,’’ ete., wherein 
_ the amount of zinc is dependent upon the amount of scrap used in the mix- 
ture, the degree of working to which the metal is to be subjected, etc. 


204 MATERIALS, 





| 


AMERICAN STANDARD SIZES OF DROP-SHOT. 


~ ~ rey 
28 aS 28 

wD ND ‘ oD) 
: © : Co) Diam- © 
Diameter. oa = Diameter. ‘s. eterna r= 
eG ee se 








oo 


Fine Dust.| 3-100” 107844No.-8} Trap Shot] 472 No. 2....} 15-100’ | 86 


DUSb eee 4-100 4565 ** 8} 9-100” 3999 °° 1.. .| 16-100 71 
NOwWAR ee «. 5-100 23268 * 47) Trap Shot] 338 ‘S B...| 17-100 59 
edi leg whew 6-100 13469 ** \7|10-100/ 2914 “* BB.| 18-100 50 
pearl) seh see Trap Shot] 10569 ‘* 6)11-100 2188 ‘‘ BBB) 19-100 42 
sen HA a 7-100/’ 8484 6° -5/12-100 1689 -** “TT. ..|-20=100 36 
or AUR Bas Trap Shot] 6888 ‘* 4/13-100 13828 “ TT..| 21-100 3 
$6) 9. sige |e Sal 00” 5689 ** 3/14-100 1069 ** F.. | 22-100 20 


“ FF..| 23-100 2 


COMPRESSED BUCK-SHOT. 








4 No. of Balls ‘ No. of Balls 
Diameter. 4a.the.lb. Diameter. io ted 
NOG .© leeeeell! 3205100'7 284 No. 00.... <..| 984-100” 115 
Oe ee ...| 27-100 232 $0000 Ses ien'| ee S160: Ge 98 
TSN UN Weg ai te 30-100 173 Balls.........{ 88-100 | 85 
oR Oe eis 32-100 140 Ser nike s 6 44-100 50 








SCREW-THREADS, SELLERS OB U.S. STANDARD. 


In 1864 a committee of the Franklin Institute recommended the adoption 
of the system of screw-threads and bolts which was devised by Mr. William 
Sellers, of Philadelphia. This same system was subsequently adopted as 
the standardiby both the Army and Navy Departments of the United States, 
and by the Master Mechanics’ and Master Car Builders’ Associations, so 
sna it may now be regarded, and in fact is called, the United States Stand- 
ard. 

The rule given by Mr. Sellers for proportioning the thread is as follows: 
Divide the pitch, or, what is the same thing, the side of the thread, into 
eight equal parts; take off one part from the top and fill in one part in ths 
bottom of the thread; then the flat top and bottom will equal one eighth of 
the pitch, the wearing surface will be three quarters of the pitch, and the 
diameter of screw at bottom of the thread will be expressed by the for 


mula 

1,299 
no. threads per inch 
For.a.sharp\V thread with angle of 60° the formula is 
1.733 


no. of threads per inch’ 


The angle of the thread in the Sellers system is 60°. In the Whitworth or 
English system it is 55°, and the point and root of the thread are rounded. 


Screw-Threads, United States Standard. 


diameter of bolt. — 


diameter of bolt — 























SMe ies) b= ARM DN dag) Deki Perel ec | tt ee? 
Sl eed aoe Be | Bd oe 
14 20 A. 10 114 fh 1:15=16] »5 2 '13-16) °3 
516 18 138-16 10 1 5-16 6 2 416 3 a0 
36 16 % 9 f 134 6 fay 414 f 3 314 
4-16 14 15-16 ‘) 1% 6 2 5-16 416 38 5-16 314 
as 8 fig | supe | 4 fo | 8 
9-16 12 1 1-16 iG 134 5 216 4 334 3 

11 § 1% 7 11% 5 fl 23% 4 94 3 





U. 8. OR SELLERS SYSTEM OF SCREW-THREADS. 205 


Screw-Threads, Whitworth (English) Standard. 

































































a a aj a a 
CU Pe aes Pie Gi ae Oe ee me a aoe ae 
A oF A a a a a Ay a a 
Y% 20 5g i1 1 8 134 5 3 314 
S16 | 18 11-16 | 11 114 7 1% 4146 | 344 314 
34 16 34 10 114 “4 2 416 | 314 314 
7-16 | 14 13-16 | 10 134 6 Q14 334 ie 
VA 12 % 9 1% 6 Q16 4 4 3 
9116. -|..12 15-16 | 9 § 154 5 234 314 
U.S. OR SELLERS SYSTEM OF SCREW-THREADS. 
BOLTS AND THREADS. HEX. NUTS AND ‘HEADS. ; 
eeepc eee 8 Bye eee ee ee ee eee eee Gis 
5 re) ° Sai wma 
OA im |Gsl & lor [68 Sic | 8 ea | 2d| oa se 
w |ed|e?| y As sinc) aw | Aa | Sw | seo] 82] 6 
Oo oa om (2) NM = mM 3 —_ Q 3 3 MS = M 
» |SS] -S) 4 [SEVIS S Sl) eo | es nem ot Ol eee ws 
gE jes| 88) Slgeslses| 6a | Se | Fe | sels | 2F 
S 4 | 83 2 oealtas a | 4 te ie oe = 
a = - la 4 
Ins. Ins.| Ins. ‘Ins. | Ins. Ins. | Ins. | Ins. Ins. 
14 {20 185|.0062} .049) .027] 14 "-16\ s%-64) 14 3-16 7-10 
5-16/18 | .240].0074| .077| .045) “19-82] 17-32| 11-16] 5-16] 14 10-12 
8g (16 | .294].0078] .110! .068] 11-16 51-64, 8g | 5-16] 63-64 
“-16]14 | .344/.0089] .150] .093] 25-32] 28-82] 9-10 | 7-16] 3¢ 1 +64 
1% |13 | .400/.0096] .196] .126| % 13-16| 1 6 (-16 | 115-64 
9-16|12 | .454].0104] .249| .162] 31-32] 29-32] 11¢ 9-16] 1% 1 23-64 
b6 rl 507/.0118} .307| .202] 1 1-16|1 17-32 | 5g = V4 
34 {10 | .620|,0125] .442| .302/114 |18-16 | 17-16 | 34 11-16] 1 49-64 
% |9 | .731|.0138} .601| .420] 1 7-16/13¢ 1 21-32] % 13-16] 2 1-32 
1 8 | .837|.0156} 2785] .550/15 19-16 | 1% jt 15-16] 2 19-64 
144 | 7 | .940].0178] .994] .694/1 13-16]1 23-82 [11g |1.1-16 | 29-16 
144 |7 |1.065].0178] 1.227] .§93/2 115-16] 25-16 |114 |1 8-16 | 253-64 
134 | 6 |1.160].0208] 1.485] 1.057/2 3-16 |214 2 17-32/184 |15-16 | 3 3-32 
144 | 6 |1.284/.0208] 1.767] 1.295)284 [25-16 | 234  |116 +‘|1 7-16 | 3 28-64 
15g | 516/1.389].0227| 2.074] 1.515/2°9-16 [2 2°31-32/15g |1 9-16 | 366 
134 | 5 |1.491/.0250] 2.405] 1.746/234 —|2°11-16] 3.3-16 |134 {1 11-16] 357-64 
1% | 5 |1.616|.0250] 2.%61| 2.051/2 15-16]274 3 18-32/1% |1. 13-16] 4 5-32 
Q 446|1.712| .0277| 3.142] 2.302/814  |81-16 | 85g =‘ |2 1 15-16] 4 27-64 
214 | 416/1.962] .0277| 3.976| 3.023/314  |37-16 | 41-16 |214 |23-16 | 4 61-64 
216 2.176| 0312] 4.909| 3.719|3%4 1813-16] 4146 = |216_—s*/..7-16 | _5 31-64 
234 | 4 |2.426/.0312| 5.940] 4.620/414 [43-16 | 429-32)284 |2 11-16] 6 
3 314|2.629| 0357] 7.069| 5.428/454  |49-16 | 584 2 15-16] 6 17-32 
314 | 316/2.879|.0357| 8.296} 6.510 415-16] 5 13-16'314 |3 3-16 | 71-16 
3144 | 314/3.100|.0384| 9.621| 7.548/53g [55-16 | 67-64 |316 |37-16.| 739-64 
334 | 3 |3.317|.0413111.045| 8.641534 (5 11-16] 6 21-32/384 [3 11-16] 81¢ 
4 3 |3.567|.0413/12.566| 9.993161g  |61-16 | 7.3-32 |4 3 15-16] 8 41-64 
414 | 276'3.798] .0435/14.186|11.329/614  |67-16 | 79-18 [414 |43-16.| 938-16 
Ale | 234/4,028|.0454]15.904|12.7431674 6 13-16] 7 31-32\414 |4 7-16 | 934 
434 | 256/4.256| 0476/17. 721 |14,226/714 17 3-16 | 8 13-32.434 4 11-16]1034 
5 21414 .480/ .0500]19.635 |15.763/75¢ 79-16 | 8 27-82'5 4 15-16|10 49-64 
514 | 214/4.730! .0500/21 .648 |17.572/8 7 15-16] 9.9-82 |514 [53-16 |11 28-64 
5l4 | 234/4.953] .0526/23.758 |19.267/884 185-16 | 923-325lg 157-16 |1174 
534 | 236/5.203) .0526/25.967 121.262/834 18 11-16|10 5-82 |534 + |5 11-16]1234 














6 214/5.423) .0555|28 .274 |23.098/91¢ 9 1-16 |10 aad 5 15-16|12 15-16 
( 


LIMIT GAUGES FOR IRON FOR SCREW THREADS, 

In adopting the Sellers, or Franklin Institute, or United States Standard, 
es itis variously called, a difficulty arose from the fact that it is the habit 
ef iron manufacturers to make iron over-size, and as there are no over-size 


506 MATERIALS. 


screws in the Sellers system, if iron is too large it is necessary to cut it away 
with the dies. So great is this difficulty, that the practice of making taps 
and dies over-size has become very general. If the Sellers system is adopted 
it is essential that iron should be obtained of the correct size, or very nearly 
so. Of course no high degree of precision is possible in rolling iron, and 
when exact sizes were demanded, the question arose how much allowable 
variationjthere should be from the true size. It was proposed to make limit- 
gauges for inspecting iron with two openings, one larger and the other 
smaller than the standard size, and then specify that the iron should enter 
the large end and not enter the small one. The following table of dimen- 
sions for the limit-gauges was - commended by the Master Car-Builders’ 
Association and adopted by letter ballot in 1883. 





Size of | Size of . Size of | Size of 
Size of | Large Small | Differ- §@ Size of} Large Small | Differ- 





Tron. End of | End of ence. Tron. End of | End of ence, 
Gauge. | Gauge. Gauge. | Gauge. 
Yin.| 0.2550 0.2450 0.010 3Zin.| 0.63880 0.6170 0.016 
5-16 0.3180 0.307 0.011 34 0.7585 0.7415 0.017 
3% 0.3810 0.3690 0.012 % 0.8840 0.8660 0.018 
%-16 0.4440 0.4310 0.013 | 1.0095 0.9905 0.019 
% 0.5070 0.4930 0.014 1g 1.1350 1.1150 0.020 
9-16 0.5700 0.5550 0.015 144 1.2605 1.2395 0.021 


Caliper gauges with the above dimensions, and standard reference gauges 
for testing them, are made by The Pratt & Whitney Co. 


THE WAXIMOUM VARTATION IN SIZE OF ROUGH 
IRON FOR JU. 8S. STANDARD BOLTS, 


Am. Mach., May 12, 1892. 


By the adoption of the Sellers or U.S. Standard thread taps and dies keep 
their size much longer in use when flatted in accordance with this system 
than when made sharp *' V,”’ though it has been found advisabk in practice 
in most cases to make the taps of somewhat larger outside diameter than 
the nominal size, thus carrying the threads further towards the V-shape 
and giving corresponding clearance to the tops of the threads when in the 
nuts or tapped holes. 

Makers of taps and dies often have calls for taps and dies, U.S. Standard, 
** for rough iron.”’ : 

An examination of rough iron will show that much of it is rolled out of 
round to an amount exceeding the limit of variation in size allowed. 

In view of this it may be desirable to know what the extreme variation int 
iron may be, consistent with the maintenance of U.S. Standard threads, i.e., 
threads which are standard when measured upon the angles, the only place 
where it seems advisable to have them fit closely. Mr. Chas. A. Bauer, the 
general manager of the Warder, Bushnell & Glessner Co., at Springfield, 
Ohio, in 1884 adopted a plan which may be stated as follows: All bolts, 
whether cut from rough or finished stock, are standard size at the bottom 
and at the sides or angles cf the threads, the variation for fit of the nut and 
allowance for wear of taps being made in the machine taps. Nuts are 
punched with holes of such size as to give 85 per cent of a full thread, expe- 
rience showing that the metal of wrought nuts will then crowd into the 
threads of the taps sufficiently to give practically a full thread, while if 
punched smaller some of the metal will be cut out by the tap at the bottom 
of the threads, which is of course undesirable. Machine taps are made 
enough larger than the nominal to bring the tops of the threads up sharp, 
plus the amount allowed for fit and wear of taps. This allows the iron to 
be enough above the nominal diameter to bring the threads up full (sharp) 
at top, while if i+ is small the only effect is to give a flat at top of threads ; 
neither condition affecting the actual size of the thread at the point at whieh 
it is intended to bear. Limit gauges are furnished to the mills, by which the 
iron is rolled, the maximum size being shown in the third column of the 
table. The minimum diameter is not given, the tendency in rolling being 
nearly always to exceed the nominal diameter. 

In making the taps the threaded portion is turned to the size given in the 
eighth column of the table, which gives 6 to 7 thousandths of an inch allow- 
ance for fit ond wear of tap. Just above the threaded portion of the tap a 


SIZES OF SCREW-THREADS‘FOR BOLTS AND TAPS, 207 


place is turned to the size given in the ninth column, these sizes being the 
saine as those of the regular U. 8. Standard bolt, at the bottom of the 
thread, plus the amount allowed for fit and wear of tap ; or, in other words, 
d’ = U.S. Standard d+ (D’— D). Gauges like the one in the cut, Fig. 
72, are furnished for this sizing. In finishing the threads of the tap a tool 





Fig. 72. 
is used which has a removable cutter finished accurately to gauge by grind- 


_ ing, this tool being correct U.S. Standard as to angle, and flat at the point. 


Tt is fed in and the threads chased until the flat point just touches the por- 
tion of the tap which has been turned to size d’. Care having been taken 
with the form of the tool, with its grinding on the top face (a fixture being 


_ provided for this to insure its being ground properly), and also with the set- 


ting of the tool properly in the lathe, the result is that the threads of the tap 
are correctly sized without further attention. 

It is evident that one of the points of advantage of the Sellers system is 
sacrificed. i.e., instead of the taps being flatted at the top of the threads 
they are sharp, and are consequently not so durable as they otherwise would 
be ; but practically this disadvantage is not found to be serious, and is far 


~ overbalanced by the greater ease of getting iron within the prescribed 
limits ; while any rough bolt when reduced in size at the top of the threads, 


by filing or otherwise, will fit a hole tapped with the U.S. Standard hand 


t taps, thus affording proof that the two kinds of bolts or screws made for the 


two different kinds of work are practically interchangeable. By this system 
2” jron can be .005/’ smaller or .0108’” larger than the nominal diameter, or, 


_ in other words, it may have a total variation of .0158’’, while 12’’ iron can be 


.0105’" smaller or .0309’ larger than nominal—a total variation of .0414/”/— 


and within these limits it is found practicable to procure the iron. 


STANDARD SIZES OF SCREW-THREADS FOR BOLTS 


AND TAPS. 
(CHaAas. A. BAUER.) 











al 2 3 4 5 6 i 8 9 10 

20, Aen ae d h Feo pr Tee dl’ H 
Inches. Inches | Inches.| Inches.| Inches. Inches! Inches. Tnches, 

VY 20 .2608 . 1855 .0379 .0062 .006 . 2668 .1915 . 2024 


5-16 | 18 28245 «2403 0421 007 006 .3305 .2463 2589 
3g | 16 3885 2938 0474 0078 006 8945 2998 .81389 
7-16 | 14 -4530 8447 0541 .0089 .006 4590 8507 8670 
ly | 13 .5166 4000 0582 0096 006 -5226 4060 4236 
9-16 | 12 5805 4543 .0631 -0104 007 5875 4613 4802 
56 | 11 6447 5069 .0689 -0114 007 6517 .5139 5846 
Of HelDe 7717 6201 .0758 0125 .007 T7187 6271 .6499 
% 9 -8991 1307 .0842 -0139 007 9061 1307 . 7630 














1 8 | 1.0271 8376 .0947 .0156 .007 1.0841 .5446 .8731 

11g dalmlet OOO .9394 - 1083 .0179 007 1.1629 . 9464 .9789 
—«1%4 7 | 1.2809 | 1.0644 -1083 .0179 .007 1.2879 | 1.0714 | 1.1039 

A = nominal diameter of bolt. = yas 2165 

D = actual diameter of bolt. = : 

d = diameter of bolt at bottom of Pap Y eke Ls die 

thread. Ma 

m = number of threads per inch. h= des yy i a 

f = flat of bottom of thread. 125 
_ h= depth of thread. ie ee 

D' and d’ = diameters of tap. Hey’ 1.288 _ D’ 

H = hole in nut before tapping. Levee q <a S5(2he} 


208 MATERIALS. 


STANDARD SET-SCREWS AND CAP-SCREWS. 


American, Hartford, and Worcester Machine-Serew Companies. 
(Compiled by W. 8. Dix.) 


— 



































(A) (B) (C) (D) (E) | (F) | (G) 
Diameter of Screw....| % 3-16 V4 | 5-16 36 | T=16 Ig 
Threads per Inch..... 40 24 20 18 16 14 12 
Size of Tap Drill*.....| No. 43 }No.30| No.5 17-64 | 21-64}: 3g | 27-64 
(H) (I) (J) (K) (L) | (M) |} (N) 
Diameter of Screw..:.} 9-16 5g 34 % 1 144 114 
Threads per Inch.... 12 11 10 9 8 7 7 
Size of Tap Drill*.... | 31-64 | 17-32) 21-32 49-64 % | 63-64 14 
Set Screws. Hex. Head Cap-serews.| Sq. Head Cap-screws. 
Short} Long Short | Long 
Short | Long | Lengths F : Lengths | 7; ‘ Lengths 
Diam. | Diam. | (under gl ei (ander | Piam.| Diam. (ander 


of Head|of Head) Head). | oaq| Heaa.| Hed) | treaa.| Head! eae). 


ae a es ft eee 


(C) 4| .35 | %to8 | 7-16| .51 | 34 t08 3% | .b3 | %to3 
(D) 5-16, .44 | 34t0 314} % | .58 | 3% to 34) 716] .62 | 34 to 34 





eS et et st Et 
a 
Or 
— 
we 
RSS 
s+ 
° 
Or 
— 
RS 





Round ee. Head Flat Head Cap-screws. Button-head Cap- : 




















screws. 
: Lengths , Lengths : Lengths 
Diam. of Diam. of | ;“<8 Diam, of ore 
(under (including : (under 
Head Head). Head. Head). Head. Head). 
(A) 3-16 34 to 214 14 34 to 184 _-| 7-82 (.225) | 34 to 134 
(B) % 34 to 284 Be 34 to 2 5-16 34 to 2 
(C) 38 | 34to03 15-32 34 to 214 7-16 34 to 214 
(D) ‘7-16 34 to 314 56 34 to 234 9-16 34 to 244 
(E) 9-16 34 to 3144 34 34 to 3 By4 | 34 to 234 
(F) 56 34 to 334 13--16 1to38 4, 34 to 
{G 34 to 4 % 114 to 3 13-16 1 to3 
(H) 13-16 1 to 414 14% to 3 15-16 1144 to3 
(I) % 114 to 416 1g 134 to 3 1 1144 to3 
(J #1 144 to 434 13g 2 tod 134 134 to3 
(K) 11g 34 to 5 
(L) 114 2 tod : 
* Kor cast iron. For Numbers oi tC wireeiL tits or 


Threads are U.S. Standard. Cap-screws are threaded on th tt 9 to and 
including 1’ diam. x 4’’ long, and 44 length above. aves iochsake by 14” 
each regular size between the limits given. Lengths of heads, except flat 
Tepe a hp diam. of screws. 

e angle of the cone of the flat-head screw is 76°, the sides maki i 
of 52° with the top. ts ded 


STANDARD MACHINE SCREWS. 209 


STANDARD MACHINE SCREWS. 


Diam. |Diam. of|Diam. of Lengths. 























No. Setar est trad of of Flat | Round | Filister | ——————_—_—— 
Y- | Head. | Head. | Head. From To 
2 56 .0842 .1631 1544 sidae | o=16 ¥% 
Bi 48 .0973 ~1894 .1786 1545 8-16 py 
4 32, 36, 40 .1105 .2158 .2028 1747 3-16 34 
5 32, 36, 40 1236 2425 | .2270 1985 3-16 % 
6 30, 32 .1368 . 2684 .2512 .2175 3-16 1 
7 30, 32 1500 22947 22754 .2892 4 14% 
8 30, 32 . 1631 .8210 .29386 | .2610 | 14 114 
9 24, 30, 32 1763 3474 -0208 .2805 14 13% 
10 24, 30, 32 .1894 .3737 .3480 .8035 4 1% 
12 20, 24 -2158 | .4263 3922 .3445 34 134 
14 20, 24 2421 .4790 .4364 8885 | 86 2 
16 16, 18, 20 2684 .5316 4866 .4300 | 3% 214 
18 16, 18 .2947 5842 .5248 .4710 VA 216 
20 16, 18 8210 .6368 -56690 |} .5200 ly 234 
22 16, 18 .8474 .6894 .6106 .5557 4% 3 
24 ood ge poh as <olot . 7420 6522 . 6005 % 3 
26 14, 16 .4000 | .7420 .6938 .6425 34 3 
28 14, 16 .4263 . 7946 «(854 .6920 % 3 
30 14, 16 -4520 8473 7770 7240 i 3 





ti a vary by 16ths from 3-16 to 14, by 8ths from 1% to 1%, by 4ths from 

to 3 

SIZES AND WEIGHTS OF Faceted AND 
HEXAGONAL NUT 


United States Standard Sizes. cnediaeeoda and trimmed, 
Punched to suit U. S. Standard Taps. 



































s a $ a 3 
2 3 wn dui Square. Hexagon. 
a) ? . 8) 
a a ae ga Cel ee “a So = 
© : FI ¢ ers 80 54 ‘vied gS 2 =“ >i ae 
; a ae a A ak Sw o2 du ¢2 
| a= 3) q 0 oe ay = ty 
SEP eee te ee 5 a BS hs gy Sa 
a E = la 4 Ps E Z, Ee 
VY % 14 13-64 1116 9-16} 7270 .0138 | 7615 0131 
5-16 19-82} 5-16) 4 138-16 11-16) _ 4700 .0231 | 5200 0192 
36 11-16) 3% 19-64 13-16) 2350 .0426 | 3000 0333 
7-16 | 25-82} 7-16] 11-32] 114 % 1630 .0613 | 2000 | .050 
% % 4% 25-64) 114 i 1120 .0893 | 1430 07 
9-16 | 31-32! 9-16] 29-64] 13g 1% 890 1124 | 1100 | .091 
Beal d 1 16h 166, me Ral te 114 640 156 | 740 | 2135 
8, | 1% 34 | 39-64] 134 1 7-16] 380 263 | 450 | .222 
% 1 7-16) *% 47-64) 2 1-16] 111-16 280 6057 309 824 
1 15 1 58-64] 2 5-16| 1% 170 .588 216 463 
1g {1 13-16) 1% 59-64) 2 9-16! 2 1-16 130 769 148 676 
14 2 1144 ~-|1 1-16} 2 18-16) 2 5-16 96 1.04 Ace 901 
134 | 23-16] 13g |1 5-32] 314 Qe ql 1.43 85 | 1.18 
144 | 23 144 |1 9-32) 384 2 58 1.7 68 | 1.47 
15¢ 2 9-16} 15g |1 13-82) 354 2 15-16 44 2280 56 1.79 
134 | 234 | 134. |1% 3% 3 3-16) 34 | 2.94 40 | 2.50 
1% |2 15-16|'1%% |154 4 38% 30 | 3.33 87 1 24 
1 2 1 23-382) 4 716} 35g 23 4.35 29 3.45 
214 846 214 |1 15-16) 4 15-16} 4 1-16 19 5.26 21 4.7 
24 | 3% | 214 [2 3-16] 51% 46 12 | 8.33 15 | 6.67 
234 4h, 234 |2 7-16) 6 4 15-16 9 Lint r FE- | 9.09 
454 |3 (286 | 6% | 5 5-16 | 13.64 814|11.76 











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TRACK BOLTS. 
With United States Standard Hexagon Nuts, 


~ 


oO feinae Kor 
. . . . ° . . . . . . . . ° 
19101010 MOND eD EVCrORCe 


Kegs per Mile. 


| 


No. in Ke 
200 Ibs. 




















45 to 85 lbs 


RIVETS—TURN BUCKLES, Bit 


CONE-HEAD BOILER RIVETS, WEIGHT PER 100.: 
(Hoopes & Townsend.) 





Diam. in.) 1/2 | 96 | 5/8 |11/16| 94 | 18/16) 9 | 1 | 136% | 134" 


———$—$<—<— |§ — ——————§|_— ——— | — | | | | | | 


Length. | lbs. | Ibs. | lbs. | Ibs. | ibs. | lbs. | Ibs. | Ibs. | Ibs. | Ibs. 
34 inch 8.75| 13.7 | 16. 
6s 9. 











% 35] 14.4 | 17.22 
te 10.00] 15.2 | 18.25] 21.70] 26.55 
11g 10.70| 16.0 | 19.28] 23.10] 28.00 
144“ 11.40] 16.8 | 20.31] 24.50] 29.45] 387.0] 461 60 
184 .¢ 12.10] 17.6 | 21.34] 25.90) 30.90] 38.6) 48] 63] 95 
tices 12.80| 18.4 | 22.37] 27.30] 82.35) 40.21 50] 65] 98] 133 
15g * 13.50] 19.2 | 23.40] 28.70] 33.80] 41.9] 52] 67] 101] 187 
134“ 14.20] 20.0 | 24.43] 30.10] 85.25] 43.5, 54] 69] 104] 141 
1%“ 14.90] 20.8 | 25.46] 31.50] 36.70] 45.21 56] v1] 107 | 145 
“ 15.60] 21.6 | 26.49] 82.90] 38.15] 47.0} 58| 74] 110] 149 
14 16.30] 22.4 | 27.52] 34.80] 39.60) 48.71 60] 7] 114] 153 
Wg « 17.00} 23.2 | 28.55] 85.70] 41.05] 50.3] 62] 80] 118] 157 
284 ¢ 17.70| 24.0 | 29.58) 37.10] 42.50] 51.9] 64] 83] 121] 161 
ean 18.40] 24.8 | 30.61] 38.50] 43.95] 53.5 66] 86] 124] 165 
25g « 19.10] 25.6 | 31.64] 39.90] 45.40) 55.11 68] 89] 127]. 169 
234. + 19.80] 26.4 | 32.67| 41.30] 46.85] 56.8} 70] 92] 130] 178 
ies 20.50] 27.2 | 83.70 42.70] 48.30] 58.41 72] 95] 133] 177 
“ 21.20] 28.0 | 34.73] 44.10] 49.75] 60.0) 74 | 98] 137] 181 
Bigiis 22.60] 29.7 | 36.79} 46.90] 52.65} 63.3] 78 | 103 | 144 | 189 
She 24.00] 31.5 | 38.85).49.70] 55.55] 66.5 82] 108| 151] 197 
334“ 25.40] 83.3 | 40.91] 52.50] 58.45} 69.8) 86] 113] 158 | 205 
ss 26.80] 35.2 | 42.97| 55.30] 61.35} 73.0] 90] 118] 165] 213 
444“ 28.20| 36.9 | 45.03} 58.10] 64.25] 76.3] 94] 124] 172] 921 
4g 29.60] 38.6 | 47.09] 60.90] 67.15} 79.5] 98 | 130] 179} 929 
434“ 31.00] 40.3 | 49.15] 63.70] 70.05) 82.8] 102] 136 | 186 237 
32.40] 42.0 | 51.21] 66.50] 72.95] 86.0} 106 | 142] 193] 245 
Big“ 33.80] 43.7 | 53.27] 69.20] 75.85} 89.3] 110] 148] 200 | 954 
oe 35.20| 45.4 | 55.33] 72.00] 78.75] 92.5] 114] 154] 206] 263 
534‘ 36.60| 47.1 | 57.39] 74.80! 81.65] 95.7] 118] 160] 212] 272 
pe 38.00| 48.8 | 59.45] 77.60] 84.55] 99.0] 122] 166] 218] 281 
64“ 40.80] 52.0 | 63.57] 83.30] 90.35! 105.5] 130] 177 | 231] 297 
ime! 43.60] 55.2 | 67.69] 88.90] 96.15] 112.0] 138] 188| 245] 3814 
Heads...... 5.50| 8.40] 11.50] 13.20] 18.00] 23.0} 29.0 | 38.0 | 56.0 | 77.5 


a 


* These two sizes are calculated for exact diameter. 
Rivets with button heads weigh approximately the same as cone-head 
rivets. 
TURNBUCK LES. 
(Cleveland City Forge and Iron Co.) 
Standard sizes made with right and left threads. D = outside diameter 














of screw. 4A = length in clear between heads = 6 ins. for all sizes, B= 
length of tapped heads = 144D nearly. C= 6ins. + 3D nearly. 


212 MATERIALS, 


SIZES OF WASHERS. 








Thickness, 











Diameter in |Size of Hole, in| pienin Bolt in A 
qekere , ? gham : No. in 100 Ibs, 
inches. inches. Wire-gauge. inches, 
5-16 No. 16 4 29,300 
4, 3 £16 5-16 18,000 
¢-16 6 14 34 4,600 
1% 9-16 apa 4% 8,300 
114 56 eri? 9-16 2,180 
1% 11-16 11 5% 2,350 
134 13-16 ee | 34 1,680 
2 31-82 “* 10 % 1,140 
214 14% && 58 1 580 
234 14 * 8 144 470 
3 13% an § 14 860 
3 114 “ 6 196 360 








TRACK SPIKES, 





4 Kegs per Mile 
Rails used. Spikes. Number in Keg, Ties 24in. 








200 Ibs. between Centres, 
45 to 85 516 x 9-16 880 80 
' 40 ** 52 5 x9-16 400 27 
B5.'* 40 5 xk * 490 22 
24.5 85 416 x16 550 20 
24 -** 30 416 x 7-16 925. 15 
pe | Soa? | a F 
5 x3% 

14.“ 16 ph 1350 8 
8. 12 W146 x36 1550 f 
8 ‘10 216 x 5-16 220 5 








STREET RAILWAY SPIKES. 











: ; ; Kegs per Mile, Ties 24 in. 
Spikes. Number in Keg, 200 Ibs. belwoenlGcntrea 
516 x 9-16 400 30 
5 xl 545 19 
416 x 7-16 800 13 


ee 


BOAT SPIKES. 
Number in Keg of 200 Ibs. 











Length. 1% 5-16 | 34 % 
4 ineh. 9375 e@eeeeeerssreooeese eeeeeoeer ce ee eeoe e@eeeeeeoeveseo 
Dar. 2050 1230 940 sine e aioteereneee os 
a 1825 1175 800 450 
7 hy | eee. 990 650 375 
Ses BORO oco SO0U Gen 880 600 335 
Oe es sree seeePttatre sist | sceslasiees ¢ cles 525 800 
10 Ad eeoeoee e@eeee@ae+eeor ee eer eeGeeceerees 4% 275 


SPIKES; CUT NAILS. 213 


WROUGHT SPIKES, 
Number of Nails in Keg of 150 Pounds. 























Size. 4 in. 5-16 in. 34 in. 7-16 in. 4 in. 
3 inches...... 2950 eeeee e@eerecrieeoeeeeee 288 ee ed ee ee ee ed 
314 ° eereece 1890 1208 eeeeeeSeeeer] eeSs Gee COSC eeeG esses oees 
4 . e@eeeee 1650 1135 seer eeeer+e- eeeeCeeevese e@eeeneees oer. 
414 oe @eeeee 1464 1064 e@eeeeeer eager ee@. ©00@@>@6@88 s@eeeeee vate. 
5 Sed a ais setek 1380 930 742 SBR OOSO NOs 002 Gu0 moe 
6 te ees 1292 868 570 OOOO GOOOIO) (COOUGOOG rs L 
e 7a Cease 1161 662 482 445 306 
8 ot TO onal nice: POngerEe 635 455 384 256 
OMe et lawse ct beveeets rete 573 424 300 240 
10 = ee @@e> #@e@eeeeeeeeer eeeeteseoreee: 391 270 222 
11 Wo @eree eeee Sete eeeetceeeceeee eoeeos *eOreet@ered 249 203 
12 C eeeoeesr eeeeeeeeoeeeoe @eeervreeeSeeeeoiecees eee sanoes 236 180 





WIRE SPIKES. 








Approx. Size/Ap. No. Approx. Size/Ap. No, 











Size. of Wire Nails.| in 1 Ib. Size. of Wire Nails.| ind Ib: 
10d Spike.... .|3 in. No.7 50 60d Spike...... 6 in. No.1 10 
Tene ete | Bid gL gee ela in Pa ekh Bigatti Soy 9 
Sie? A ene FW ES TN ea OE PA ae BE RB) 2 
Sider $25 2c Aig TA geen On! ign sees tee ee nee Sn OU LenS 
AUR ae Spree, ie Stee 155s flo oie aes 0 0 echt deat.6) Bile 6 
BO Sod. eh DiS SS. #8 Ot 19 





LENGTH AND NUMBER OF CUT NAILS TO THE 








POUND. 

‘ &p D n 
ee B ce cae 
Size. to Fach rede, be Se. bt Se z 5 = @ | a 
af Se StSe ee here fe te |S 
| OeOrl ey tome henner chm. |e} & 
et tae ete fe LN vy: Dctelane oes pricier BOOM Mtr odes occ. ee le Mee aloes 
RPS DS W025 ll a A i 
800 -.| 1100 | 1000 HME Fetes o's, figis aieie's- ee axe ol ttetere 
480 720 %60 D2 eee ie eater Poa see 
288 . 523 368 180 BIB! [ete creer lhe Rare ore 

200 410 earns live 130 

168 } 95 | 84 DOG eects eee ote 224 126 96 

124°| 94 | 64 f 18B)oc..c tle. 98 | 82 

88 | 62 | 48 W496) | Ses cS. le fed 128 "5 68 
f 53 | 36 SOM Rictett Ueare " 110 6D). [eds o's [ie come 
58 | 46 | 380 102 Ske See oes 91 Dt fe seer. 28 
44} 42}24¢] 6]..... ae CB he | ao eae 
384 | 38 | 20 G24 lyrce calles wes 54 PY Goal be airae Q2 
23 | 33 | 16 OA oe oe ar 40 lessee eee [1446 
18 | 20 Me Miseres\eor. ..| 83 |.cckesfodeeeiene 
1G NRO CA orc pclecac..| 28 becass ELD 98g 
10 eersefoecefoceeces|seoesesiecseee |seesteoei|oesoerievers 8 





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MATERIALS. 


214 





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APPROXIMATE NUMBER OF WIRE NAILS PER POUND. 215 








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x16 MATERIALS, 


SIZE, WEIGHT, LENGTH, AND STRENGTH OF IRON 
WIRE, 


(Trenton Iron Co.) 











Bihar Tensile ee can 
‘ proximate) of Charcoa 
No. by | in Deci- aren Ce Feet to | Weight of | Iron Wire in Pounds. 











Wire |mals of he One Mile 
Gauge. | One pedinae ei fl Pound, | in pounds, eM HMR ON Taal Re. 
Inch F 
Ai 8 Bright. | Annealed, 
———————|- | FS 
00000 | .450 15904 1.863 | 2833.248 12598 9449 
0000 =| .400 ~ 12566 2.358 | 2238.878 9955 7466 
008 .360 10179 «|= 2.911 | 1818.574 8124 6091 
00 .330 . 08553 8.465 | 1523.861 6880 5160 
0 805 .07306 4.057 | 1301.678 5926 4445 
1 »285 -06379 4.645 | 1136.678 5226 3920 
2 265 £05515 5.874 | 982.555 4570 342 
3 «245 .04714 6.286 | 839.942 3948 2960 
4 225 | .038976 | 7.454 | 708.365 3374 2530 
5 205 .03301 8.976 | 588.139 2839 2130 
6 .190 02835 10.453 | 505.084 247 1860 
v4 1% .02405 12.322 | 428.472 2136 1600 
8 .160 .02011 14.736 | 358.3008 1813 1360 
9 2145 .01651 | 17.950 | 294.1488 1507 =| ~~ 1180 
10 .130 .01327 22.333 | 236.4384 12383 925 
11 1175 | .01084 27.340 | 193.1424 1010 758 
12 105 -00866 84.219} 154.2816 | - 810 607 
13 .0925 | .00672 | 44.092} 119.7504 631 473 
14 .080 .00503 58.916 | 89.6016 414 356 
15 .070 .00385 76.984 | 68.5872 S7at 280 
16 .061 00292 | 101.488} 52.0080 902. | 326 
17 0525 | .00216 137.174 | 38.4912 222 165 
18 045 | .00159 | 186.3385 | 28.3378 169 127 
19 040 | 0012566 | 235.084 | 22.3872 137 103 
20 .035 | .0009621 | 308.079 | 17.1389 107 80 
21 .031 0007547 | 392.772 | 13.4429 
22 .028 .0006157 | 481.234 10.9718 Boze © 
23 025 0004909 | 603.863 8.7437 Peas ct 
24 0225 | .0003976 | 745.710 7.0805 oP ou OF: 
25 -020 .0003142 | 943.396 5.5968 wet ossak & 
26 .018 | 0002545 | 1164.689 4.5334 orss 8 8B 8 
27 017 | = =.0002270 | 1305.670 4.0439 Bond Se8aah 
28 .016 0002011 | 1476.869 3.5819 BULoR ass F 
29 015 | .0001767 | 1676.989 | 3.1485 PERRO RaAG 
30 O14 .00015389 | 1925. 321 2.7424 ag Efsaaen & 
31 013 .0001327 | 2232.653 2.3649 naa aneRS a 
32 012 | 0001131 | 2620.607 } 2.0148 eS oes akon S 
33 Olt 0000950 | 8119.092 1.6928 poten enme | & 
34 .010 00007854 | 3773.584 1.3992 aoteoaese s 
35 .0095 | .00007088 | 4182.508 1.2624 oPSaes555 wy 
36 .009 00006362 | 4657.728 1.1336 SaHlG aero & 
37 .0085 | 00005675 | 5222.035 1.0111 Beau haasd & 
38 .008 .00005027 | 5896.147 .89549 oSSSSszeZ 
39 0075 | .00004418 } 6724.291 - 78672 Sf okesesce 
007 00003848 | 7698.253 . 68587 chap a 





f TESTS OF TELEGRAPH WIRE. 217 


' GALVANIZED IRON WIRE FOR TELEGRAPH AND 
TELEPHONE LINES, 


(Trenton Iron Co.) 

WEIGHT PER MILE-OHN.—This term is to be understood as distinguishing 
the resistance of material only, and means the weight of such material re- 
quired per mile to give the resistance of one ohm. To ascertain the mileage 
resistance of any wire, divide the ‘‘ weight per mile-ohm "’ by the weight of 
the wire per mile. Thus in a grade of Extra Best Best, of which the weight 

er mile-ohm is 5000, the mileage resistance of No. 6(weight per mile 525 

bs.) would be about 9144 ohms; and No. 14 steel wire, 6500 lbs. weight per 
mile-ohm (95 lbs. weight per mile), would show about 69 ohms, 


Sizes of Wire used in Telegraph and Telephone Lines, 


No. 4. Has not been much used until recently; is now used on important 
lines where the multiplex systems are applied. 

No. 5. Little used in the United States. 

No. 6. Used for important circuits between cities, 

No. 8. Medium size for circuits of 400 miles or less. 

No. 9. For similar locations to No. 8, but on somewhat shorter circuits ¢ 
until lately was the size most largely used in this country. 

Nos. 10, 11. For shorter circuits, railway telegraphs, private lines, police 
and fire-alarm lines, etc. 

No. 12. For telephone lines, police and fire-alarm lines, etc. 

Nos, 138, 14. For telephone lines and short private lines: steel wire is used 
most generally in these sizes, 

The coating of telegraph wire with zine as a protection against oxidation 
is now generally admitted to be the most efficacious method. 

The grades of line wire are generally known to the trade as ‘‘ Extra Best 
Best ’’ (E. B. B.), ‘* Best Best ’’ (B. B.), and ‘‘ Steel.” 

“ Hxtra Best Best” is made of the very best iron, as nearly pure as any 
commercial iron, soft, tough, uniform, and of very high conductivity, its 
weight per mile-ohm being about 5000 lbs. 

‘The ‘* Best Best” is of iron, showing in mechanical tests almost as good 
results as the E. B. B., but not quite as soft, and being somewhat lower in 
eonductivity; weight per mile-ohm about 5700 lbs. 

The Trenton ‘‘ Steel”? wire is well suited for telephone or short telegraph 
lines, and the weight per mile-ohm is about 6500 lbs. 

The following are (approximately) the weights per mile of various sizes of 
galvanized telegraph wire, drawn by Trenton Iron Co.’s gauge: 

No. 4, 5, 6, 7, 8, 9, AO. else es ae eee dS, bk, 


Lbs. 720, 610, 525, 450, 375, 310, 250, 200, 160, 125, 95. 


TESTS OF TELEGRAPH WIRE. 
The following data are taken from a table given by Mr. Prescott relating 
to tests of E. B. B. galvanized wire furnished the Western Union Telegraph 
Co.: 





; “| . Resistance. | Ratio of 
: Diam. Weight. Length. ee ae ll tyatet 
Size : Temp. %5.8° Fahr. || Breaking 
f Parts of Feet | Weight to 


Wire. a Grains, | Pounds LS Feet Ohms | Weight 
per foot.|per mile. per ohm.| per mile, per mile, 





4 £238 1043.2 886.6 6.00 958. 5.51 

5 | ~ 220 891.3 | 673.0 7 85 (27 7 26 | 

6 203 758.9 572.2 9.20 618 8.54 || 3.05 
if .180 596.7 449.9 11-70 578 10.86 | 3.40 
8 165 501.4 378.1 14.00 409 12.92 3.07 
9 148 403.4 1 804.2 17.4 328 16.10 3.38 
10 .134 330.7 249.4 91.2 269 19.60 8.37 
11 .120 265.2 ¢ 200.0 26.4 216 24.42 2.97 
12 .109 218.8 165.0 32.0 179 29 60 3.43 
14 .083 126.9 95.7 55.2 104 51.00 8.05 


JOINTS IN TELEGRAPH WIRES.—The fewer the joints in a line the better. 
All joints should be carefully made and well soldered over, for a bad joint 
may cause as much resistance to the electric current as several miles of 
wire. 


MATERIALS, 


218 


—————————— ee eee 






































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HARD-DRAWN COPPER WIRE} INSULATED WIRE. 221 


HARD-DRAWN COPPER TELEGRAPH WIRE, 
(J. A. Roebling’s Sons Co.) 
Furnished in half-mile coils, either bare or insulated. 





Approximate 
Size, B. & S. rar in Breaking Weight Sizeot ti B. 
m : = ron Wire 

Gauge. per Mile. Strength. per Mile. equal to 
Copper 
9 4.30 625 209 Fen 
10 5.40 525 166 3 = 
11 6.90 420 131 ge ts 
12 8.70 330 104 eS 
13 10.90 270 83 6146 
14 13.70 213 66 8° oS 
15 17.40 170 52 9 ®& 
16 22.10 180 41 10 & 
oO 


‘In handling this wire the greatest ¢éare should be observed to avoid kinks, 
bends, scratches, or cuts. Joints should be made only with McIntire Con- 
nectors. 

On account of its conductivity being about five times that of Ex. B. B. 
Iron Wire, and its breaking strength over three times its weight per mile, 
copper may be used of which the section is smaller and the weight less than 
a Ae aay iron wire, allowing a greater number of wires to be strung on 
the poles. 

Besides this advantage, the reduction of section materially decreases the 
eléctrostatic capacity, while its non-magnetic character lessens the self-in- 
duction of the line, both of which features tend to increase the possible 
speed of signalling in telegraphing, and to give greater clearness of enunci- 
ation over telephone lines, especially those of great length. 


ENSULATED COPPER WIRE, WEATHERPROOF 


























INSULATION. 
' Double Braid. Triple Braid. ; 
oa. Beat Scores. Approximate 
Num- j Weights, 
bers, |Outside Weights, Outside Weights, Pounds. 
B. & S.| Diame- Pounds. Diame- Pounds. 
Gauge.| ters in ; ee 
82ds f 32ds ( 
Inch. eet: Mile. | Inch. aoee Mile. Reel. Coil. 
0000 20 716 781 24 v7 4092 2000 250 
000 18 lay 8036 22 680 3826 2000 250 
00 17 465 | 2455 18 490 | 2587 500 250 
Q 16 875 1980 17 400 2112 500 250 
1 15 285 1505 16 306 1616 5u0 250 
2 14 245 1294 15 268 1415 500 250 
3 13 190 1003 14 210 1109 500 250 
4 11 152 803 12 164 866 250 125 
5 10 120 634 11 145 766 260 130 
6 9 98 518 10 1k 591 275 140 
8 8 66 349 9 78 412 200 100 
10 7 45 238 8 55 290 200 100 
12 6 30 158 7 35 185 Bay 25 
14 5 20 106 6 26 137 25 
16 4 14 74 5 2 106 : 25 


—= 


Pap ie MATERIALS 


Power Cables. Lead Incased, Jute or Paper Insulated, 


(John A. Roebling’s Sons Co.) 





Outside} Weights, Outside| Weights, 









































Nos,. | Circular : Nos. Circular : 

4 : Diam. {1000 feet. ) vi Diam. |1000 feet, 
B.&5.G.|  Mils. Inches. | Pounds. B.&8.G.| Mils. Inches. | Pounds. 
BGA ad 1000000 1 138/16 6685 sielainstantels 600000 114 3060 
racic ROC 900000 1 23/32 6228) By eee os Sein 20000 1 3/16 2732 
Ste sii ieleie's 800000 1 21/32 5713 0000 211600 1 3/32 2533 
head 750000 § 154 5543 000 |} 168100 | 1 1/16 2300 
mierots wae ss0y 700000 1 19/32 5315 00 133225 1 2021 
Rafe ate 650000 1 9/16 5088 0 105625 15/16 W723 
etelenia ota d 600000 1 17/32 4857 1 83521 29/32 1633 
AARC 550000 ‘ 4630 2 66564 % 1482 
Biers Caecayetas 500000 1 7/16 4278 3 52441 20/32 1360 
Ae yee oF 450000 134 3923 4 41616 34 1251 
mises Gere ete © 400000 | 1 11/82 8619 6 26244 11/16 1046 
@COveecrces 350000 1 5/16 3416 4 

Stranded Weather-proof Keed Wire. 
3a E 
Weights. | oS ‘Weights. |o@ 
pac Pounds. |g rhea Pounds. |@& 
Circular Di er £8 @ Circular Di np BS 
Mils. mc Mils. ride Kg 
Inches. Oo. Ys Inches, Oo: 
4000 | mite. | 2 1000 | mile. | 5.48 
ry 2, ®o e 
ie a fy 
1000000 8550 | 18744! 800 550000 1 3/16 | 2043 | 10787] 1200 
900000 1 13/32| 38215 | 16975, 800 500000 14% 1875 9900| 1320 
§00000 1 11/32) 2880 | 15206) 850 450000 1 3/82 | 1703 8992) 1400 
750000 1 5/16 | 2713 | 14325) 850 400000 1 1/16 | 1530 8078} 1450 
700000 1 9/82 | 2545 | 13438} 900 350000 1 1358 7170) J50C - 
650000 ye 23878 | 12556) 900 800000 15/16, 1185 6257} 1600 
600000 1. 7/82 | 2210 | 11668] 1000 250000 29/82) 1012 5843} 1600 


The table is calculated for concentric strands. MRope-laid strands are 


larger. 

Approximate Rules for the Resistance of Copper Wire, 
—The resistance of any One ae at 20° C. or 68° F’., according to Mat- 
100 
a2 
national ohms, / the length of the wire in feet, and d its diameter in mils. 

41 mil = 1/1000 inch.) 

A No. 10 Wire, A.W.G., .1019 in. diameter (practically 0.1 in.), 1000 ft. in 
length, has a resistance of 1 ohm at 68° F. and weighs 31.4 lbs. 

If a wire of a given length and size by the American or Brown & Sharpe 
gauge has a certain resistance, a wire of the same jength and three numbers 
higher has twice the resistance, six numbers higher four times the resist- 
ance, etc. 


thiessen’s standard, is R = , in which F# is the resistance in inter- 


Wire gauge, A.W.G. No..... O00) (1. | apa 10, 13, Peles 19 22 
Relative resistance.......-.. oe eLODn AG.) 4 ene 1 “1/25q174. 1/8 24/16 
og section or weight.. 1/16 1/8 1/4 1/2 1 “gee 4 8 16 


Approximate rules for resistance at any temperature: 


9.6(1 + .0040)2 
R, = Ro(t + .004); be oo ey 


Ro = resistance at 0°, R, = resistance at the temperature 7° C., 1 = length 
in feet, d = diameter in mils. (See Copper Wire Table, p. 1034,) 


i; 


STEEL WIRE CABLES, 295 


GALVANIZED STEEL-WIRE STEAND. 
For Smokestack Guys, Signal Strand, ete. 
(J. A. Roebling’s Sons Co.) 
This strand is composed of 7 wires, twisted together into a single strand. 


——— 











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15/32} 48 | 7.500 8 17/64| 15 2950 f 9/64 | 314 525 
7/16 37 6,000 4 11% 1,750 7 2% one 
3 30 4,700 4/32 834 1.300 3/32 2 820 


8 5 
5/16 21 3,300 # 38/16 | 644 | 1,000 








For special purposes these strands can be made of 50 to 100 per cent 
greater tensile strength. When used to run over sheaves or pulleys the use 
of soft-iron stock is advisable. 


FLEXIBLE STEEL-WIRE CABLES FOR VESSELS, 
(Trenton Iron Co., 1886.) 


With numerous disadvantages, the system of working ships’ anchors with 
chain cables is stillin vogue. A heavy chain cable contributes to the hold- 
ing-power of the anchor, and the facility of increasing that resistance by 
paying out the cable is prized as an advantage. The requisite holding- 
power is obtained, however, by the combined action of a comparatively 
light anchor and a correspondingly great mass of chain of little service in 
proportion to its weight or to the weight of the anchor. If the weight and 
size of the anchor were increased so as to give the greatest holding-power 
required, and it were attached by means of a light wire cable, the combined 
weight of the cable and anchor would be much less than the total weight of 
the chain and anchor, and the facility of handling would be much greater. 
English shipbuilders have taken the initiative in this direction, and many of 
the largest and most serviceable vessels afloat are fitted with steel-wire 
cables. They have given complete satisfaction. 

The Trenton Iron Co.’s cables are made of crucible cast-steel wire, and 
guaranteed to fulfil Lloyd’s requirements. They are composed of 72 wires 
subdivided into six strands of twelve wires each. In order to obtain great 
flexibility, hempen centres are introduced in the strands as well as in the 
completed cable. 


FLEXIBLE STEEL-WIBRE HAWSERS, 


These hawsers are extensively used, They are made with six strands of 
twelve wires each, hemp centres being inserted in the individual strands as 
well asin the completed rope. The material employed is crucible cast steel, 
galvanized, and guaranteed to fulfil Lloyd’s requirements. They are only 
one third the weight of hempen hawsers; and are sufficiently pliable to work 
round any bitts to which hempen rope of equivalent strength can be applied. 

13-inch tarred Russian hemp hawser weighs about 39 lbs. per fathom, 

10-inch white manila hawser weighs about 20 lbs. per fathom. 

114g-inch stud chain weighs about 68 lbs. per fathom. 

4-inch galvanized steel hawser weighs about 12 lbs. per fathom. 

Each of the above named has about the same tensile strength, 


224 MATERIALS, 


SPECIFICATIONS FOR GALVANIZED IRON WIRE. 
Issued by the British Postal Telegraph Authorities, 


Tests for Strength and 


Weight per Mile, Diameter. Ductility 








3 


Weight. 
No. of Twists 


Allowed. Allowed. 


. of Twists 


.in 6in 
in 6 in. 

For Breaking Weight not 
in 6 in. 


For Breaking Weight not 
of the Standard 


o. of Twists 
Size at 60° Fahr. 
Constant, being Standard 
Weight X Resistance. 


Breaking 
Resistance per Mile 














Required Standard. 
Required Standard. 
less than— 
less than— 


Maximum. 
Minimum, 
Minimum. | No 
Minimum. | N 
Maximum. 





——o 
— |—————_—_—_—_——- | | | — | —_—__ | ———__ ] —__ |] ————} | — 


Ibs. | Ibs. | Ibs. | mils. | mils. | mils. | Ibs. lbs. lbs. ohms. 


300 | 767 | 833 242 | 237 | 247 |2480) 15 }2550) 14 | 2620) 18 | 6.75 |5400 
600 | 571 | 629 209 | 204 | 214 |1860) 17 |1910) 16 | 1960} 15 | 9.00 |5400 
450 | 424 | 477 181 } 176} 186 /1390) 19 |1425) 18 | 1460) 17 | 12.00 |5400 
400 | 377 | 424 171 { 166 | 176 {1240} 21 |1270) 20 | 1300) 19 | 18.50 |5400 
200 | 190 | 213 121 | 118 | 125 | 620) 30 | 638) 28 | 655) 26 | 27.00 | 5400 





STRENGTH OF PIANO-WIRE. 


The average strength of English piano-wire is given as follows by Web 
ster, Horsfals & Lean: 





Numbers | Equivalents} Ultimate { Numbers | Equivalents} Ultimate. 





in Music- |in Fractions} Tensile in Music- Jin Fractions} Tensile 
wire of Inches in|} Strength in wire of inches in | Strength in 

Gauge. Diameters. Pounds, Gauge. Diameters. Pounds. 

12 029 225 18 0041 395 

13 .031 250 19 043 425 

14 + °3028 285 20 .045 500 

15 035 3805 21 047 540 

16 037 840 22 2052 650 

17 -039 360 








These strengths range from 300,000 to 340,000 lbs. per sq. in. The compo- 
sition of this wire is as follows: Carbon, 0.570; silicon, 0.090; sulphur, 0.011; 
phosphorus, 0.018; manganese, 0.425. 


‘“ PLOUGH”-STEEL WIRE. 


The term “plough,” given in England to steel wire of high quality, was 
derived from the fact that such wire is used for the construction of ropes 
used for ploughing purposes. It is to be hoped that the term will not be 
used in this country, as it tends to confusion of terms. Plough-steel is 
known here in some steel-works as the quality of plate steel used for the 
mould-boards of ploughs, for which a very ordinary grade is good enough. 

Experiments by Dr. Percy on the English plough-steel (so-called) gave the 
following results: Specific gravity, 7.814; carbon, 0.828 per cent; manga- 
nese, 0.587 per cent; silicon, 0.143 per cent; sulphur, 0.009 per cent; phos 
phorus, nil; copper, 0.030 per cent. No traces of chromium, titanium, or 
tungsten were found. The breaking strains of the wire were as follows: 


Diameter, inch............ 093 + 132 2159 191 
Pounds per sq. inch........ 344,960 257,600 224,000 201,600 


The elongation was only from 0.75 to 1.1 per cent. 


SPECIFICATIONS FOR HARD-DRAWN COPPER WIRE. 225 


WIRES OF DIFFERENT METALS AND ALLOYS. 
(J. Bucknall Smith’s Treatise on Wire.) 


Brass Wire is commonly composed of an alloy of 13/4 to 2 parts of 
copper tol part of zinc. The tensile strength ranges from 20 to 40 tons per 
square inch, increasing with the percentage of zinc in the alloy. 

German or Nickel Silver, an alloy of copper, zinc, and nickel, is 
practically brass whitened by the addition of nickel. It has been drawn into 
wire as fine as .002/’ diam. 

Platinum wire may be drawn into the finest sizes. Qn account of its 
high priceits use is practically confined to special scientific instruments and 
electrical appliances in which resistances to high temperature, oxygen, and. 
acids are essential. It expands less than other metals when heated, which 
property permits its being sealed in glass without fear of cracking. It is 
therefore used in incandescent electric lamps. 

Phosphor-bronze Wire contains from 2 to 6 per cent of tin and 
from 1/20 to 1/8 per cent of phosphorus. The presence of phosphorus is 
detrimental to electric conductivity, : 

°° Delta=metal » wire is made from an alloy of copper, iron, and zine. 
Its strength ranges from 45 to 62 tons per square inch. It is used for some 
kinds of wire rope, also for wire gauze, - It is not subject to deposits of ver- 
digris. It has great toughness, even when its tensile strength is over 60 
tons per square inch. 

Aluminum Wire.— Specific gravity .268. Tensile strength only 
about 10 tons per square inch. It has been drawn as fine as 11,400 yards to 
the ounce, or .042 grains per yard. 

Aluminum Bronze, 90 copper, 10 aluminum, has high strength and 
ductility; is inoxidizable, sonorous. Its electric conductivity is 12.6 percent. 

Silicon Bronze, patentee in 1882 by L. Weiler of Paris, is made as 
follows: Fluosilicate of potash, pounded glass, chloride of sodium and eal- 
cium, carbonate of soda and lime, are heated in a plumbago crucible, and 
after the reaction takes place the contents are thrown into the molten 
bronze to be treated. Silicon-bronze wire has a conductivity of from 40 to 
98 per cent of that of copper wire and four times more than that ofiron, 
while its tensile strength is nearly that of steel, or 28 to 55 tons per square 
inch of section. The conductivity decreases as the tensile strength in- 
creases. Wire whose conductivity equals 95 per cent of that of pure copper 
gives a tensile strength of 28 tons per square inch, but when its conductivity 
is 834 per cent of pure copper, its strength is50 tons per square inch. Itis 
being largely used for telegraph wires. It has great resistance to oxidation. 

Ordinary Drawn and Annealed Copper Wire has astrength 
of from 15 to 20 tons per square inch, 


SPECIFICATIONS FOR HARD-DRAWN COPPER 
WIRE 


The British Post Office authorities require that hard-drawn copper wire 
supplied to them shall be of the lengths, sizes, weights, strengths, and con- 
ductivities as set forth in the annexed table, 




















&0 ; = 
Weight per Statute | Approximate Equiya- i 3 3 2Oz £58 

Mile, lent Diameter, 3 ea fuca | og 

® ,3 Ss, Bj2Scxu/ Por 

: as me iMod) Sic 

: e e 0 g inp) 48 Ay = 

sol ¢ q ss g H 1) s8 | 2a |ESE fon 
& 3 = Ss SF [sec Ss 

aS =| | SE | fn o95| 23° 

ss | & a 3 E B ler | 52 8323) &so 

Sa | 8 a sg E a |S Jee leakel 8x8 

Fn) a va A a |= |"e S 

lbs lbs lbs mils mils. | mils. | Ibs ohms. | fos 
100 97 102% 79 18 80 330 30 9.10 50 
150 | 14634 | 15384| 97 | 9511 98 | 490] 25 | 6.05 50 
200 195 205 112 110144 11314 650 20 4.53 | 650 
400 | 390 410 158 15516 16014 } 1300 10 2.26 50 


rr rT, 


bad 


226 MATERIALS, 
| 


WIRE ROPES. 
List adopted by manufacturers in 1892. See pamphlets of Johm A. 
Roebling’s Sons Co., Trenton Iron Co., and other makers, 
Pliable Hoisting Rope, 
With 6 strands of 19 wires each, 























‘ IRON. 
g Hm. aa S43 
. con wod * yy} dou ° D 
re oO 66,8 Ao BO o ED 
2 5 | ga | Es | #2 fae | 8 
S| ° be 5 nS oS REO op 
x 5 OS |e woe Fag | Saud | of 
ie | We a Pd Winton Persist dae seer ce oy 
3 f | 33 | PBS, | e8 | 88s | SBR | sa 
Sis ae q ae sea tee 
5 aA | se | eabs | FS | EAR | Sama | SS, 
1 Qu4 634 8.00 74 15 14 13 
| $8 [8 | Bo | eB Le 
3 134 5lé 125, 5 1 
4 154 5 4.10 44 9 11 814 
5 114 434 3.65 2 8 10 le 
56 134 434 3.00 33 614 9 
6 114 4 2.50 ' Bin 8 6% 
” 144 314 2.00 20 4 ie 
8 1 314 1.58 16 3 614 54 
9 % 234 1.20 11.50 QU 5 4a 
10 34 214 0.88 8.64 134 434 4 
1014 56 0.60 5.13 114 334 314 
104% 9-16} 154 0.48 4.27 34 84 234 
1034 6 14 0.39 3.48 i 3 ai 
10a 7-16 136 0.29 3.00 84 234 2 
10% 36 114 0.23 2.50 i 6 1% 
CAST STEEL. 
1 Pay, 6 8.00 155 31 Le ee ate 
Q ie te 6.30 125 25 Ph ee He 
3 134 Bl 5.25 1 2 RE SU ie 
4 nee 1 6 4.10 86 17 15 614 
5 é 434 3.65 77 15 14 534 
5M 18% 436 3.00 63 12 13 56 
6 144 4 2.50 52 10 12 
? 114 34 2.00 42 8 11 4\6 
9 % 234 
10 y 214 0.88 18 314 3 
1014 54 . 0.60 12 216 534 214 
1014 9-16] 15 0.48 9 134 13% 
1034 % 04 0.39 ve 1% 4 1g 
10a 7-16] 184 0.29 Blé 11 334 144 
10% 8 VA 0.23 446 % 342 





Cabie-Traction Ropes. 


Aceording to English practice, cable-traction ropes, of about 314 in. in 
circumference, are commonly constructed with six strands of seven or fif- 
teen wires, the lays in the strands varying from, say. 3 in. to 344 in., and the 
lays in the ropes from, say, 7}4in. to9in. In the United States, however, 
strands of nineteen wires are generally preferred, as being more flexible; 
but, on tke other hand, the smaller external wires wear out more rapidly. 
The Market-street Street Railway Company, San Francisco, has used ropes 
114 in. in diameter, composed of six strands of nineteen steel wires, weighing 
214 lbs. per foot, the longest continuous length being 24,125 ft. The Chicago 
City Railroad Company has employed cables of identical construction, the 
longest length being 27,700 ft. On the New York and Brooklyn Bridge cable 
railway steel ropes of 11,500 ft. long, containing 114 wires, have been used. 


WIRE ROPES. 227 


Transmission and Standing Rope, 


With 6 strands of 7 wires each. 














IRON, 

Bos & Ba) - 
ss o 6 ae 4 ye) ‘ Sel : ® 
ra) 3) rte) ex ie Ss as 
2 =| = ha roy bo as Set a 
E . | S3e | #28 | Ss S23, | So 
5 oD pes iad le i Bobe 02.4 5 
A 2 ‘a 42 Shr a =p SS ot NS 
® a 5 mae ae Som F=on | we 
S | 5 Os ses oie LgS Be aD a7) 
S S A= SSes pate £Ss 0 O38 oleae & 
Es A 6) eo eg Ane Bama | So 
if! 1% 434 3.37 36 9 10 13 
12 136 436 2.77 30 Wl, 9 12 
13 1144 4 2.28 25 614 814 1034 
14 114 314 1.82 20 5 We 914 
15 1 31g 1.50 16 4 614 814 
16 % 234 1.12 12.3 3 534 f 

? 34 Q\4 0.92 8.8 214 434 634 
18 11-16] 214 on 7.6 Q 41 6 
19 6 a 0.57 5.8 1144 4 514 
20 9-16] 15 0.41 4.1 1 314 414 
21 M4 Ile 0.31 2.83 34 23 4 
22 (16 134 0.23 2.13 14 16 314 
23 3% 114 0.21 1.65 fc ag 214 234 
24 5-16] 1 0.16 Frat tetas toer ee 2 he 
25 9-32 % 0.125 1.03 esos evs 134 2144 

CAST STEEL. 

ry 1% 434 3.37 62 3 13 84 
12 134 43¢ 2.77 52 10 12 8 
13 114 4 2.28 44 9 11 714 
14 114 314 1.82 36 M% 10 614 
15 1 aig 1.50 30 6 9 534 
16 % 24 1.12 22 44 8 

17 54 214 0.92 17 3g 3 4 
18 11-161 214 0.70 14 3 6 4 
19 Bg 2 0.57 11 214 Bi 316 
20 9-16} 154 0.41 8 134 434 3 
21 6 146 0.31 6 114 4 214 
22 (-16] 184 0.23 44 114 314 Qi 
23 36 | 1% 0.21 4 1 314 2 
24 5-16] J 0.16 3 34 234 134 
25 9-32) 3% | 0:12 2 14 214 114 





Plough-Steel Rope. 


Wire ropes of very high tensile strength, which are ordinarily called 
“Plough-steel Ropes,” are made of a high grade of crucible steel, which, 
when put in the form of wire, will bear a strain of from 100 to 150 tons per 
square inch. 

Where it is necessary to use very long or very heavy ropes, a reduction of 
the dead weight of ropes becomes a matter of serious consideration. 

It is advisable to reduce all bends to a minimum, and to use somewhat 
larger drums or sheaves than are suitable for an ordinary crucible rope hav 
ing a strength of 60 to 80 tons per square inch. Before using Plough-stee 
Ropes it is best to have adyice on the subject of adaptability. . 


228 MATERIALS. 


Plough-Steel Rope, 


With 6 strands of 19 wires each. 





> 











A Breaking Min. Size of 
Trade | Diameter in user D €Y! Strain in Proper Work-| Drum or 
Number. inches. ounds tons of ing Load. Sheave in 

Pp *~} 2000 Ibs. feet. 
1 214 8.00 240 46 9 
2 2 6.30 189 37 8 

3 134 5.25 15% 31 ves 
4 154 4.10 123 25 6 

Bi 183 3°00 790 is ig 
1 : 9 1 5 

6 114 2.50 "5 15 
7 11g 2.00 60 12 4 

8 1 1.58 47 9 4\4 

9 % 1.20 37 ? 334 
10 34 0.88 a7 5 3 
10% 56 0.60 18 314 3 

10% 9-16 0.44 13 216 214% 
1034 u% 0.39 10 9 Q 

With 7 Wires to the Strand. 

15 1 1.50 45 9 54 
16 % 1.12 33 6% 5 
17 34 0.92 25 5 4 

18 11-16 0.70 21 4 3K 
19 34 0.57 16 334 3 

20 9-16 0.41 12 Ql4 234 

21 16 0.31 9 1% 24a 
22 7-16 0.23 5 1% 2 

23 34 0.21 4 1 1g 





Galvanized Iron Wire Rope. 
For Ships’ Rigging and Guys for Derricks. 
CHARCOAL ROPE. 








ea ont Cir. of | Break- Weight Cir, of | Break- 
= eig new ing + ew ing 
Circum- |her Fath-| Manila | Straing CiCUM-|_ per | wanila | Strain 
ference |" om in | Rope of | in tons ference | Fathom) pone of | in tons 
in inches. pounds. Baal of 2000 12 inches ad sail of 2000 
Strength.|pounds pounes:/Strength,| pounds 
516 2614 11 43 a4 | 516 5 9 
ceil WeTmmmeio ys 86 | baa vale = ee 
6 a pO} 
ele | ee] me) ee) 
414 1644 814 26 114 134 214 Le 
|i | ae | BL | el | 
A. 2 
3 1034 ora 16 % 34 134 1 


(st) 
AS 
We) 
= 
ps 
aN 
annus 





WIRE ROPES. 229 


Galvanized Cast-steel Yacht Bigginge. 

















Teee Cir. of | Break- Weight | Cir. of | Break- 
. eig new in . new ing 
Circum- per Fath-| Manilla Strain Cireum-|__ per Manilla | Strain 
ference omen tite f ti ference | Fathom) , étint 
in inches. ope of fin tons] in inches| in eater the he 
pounds. | equal | of 2000 mid equal | of 2000 
Strength.|pounds pounds.'Strength.|pounds 
4 1414 13 66 2 B16 614% 14 
314 1034 +1. 43 134 ai6 54 10 
3 8 9lé 32 116 434 8 
234 634 8144 27 13g 1% 414 614 
2 bee tl a8 22 114 134 334 56 
214 | 46 7 18 1 % 3 34 
Steel Hawsers. 
For Mooring, Sea, and Lake Towing. 
Size of ; Size of 
Circumfer-| Breaking |Manilla Haw-{ Circumfer-| Breaking |Manilla Haw- 
ence. Strength. | ser of equal ence. Strength. | ser of equal 
Strength. Strength. 
Inches. Tons. Inches. Inches. Tons, Inches. 
24 15 614 3% 29 9 
234 18 7 4 35 10 
3 22 814 





Steel Flat Ropes. 
(J. A. Roebling’s Sons Co.) 

Steel-wire Flat Ropes are composed of a number of strands, alternately 
twisted tothe right and left, laid alongside of each other, and sewed together 
with soft iron wires, These ropes are used at times in place of round ropes 
in the shafts uf mines. They wind upon themselves on a narrow winding- 
drum, which takes up less room than one necessary for around rope. The 
soft-iron sewing-wires wear out sooner than the steel strands, and then it 
beeomes necessary to sew the rope with new iron wires. 


oa ; wary 
Width and|Weight per . Width and | Weight per] qa. : 
Thickness foot in | Strengthin | mnickness | foot in | Stensth in 














in inches. | pounds. pounds. in inches. | pounds. | pounds. 
eK wee ees ages ne t= tet. Dee overs 
36 x2 1.19 35,700 144x3 2.38 71,400 
84 x 216 1.86 55.800 46x 314 2.97 89,000 
36x3 2.00 60,000. 4ox4 3.30 99,000 
36x 316 2.50 75,000 16x46 4.00 120,000 
Bex 4 2.86 85,800 46x5 4.27 128,000 
36x 414 3.12 93,600 14x54 4.82 144,600 
36x 5 3.40 100,000 14 x6 5.10 158,000, 
36 x 513 3.90 110,000 4x7 5.90 177,000 


For safe working load allow from one fifth to one seventh of the breaking 


stress. 
‘Lang Lay? Rope. 

In wire rope, as ordinarily made, the component strands are laid up into 
rope in a direction opposite to that in which the wires are laid into strands; 
that is, if the wires in the strands are laid from right to left, the strands are 
laid into rope from left to right. Im the ‘‘ Lang Lay,” sometimes known as 
’* Universal Lay,”’ the wires are laid into strands and the strands into repe 
in the same direction; that is, if the wire is laid in the strands from right to 
left, the strands are also laid into rope from right to left. Its use has been 
found desirable under certain conditions and for certain purposes, mostly 
for haulage plants, inclined pene, and street railway cables, although it 
has also been used for vertical hoists in mines, etc. Its advantages are that 


230 





MATERIALS, 


GALVANIZED STEEL CABLES. 
Vor Suspension Bridges, (Roebling’s.) 


Weight per foot. 


Diameter in inches, 


h 


SR SE 


yo SE || ee ORS) CSS FE 


a | s a | a 

s| fe | 8.) 2| fe 
& | ER es | Be 
S|} ny S 7 3 mas 
be 2 au aad hy ona 
S | gay S Sa oe 
2 | 888 bp 2 Ese 
@ | =s8 : @ | #82 
mete Ss ea Bi a 
25g | 220 13 244 | 155 
214 | 200 11.8 2 110 
234 | 180 10 1% | 100 


rx 


Oro CO 
Mora 





we 3 
aS } 
OS a 
b4 G2 
aps be 
EN ® 
Orcs on 
aa 02,2 Fey 
gat a 
a2s bo 
eiacs e 
SS aply eS 
95 5.6 
75 4.85 
65 3.7 


COMPARATIVE STRENGTHS OF FLEXIBLE GAL-= 
VANIZED STEEL-WIiIRE HAWSERS, 


With Chain Cable, Tarred Russian Hemp, and White 
Manila Ropes. 


Patent Flexible 
Steel-wire Hawsers 














and Cables. 

A : fol) ‘ 
Sjdie jee 
a) S13 o Aa 
S731 38 jae 
o| s sane, (Oy = 
“a al FQ a as e 
Sie lathe. Ove 
=} o oes) Fed 
oO [oy Oo ./8 FS 
ih re) isos Ore (S} 

fe) 3st ~ 
OS | ee |}Oae 
o|- | s8 Eso 
aS o 32 1.8 HQ 
NM Els A 
1 34) 134 6 
114} 1 216 6 
144} 134) 4 9 
134| 2 51g | 1014 
2 234) 7 12 
214| 334) 9 13144 
214) 4146! 12 15 
234| 516) 15 16% 
3 7 18 18 
3141 8 | 22 1914 
314| 9 26 & 
ae wie, 33 24 
416/15 39 Bat 
5 |2344) 64 30 
516/28 74 33 
6 |33 §8 36 
614)37 |102 39 
fe Sb le 42 
T146/47 = |130 45 
8 |53 {150 48 


Notr.—This is an old table, and its authority is uncertain. 


Chain Cable. 


Size. 
Re | Weight per Fathom. 


9-16) 17 
10-16} 21 


11-16) 25 
12-16} 30 
138-16] 35 
15-16} 48 
54 
68 
732/112 
143 





1 
148 
1.1 
196 
134 
1 15-16)204 
1-16]23! 
16|256 


2 
2 3- 
2 516/280 


166)5 





| Proof Strain, tons. 





Tarred Rus- White 
sian Hemp Manilla 
Rope. Ropes. 
q gS ja —E|¢ 
2 g|s g}F 
g 3 | a 2 | 2 
‘s |e & | 3 
oo Pa ee w |S 
MD 8) mM o mM 
ao Or | op ies 
a pl: 28 
ed ah NRE: Tic) Pas Uae peed 
a |S/2/ei81 213 
6 |S2/F |g l|a2lE ls 
234 114] 246] 114] 2 
6 316} 3 | 216] 8 | 184] 2384 
4 | 814] 314! 334] 2 aie 
re See Bae | tae as 
534 8 | 7 | 5 | 414) 784 
916 644} 10 9 | 534] 6 104 
744] 13 [1146] 644] 7 11214 
1234 8l6| 16 | 14] 7 | 884/15 
151g 9 | 19 11616] %16]1016]18 
17 8-10/10 23 | 20 | Sl6)138 (2234 
23 7-10)11 28 12416) 9 |14146)25 
27 12 83. | 29 410° |18 |/81 
sag [18 | 39 | 34 [11 [22 [88 
5514 |15 | 56 | 50 |1284/2914/51 
6614 17 67 | 60 |1814/8514)/62 
71% 19 84 | 72 |15 [42 |73lg 
9416 21 1106 } 89 
107 1-10/23 123 |106 
12014 |24 1134 [115 
13434 25 {146 {125 





the fourth column are probably much too small for durability, 


The figures in 


WIRE ROPES. . 231 


it is somewhat more flexible than rope of the same diameter and composed 
cof the same number of wires laid up in the ordinary manner; and (especi- 
ally) that owing to the fact that the wires are laid more axially in the rope, 
longer surfaces of the wire are exposed to wear, and the endurance of the 
rope is thereby increased. (Trenton Iron Co.) 


Notes on the Use of Wire Rope. 
(J. A. Roebling’s Sons Co.) 

Several kinds of wire rope are manufactured. The most pliable variety 
contains nineteen wires in the strand, and is generally used for hoisting and 
running rope. The ropes with twelve wires and seven wires in the strand 
are stiffer, and are better adapted for standing rope, guys, andrigging. Or- 
ders should state the use of the rope, and advice will be given. Ropes are 
made up to three inches in diameter, upon application. 

For safe working load, allow one fifth to one seventh of the ultimate 
strength, according to speed, so as to get good wear from the rope. When 
substituting wire rope for hemp rope, it is good economy to allow for the 
sO aasg the same weight per foot which experience has approved for the 
atter. . 

Wire rope is as pliable as new hemp rope of the same strength; the for- 
mer will therefore run over the same-sized sheaves and pulleys as the latter. 
But the greater the diameter of the sheaves, pulleys, or drums, the longer 
wire rope will last. The minimum size of drum is given in the table. 

Experience has demonstrated that the wear increases with the speed. It 
is, therefore, better to increase the load than the speed. 

Wire rope is manufactured either with a wire ora hemp centre. The lat- 
ter is more pliable than the former, and will wear better where there is 
short bending. Orders should specify what kind of centre is wanted. 

Wire rope must not be coiled or wncoiled like hemp rope. 

When mounted on a reel, the latter should be mounted on a spindle or flat 
turn-table to pay off the rope. When forwarded in a small coil, without reel, 
roll it over the ground like a wheel, and run off the rope in that way. All 
untwisting or kinking must be avoided. 

To preserve wire rope, apply raw linseed-oil with a piece of sheepskin, 
wool inside; or mix the oil with equal parts of Spanish brown or lamp-black. 

To preserve wire rope under water or under ground, take mineral or vege- 
table tar, and add one bushel of fresh-slacked lime to one barrel of tar, 
which will neutralize the acid. Boil it well, and saturate the rope with the 
hot tar. To give the mixture body, add some sawdust. 

The grooves of cast-iron pulleys and sheaves should be filled with well- 
seasoned blocks of hard wood, set on end, to be renewed when worn out. . 
This end-wood will save wear and increase adhesion. The smaller pulleys 
or rollers which support the ropes on inclined planes should be constructed 
on the same plan. When large sheaves run with very great velocity, the 
grooves should be lined with leather, set on end, or with India rubber. This 
is done in the case of sheaves used in the transmission of power between 
distant points by means of rope, which frequently runs at the rate of 4000 
feet per minute. 

Steel ropes are taking the place of iron ropes, where it is a special object 
to combine lightness with strength. 

But in substituting a steel rope for an iron running rope, the object in view 
should be to gain an increased wear from the rope rather than to reduce the 


size. 
‘ _ Locked Wire Rope. 
Fig. 74 shows what is known as the Patent Locked Wire Rope,-made by 
the Trenton Iron Co. It is claimed to wear two to three times as long as an 



































Fig. 74: 


ordinary wire rope of. equal diameter and of like material. Sizes made are 
trom 14 to 1 inches diameter, : 


232 MATERIALS, 


CRANE CHAINS, 
(Bradlee & Co., Philadelphia.) 








“1D. B. G.’’ Special Crane. Crane 

= & a bo 3 

R 3 2 oR] au io. & 8 
4 | 8,13 8| 3 |#. | 3B 8 |2.18 0 4g. 
Sul sa |B4¥s)] Bu og £5 ees] o8 | os2 |epg 
yo a2 5 eS: aS sete) GBH es M's 8 ae 
So | aa | OER] oS 6% og |p 82/ 05 | O88 | ,keS 
oy Aor eS See © 2 we |koe| Sa] oa | eee 

= Bb S a » & GS 3 i) a s la} Oo 
om ak Hae Sad BS OS lec | & a as 

wR C oo g tco PQ |g = 3 

a = < & & 
Y% 25-32 % % 1932 38864 1288} 1680 3360 1120 
A 27-32 4 1 1-16 2898 5796 1982) 2520 5040 1680 
3 31-382 | 17-10) 14 4186 83872 2790] 3640 7280 2427 
7-16} 1 5-82 138 5796 11592 8864} 5040} 10080 8360 
¥ |111-82) 2 111-16} %728 15456 5182) 6720! 13440 4480 
9-16] 115-382} 382-10] 1% 2660 19320 6440] 8400} 16800 5600 
5 1 23-82) 414 21-16 | 11914 23828 7942| 10360} 20720 6907 
41-16] 1 27-32 214 14490 28980 9660) 12600} 25200 8400 
34 |181-382| 5% 214 17388 84776 | 11592) 15120} 30240 | 10080 
18-16} 2 3-382 6 %-10 | 211-16} 20286 40572 | 13524) 17640) 385280 | 11760 
%. | 2 7-82 8 2% 22484 44968 | 14989| 20440} 40880 | 13627 
15-16} 2 15-382] 9 381-16 | 25872 51744 | 17248] 238520} 47040 | 15680 
1 219-32 | 10 7-10 | 3814 29568 59186 | 19712) 26880} 53760 7920 
1 1-16] 2 238-32 | 112-10] 35-16 | 33264 66588 | 22176) 380240} 60480 | 20160 
14 2 27-82 | 1214 334 3757 75152 | 25050} 34160} 68820 | 22773 
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14 3 81-32 | 21 7-10 | 5 66528 | 133056 | 44352) 60480; 120960 | 40320 





~ 


The distance from centre of one link to centre of next is equal to the in- 


side length of link, but in practice 1/32 inch is allowed for weld. This is ap- 
proximate, and where exactness is required, chain should be made so. 
For CHAIn SHEAVES.—The diameter, if possible, should be not less than 
twenty times the diameter of chain used. ; 
ExAMPLE.—For 1-inch chain use 20-inch sheaves. 


WEIGHTS OF LOGS, LUMBER, ETC. 
Weight of Green Logs to Scale 1,000 Feet, Board Measure, 


TY OlLO WMOEIVO CI OULITOLT Jy, 0-9: oy :c a mtb, cuss ously sara cleremniejeiewiele® ary 8,000 to 10,000 Ibs, 
Norway pine (Michigan) Pyaar yd 8% eeeines ia to 8,000 ‘ 
: : rae oe Off Of stumM pi ser. 32.0 Rise cat eitele ct ,000 to 7,000 °° 
White pine (Michigan) { out of water....... ble Siew sive Seebiont 7,000 to 8,000 ‘* 
White pine (Pennsylvania), bark Off.........seeceee e--«s* 5,000 to: 6,000 
Hemlock (Pennsylvania), bark off..............26 2. vee 6,600 to 7,000 * 


Four acres of water are required to store 1,000,000 feet of logs. 
Weight of 1,000 Feet of Lumber, Board Measure, 


Yellow or Norway pine@..........6....... Dry, 3,000 lbs. Green, 5,000 Ibs, 
White pine... Pegieeemebees sc. cde se sens 2500 * “ "4,000 “ 
Weight of 1 Cord of hk ch) jah Pad 2 yk 128 Cubic Feet per 
ord. 
Hickory. OF BUSA MADierare is csc thus cess ssseseeutens soeeeeee ss 4,500 lbs. 
White oak........ .o0seewn- {SOGOU DUGO OCCMDOOG valerate BAO oc. cnet 8,850 ‘*: 
Beech; red-odk or DIBCIOAR. 08 iid eve cies ces edeleceeaieseess» 3,250) *¥ 
Poplar, chestnut or elm.......... 20) cesserecsccses seebbestecsocscs 2,000 ‘f 
Pine (white or Norway)........+-.. oeeesipe ese ccc scsuiceeminecisecs os 000MMEE 


He@inlock bark, Cryo. sccmgueees sss. ccscuucaccssccccssesheceessiecs O,c00ume 


SIZES OF FIRE-BRICK. 233 


SIZES OF FIRE-BRICK, 


Pia i straight..... SENS 9x 414 x 214 inches. 
OUP ote ls Here secevecesed GING s ele rs 
Checker... .ssscsesessssss 9X8 xB 
2-inch.. erverereseeeeesese 9x41gx2 ue 
Splietee ese vel gegaes Ox dae lagi wes 
ed SUL as ed he tom eee 9x 416 x2 sé 


118 bricks to circle 12 feet inside diam. 
INO: © ROY ak wis tnacial tes 9 x 214 thick x 414 to 84% 
inches wide. 
63 bricks to circle 6 ft. inside diam. 
INO. AIROY gS 4 oh qos tase « 9 x 216 thick x 414% to 3 
inches wide. 
388 bricks to circle 3 ft. inside diam. 
NOW 4 keys hd. 9x2% thick x 41% to 24% 
inches wide. 
25 bricks to circle 11% ft. inside diam. 
No. 1 wedge (or bullhead). 9x 414 wide x 24 to 2 in. 
thick, tapering lengthwise. 
98 bricks to circle 5 ft. inside diam. 


No. 2 wedge.......:-..040- 9x 414 x 214 to 11% in. thick. 
60 bricks to circle 214 ft. inside diam. 
INO. barely. tue isha 9x 416x2l4 to 2 in. thick, 


tapering breadthwise. 
72 bricks to circle 4 ft. inside diam. 


INO: 2 UG)... hip eas wade ee 9 x 414 x 216 to 114. 
42 bricks to circle 2 ft. inside diam. 
Nop 1 SEOw.. ihe... . 4. Fee 9to7x 414 to 214, 
Bevel on one énd. 
ING) 2 SEOW .) le leice ade Gee = 9x 214 x 44% to 24. 
Equal bevel on both edges. 
Nor Siskew .4..0%)-).: «02.904 - 9x 216x 4% to 14. 
Taper on one edge. 
APINCH (Gir Cle sep seston 814 to BIZ x 414 x 244. 
Edges curved, 9 bricks line a 24-inch circle, 
36-inch Gircle 7 4...) 3) 834 to 644 x 414 x 214, 
9X Qhex (444-214) 13 bricks line a 36-inch circle. 
| 48-inch Circles. Jo... ie 24 834 to 714 x 414 x 2. 
17 bricks line a 48-inch circle. 


13l4-inch straight.........1314x 214x 6. 

13l4-inch key No.1 .. .... 1314 x 244 x 6 to 5 inch. 
90 bricks turn a 12-ft. circle. 

18l4-inch key No, 2.... ...138144x 24 x 6 to 43 inch. 
52 bricks turn a 6-ft. circle. 





Bridge wall, No. 1......... 13 x 614 x 6. 
Bridge wall, No. 2.........13X614x 3. 
36'in. Circle Mill tile ... «. 8. it 0.5) UE) e < 18, 20, or 24x 6x93. 
83% Stock-hole tiles............ 18, 20, or 24x9x4, 
\ 18-inch) DlOGK yee. <6 Panes tele oR 
6% Hlat DACK I Ta52 Soeaas asic cee) 2X 0 X250; 
Hlat backiarchy. cn... 9x6x 314 to 214. 
PRR f, 22-inch radius, 56 bricks to circle. 
Locomotive tile .......... 82x 10x 3. 
34x 10x3. 
84x 8x3. 
86x 8x3. 
40x 10x 3. 





Tiles, slabs, and blocks, various sizes 12 to 30 inches 
long, 8 to 80 inches wide, 2 to 6 inches thick. 

Cupola brick, 4 and 6 inches high, 4 and 6 inches radial width, to line shells 
23 to 66 in diameter. 

A 9-inch straight brick weighs 7 lbs. and contains 100 cubic inches, (=120 
lbs. per cubic foot. Specific gravity 1.93.) P 

One cubic foot of wall requires 17 9-inch bricks, one cubic yard requires 
460. Where keys, wedges, and other “ shapes”’ are used, add 10 per cent in 
estimating the number required, 


234 MATERIALS. 


One ton of fire-clay should be sufficient to lay 3000 ordinary bricks. Ta 
secure the best results, fire-bricks should be laid inthe same clay from which 
they are manufactured. It should be used as a thin paste, and not as mor. 
tar. The thinner the joint the better the furnace wall. In ordering bricks 
the service for which they are required should be stated. 


NUMBER OF FIRE-BRICK REQUIRED FOR 
VARIOUS CIRCLES. 





———$——, 

















AG KEY BRICKS. ARCH BRICKS. WEDGE BRICKS. 
®o 
acd A pay MC Gal | eee 
chaise belek aE ee oe ie d 
oy he Ae) } ro) 6 | o PY 6 ar lio ~ 5 
4Z\|4/1B A i Zoe tr) HH 4lGa > a 
ft. in. 
he Oe: ON pee AL hd A ak QO Seah Sere Das | Poiecuece. | Wekarnil ietee a iets eseetim hea aes 
Sie Oa elgg lio SOAS eee ee als 42a tesleeee 
2 6 Qa 25 Bd ASU LB seeders. AQ? GOgeot= eae 60 
BO: 388 Som elise. teeny Ot) 48. | QO es 68 
3 Ol. 82 | 10 42 | 10 | 54 eee 64> OG 40 Rete 76 
Ae Oral U5) 46 hea Nuteeo ee (2h | Awe ane ae 83 
aunts 19 | 82 51 72 8 80) 125279 al eee 91 
0 ae Tomeae 55 ff 15 87 O Brae as 98 
5k Wh 6 | 53 59 ae 23 95 98 8 106 
Coe OES Ey Aes 63 63 ie 30 102 98 15 113 
6 6 58 9 67 Us 388 110 98 23 121 
dS) Beer | ties, 52 19 71 le 45 spare 98 30 {28 
Uae Ou le -ceualess de 47 29 76 ae 53 225 98 88 136 
8 0 42 38 80 [2 60 132 98 46 144 
8 6 37 47 84 fp 68 140 98 53 {51 
Oe ON ites oi os eke 31 57 88 Yep 15 147 98 61 159 
9 6 26 66 92 72 83 150 98 68 166 
ODEO Wks wes ttstraes 21 76 Vi "2 90 162 98 76 174 
TOPEG |. Sapeitee tee 16 85 101 ey 98 170 98 838 181 
11 O 11 94 105 72 105 n Were 98 91 189 
a) Pies yeiaterlae atege 5 104 109 72 113 185 98 98 196 
DO assests |e SE eae 113 113 72 121 1938 98 106 204 
OMe ae; vie aay! Beret 113 117 See 











For larger circles than 12 feet use 113 No. 1 Key, and as many 9-inch brick 
as may be needed in addition. 


ANALYSES OF MT. SAVAGE FIRE-CLAY. 


(1) (2) (8) (4) 
1871 1877. 1878. 1885. 
Report on Second 
Iustitute of clays of Geological “HGH 

Technolo er sey Survey of Wath 
SeNAOeY Prof, GkHeCook. | Pennsylvania, he 

50.457 HOroUm Ollica..... soaee ela lores near 44.395 56.15 
35.904 SOROS Me AIUMINA 2.6 e. o. ea belts cees 33.558 33.295 
pees iitoge Litanic acid... ci. ..o0% 1.5380 See 5 

1.504 Lee eeroxide Hron.« . dss 1.080 0.59 

9.133 MMMM TIA C2 2! 5s 4's we od eae crs trace 0.17 
0.018 et PANES TI CSID) oes jars die bis, « ssa abeveiote 0.108 0.115 
trace 0.80 Potash (alkalies). ohare ONBA Tie if aera 

12.744 10.50 Water andinorg. matter. 14.575 9.68 











100.760 100.450 100.493 100.000 


EE 


MAGNESIA BRICKS, 230 


MAGNESIA BRICKS, 


“Foreign Abstracts’ of the Institution of Civil Engineers, 1893, gives a 
paper by ©. Bischof on the production of magnesia bricks. The material 
most in favor at present is the magnesite of Styria, which, although less 
pure considered as a source of magnesia than the Greek, has the property 
of fritting at a high temperature without melting. The composition of the 
two substances, in the natural and burnt states, is as follows: 


Magnesite. Styrian. Greek. 

Carbonate of magriesia............ 90.0 to 96.0% 94.46% 

8 seein ates Bed Ro nae 0.5to 2.0 . 4.49 

cs SUDETO NM sat. Hamewe canes os 3.0 to 6.0 FeO 0.08 
SiliGals ae eee sale ee ASE IRSO 1.0 0.52 
Manganous oxide ........... Adddicac’ oR Water 0.54 

Burnt Magnesite, 

Magonesiay cacmerits.s <tsias/s site ates =e ete 3 82.46—95.36 
AI Oe steer ee caetihy Aas cee See es: te} 0.83—10.92 
Alumina and ferric oxide........ 2. 18.0 0.56— 3.54 
SilCA ona Go seve sie ores tisleiascio aratnarseercts 1.2 0.73— 7.98 


At ared heat magnesium carbonate is decomposed into carbonic acid and 
caustic magnesia, which resembles lime in becoming hydrated and recar- 
bonated when exposed to the air, and possesses a certain plasticity, so that 
it can be moulded when subjected to a heavy pressure. By long-continued 
or stronger heating the material becomes dead-burnt, giving a form of mag- 
nesia of high density. sp. gr. 3.8, as compared with 3.0 in the plastic form, 
which is unalterable in the air but devoid of plasticity. A mixture of two 
volumes of dead-burnt with one of plastic magnesia can be moulded into 
bricks which contract but little in firing. Other binding materials that have 
been used are: clay up to 10 or 15 per cent; gas-tar, perfectly freed from 
water, soda, silica, vinegar as a solution of magnesium acetate which is 
readily decomposed by heat, and carbolates of alkalies or lime. Among 
magnesium compounds a weak solution of magnesium chloride may also be 
used. For setting the bricks lightly burnt, caustic magnesia, with a small 
proportion of silica to render it less refractory, is recommended. The 
strength of the bricks may be increased by adding iron, either as oxide or 
silicate. If a porous product is required, sawdust or starch may be added 
to the mixture. When dead-burnt magnesia is used alone, soda is said to be 
the best binding material. 

See also papers by A. E. Hunt, Trans. A. I. M. E., xvi, 720, and by T. Egles- 
ton, Trans. A. I. M. E., xiv, 458, 

Asbestos.—J. T. Donald, Hng. and M. Jour., June 27, 1891. 





ANALYSIS. 
Canadian. 

Italian. Broughton, Templeton. 
SiliCA. uss tatinschesa ie aeeimer e.--- 40.80% 40.57% 40.52% 
Maenesia... o.'52 esac ereieneia nisi 43.37 41.50 42.05 
Ferrous oxide........ sic s fairs .87 2.81 1.97 
Alumina...... Shtcustere sisiveciee om Pea 6 .90 2.10 
Water........ sterare sl evalarereeaseiers 13.72 13.55 13.46 

100.53 99.33 100.10 


Chemical analysis throws light upon an important point in connection 
with asbestos, i.e., the cause of the harshness of the fibre of some varieties, 
Asbestos is principally a hydrous silicate of magnesia, i.e., silicate of mag- 
nesia combined with water. When harsh fibre is analyzed it is found to 
contain less water than the soft fibre. In fibre of very fine quality from 
Black Lake analysis showed 14.38% of water, while a harsh-fibred sample 
gave only 11.70%. If soft fibre be heated to a temperature that will drive off 
a portion of the combined water, there results a substance so brittle that it 
may be crumbled between thumb and finger. There is evidently some con- 
nection between the consistency of the fibre and the amount of water in its 
composition. 


936 STRENGTH OF MATERIALS. 


STRENGTH OF MATERIALS. 


Stress and Straim.—There is much confusion among writers on 
strength of materials as to the definition of these terms. An external force 
applied to a body, so as to pull it apart, is resisted by an internal force, or 
resistance, and the action of these forces causes a displacement of the mole- 
cules, or deformation. By some writers the external force is called a stress, 
and the internal force a strain; others call the external force a strain, and 
the internal force a stress: this confusion of terms is not of importance, as 
the words stress and strain are quite commonly used synonymously, but the 
use of the word strain to mean molecular displacement, deformation, or dis- 
tortion, as is the custom of some, is a corruption of the language. See Hn- 
gineering News, June 28, 1892. Definitions by leading authorities are given 
below. 

Stress,—A stress is a force which acts in the interior of a body, and ree 
sists the external forces which tend to change its shape. A deformation is 
the amount of change of shape of a body caused by the stress. The word 
strain is often used as synonymous with stress and sometimes it is also used 
to designate the deformation. (Merriman.) 

The force by which the molecules of a body resist a strain at any point is 
called the stress at that point. 

The summation of the displacements of the molecules of a body for a 
given point is called the distortion or strain at the point considered. (Burr). 

Stresses are the forces which are applied to bodies to bring into action 
their elastic and cohesive properties. These forces cause alterations of the 
forms of the bodies upon which they act. Strain is a name given to the 
kind of alteration produced by the stresses. The distinction between stress 
and strain is not always observed, one being used for the other. (Wood.) 

Stresses are of different kinds, viz.: tensile, compressive, transverse, tor- 
sional, and shearing stresses. 

A tensile stress, or pull, is a force tending to elongate a piece. A com- 

ressive stress, or push, is a force tending to shorten it. A transverse stress 
ends to bend it. A torsional stress tends to twist it. A shearing stress 
tends to force one part of it to slide over the adjacent part. 

Tensile, compressive, and shearing stresses are called simple stresses. 
Transverse stress is compounded of tensile and compressive stresses, and 
torsional of tensile and shearing stresses. 

To these five varieties of stresses might be added tearing stress, which is 
either tensile or shearing, but in which the resistance of different portions 
of the material are brought into play in detail, or one after the other, in- 
stead of simultaneously, as in the simple stresses. 

Effects of Stresses.—The following general laws for cases of simple 
tension or compression have been established by experiment. (Merriman): 

1. When a small stress is applied to a body, a small deformation is pro- 
duced, and on the removal of the stress the body springs back to its original 
fore For small stresses, then, materials may be regarded as perfectly 
elastic. 

2. Under small stresses the deformations are approximately proportional 
to the forces or stresses which produce them, and also approximately pro- 
portional to the length of the bar or body. 

38. When the stress is great enough a deformation is produced which is 
partly permanent, that is, the body does not spring back entirely to its 
original form on removal of the stress. This permanent part is termed a 
set. In such cases the deformations are not proportional to the stress. 

4, When the stress is greater still the deformation rapidly increases and 
the body finally ruptures. 

5, A sudden stress, or shock, is more injurious than a steady stress or than 
a stress gradually applied. 

Elastic Limit,—The elastic limit is defined as that point at which the 
deformations cease to be proportional to the stresses, or, the point at which 
the rate of stretch (or other deformation) begins to increase. It is also 
defined as the point at which the first permanent set becomes visible. The 
last definition is not considered as good as the first, as it is found that with 
some materials a set occurs with any load, no matter how small, and that 
with others a set which might be called permanent vanishes with lapse of 
time, and as it is impossible to get the point of first set without removing 


STRESS AND STRAIN, te 237 


the whole load after each increase of ioad, which is frequently inconvenient. 
The elastic limit, defined, however, as the point at which the extensions be- 
gin to increase at a higher ratio than the applied stresses, usually corresponds 
very nearly with the point of first measurable permanent set. 

Apparent Elastic Limit.—Prof. J. B. Johnson (Materials of Con- 
struction, p. 19) defines the ‘apparent elastic limit” as ‘the point on the 
stress diagram [a plotted diagram in which the ordinates represent loads 
aud the abscissas the corresponding elongations] at which the rate of de- 
formation is 50% greater than it is at the origin,” [the minimum rate]. An 
equivalent definition, proposed by the author, is that point at which the 
modulus of extension (length < increment of load per unit of section + in- 
crement of elongation) is two thirds of the maximum. For steel, witha 
modulus of elasticity of 30,000,000, this is equivalent to that point at which 
the increase of elongation in an 8-inch specimen for 1000 Ibs. per sq. in. 
increase of load is 0.0004 in. 

Vield-point.—The term yield-point has recently been introduced into 
the literature of the strength of materials. It is defined as that point at 
which the rate of stretch suddenly increases rapidly. The difference be- 
tween the elastic limit, strictly defined as the point at which the rate of 
stretch begins to increase, and the yield-point, at which the rate increases 
suddenly, may in some cases be considerable. This difference, however, will 
not be discovered in short test-pieces unless the readings of elongations are 


made by an exceedingly fine instrument, as a micrometer reading to T0008 
of aninch. In using a coarser instrument, such as calipers reading to 1/100 
of an inch, the elastic limit and the yield-point will appear to be simultane- 
ous. Unfortunately for precision of language, the term yield-point was not 
introduced until long after the term elastic limit had been almost univer- 
sally adopted to signify the same physical fact which is now defined by the 
term yield-point, that is, not the point at which the first change in rate, 
observable cnly by a microscope, occurs, but that later point (more or less 
indefinite as to its precise position) at which the increase is, great enough to 
be seen by the naked eye. A most convenient method of determining the 
point at which a sudden increase of rate of stretch occurs in short spect- 
mens, when a testing-machine in which the pulling is done by screws is 
used, is to note the weight on the beam at the instant that the beam “ drops.”” 
During the earlier portion of the test, as the extension is steadily increased 
by the uniform but slow rotation of the screws, the poise is moved steadily 
along the beam to keep it in equipoise; suddenly a point is reached at which 
the beam drops, and will not rise until the elongation has been considerably 
inereased by the further rotation of the screws, the advancing of the poise 
meanwhile being suspended. This point corresponds practically to the point 
at which the rate of elongation suddenly increases, and to the point at 
which an appreciable permanent set is firstfound, Itisalsothe point which 
has hitherto been called in practice and in text-books the elastic limit, and 
it will probably continue to be socalled, although the use of the newer term 
‘* vield-point ” for it, and the restriction of the term elastic limit to mean 
the earlier point at which the rate of streteh begins to increase, as determin- 
able only by micrometric measurements, is more precise and scientific. 

Tn tables of strength of materials hereafter given, the term elastic limit is 
used in its customary meaning, the point at which the rate of stress has be 
gun to increase, as Observable by ordinary instruments or by the drop of 
the beam. With this definition it is practically synonymous with yield- 

oint, 

3 Coefficient (or Modulus) of Elasticity.—This is a term express- 
ing the relation between the amount of extension or compression of a mate» 
rial and the load producing that extension or compression. 

It is defined as the load per unit of section divided by the extension per 
unit of length. 

Let P. be the applied load, k the sectional area of the piece, / the length of 
the part extended, A the amount of the extension, and EF the coefficient of 
elasticity. Then P +k = the load ona unit of section; A + ¢ = the elonga- 
tion of a unit of length. 

D aaa Pl 


B=7 +45 iy 


The coefucient of elasticity is sometimes defined as the figure egpressin 
the load which would be necessary to elongate a piece of one square inch 
section to double its original length, provided the piece would not break, and 
the ratio, of extension to the force producing it remained constant. This 
definition follows from the formula above given, thus: If k= one square 
inch, / and 4 each = one inch, then H = P. ; 

Within the elastic limit, when the deformations are proportional] to the 


238 STRENGTH OF MATERIALS. 


stresses, the coefficient of elasticity is constant, but beyond the elastic limit 
it decreases rapidly. 

In cast iron there is generally no apparent limit of elasticity, the deforma- 
tions increasing at afaster rate than the stresses, and a permanent set being 
produced by smallloads. The coefficient of elasticity therefore is not con- 
stant during any portion of a test, but grows smaller as the load increases. 
The same is true in the case of timber. In wrought iron and steel, however, 
there is a well-defined elastic limit, and the coefficient of elasticity within 
that limit is nearly constant. 

Resilience, or Work of Resistance of a Material,—Within 
the elastic limit; the resistance increasing uniformly from zero stress to the 
stress at the elastic limit, the work done by a load applied gradually is equal 
to one half the product of the final stress by the extension or other deforma- 
tion. Beyond the elastic limit, the extensions increasing more rapidly than 
tne loads, and the strain diagram approximating a parabolic form. the work 
is approximately equal to two thirds the product of the maximum stress by 
the extension. 

The amount of work required to break a bar, measured vopyantd in inch- 
pounds, is called its resilience; the work required to strain it to the elastic 
limit is called its elastic resilience. (See page 270.) 

Under a load applied suddenly the momentary elastic distortion is equal 
to twice that caused by the same load applied gradually. 

When a solid material is exposed to percussive stress, as when a weight 
falls upon a beam transversely, the work of resistance is measured by the 
product of the weight into the total fall. 

Elevation of Ultimate Resistance and Elastic Limit,.—Iit 
was first observed by Prof. R. H. Thurston, and Commander L. A. Beards- 
lee, U. S. N., independently, in 1878, that if wrought 1ron be subjected to a 
stress beyond its elastic limit, but not beyond its ultimate resistance, and 
then allowed to “ rest’ for a definite interval of time, a considerable in- 
crease of elastic limit and ultimate resistance may be experienced. In other 
words, the application of stress and subsequent ‘* rest” increases the resist- 
ance of wrought iron. 

This ‘“‘ rest’ may be an entire release from stress or a simple holding the 
test-piece at a given intensity of stress. 

Commander Beardslee prepared twelve specimens and subjected them to 
an intensity of stress equal to the ultimate resistance of the material, witb- 
out breaking the specimens, These were then allowed to rest, entirely free 
from stress, from 24 to 30 hours, after which period they were again stressed 
until broken. The gain in ultimate resistance by the rest was found to vary 
from 4.4 to 17 per cent. 

This elevation of elastic and ultimate resistance appears to be peculiar to 
iron and steel: it has not been found in other metals. 

Relation of the Elastic Limit to Endurance under Re= 
peated Stresses (condensed from Hngineering, August 7, 1891).— 
When engineers first began to test materials, it. was soon recognized that 
if a specimen was loaded beyond a certain point it did not recover its origi- 
nal dimensions on removing the load, but took a permanent set; this point 
was called the elastic limit. Since below this point a bar appeared to recover 
completely its original form and dimensions on removing the load, it ap- 
peared obvious that it had not been injured by the load, and hence the work- 
ine ped might be deduced from the elastic limit by using a small factor of 
safety. 

Experience showed, however, that in many cases a bar would not carry 
safely a stress anywhere near the elastic limit of the material as determined 
by these experiments, and the whole theory of any connection between the 
elastic limit of a bar and its working load became almost discredited, and 
engineers employed the ultimate strength only in deducing the safe working 
load to which their structures might besubjected. Still, as experience accu- 
mulated it was observed that a higher factor of safety was required for a live 
load than for a dead one. 

In 1871 Wohler published the results of a number of experiments on bars 
of iron and steel subjected to live loads. In these experiments the stresses 
were put on and removed from the specimens without impact, but it was, 
nevertheless, found that the breaking stress of the materials was in every 
case much below the statical breaking load. Thus, a bar of Krupp’s axle 
steel having a tenacity of 49 tons per square inch broke with a stress of 28.6 
tons per square inch, when the load was completely removed and replaced 
without impact 170,000 times. These experiments were made on a large 


STRESS AND STRAIN, 239 


number of different brands of iron and steel, and the results were concor- 
dant in showing that a bar would break with an alternating stress of only, 
say, one third the statical breaking strength of the material, if the repetitions 
of stress were sufficiently numerous. At the same time, however, it ap- 
peared from the generaltrend of the experiments that a bar would stand an 
indefinite number of alternations of stress, provided the stress was kept 
below the limit. 

Prof. Bauschinger defines the elastic Kmit as the point at which stress 
ceases to be sensibly proportional to strain, the latter being measured with 


a mirror apparatus reading to 00088 of a millimetre, or about Too000 12+ 


This limit is always below the yield-point, and may on occasion be zero. On 
loading a bar above the yield-point, this point rises with the stress, and the 
rise continues for weeks, months, and possibly for years if the bar is left at 
rest under its load. Onthe other hand, when a bar is loaded beyond its true 
elastic limit, but below its yield-point, this limit rises, but reaches a maxi- 
mum as the yield-point, is approached, and then falls rapidly, reaching even 
to zero. On leaving the bar at rest under a stress exceeding that of its 
primitive breaking-down point the elastic limit begins to rise again, and 
may, if left a sufficient time, rise to a point much exceeding its previous 
value. 

This property of the elastic limit of changing with the history of a bar has 
done more to discredit it than anything else, nevertheless it now seems as if 
it, owing to this very property, were once more to take its former place in 
the estimation of engineers, and this time with fixity of tenure. It had long 
been known that the limit of elasticity might be raised, as we have said, to 
almost any point within the breaking load of a bar. Thus, in some experi- 
ments by Professor Styffe, the elastic limit of a puddled-steel bar was raised 
16,000 lbs. by subjecting the bar to a load exceeding its primitive elastic 
limit. 

A bar has two limits of elasticity, one for tension and one for compression. 
Bauschinger loaded a number of bars in tension until stress ceased to be 
sensibly proportional to strain. The load was then removed and the bar 
tested in compression until the elastic limit in this direction had been ex- 
ceeded. This process raises the elastic limit in compression, as would be 
found on testing the bar in compression a second time. In place of this, 
however, it was now again tested in tension, when it was found that the 
artificial raising of the limit in compression had lowered that in tension be- 
low its previous value. By repeating the process of alternately testing in 
tension and compression, the two limits took up points at equal distances 
from the line of no load, both in tension and compression. These limits 
Bauschinger calls natural elastic limits of the bar, which for wrought iron 
correspond to astress of about 814 tons per square inch, but thisis practically 
the limiting load to which a bar of the same material can be strained alter- 
rately in tension and compression, without breaking when the loading is 
repeated sufficiently often, as determined by Wéhler’s method. 

As received from the rolls the elastic limit of the bar in tension is above 
the natural elastic limit of the bar as defined by Bauschinger, having been 
artificially raised by the deformations to which it has been subjected in the 
process of manufacture. Hence, when subjected to alternating stresses, 
the limit in tension is immediately lowered, while that in compression is’ 
raised until they both correspond to equal loads. Hence, in Wohler’s ex- 
periments, in which the bars broke at loads nominally below the elastic 
limits of the material, there is every reason for concluding that the loads 
were really greater than true elastic limits of the material. This is con- 
firmed by tests on the connecting-rods of engines, which of course work 
under alternating stresses of equal intensity. Careful experiments on old 
rods show that the elastic limit in compression is the same as that in ten- 
sion, and that both are far below the tension elastic limit of the material as 
received from the rolls. 

The common opinion that straining a metal beyond its elastic limit injures 
it appears to be untrue. It is not the mere straining of a metal beyond one 
elastic limit that injures it, but the straining, many times repeated, beyond 
its two elastic limits. Sir Benjamin Baker has shown that in bending a shell 
plate for a boiler the metal is of necessity strained beyond its elastic limit, 
so that stresses of as much as 7% tons to 15 tons per square inch may obtain 
in it as it comes from the rolls, and unless the plate is annealed, these 
stresses will still exist after it has been built into the boiler. In such a case, 
however, when exposed to the additional stress due to the pressure inside 


240 STRENGTH OF MATERIALS, 


the boiler, the overstrained portions of the plate will relieve themselves by 
stretching and taking a permanent set, so that probably after a year’s work- 
ing very little difference could be detected in the stresses in a plate built in- 
to the boiler as it came from the bending rolls, and in one which had been 
annealed, before riveting into place, and the first, in spite of its having been 
strained beyond its elastic limits, and not subsequently annealed, would be 
as strong as the other. 


Resistance of Metals to Repeated Shocks, 


More than twelve years were spent by Wohler at the instance of the Prus- 
sian Government in experimenting upon the resistance of iron and steel to 
repeated stresses. The results of his experiments are expressed in what is 
known as Wobler’s law, which is given in the following words in Dubois’s 
translation of Weyrauch: 

‘‘Rupture may be caused not only by a steady load which exceeds the 
carrying strength, but also by repeated applications of stresses, none of 
which are equal to the carrying strength. The differences of these stresses 
are measures of the disturbance of continuity, in so far as by their increase 
the minimum stress which is still necessary for rupture diminishes.”’ 

A practical illustration of the meaning of the first portion of this law may 
be given thus: If 50,000 pounds once applied will just break a bar of iron or 
steel, a stress very much less than 50,000 pounds will break it if repeated 
sufficiently often. 

This is fully confirmed by the experiments of Fairbairn and Spangenberg, 
as well as those of Wéhler; and, as is remarked by Weyrauch, it may be 
considered as a long-known result of common experience. It partially ac- 
counts for what Mr, Holley has called the “‘ intrinsically ridiculous factor of 
safety of six.” 

Another “‘long-known result of experience” is the fact that rupture may 
be caused by a succession of shocks or impacts, none of which alone would 
be sufficient to cause it. Iron axles, the piston-rods of steam hammers, and 
other pieces of metal subject to continuously repeated shocks, invariably 
ga after acertain length of service. They havea “life” which is lime 
ited. 

Several years ago Fairbairn wrote; ‘* We know that in some cases wrought 
iron subjected to continuous vibration assumes a crystalline structure, and 
that the cohesive powers are much deteriorated, but we are ignorant of the 
causes of this change.” We are still ignorant, not only of the causes of this 
change, but of the conditions under which it takes place. Who knows 
whether wrought iron subjected to very slight continuous vibration will en- 
dure forever? or whether to insure final rupture each of the continuous small 
shocks must amount at least to a certain percentage of single heavy shock 
(both measured in foot-pounds), which would cause rupture with one applica- 
tion ? Wohler found in testing iron by repeated stresses (not impacts) that 
in one case 400,000 applications or a stress of 500 centners to the square inch 
caused rupture, while a similar bar remained sound after 48,000,000 applica- 

‘tions of a stress of 300 centners to the square inch (1 centner = 110.2 lbs.). 

Who knows whether or not a similar law holds true in regard to repeated 
shocks ? Suppose that a bar of iron would break under a single impact of 
1000 foot-pounds, how many times would it be likely to bear the repetition 
of 100 foot-pounds, or would it be safe to allow it to remain for fifty years 
subjected to a continual succession of blows of even 10 foot-pounds each ? 

Mr. William Metcalf published in the Metallurgical Review, Dec. 1877, the 
results of some tests of the life of steel of different percentages of carbon 
under impact. Some small steel pitmans were made, the specifications for 
which required that the unloaded machine should run 44 hours at the rate 
pf 1200 revolutions per minute before breaking. 

The steel was all of uniform quality, except asto carbon. Here are the 
results; The 

.30 C- rani1h. 21m. Heated and bent before breaking. 
A9C. ‘* 1h. 28m., * $9 4 488 “s “6 
430. * 4h.57m. Broke without heating. 

65C, ‘* 3h.50m. Broke at weld where imperfect. 
80C. ** 5h. 40m. 

84C. ‘18h. 

«87 C. Broke in weld near the end. 

.96 C, Ran 4.55 m., and the machine broke down. 


Some other experiments by Mr. Metcalf confirmed his conclusion, viz.. 





STRESS AND STRAIN. 241 


that high-carbon steel was better adapted to resist repeated shocks and vi- 
brations than low-carbon steel. 

These results, however, would scarcely be sufficient to induce any en- 
gineer to use .84 carbon steel in a car-axle or a bridge-rod. Further experi- 
ments are needed to confirm or overthrow them. 

(See description of proposed apparatus for such an investigation in the 
author’s paper in Trans. A, I. M. E., vol. viii, p. 76, from which the above 
extract is taken.) 


Stresses Produced by Suddenly Applied Forces and 
Shocks, 


(Mansfield Merriman, Rk. R. & Eng. Jour., Dec. 1889.) 


Let P be the weight which is dropped from a height h upon the end of a 
bar, and let y be thé maximum elongation which is produced. The work 
performed by the falling weight, then, is 

W=Ph+y), 
and this must equal the internal work of the resisting molecular stresses. 
The stress in the bar, which is at first 0, increases up toa certain limit Q, 
which is greater than P; and if the elastic limit be not excéeded the elonga- 
tion increases uniformly with the stress, so that the internal work is equa] 
to the mean stress 1/2Q multiplied by the total elongation y, or 


W = 1/2 Qy. 
Whence, neglecting the work that may be dissipated in heat, 


1/2Qy = Ph+ Py. 
If e be the elongation due to the static load P, within the elastic limit 


y= Se: whence 
h 
e= P(r 44/1424), side ees Sate) 


ae 
which gives the momentary maximum stress. Substituting this value of Q, 


there results 
h 
y= o(1 44/1424), ase of 6 6. 8 re re (2) 


which is the value of the momentary maximum elongation. 

A shock results when the force P, before its action on the bar, is moving 
with velocity, aS is the case when a weight P falls from a height h. The 
above formulas show that this height h may be smiall if e is a small quan- 
tity, and yet very great stresses and deformations be produced. For in- 
stance, let h = 4e, then Q=4P and y = 4e; also let h=12e, then Q=6P 
and y=6e. Or take a wrought-iron bar 1 in. square and 5 ft. long: under a 
steady load of 5000 lbs. this will be compressed about 0.012 in., supposing 
that no lateral flexure occurs; but if a weight of 5000 lbs. drops upon its end 
Sud the small height of 0.048 in. there will be produced the stress of 20,000 





Ss. 

A suddenly applied force is one which acts with the uniform intensity P 
upon the end of the bar, but which has no velocity before acting upon it.- 
This corresponds to the case of h =0in the above formulas, and gives Q= 
2P and y = 2e for the maximum stress and maximum deformation. Probe 
ably the action of a rapidly-moving train upon a bridge produces stressez 
of this character. 

Increasing the Tensile Strength of Iron Bars by Twist= 
ing them.—Ernest L. Ransome of San Francisco has obtained an English 
Patent, No, 16221 of 1888, for an ‘* improvement in strengthening and testing 
wrought metal and steel rods or bars, consisting in twisting the same in a 
cold state. . . . Any defect in the lamination of the metal which would 
otherwise be concealed is revealed by twisting, and imperfections are shown 
at once. The treatment may be applied to bolts, suspension-rods or bars 
subjected to tensile strength of any description.” 4 

Results of tests of this process were reported by Lieutenant F. P, Gilmore, 
U.S. N.,in a paper read before the Technical Society of the Pacific Coast, 
published in the Transactions of the Society for the month of December, 
1888. The experiments include trials with thirty-nine bars, twenty-nine of 
which were variously twisted, from three-eighths of one turn to six turns per 
foot. The test-pieces were cut from one and the same bar, and accurately 


BaD eh ie STRENGTH OF MATERIALS, 


measured and numbered. From each lot two pieces without twist were 
tested for tensile strength and ductility. One group of each set was twisted 
until the pieces broke, as a guide for the amount of twist to be given those 
to be tested for tensile strain. 

The following is the result of one set of Lieut. Gilmore’s tests, on iron 
bars 8 in. long, .719 in. diameter. 


Twists 


No. of ees Twists} Tensile Tensile | Gain per 
Bars. Conditions, Micka per ft. | Strength. | per sq. in. cent. 

2 Not twisted. 0 0 22,000 54,180 

2 Twisted cold. % 34 23,900 59,020 9 

2 Me "E 1 14% 25,800 63,560 17 

2 we of 2 3 26,300 64,750 19 

1 r .. 216 334 26,400 65,000 20 





Tests that corroborated these results were made by the University of 
California in 1889 and by the Low Moor Iron Works, England, in 1890. 


TENSILE STRENGTH. 

The following data are usually obtained in testing by tension in a testing: 
machine a sample of a material of construction: 

The load and the amount of extension at the elastic limit. 

The maximum load applied before rupture. 

The elongation of the piece, measured between gauge-marks placed a 
stated distance apart before the test; and the reduction of area at the 
point of fracture. 

The load at the elastic limit and the maximum load are recorded in pounds 
per square inch of the original area. The elongation is recorded as a per- 
centage of the stated length between the gauge-marks, and the reduction 
area as a percentage of the original area. The coefficient of elasticity is cal- 
culated from the ratio the extension within the elastic limit per inch of 
length bears to the load per square inch producing that extension. 

On account of the difficulty of making accurate measurements of the frac- 
tured area of a test-piece, and of the fact that, elongation is more valuable 
than reduction of area as a measure of ductility and of resilience or work 
of resistance before rupture, modern experimenters are abandoning the 
custom of reporting reduction of area. The ‘‘strength per square inch of 
fractured section” formerly frequently used in reporting tests is now almost 
entirely abandoned. Thedata now calculated from the results of a tensile 
test for commercial purposes are: 1. Tensile strength in pounds per square 
inch of original area. 2. Elongation per cent of a stated length between 
gauge-marks, usually 8 inches. 3, Elastic limit in pounds per square inch 
of original area. 

The short or grooved test specimen gives with most metals, especially 
with wrought iron and steel, an apparent tensile strength much higher 
hen phe real strength. This form of test-piece is now almost entirely aban. 

oned, 

The following results of the tests of six specimens from the same 114’’ stee} 
bar illustrate the apparent elevation of elastic limit and the changes in 
other properties due to change in length of stems which were turned down 
a each uate to .798’’ diameter. (Jas. E. Howard, Eng. Congress 18938. 

ection G. 





;A56 x Elastic Limit, |Tensile Strength,| Contraction of 
Description of Stem. | rh. “per Sq. In. | Lbs. per Sq. in. | Area, per cent. 





1200 TOM oye a eteeteial: 64,900 94,400 ' 49.0 

DOL ues csistereeeuteeter 65,320 97,800 43.4 

ROD MEE a 2h, eee -.---| 68,000 102,420 39.6 
Semicircular groove, 

4”) radius 3... eee 75,000 116,380 81.6 
Semicircular groove, 

16" radius ........6.. 86,000, about 134,960 28.0 
V-shaped groove...... 90,000, about 117,000 Indeverminate, 


a a 


TENSILE STRENGTH. 243 


Tests plate made by the author in 1879 of straight and grooved test-pieces 
of boiler-plate steel cut from the same gave the following results :° 


5 straight pieces, 56,605 to 59,012 lbs. T.S. Aver. 57,566 Ibs, 
4grooved “ 64,341 to 67,400 ‘ “© 65,452 *¢ 
Excess of the short or grooved specimen, 21 per cent, or 12,114 Ibs. 


Measurement of Elongation.—In order to be able to compare 
records of elongation, it is necessary not only to have a uniform length of 
section between gauge-marks (say 8 inches), but to adopt a uniform method 
of measuring the elongation to compensate for the difference between the 
apparent elongation when the piece breaks near one of the gauge-marks, 
and when it breaks midway between them. The following method is rec- 
ommended (Trans. A. S. M. E., vol. xi., p. 622): 

Mark on the specimen divisions of 1/2 inch each. After fracture measure 
from the point of fracture the length of 8 of the marked spaces on each 
fractured portion (or 7 + on one side and 8 + on the other if the fracture is 
not at one of the marks). The sum of these measurements, less 8 inches, is 
the elongation of 8 inches of the original length. If the fracture is so 
near one end of the specimen that 7-++-spaces are not left on the shorter 
portion, then take the measurement of as many spaces (with the fractional 
part next to the fracture) as are left, and for the spaces lacking add the 
measurement of as many corresponding spaces of the longer portion as are 
necessary to make the 7-+ spaces. 

Shapes of Specimens for Tensile Tests.,—The sbapes shown 
in Fig. 75 were recommended by the author in 1882 when he was connected 


[— - —~—-- —-—16"'to 20" -— -—-—- 























V4 No.1. Square or flat bar, as 
: rolled. 


eee eee 16g KL 
















Q No. 2. Round bar, as rolled. 


-——_- —--——_-] fr (jee he a eae 
6-to 20 No. 3. Standard shape for 


flats or squares. Fillets 4% 











{US 












































 -—- 3" - — - | inch radius. 
k— -— - —-~16"'to-20— -———-=>] 
No. 4. Standard shape for 
rounds. Fillets 14 in. radius. 
a Re Tha Gag TL 
ie ay hala Sele Oe iA No. 5. Government. shape for 
Z marine boiler-plates of. iron. 
Z Not recommended for other 
per a tests, as results are generally 
11 in error, 
Fie. 75. 


with the Pittsburgh Testing Laboratory. They are now in most general 
use, the earlier forms, with 5 inches or less in length between shoulders, 
being almost entirely abandoned. J A 

Precautions Required in making Tensile Tests.—The 
testing-machine itself should be tested, to determine whether its weighing 
apparatus is accurate, and whether it is so made and adjusted that in the 
test of a properly made specimen the line of strain of the testing-machine 
is absolutely in line with the axis of the specimen. | ‘ 

The specimen should beso shaped that it will not give an incorrect record 
of strength. ‘ ¢ 

It should be of uniform minimum section for not less than five inches of 
its length. ‘ 

Regard must be had to the time occupied in making tests of certain mate- 
rials. Wrought iron and soft steel can be made to show a higher than their 
actual apparent strength by keeping them under strain for a great length 
of time. ~» iad : ; 

In testing soft alloys, copper, tin, zinc, and the like, which flow under con- 
stant strain their highest apparent strength is obtained by testing them 
rapidly. In recording tests of such materials the length of time occupied in 
the test should be stated. 


244 STRENGTH OF MATERIALS. 


For very accurate measurements of elongation, corresponding to incre- 
ments of load during the tests, the electric contact micrometer, described 
in Trans. A. S. M. E., vol. vi., p. 479, will be found convenient. When read- 
ings of elongation are then taken during the test, a strain diagram may be 
plotted from the reading, which is useful in comparing the qualities of dif- 
ferent specimens. Such strain diagrams are made automatically by the new 
Olsen testing-machine, described in Jour. Frank, Inst. 1891. 

The coefficient of elasticity should be deduced from measurement ob- 
served between fixed increments of load per unit section, say between 2000 
and 12,000 pounds per square inch or between 1000 and 11,000 pounds instead 
of between 0 and 10,000 pounds. 


COMPRESSIVE STRENGTH. 


What is meant by the term ‘‘compressive strength ” has not yet been 
settled by the authorities, and there exists more confusion in regard to this 
term than in regard to any other used by writers on strength of materials, 
The reason of this may be easily explained. The effect of a compressive 
stress upon a material varies with the nature of the material, and with the 
shape and size of the specimen tested. While the effect of a tensile stress is 
to produce rupture or separation of particles in the direction of the line of 
strain, the effect.of a compressive stress on a piece of material may be either 
to cause it to fly into splinters, to separate into two or more wedge-shaped 
pieces and fly apart, to bulge, buckle, or bend, or to flatten out and utterly re- 
sist rupture or separation of particles. A piece of speculum metal under 
compressive stress will exhibit no change of appearance until rupture takes 
place, and then it will fiy to pieces as suddenly as if blown apart by gun- 
powder.’ A piece of cast iron or of stone will generally split into wedge- 
shaped fragments. A piece of wrought iron will buckle orbend. A piece of 
wood or zine may bulge, but its action will depend upon its shape and size. 
A piece of lead will flatten out and resist compression till the last degree; 
that is, the more it is compressed the greater becomes its resistance. 

Air and other gaseous bodies are compressible to any extent as long as 
they retain the gaseous condition. Water not confined in a vessel is com- 
pressed by its own weight to the thickness of a mere film, while when con- 
fined in a vessel it is almost incompressible. 

' It is probable, although it has not been determined experimentally, that 
solid bodies when confined are at least as incompressible as water. When 
they are not confined, the effect of a compressive stress is not only to 
shorten them, but also to increase their lateral dimensions or bulge them. 

Lateral strains are therefore induced by compressive stresses. 

The weight per square inch of original section required to produce any 
given amount or percentage of shortening of any material is not a constant 

uantity, but varies with both the length and the sectional area, with the 
shape of this sectional area, and with the reiation of the area to the length. 
The ‘‘compressive strength” of a material, if this term be supposed to mean 
the weight im pounds per square inch necessary to cause rupture, may vary 
with every size and shape of specimen experimented upon. Still more diffi- 
cult would it be to state what is the ‘‘compressive strength’ of a material 
which does not rupture at all, but flattens out. Suppose we are testing a 
cylinder of a soft metal like lead, two inches in length and one inch in diam- 
eter, a certain weight will shorten it one per cent, another weight ten per 
cent, another fifty per cent, but no weight that we can place upon it will 
rupture it, for it will flatten out to a thin sheet. What, then, is its compres- 
sive strength? Again, a similar cylinder of soft wrought iron would prob- 
ably compress. a few per cent, bulging evenly all around; it would then com- 
mence to bend, but at first the bend would be imperceptible to the eye and 
too small to be measured. Soon this bend would be great enough to be 
noticed, and finally the piece might be bent nearly double, or otherwise dis- 
torted. What is the ‘‘compressive strength’’ of this piece of iron? Is it 
the weight per square inch which compresses the piece one per cent or five 
per cent, that which causes the first bending (impossible to be discovered), 
or that which causes.a perceptible bend? , 

As showing the confusion concerning the definitions of compressive 
strength, the following statements from different authorities on the strength 
of wrought iron are of interest. 

Wood’s Resistance of Materials states, ‘‘ comparatively few experiments 
have been made to determine how much wrought iron will sustain at the 
point of crushing. Hodgkinson gives 65,000, Rondulet 70,800, Weisbach 72,000 


COMPRESSIVE STRENGTH. 245 


Rankine 30,000 to 40,000. Itis generally assumed that wrought iron will resist 
about two thirds as much crushing as to tension, but the experiments fail 
to give a very definite ratio.” 

Mr. Whipple, in his treatise on bridge-building, states that a bar of good 
wrought iron will sustain a tensile strain of about 60,000 pounds per square 
inch, and a compressive strain, in pieces of a length not exceeding twice the 
least diameter, of about 90,000 pounds. 

The following values, said to be deduced from the experiments of Major 
Wade, Hodgkinson, and Capt. Meigs, are given by Haswell: 


American WrougheE I7OD. ..5 0.00 recesescscrdscsccess 12h,t2) IDM 
OU 22 WL (MEAN) jasWectiens ace cence secs .500 LL 
65,200 * 


English = ee sivtoeslesvsistevtesbd steed 40,000 ry 3 
b] 


Stoney states that the strength of short pillars of any given material, all 
having the same diameter, does not vary much, provided the length of the 
piece is not less than one and does not exceed four or five diameters, and 
that the weight which will just crush a short prism whose base equals one 
square inch, and whose height is not.less than 1 to 14 and does not exceed 
4 or 5 diameters, is called the crushing strength of the material. It would 
be well if experimenters would all agree upon some such definition of the 
term ‘‘ crushing strength,” and insist that all experiments which are made 
for the purpose of testing the relative values of different materials in com- 
pression be made on specimens of exactly the same shape and size. An 
arbitrary size and shape should be assumed and agreed upon for this pur- 
pose. The size mentioned by Stoney is definite as regards area of section, 
viz,, one square inch, but is indefinite as regards length, viz., from one to 
five diameters. In some metals a specimen five diameters long would bend, 
and give a much lower apparent strength than a specimen having a length of 
one diameter. The words ‘ will just crush ”’ are also indefinite for ductile 
materials, in which the resistance increases without limit if the piece tested 
does not bend. In such cases the weight which causes a certain percentage 
ot compression, as five, ten, or fifty per cent, Should be assumed as the 
crushing strength. 

For future experiments on crushing strength three things are desirable : 
First, an arbitrary standard shape and size of test specimen for comparison 
of all materials. Secondly, a standard limit of compression for ductile 
materials, which shall be considered equivalent to fracture in brittle mate- 
rials. Thirdly, an accurate knowledge of the relation of the crushing 
strength of a specimen of standard shape and size to the crushing strength 
of specimens of all other shapes and sizes. The latter can only be 
secured by a very extensive and accurate series of experiments upon all 
kinds of materials, and on specimens of a great number of different shapes 
and sizes. 

The author proposes, as a standard shape and size, for a compressive test 
specimen for all metals, a cylinder one inch in length, and one half square 
inch in sectional area, or 0.798 inch diameter; and for the limit of compres- 
sion equivalent to fracture, ten per cent of the original length. The term 
‘compressive strength,” or ‘‘ compressive strength of standard specimen,” 
would then mean the weight per square inch required to tracture by com- 
pressive stress a cylinder one inch long and 0.798 inch diameter, or to 
reduce its length to 0.9 inch if fracture does not take place before that reduc- 
tion in length isreached. If sucha standard, or any standard size whatever, 
had been used by the earlier authorities on the strength of materials, we 
never would have had such discrepancies in their statements in regard t@ 
the compressive strength of wrought iron as those given above. 

The reasons why this particular size is recommended are: that the sectional 
area, one-half square inch, is as large as can be taken in the ordinary test- 
ing-machines of 100,000 pounds capacity, to include all the ordinary metals 
of construction, cast and wrought iron, and the softer steels; and that the 
length. one inch, is convenient for calculation of percentage of compression, 
If the length were made two inches, many materials would bend in testing, 
and give incorrect results. Even incast iron Hodgkinson found as the méan 
of several experiments on various grades, tested in specimens 34 inch in 
height, a compressive strength per square inch of 94,730 pounds, while the 
mean of the same number of specimens of the same irons tested in pieces 114 
inches in height was only 88,800 pounds. The best size and shape of standard 
specimen should, however, be settled upon only after consultation and 
agreement among several authorities. 


246 STRENGTH OF MATERIALS. 


The Committee on Standard Tests or the American Society of Mechanical 
Engineers say (vol. xi., p. 624): 

‘* Although compression tests have heretofore been made on diminutive 
sample pieces, it is highly desirable that tests be also made on long pieces 
from 10 to 20 diameters in length, corresponding more nearly with actual 
practice, in order that elastic strain and change of shape may be determined 
by using proper measuring apparatus. 

The elastic limit, modulus or coefficient of elasticity, maximum and ulti- 
mate resistances, should be determined, as well as the increase of section at 
various points, viz., at bearing surfaces and at crippling point. 

The use of long compression-test pieces is recommended, because the in- 
vestigation of short cubes or cylinders has led to no direct application of 
the constants obtained by their use in computation of actual structures, 
which have always been and are now designed according to empirical for 
mule obtained from a few tests of long columns.”’ 


COLUMNS, PILLARS, OR STRUTS. 


Hodgkinson’s Formula for Columns, 


P = crushing weight in pounds; d = exterior diameter in inches; d, = in- 
terior diameter in inches; L = length in feet, 


Kind of Column, 


Both ends rounded, the 
length of the column 
exceeding 15 times 
its diameter. 





Both ends flat, the 
length of the column 
exceeding 30 times 
its diameter, 


Fame of eaaklroni,cii$ Fir ate P= W800 Ts 
“umng of east iron..... | P= 20 pig — | P= 99,80 
Tama oe wrdupueteony: I Ta P = 200,000 
acc nuvince plans | dissident oat Petal eotiag 
Pace of seers | Pa i710 


The above formule apply only in cases in which the length is so great that 
the column breaks by bending and not by simple crushing. If the column 
be shorter than that given in the table, and more than four or five times its 
diameter, the strength is found by the following formula ; 


PCK 
P + 34CK’ 


‘in which P = the value given by the preceding formule, K = the transverse 
section of the column in square inches, C = the ultimate compressive resis- 
tance of the material, and W = the crushing strength of the column. 

Hodgkinson’s experiments were made upon comparatively short columns, 
the greatest length of cast-iron columns being 60% inches, of wrought iron 
9034 inches. 

The following are some of his conclusions: 

1. In all long pillars of the same dimensions, when the force is applied in 
the direction of the axis, the strength of one which has flat ends is about 
three times as great as one with roun |ed ends. 

2. The strength of a pillar with ~ne nd rounded and the other flat is an 
arithmetical mean between the two given inthe preceding case of the same 
dimensions, ; 

3. The strength of a pillar having both ends firmly fixed is the same as 
one of half the length with both ends rounded, 

4. The strength of a pillar is not increased more than one seventh by en- 
larging it at the middle, 


W= 


MOMENT OF INERTIA AND RADIUS OF GYRATION. 247 


Gordon’s formule deduced from Hodgkinson’s experiments are more 
generally used than Hodgkinson’s own. They are: 


Columns with both ends fixed or flat, P = —~—, 


SS 


Columns with one end fiat, the other end round, P SS serrmeay 
1+ 1.805 
Columns with both ends round, or hinged, P = —fS_,; 
1 + 4a, 
S = area of cross-section in inches; 
P= ultimate resistance of column, in pounds; 


f = crushing strength of the material in lbs. per square inch; 
Moment of inertia, 


area of section ’ 





ry = least radius of gyration, in inches, r? = 


l= length of column in inches; 
a = a coefficient depending upon the material; 

f and a are usually taken as constants; they are really empirical variables, 
dependent upon the dimensions and character of the column as well as upon 
the material. (Burr.) 

For solid wrought-iron columns, values commonly taken are: f = 36,000 to 
40,000; a = 1/36,000 to 1/40,000. 

For solid cast-iron columns, f = 80,000, a = 1/6400. 

80,000 

100 [a2 
ae 800 d2 
d = diameter in the same unit, and p = strength in lbs. per square inch. 

The coefficient of 1?/d? is given various values, as 1/400, 1/500, 1/600, and 
1/800, by different writers. The use of Gordon’s formula, with any coef- 
ficients derived from Hodgkinson’s experiments, for cast-iron columns is to 
be deprecated. See Strength of Cast-iron Columns, pp. 250, 251. 

Sir Benjamin Baker gives, 

For mild steel, f= 67,000 lbs., a = 1/22,400. 
For strong steel, f = 114,000 lbs , a = 1/14,400 

Prof. Burr considers these only loose approximations for the ultimate 
resistances. See his formule on p. 259. 

For dry timber Rankine gives f = 7200 lbs., a = 1/3000. 


MOMENT OF INERTIA AND RADIUS OF GYRATION. 


The moment of inertia of a section is the sum of the products of 
each elementary area of the section into the square of its distance from an 
assumed axis of rotation, as the neutral axis. 

The radius of gyration of the section equals the square root of the 
quotient of the moment of inertia divided by the area of the section. If 
R = radius of gyration, J= moment of inertia and A = area, 


I I 
Ra4/t. qa F. 


The moments of inertia of various sections are as follows: 
d = diameter, or outside diameter; d, = inside diameter; b = breadth; 
i = depth; b,, h,, inside breadth and diameter; 


For hollow cast-iron columns, fixed ends, p = 1 = length and 


Solid rectangle J = 1/12bh3; Hollow rectangle I = 1/12(bh3 — b,h,3); 
Solid square J = 1/12b4; Hollow square J = 1/12(b4 — b,4); 
Solid cylinder I= 1/647d+; Hollow cylinder I= 1/647(d4 — d,4). 


Woments of Inertia and Radius of Gyration for Various 
Sections, and their Use in the Formulas for Strength of 
Girders and Columns,—‘he strength of sections to resist strains, 
either as girders or as columns, depends not only on the area but also on the 
form of the section, and the property of the section which forms the basis 
of the constants used in the formulas for strength of girders and columns 
to express the effect of the form, is its moment of inertia about its neutral 
axis. The modulus of resistance of any section to transverse bending is its 


848 STRENGTH OF MATERIALS. 


moment of inertia divided by the distance from the neutral axis to the 
fibies farthest removed from that axis; or 
Moment of inertia I 


i pa es i Ea see ee reed A eae 
Rection modulus Distance of extreme fibre from axis y 


Moment of resistance = section modulus X unit stress on extreme fibre. 


Moment of Inertia of Compound Shapes. (Pencoyd Iron 
Works.)—The moment of inertia of any section about any axis is equal to the 
I about a parallel axis passing through its centre of gravity + (the area of 
the section x the square of the distance between the axes). i 

By this rule, the moments of inertia or radii of gyration of any single sec- 
tions being known, corresponding values may be obtained for any combina- 
tion of these sections. 

Radius of Gyration of Compound Shapes,-—In the case of a 
pair of any shape without a web the value of R canalways be found with- 
out considering the moment of inertia. 

The radius of gyration for any section around an axis parallel to another 
axis passing through its centre of gravity is found as follows: 5 

Let r = radius of gyration around axis through centre of gravity; k= 
radius of gyration around another axis parallel to above; d = distance be- 
tween axes: R = Vd? + 72, 

When r is small, & may be taken as equal to d without material error. 

Graphical Method for Finding Radius of Gyration.—Benj. 
F, La Rue, Eng. News, Feb. 2, 1898, gives a short graphical method for 
finding the radius of gyration of hollow, cylindrical, and rectangular col. 
umns, as follows: 

For cylindrical columns: 

Lay off to a scale of 4 (or 40) a right-angled triangle, in which the base 
equals the outer diameter, and the altitude equals the inner diameter of the 
column, or vice versa. The hypothenuse, measured to a scale of unity (or 
10), will be the radius of gyration sought, 

This depends upon the formula 


G- fo of Inertia _ VD2 + d2 


=| = ST 


Area 4 
in which A = area and D = diameter of outer circle, a = area and d = dia- 


meter of inner circle, and G = radius of gyration. 4D? + d? is the expres- 
sion for the hypothenuse of a right-angled triangle, in which D and @ are the 
base and altitude. 

The sectional area of a hollow round column is .7854(D2 — d?). By con- 
structing a right-angled trianglein which D equals the hypothenuse and d@ 


equals the altitude, the base will equal 4/D? — d?,_ Calling the value of this 
expression for the base B, the area will equal .7854B2, 

Value of G for square columns: 

Lay off as before, but using a scale of 10, a right-angled triangle of whicl: 
the base equals D or the side of the outer square, and the altitude equals d, 
the side of the inner square. With a scale of 8 measure the hypothenuse, 
which will be, approximately, the radius of gyration. 

This process for square columns gives an excess of slightly more than 4%. 
By deducting 4% from the result, a close approximation will be obtained. 

A very close result is also obtained by measuring the hypothenuse with 
the same scale by which the base and altitude were laid off, and multiplying 
by the decimal 0.29; more exactly, the decimal is 0.28867. 

The formula is 


jg Mom, of inertia 1 sae tra Se | ee tt 
ee / Bea. Vy ee 
This may also be applied to any rectangular column by using the lesser 


diameters of an unsupported column, and the greater diameters if the col- 
ump is supported in the direction of its least dimensions. 


ELEMENTS OF USUAL SECTIONS, 

Moments refer to horizontal axis through centre of gravity. This table is 
intended for convenient application where extreme accuracy is not impor- 
tant. Some of the terms are only approximate; those marked * are correct, 
Values for radius of gyration in flanged beams apply to standard minimum 
sections only. 4 = area of section; b = breadth; h = depth; D= diameter. 





ELEMENTS OF USUAL. SECTIONS, 249 





Shape of Section. 


= $$$ | —————————__ | 


Solid Rect- 
angle. 


‘:| Hollow Rect- 
angle. 





Solid Circle. 


Hollow Circle. 
A, area of 
large section ; 
a, area of 
small section. 





Solid Triangle. 


Even Angle. 














Distance of base from centre of gravity, solid triangle, 3 even angle 


uneven angle, pane even tee, on deck beam, mat 


the table, or re 


2.3" 





Square of 























Moment | Section Least Least 
of Inertia. | Modulus. | Radius of | Radius of 
Gyration, | Gyration, 
bh3 * bh? *  |(Least side)2*| Least side # 
12 6 12 3.46 
bh3—b,h,9 *| bh3—b,h,8*| h2+hy2*| hen 
AD? * AD * D2 * D* 
16 8 16 Z 
AD?—ad? | AD?—ad?| D?+d2*| ptg 
16 8D 16 364" 
Soko The least of 
Bhs bh2 of the two:| the two: 
Tioga Jer Tgealm ges bE Te 
18 4.24 4.9 
Ah? Ah b2 b 
10.2 a 25 5 
Abt Ah (hb)? hb 
web 6.5 | 13(h? + 02) | 2.6 +b) 
19 9.5 92.5 a04 
Ah2 Ah b2 yy 
11.1 8 22.5 4.74 
Ah? Ah b2 b 
6.66 3.2 9] 4.58 
Ah? Ah b2 5 
7.34 3.67 12.5 3.54 
Ah? Ah b2 b 
6.9 4 36.5 6 


—_——___ — 


h, 
’ 3.3? 


all other shapes given in 


250 STRENGTH OF MATERIALS, 


The Strength of Cast-iron Columns, 


Hodgkinson’s experiments (first published in Phil. Trans. Royal Socy., 
1840, and condensed in Tredgold on Cast Iron, 4th ed., 1846), and Gordon’s 
formula, based upon them, are still used (1898) in designing cast-iron col- 
umns. That they are entirely inadequate as a basis of a practical formula 
suitable to the present methods of casting columns will be evident from 
what follows. 

Hodgkinson’s experiments were made on nine ‘‘ long ”’ pillars, about 714 
ft. long, whose external diameters ranged from 1.74 to 2.23 in., and average 
thickness from 0.29 to 0.35 in., the thickness of each column also varying, 
and on 18 ‘‘short ’’ pillars, 0.733 ft. to 2.251 ft. long, with external diameters 
from 1.08 to 1.26 in., all of them less than 14 in. thick. . The iron used was 
Low Moor, Yorkshire, No. 3, said to be a good iron, not very hard, earlier 
experiments on which had given a tensile strength of 14,535 and a crushing 
strength of 109,801 lbs. per sq.in. The results of the experiments on the 
“long ’’ pillars were reduced to the equivalent breaking weight of a solid 
pillar 1 in. diameter and of the same length, 7144 ft., which ranged from 2969 
to 3587 lbs. per sq. in., a range of over 12 per cent, although the pillars were 
made from the same iron and of nearly uniform dimensions. From the 13 
experiments on ‘‘short’’ pillars a formula was derived, and from it were 
obtained the ‘‘ calculated” breaking weights, the actual breaking weights 
ranging from about 8 per cent above to about 8 per cent below the ealcu- 
lated weights, a total range of about 16 per cent. Modern cast-iron columns, 
such as are used in the construction of buildings, are very different in size, 
proportions, and quality of iron from the slender ‘‘long’’ pillars used in 
Hodgkinson’s experiments. There is usually no check, by actual tests or by 
disinterested inspection, upon the quality of the material, The tensile, com- 
pressive, and transverse strength of cast iron varies through a great range 
(the tensile strength ranging from less than 10.000 to over 40.000 lbs. per sq. 
in.), with variations in the chemical composition of the iron, according to 
laws which are as yet very imperfectly understood, and with variations in 
the method of melting and of casting. There is also a wide variation in the 
strength of iron of the same melt when cast'into bars of different thick- 
nesses, It is therefore impossible to predict even approximately, from the 
data given by Hodgkinson of the strength of columns of Low Moor iron in 
pillars 744 ft. Jong, 2in. diam., and 4 in. thick, what will be the strength of 
a column made of American cast iron, of a quality not stated, ina column 
16 ft. long, 12 or 15 in. diam., and from 34 in. to 114 in. thick. 

Another difficulty in obtaining a practical formula for the strength of cast- 
iron columns is due to the uncertainty of the quality of the casting, and the 
danger of hidden defects, such as internal stresses due to unequal cooling, 
cinder or dirt, blow-holes, ‘‘ cold-shuts,”? and cracks on the inner surface, 
which cannot be discovered by external inspection. Variation in thick- 
ness, due to rising of the core during casting, is also a common defect. 

In addition to,the above theoretical or a priori objections to the use of 
Gordon’s formula, based on Hodgkinson’s experiments, for cast-iron 
columns, we have the data of recent experiments on full-sized columns. 
made by the Building Department of New York City (Hng’g News, Jan. 18 
and 20, 1898). Ten columns in all were tested, six 15-inch, 1901 inches long, 
two 8-inch, 160 inches long, and two 6-inch, 120 inches long. The tests were 
made on the large hydraulic machine of the Phoenix Bridge Co., of 2,000,000 
pounds capacity, whicn was calibrated for frictional error by the repeated 
testing within the elastic limit of a large Phoenix column, and the compayri- 
son of. these tests with others made on the government machine at the 
Watertown Arsenal. The average frictional error was calculated to be 
15.4 per cent, but Hngineering News, revising the data, makes it 17.1 per 
cent, with a variation of 3 per cent either way from the average with differ- 
ent loads. The results of the tests of the volumes are given on the opposite 
page. 

Column No. 6 was not broken at the highest load of the testing machine. 

Columns Nos. 3 and 4 were taken from the Ireland Building, which col- 
lapsed on August 8, 1895; the other four 15-inch columns were made from 
drawings prepared by the Building Department, as nearly as possible 
duplicates of Nos.3 and4. Nos. 1 and 2 were made by a foundry in New 
York with. no knowledge of their ultimate use. Nos. 5 and 6 were made by 
a foundry in Brooklyn with the knowledge that they were to be tested. 
Nos. 7 to 10 were made from drawings furnished by the Department, 


THE STRENGTH OF CAST-IRON COLUMNS. 251 


TESTS OF CAST-IRON COLUMNS. 





Thickness. Breaking Load. 
Number Dei riers eee. teen tee ba ek ST TARE Ore Ate: on eee Pa gC eh oe 
Inches. Pounds 
Max. Min. | Average. Pounds. per sq. in. 
1 15 1 1 1 1,856,000 80,830 
2 15 15/16 1 11g 1,330,000 27,700 
8 15 14 1 114 1,198,000 24,900 
4 15% 17/32 1 114 1,246,000 25,200 
5 15 a Sse 1 11/64 | 1,632,000 32,100 
6 15 1144 144 1 8/16 | 2,082,000 + 40,400 + 
734 to 8144] 144 54 1 651,000 31,900 
8 8 1 3/32 1 1 3/64 612,800 26,800 
9 61/16 | 15/32 114 1 9/64 400,000 22.700 
10 6 3/32 1k 1 1/16 1 7/64 455,200 26,300 
“Applying Gordon's formula, as used by the Building Department, 
00a Z| F 
ile air 92° to these columns gives for the breaking strength per square 
1+ a0 


inch of the 15-inch columns 57,143 pounds, for the 8-inch columns 40,000 
pounds, and for the 6-inch columns 40,000. The strength of columns Nos. 3 
and 4 as calculated is 128 per cent more than their actual strength; their 
actual strength is less than 44 per cent of their calculated strength; and the 
factor of safety, supposed to be 5in the Building Law, is only 2.2 for central 
loading, no account being taken of the likelihood of eccentric loading. 

Prof. Lanza, in his Applied Mechanics, p. 372, quotes the records of 14 
tests of cast-iron mill columns, made on the Watertown testing-machine in 
1887-88, the breaking strength per square inch ranging from 25,100 to 63,310 
pounds, and showing no relation between the breaking strength per square 
inch and the dimensions of the columns. Only 3 of the {4 columns had a@ 
strength exceeding 83,500 pounds per square inch, The average strength of 
the other 1! was 29,600 pounds per square inch. Prof. Lanza says that it is 
' evident that in the case of such columns we cannot rely upon a crushing 
strength of greater than 23,000 or 30,000 pounds per square inch of area of 
section. 

He recommends a factor of safety of 5 or 6 with these figures for crush- 
ing strength, or 5000 pounds per square inch of area of section as the highest 
allowable safe load, and in addition makes the conditions that the length of 
the column shall not be greatly in excess of 20 times the diameter, that the 
thickness of the metal shall be such as to insure a good strong casting, and 
that the sectional area should be increased if necessary to insure that the 
extreme fibre stress due to probable eccentric loading shall not be greater 
than 5000 pounds per square inch. 

Prof. W. H. Burr (Hng’g News, June 30, 1898) gives a formula derived 
from plotting the results of the Watertown and Phoenixville tests, above 
described, which represents the average strength of the columns in pounds 
per square inch. It is p = 30,500 -- 1601/d. It is to be noted that this is an 
average value, and that the actual strength of many of the columns was 
much lower. Prof. Burr says: ‘“‘If cast-iron columns are designed with 
anything like a reasonable and real margin of safety, the amount of metal 
required dissipates any supposed economy over columns of mild steel.” 

Wransverse Strength of Cast-iron Water-pipe. (Technology 
Quarterly, Sept. 1597.)—Tests of 31 cast-iron pipes by transverse stress 
gave a maximum outside fibre stress, calculated from maximum load, 
assuming each half of pipe as a beam fixed at the ends, ranging from 12,800 
lbs. to 26,300 Ibs. per sq. in. 

Bars 2 in, wide cut from the pipes gave moduli of rupture ranging from 
28,400 to 51,400 lbs. per sq. in. Four of the tests, bars and pipes: 

Moduli of rupture of bar............ 28,400 34,400 40,000 51,400 
IDLO SILESsIOl PIPE’. .. c's «scatterers 18,300 12,800 14,500 26,300 

These figures show a great variation in the strength of both bars and 
pipes, and also that the strength of the bar does not bear any definite rela- 
tion to the strength of the pipe. 


R52 STRENGTH OF MATERIALS, es 


Safe Load, in Tons of 2000 Lbs., for Round Cast-iron 
Columns, with Turned Capitals and Bases, 
Loads being not eccentric, and length of column not exceeding 20 times 


the diameter. Based on ultimate crushing strength of 25,000 lbs. per sq. in. 
and a factor of safety of 5. (For eccentric loads see page 254.) 








Thick- Diameter, inches. 
ness, 
mehes. | ¢ 17] 8{91/10| 11 | 19 | 18 | 14 |:15 | 16 | 18 
54 — |26.4/31.3 
8% —_|30.9/36.8)42. 7/48. 654.5 
3 35.2/42.1/48.9/55.8162.7| 69.6] 76.5 3 ) 
1 39.2147.1155.0/62.8]70.7| 78.5} 86.4] 94.2] 102.1] 110.0 
144 ~‘(|.,..|....160.8/69.6178.4] 87.2] 96.1| 104.9] 113.8] 122.6] 131.4 
144 a Be 76.1/85.9| 95.7| 105.5] 115.3) 125.2] 135.0] 144.8] 164.4 
eas ee ee TS los:a| 10829] 114.7] 125.5] 136/38] 147.1] 157.9] 179.5 
We |occcd cs]accefareslon-s{sosede| 128-7] -485,6]-147.8] 150.0] 170.8] 10404 
ao i peels cart Pelt eee ea at vevesaleeeeee| 168.4] 182.1] 195.8] 223.3 
ie as cine lary Vela ee BA Datel Piatto Cele veeese| 204.2] 219.9] 251.3 


For lengths greater than 20 diameters the allowable loads should be 
decreased. How much they should be decreased is uncertain, since suf. 
ficient data of experiments on full-sized very long columns, from which 
a formula for the strength of such columns might. be dérived, are as yet 
lacking. There is, however, rarely, if ever, any need of proportioning cast. 
iron columns with a length exceeding 20 diameters. 


Safe Loads in Tons of 2000 Pounds for Cast-iron Columns, 
(By the Building Laws of New York City, Boston, and Chicago, 1897.) 
New York, Boston. Chicago. 


8a 5a 5a 
Square columns...... : 12 12 ; 13 
1+ ioe = + iperaa + §00a2 
8a 5a 5a 


13 3 


Round columns.,...... l 
1 1+ a2 tap «= t+ Goa 


a = sectional area in square inches; 7 = unsupported length of column in 
* {nches; d = side of square Column or thickness of round column in inches. 

The safe load of a 15-inch round column 1} inches diameter, 16 feet long, 
according to the laws of these cities would be, in New York, 861 tons; in 
Boston, 264 tons; in Chicago, 250 tons. 

The allowable stress per square inch of area of such a column would be, 
in New York, 11,350 pounds; in Boston, 8300 pounds; in Chicago, 7850 pounds. 
A safe stress of 5000 pounds per square inch would give for the safe load on 
the column 159 tons. 

Strength of Brackets on Cast-iron Columns,.—The columns 
tested by the New York Building Department referred to above had 
brackets cast upon them, each bracket consisting of a rectangular shelf 
supported by one or two triangular ribs. These were tested after the 
columns had been broken in the principal tests. In 17 out of 22 cases the 
brackets broke by tearing a hole in the body of the column, instead of by 
shearing or transverse breaking of the bracket itself. The results were 
surprisingly low and veryitreguiar. Reducing them tostrength per square 
inch of the total vertical section through the shelf and rib or ribs, they 
ranged from 2450 to 5600 lbs., averaging 4200 Ibs., for a load concentrated 
at the end of the shelf, and 4100 to 10,900 lbs,, averaging 8000 lbs., for a dis- 
tributed load. (#ng’g News, Jan. 20, 1898.) 


SAFE LOAD OF CAST-IRON COLUMNS. 253 


Safe Loads, in Tons, for Round Cast Columns. 
(In accordance with the Building Laws of Chicago.*) 





Diame-| Thick- | Unsupported Length in Feet. 


terin | nessein { 


Peehes-» Inher: “10, | s |10| 12/14/16! 18| 20/22] 24/26/98 | 30 

















50| 43} 37] 32] 27 
6 i Bi] 50| 42| 36] 31 Formula: w= 1 
62} 56] 49] 43! 38} 33 Lhe 
7 5 AAA Oe 9 iia | 
% 1) 64) 57) 49) 43) 38 w = safeload in tons of 
34 75] 69} 62] 56] 50] 44] 39 2000 pounds; 
8 % 86; 79) %1] 64) 57) 50} 44) a = cross- REE HOR of col- 
3 97/ 89] 81, 72] 63] 56] 50 um 
7% | 101] 94) 986} 78} 70) 63} 57 1 = unsupported length 
94|° 1 113] 105} 97| 88] 79) 71| 64 in inches; 
1% 126] 117] 107/971 88} 79| 71| @ = diameter in inches. 
f % | 116) 109] 101} 93] 85} 78} 71) 64 Dar 
104 1 130] 122} 114] 105} 96} 88! 80] 72 
1 145) 136} 126] 117| 107} 97| 88| 80 
L 1144 | 158] 149] 139} 128] 117} 107] 97] 88 
( 1 147] 139] 131} 122] 113] 104) 96] 88] 80 
11 144 | 163] 155] 146] 136] 126] 116] 106] _97| 89 
| 144 | 179] 170] 160] 149] 138] 127| 117] 107] 98 
134 195] 185} 174] 162] 150] 138} 127] 117) 106 
( 114 | 181] 174] 165} 155] 145] 135] 125] 115] 106] 98 
124 14 199] 191] 181] 170} 159) 148} 187; 127) 117) 108 
ae 18 217] 207] 197] 185} 173] 161) 149] 138] 127) 117 
L 13g | 284) 224] 212] 200] 187] 173] 161] J49| 187] 126 
( 1144 | 200} 192] 194) 174] 164] 154 144} 134) 125) 116] 107 
13 134 | 219} 211] 202] 191] 180] 169) 158} 147} 187) 127] 117 
134 239] 230] 220} 208] 196] 184] 172] 160] 149) 138] 128 
| 144 | 258] 248] 237] 225] 212] 199] 186] 173) 161] 149] 138 
114 232] 293] 213] 202] 191} 180} 168] 157] 147] 137] 128 
144 13g 253] 243] 232] 220] 207] 195} 183] 171} 160] 149] 139 
1h4 273] 263] 251] 238} 224] 211) 198] 185} 173} 161] 150 
l 15 293] 982| 269] 255] 241) 227] 212] 198] 185] 173] 161 
( 134 266| 2535] 243] 231] 219] 206} 194] 182] 171] 160] 150 
15 1 987| 276] 263} 250} 236] 223] 210) 197] 185] 173] 162 
154 309] 296] 283] 268] 254] 239] 225] 211] 198} 186] 174 
134 29} 316] 301] 286} 271] 255} 240] 225] 211] 198} 185 
114 301] 288, 275] 262] 248} 235] 222] 209] 197] 185 
16 15g 328] 310} 296] 282] 267) 253] 239] 225] 212) 199 
1 134 345| 331| 316] 300] 285} 270} 254] 239] 225) 212 
154 366] 351) 337] 322) 307} 293] 279] 264) 251 
18 134 391] 375] 360] 344} 328} 313] 298] 282] 268 
1% 415] 399) 883] 366, 349] 333] 317] 300! 285 
134 435] 420] 404] 389) 373] 357| 841] 326 
20 1% 463] 447| 431] 414) 397] 380] 863) 347 
- Q 490| 473| 456] 438! 420) 402] 384] 367 
{| 2% 517| 499| 481] 462| 443] 425, 406] 387 
i 134 480} 464] 448] 432] 416) 400] 384 
994 1% 511| 494] 478] 461] 443] 426] 409 
24 B41] 524| 506] 488] 470) 452) 434 
a4 581} 562] 543} 524] 504) 485) 465 
Ql4 626} 608] 589] 570} 550] 531 
234 668] 639] 620} 600) 579] 559 
241) 036 691| 671] 650] 629] 608| 587 
{ 214 724] 703] 681] 659) 637, 614 








From tables published by The Expanded Metal Co., Chicago, 1897,) __ 


Rot STRENGTH OF MATERIALS, 


ECCENTRIC LOADING OF COLUMNS. 


In a given rectangular cross-section, such as a masonry joint under pres& 
ure, the stress will be distributed uniformly over the section only when the 
resultant passes through the centre of the section; any, deviation from such 
a central position will bring a maximum unit pressure to one edge and a 
minimum to the other; when the distance of the resultant from one edge is 
one third of the entire width of the joint, the pressure at the nearer edge is 
twice the mean pressure, while that at the farther edge is zero, and that 
when the resultant approaches still nearer to the edge the pressure at the 
farther edge becomes less than zero; in fact, becomes a tension, if the 
materiai (mortar, ete., there is capable of resisting tension. Or, if, as usual 
in masonry joints, the material is practically incapable of resisting tension, 
the pressure at the nearer edge, when the resultant approaches it nearer 
than one third of the width, increases very rapidly and dangerously, becom- 
ing theoretically infinite when the resultant reaches the edge. 

With a given position of the resultant relatively to one edge of the joint or 
section, a similar redistribution of the pressures throughout the sectien may 
be brought about by simply adding to,or diminishing the width of the 
section. 

Let P = the total pressure on any section of a bar of uniform thickness. 

w = the width of that section = area of the section, when thickness =: 1. 

p = P/w = the mean unit pressure on the section. 

M = the maximum unit pressure on the section. 

n= the minimum unit pressure on the section. 

d = the eccentricity of the resultant = its distance from the centre o 
the section. 


Then M = p (14%) ana hi =p che “ . 


When d = Fw then M = 2p and m = 0. 


When d is greater than 1/6w, the resultant in that case being less than 
one third of the width from one edge. » becomes negative. (J. C. Traut- 
wine, Jr., Engineering News, Nov. 23, 1893.) 

Eccentric Loading of Cast-irom Columms,. — Prof. Lanza 
writes the author as follows: The table ou page 252 applies when the resultant 
of the loads upon the column acts along its central axis, i.e., passes through 
the centre of gravity of every section. In buildings and other construc- 
tions, however, cases frequently occur when*the resultant load does not 
pass through the centre of gravity of the section; and then the pressure is 
not evenly distributed over the section, but is greatest on the side where 
the resultant acts. (Examples occur when the loads on the floors are not 
uniformly distributed.) In these cases the outside fibre stresses of the 
column should be computed as follows, viz.: ; 
Let P = total pressure on the section; 

d = eccentricity of resultant = its distance from the centre of gravity 
of the section; 

A = area of the section, and Jits moment of inertia about an axis in its 
plane, passing through its centre of gravity, and perpendicular 
to d (see page 267); 

Cc, = distance of most compressed and cg = that of least compressed 
fibre from above stated axis; 

8; = Maximum and sg = minimum pressure per unit of area. Then 


Rae and FA ibe et ES 
A I A L 

Having assumed a certain ftréal section for the column to be designed, sy 
should be computed, and,if it exceed the proper safe value, a different 
section should be used for which s, does not exceed this value. 

The proper safe value, in the case of cast-iron columns whose ratio of 
length to diameter does not greatly exceed 20, is 5000 pounds per square inch 
when the eccentricity used in the computation of s, is liabie to occur fre- 
quently in the ordinary uses of the structure; but when it. is one which can 
only occur in rare cases the value 8000 pounds per square inch may be used. 

A long cap ona column is more conducive to the production of eccen- 
tricity of loading than a short one, heuce a long cap is a source of weakness 
in a column. 


ULTIMATE STRENGTH OF WROUGHT-IRON COLUMNS. 255 


ULTIMATE STRENGTH OF WROUGHT-IRON |: 
COLUMNS. 
(Pottsville Iron and Steel Co.) 


Computed by Gordon’s formula, p = 


dh. ede tberbe 
t\* 
1+ o(4) 
p = ultimate strength in lbs. per square inch; 
Bs length of column in inches; 
=: least radius of gyration in inches; 
f= = 40,000; 
7 0 000 for square end-bearings; 1/30,000 for one pin and one square 
beari ing; 1/20,000 for two pin-bearings. 
For safe working load on these columns use a factor of 4 when used in 
buildings, or when subjected to dead load only; but when used in bridges 
the factor should be 5. 


WROUGHT-IRON COLUMNS. 








Ultimate Strength in lbs. Safe Strength in Ibs. per 

; per square inch. , | square inch—Factor of 5. 
E Pi 1 3 Pi d 
Square ee Pin Square Bian: in 
Ends. Bane " Ends. Ends. aaa. © | Ends. 

10 39944 39866 39800 10 7989 797% 7960 
15 89776 89702 39554 15 7955 7940 7911 
20 39604 39472 89214 20 7921 7894 7843 
25 389384 89182 38788 25 W877 7836 T158 
30 89118 88834 38278 30 7821 7767 7656 
35 38810 38430 37690 35 7762 7686 7538 
40 38460 37974 370386 40 7692 7595 7407 
45 88072 37470 36322 45 7614 7494 7264 
50 37646 86928 85525 50 7529 7386 7105 
55 37186 36336 34744 55 7437 7267 6949 
60 36697 35714 83898 60 7339 7143 6780 
65 86182 34478 33024 65 7236 6896 6605 
fl 35634 84384 82128 70 7127 6877 6426 
5 35076 33682 31218 5 7015 6736 6244 
80 34482 82966 80288 80 6896 6593 6058 

85 83883 82236 29384 85 77 6447 587 
90 33264 31496 28470 90 6653 6299 5694 
95 32636 80750 27562 95 6527 6150 Hole 
100 32000 30000 26666 100 6400 6000 5333 
105 813857 29250 25786 105 6271 5850 5157 








Maximum Permissible Stresses in columns used in buildings. 
[Building Ordinances of City of Chicago, 1893.) 
For riveted or other forms cf wrought-iron columns: 
12000c 





games Be lt = length of coluinn in inches; 
j2 ry = least radius of gyration in inches; 
a 36000r2 a = area of column in square inches. 
For riveted or other steel columns, if more than 607 in length: 
S = 17,000 — - 

If less than 607 in length: S = 13,500a 
For wooden posts: 

ac a@ = area of post in square inches; 

= 7 ie d = least side of rectangular post in inches;. 
1+ 350d? 1 = Jength of post in inches; 
By 


890 fer oak; 


600 for white or Norway pine; 
=} 900 for long- leaf yellow pine, 


256 STRENGTH OF MATERIALS. 


BUILT COLUMNS. 


From experiments by T. D. Lovett, discussed by Burr, the values of f and 
a in several cases are determined, giving empirical forms of Gordon’s for- 
mula as follows: p = pounds crushing strength per square inch of section, 
i = length of column in inches, + = radius of gyration in inches. 


ee {> ue 
is y os Ls 
i) 
Am. Br.Co. 


Closed Open Square Phocnis 
Fie. 76. 
Flat Ends. 
Keystone Square Phoenix American Bridge 
Columns. Columns. Columns. Co. Columns. 


39,500 39,000 42.000 36,000 a 
Beh hag tewdt eis a ake Ta bal ied atoun tica, ep a 


: + 15300 72 35,000 72 , 50,000 72 + 76,000 r2 
Flat Ends, Swelled,. 
86,000 eos @eoeoeeeeoarveser 
p = ean aes (2) ew reslee ee welee m  | taauale cleae e166 
ie 18,300 7? 
Pin Ends. 
000 42,060 36,000 
Die tet tees ee ee ee es ___ 39.000 6) | ey) a (10) 
coat ES (qe 
+ 77000 v2 22,700 +2 — * 21,500 72 
Pin Ends, Swelled. 
36,009 
p= i D (3) siete gebleten sole) 0). uc wlave le wreye ace, @sece s@eeeeneescseoe 
Let 15,000 73 
Round Ends. 
42.000 86,000 
ii eevee ses oese eaeteccerveoce sae 1(8) cn car (11) 
OIC hed yy RTE 
12,500 72 11,500 72 


With great variations of stress a factor of safety of as high as 6 or 8 may 
be used, or it may be as low as 8 or 4, if the condition of stress is uniform or 
essentially so. 

Burr gives the following general princip!es which govern the resistance of 
built columns : 

The material should be disposed as far as possible from the neutral axis 
of the cross-section, thereby increasing 1; 

There should be no initial internal stress; 

The individual portions of the column should be mutually supporting; 

The individual portions of the column should be so firmly secured to each 
other that no relative motion can take place, in order that the column may 
fail as a whole, thus maintaining the original value of r. 

Stoney says: ** When the length of a rectangular wrought-iron tubular 
column does not exceed 30 times its least breadth, it fails by the bulging or 
ee of a short portion of the plates, not by the flexure of the pillar asa 
whole.’ 

In Trans. A. 8, C. E., Oct. 1880, are given the following formule for the 
ultimate resistance of wrought-iron columns designed by C. Shaler Smith; 


BUILT COLUMNS, 257 











Flat Ends, 
Square Phoenix American Bridge Common 
Column. Column. Co. Column. Column. 

‘ 36,500 26,50 
eR ee iy Poe Cen ee tay 
ened B EBate eS eras 1G: yale 

5820 d? 4500 d? 38750 qd? 2700 d2 
One Pin End. 
38,500 40,000 86,500 86,500 
JS serrgehary he. ST a aR Bah es eek FO ATS) 4 
+3000 a2 2350 a +350 2 + i500 at 
4 Two Pin Ends, 
87,500 ; 36,600 36,500 36,500 
er ea. (14) ra bays ay wees cr (20) Leet nee (23) 
+ i900 @ 1500 a3 1760 ai 1+ 500 a 


The “common ’’ column consists of two channels, opposite, with flanges 
outward, with a plate on one side and a lattice on the other. 

The formula for ‘* square ’’ columns may be used without much error for 
the common-chord section composed of two channel-bars and plates, with 
the axis of the pin passing through the centre of gravity of the cross- 
section. (Burr). 

Compression members composed of two channels connected by zigzag 
eee may be treated by formule 4 and 5, using f = 36,000 instead of 

Experiments on full-sized Phoenix columns in 1873 showed a close agree- 
ment of the results with formule 6-8. Experiments on full-sized Phoenix 
columns on the Watertown testing-machine in 1881 showed considerable dis- 
crepancies when the value of 1 + 7 became comparatively small. The fol- 
lowing modified form of Gordon’s formula gave tolerable results through 
the whole range of experiments : 


40,000 (1-77 
Phoenix columns, flat end, p= “ ee (24) 


1+50,000 72 





Plotting results of three series of experiments on Phoenix columns, a 
more simple formula than Gordon’s is reached as follows : 


Phoenix columns, flat ends, p = 39,640 — 46, whenl-+~r is from 30 to 140; 
p = 64,700 — 4600 NA ! when 2+ risless than 30, 
r 


Dimensions of Phenix Columns, 


(Pheenix Iron Co.) 

The dimensions are subject to slight variations, which are unavoidable in 
rolling iron shapes. 

The weights of columns given are those of the 4, 6, or 8 segments of which 
they are composed. The rivet heads add from 2% to 5% to the weights given. 
Rivets are spaced 3, 4, or 6 in. apart from centre to centre, and somewhat 
more closely at the ends than towards the centre of the column, 

G columns have 8 segments, # columns 6 segments, C, B?, B!, and A have 
4segments. Least radius of gyration = D X .3636. 

The safe loads given are computed as being one-fourth of the breaking 
load, and as producing a maximum stress, in an axial direction, on asquare- 
end column of not more than 14,000 lbs, per sq. in, for lengths of 90 radij 
and under, 


258 STRENGTH OF MATERIALS. 


Dimensions of Phoenix Stee! Columns, 
(Least radius of gyration equals Dx .3626.) 































































One Segment, Diameters in Inches. | Oue Column. 
wn n w 
| So 3 . es ke . ee 
ea gol 28, . © i oF pee ee Ons 
geile tee | Bebo ee tke ee 
S ae a g ag | aoa s | gfs 
gs oh q 5 SS slese vo | 25 Be 
Pt caw nl Oo = & 7 a on moO SS 
‘BR Q cH | oo | OSs 
= < * 
3/16 9.7 4 61/16) 3.8 | 12.9 | 1.45 
VY 12.2 A 4, 63/16| 4.8 | 16.3 | 1.50 
5/16 | 14.8 354 414 65/16} 5:8 | 19.7 | 1.55 
34 17.3 434 67/16| 6.8 | 28.1 | 1.59 
V4 16.3 58% 8g 6.4 | 21.8 | 1.95 
5/16 | 19.9 54 83/16 | 7.8 | 26.5 | 2.00 
36 23.5 44 55g 85/16 | 9.2 | 31.3 | 2.04 
V6 | 27.0 - 534 87/16 | 10.6 | 36.0 | - 2.09 
Wag bee i (OTe abi aG Ble 12.0 | 40.8 | 2.13 
9/16 34.2 6 8 9/16 13.4 45.6 2.18 
bg 37.7 614 8 11/16 14.8 } 50.3 | 2.23 
V4 18.9 6 9/16 | 914 7.4 | 25.2 | 2.39 
5/16 22.9 6 11/16} 934 9.0 30.6 2.43 
36 27.0 6 138/16) 9 7/16 10.6 36.0 2.48 
W6 (SCT Sy erat | 6 15/16) 916 12.2 | 41.5 | 2.52 
j 35.2 s 71/16 | 954 13.8 | 46.9 | 2.57 
9/16 39.3 7 3/16 | 934 15.4 52.4 2.61 
% 43.3 f D/AGals GAB /NG iar 7,50 57.8 | 2.66 
14 2514 % 13/16]11 11/16} 10.0 34.0 2.84 
5/16 31 7 15/16)1134 ey i 41.3 2.88 
36 8 1/16 }11 138/16} 14.1 48.0 2.93 
7/16 41 8 3/16 }11% 16.0 54.6 2.9% 
% 46 85/16 11/15/46} 18.0 61.3 3 01 
9/16 51 8 7/16 }1 19.9 68.0 3.06 
5 56 C 8 9/16 (12 1/16 | 21.9 | 74.6 | 3.11 
11/16 62 734 8 11/16}12 3/16 24.5 82 6 3.16 
68 8 13/16}12 5/16 26.6 90.6 3.20 
13/16 73 8 15/16}12 7/16 | 28.6 ects} 3.24 
A ‘8 9 1/16 [1246 30.6 | 104.0 | 3.29 
89 9 5/16 11256 34.8 118.6 3.34 
1144 99 9 9/16 112 13/16} 38.8 132.0 3.48 
14 109 9 13/16}18 42.67 145.3 3.57 
_——— || J | a | ff ——— ee Pee a 
1 28 11 9/16 |151% 16.5 56.0 4.20 
5/16 | 326 11 11/16]1554 19.1 | 65.0 | 4.25 
36 37 11 13/16) 1534 lant 74.0 4.29 
7/16 42 11 15/16) 15% 24.7 84.0 4.34 
1% 47 121/16 |15 15/16) 27.6 94.0 4,38 
9/16 52 12 3/16 |16 1/16 20.6 104.0 4.43 
5 57 E 12 5/16 |16 3/16 33.5 114.0 4.48 
11/16 | 62 111/16 {12 7/16 |16 5/16 | 36.4 | 124.0 | 4.52 
3 6 12 9/16 |16 7/16 40.0 136.0 4.56 
13/16 fi 12 11/16]16 9/16 43.0 146.0 4.61 
% (i 12 13/1616 11/16) 45.9 156.0 4.66, 
88 13 1/16 j16 138/16). 51-7 176.0 4.7 
1% 98 13 5/16 |17 1/16 | 57.6. | 196.0 | 4.84 
114 108 13 9/16 |17 5/16 63.5 216.0 4.93 
5/16 | 31 15% — |198% o4.2 | §2.6 | 5.54 
34 36 G 158% {1914 28.1 | 96.0 | 5.59 
7/16 41 1454 1514 1954 82.0 | 109.3 5.64 
ig | 46 155g 119°'11/16' 36.0 | 122.6 ! 5.68 


Tons for 16-feet 


Safe Load in Net 
Lengths. 














FORMULZ FOR IRON AND STEEL STRUTS. 209 














One Segment. Diameters in Inches. One Column. 32 

: te Bhan. Wig ai Ra A ae ail ae Ao 

RN 7) ae) 

a 2 5 Qh Ey 38 a=ees 

: ° 5 = Oe pa 
Se luis caus S| tow VB vib Se | SE Bales ae 
® 2 — 3 -— mR b> fo q oe a8 Bis ee] 
pice eel B = 68 MS Bd ea es Pt eg) Saas 
af! ep 4 °o aie Eases eh ee arse er oea 
SI oi ° ag fod | C8 | SoS] ea4 

= <j = 4 oD) 

9/16 51 1534 1934 39.9 136.0 5.73 280.0 
56 56 15% | 19% | 43.8 | 149.38 | 5.77 | 307.4 
11/16 61 16 20 (ae 162.6 5.82 334 9 
34 66 1644 20144 Si 176.0 5.88 362.4 
13/16 71 G 1614 2074 Da. 189.3 5.91 389.8 
Z "6 1454 1634 | 203g | 59.6 | 202.6 | 5.95 | 417.3 
1 8 1654 2054 67.4 229.3 6.04 472.1 
1% 96 16% 20% 15.3 256.0 6.13 527.3 
114 106 1714 |) 21 83.1 | 2826 | 6.27 | 582.0 
134 116 173g | 21% | 90.9 | 309.3 | 6.32 | 626.9 





Working Formulz for Wrought-iron and Steel Struts 
of various Forms, —Burr gives the following practical formule, which 
he believes to possess advantages over Gordon’s: 


Pp, = Working 


p = Ultimate Strength = 
Strength, 1/5 Ultimate, 
Ibs. per sq. in. lbs. per sq. 
Kind of Strut. of Section. in. of Section. 
Flat and fixed end iron angles and tees 44000—140 4 (1) §800 —28 Ls (2) 
r 
Hinged-end iron angles and tees....... 46000—175 ce (3)  9200—35 L (4) 
r a 
Flat-end iron channels and I beams....40000—110 = (5) 8000—22 a (6) 
i 
Flat-end mild-steel angles..............52000—180 - (7)  10400—386 u (8) 
l l 
Flat-end high-steel angles.............. 76000—290 =~ (9) 15200-58 = (10) 
l 
Pin-end solid wrought-iron columns....32000— 80 e ) 6400—16 =) (12) 
(11) 
1 l 
32000—277 — 6400—55 — 
00 — 277 q q 
Equations (1) to (4) are to be used only between a = 40 and - = 200 
6s (5) and (6) 66 66 66 66 ee 66 oe — 90 66 C6 8 900 
sé 7) to (10 66 66 66 6s 66 66 GR 40 66 co 200 
a6 (11) and (12) oe 66 66 66 66 66 ce = 20 66 (a4 = 200 
or oe = 6 and aye 65 


Steel columns, properly made, of steel ranging in specimens from 65,000 to 
73,000 Ibs. per square inch should give a resistance 25 to 33 per cent in ex- 
cess of that of wrought-iron columns with the same value of | + 1, provided 
that ratio does not exceed 140. 

The unsupported width of a plate in a compression member should not 
exceed 30 times its thickness. 

In built columns the transverse distance between centre lines of rivets 
securing plates to angles or channels, ete., should not exceed 35 times the 
plate thickness, If this width is exceeded, longitudinal buckling of the 


260 STRENGTH OF MATERIALS, 


plese. takes place, and the column ceases to fail as a whole, but yields in 
etail, 

The same tests show that the thickness of the leg of an angle to which 
latticing is riveted should not be less than 1/9 of the length of that leg or 
side if the column is purely and wholly a compression member. The above 
limit may be passed somewhat in stiff ties and compression members de- 
signed to carry transverse loads. 

The panel points of latticing should not be separated by a greater distance 
than 60 times the thickness of the angle-leg to which the latticing is riveted, 
if the column is wholly a compression member. 

The rivet pitch should never exceed 16 times the thickness of the thinnest 
metal pierced by the rivet, and if the plates are very thick it should never 
nearly equal that value. 

Merriman’s Bational Formula for Columns (fg. News, 
duly 19, 1894), 


B 
= 1 nB 12 e y e e e e e e ° (1) 
~ PH 78 
C 
B no 72 e e e ° @ og 6 ° se e (2) 
nw? x? 


B = unit-load on the column = total load P + area of cross-section A; 
C = maximum compressive unit-stress on the concave side of the column’ 
l = length of the column; r = least radius of gyration of the cross-section 
E = coefficient of elasticity of the material; n = 1 for both ends round 
mn = 4/9 for one end round and one fixed; n = 44 for both ends fixed. This 
formula is for use with strains within the elastic limit only: it does not 
hold good when the strain C exceeds the elastic limit. 

Prof. Merriman takes the mean value of # for timber = 1,500,000, for cast 
iron = 15,000,000, for wrought-iron = 25,000,000, and for steel = 30,000,000, 
and 72 = 10 asa close enough approximation. With these values he com- 
putes the following tables from formula (1): 


¥.—Wrought-iron Columns with Round Ends, 





—_— —-— 








Unit- Maximum Compressive Wnit-stress C. 
load. 
1 
Fe oriB, | =3,20 pA EY ea bees = = yo0\= a y09\2. = 140\2 = 160 
A r r r r r ro. r , 





5,000 5,040 | 5,170 | 5,390 | 5,730 | 6,250 | 6.980 | 8.220 | 10,250 
6,000 6,055 | 6,240 6,560 7,090 7,890 | 9,020 | 31,830 | 15,56u 
7,000 7,080 | 7,330 | 7,780 8,530 | 9,720 | 11,610 | 15,510 | 24,720 


8,000 8,100 | 8,430 9,040 | 10,060 | 11,660 | 14,640 | £1,46e | ...... 
9,000 9,130 | 9,550 | 10,840 | 11,690 | 14,060 | 18,380 }........}....... 
10,000 10,160 | 10,680 | 11,680 | 13,440 | 16,670 | 238,090 |..-.... 


11,000 11,200 | 11,750 | 13,070 | 15,310 | 19,640 
12,000 12,240 | 13,000 | 14,500 | 17,320 | 23,080 
13,000 13,280 | 14,180 | 15,990 | 19,480 


se tale MR TS 


ceesace. Or i 





STRENGTH OF WROUGHT IRON AND STEEL COLUMNS. 26] 


Il.—Wrought-iron Columns with Fixed Ends. 
Unit- 











loath: Maximum Compressive Unit-stress C. 
ye L 29 ees 40 ep LEO © = s00\! = 120] 2 = 404 = 180 
A .) if 1; r r r r r 


13,000 | 13,070 | 13,280 | 13,640 | 14,210 | 14/940 | 15,990 | 17/440 | 19.480 
14,000 | 14,080 | 14,320 | 14,740 | 15,380 | 16,280 | 17,530 | 19,290 | 21,820 





IiI.—Steel Columns with Round Ends, 








Unit- Maximum Compressive Unit-stress C. 

load. . 
15 gg RN Sg coe aioe 8 mien pve anew As le 
A r r r " + 2 fA bi 


eeoe re eof seeecees 


28,300 eee bk ght 


18, 000 
14,000 14,250 15, 130 16, 830 


12,000 12,200 | 12,820 | 14,020 | 16,130 ‘' 20,000 
| | 19,960 











IV.—Steel Columns with Fixed Ends. 





Inga Maximum Compressive Unit-stress C, 








15,000 | 15,080 | 15,310 | 15,710 | 16,310 | 17,140 18, 290 19,870 | 22,060 





The design of the cross-section of a column to carry a given load with 
maximum unit-stress C may be made by assuming dimensions, and then 


262 STRENGTH OF MATERIALS. 


computing C by formula (1). If the agreement between the specified and 
computed vatues is not sulficiently close, new dimensions must be chosen, 
and the computation be repeated. By the use of the above tables the work 
will be shortened. 

The formula (1) may be put in another form which in some eases will ab. 
breviate the numerical work. For B substitute its value P-- A, and for 
Ar? write J, the least moment of inertia of the cross-section; then 


én which I and 7? are to be determined. 

For example, let it be required to find the size of a square oak column 
with fixed ends when loaded with 24.000 Ibs. and 16 ft. long, so that the 
maximum compressive stress C shall be 1000 Ibs. per square inch. Here 

= 24,000, C = 1000, n = 144, 72 = 10, H = 1,500,000, 2 = 16 X 12, and (8) be- 


comes 
I — 24r? = 14.75. 
Now let x be the side of the square; then 


a4 x 
ee “2 —_—- 
I= and 72= 3° 
so that the equation reduces to 24 — 24x? = 177, from which 2? is found to be 
29.92 Sq. in., and the side x = 5.47 in. Vhus the unit-load B is about 802 
lbs. per square inch. 


WORKING STRAINS ALLOWED IN BRIDGE 
MEMBERS. 


Theodore Cooper gives the following in his Bridge Specifications : 
Compression members shall be so proportioned that the maximum load 
shall in no case cause a greater strain than that determined by the follow: 
ing formula; 
8000 
P= Sega T for square-end compression members $ 
a8 40,00072 
8000 
12 
dt: 30,00027°2 
8000 : : ; ; 
P= ST for compression members with pin-bearings; 
ne 20,0007? 


(These values may be increased in bridges over 150 ft. span. See Cooper's 
Specifications.) ' 
P = the allowed compression per square inch of cross-section ; 
l = the length of compression member, in inches; 
y = the least radius of gyration of the section in inches. 
No compression member, however, shall have a length exceeding 45 times 
its least width. 
Tension Members.—All parts of the structure shall be so proportioned 
that the maximum loads shall in no case cause a greater tension than the 
fullowing (except in spans exceeding 150 feet) : 


P= for compression members with one pin and one square end; 


Pounds pet 
Sq. in. 


On lateral bracing............ RSA erie Acie Rakisace o eiciavate current: 15,000 
On solid rolled beams, used as cross floor-beams and stringers. 9,000 
On bottom chords and main diagonals (forged eye-bars)...... 10,000 
On bottom chords and main diagonals (plates or shapes), net 
SOCUION! cme se oh se sels ee eats da ks er eee - 8,000 
On counter rods ana long verticals (forged eye-bars).......... 8,000 
On counter and long verticals (plates or shapes), net section.. 6.£0C 
On bottom flange of riveted cross-girders, net section ........ 8,000 


20 ft.long,(neb SECHOU:: ... ves oainles cd PL a es, 


WORKING STRAINS ALLOWED IN BRIDGE MEMBERS, 2638 


On bottom flange of riveted longitudinal plate girders under 
20 ft. long; net section ........'.... Rae eee et ire Voter ets . %,000 
On floor-beain hangers, and other similar members liaule to 
sudden loading (bar iron with forged ends)................ 
On floor beam hangers, and other similar members liable to 


sudden loading (plates or shapes), net section............. 3 


Members subject to alternate strains of tension and compression shall be 
proportioned to resist each kind of strain. Both of the strains shall, how- 
ever, be considered as increased by an amount equal to 8/10.0f the least of 
the two strains, for determining the sectional area by the above allowed 
strains. 

_ The Phoenix Bridge Co. (Standard Specifications, 1895) gives the follow- 
ing: 

The greatest working stresses in pounds per square inch shall be as fol- 
Ows: 


Tension. 
Steel. Tron. 


Min. stress For bars, 4 Min. stress 
sit 9,000 Inte stress_} forged ends. iain 600] 4 + Max. stress | 





Min. stress] P:ates or a Min. stress 
AAR on [1 2 Max. a shapes net. diets 000 1 i Max. oY 
8,500 pounds. Floor-beam hangers, forged ends........... 7,000 pounds: 
7,000 nS Floor-beam hangers, plates or shapes, net 
SCCIIOUG..vie tee eeit ta eee mit eiremas sce emitters 6 COOTF ies 
10,000 4 Lower flanges of rolled beams. .. .......... OOO Mme se 
20,000 se OUtSIDe MDres OL DiiSece sense state aie seca cco ee 15,000 hy 
80,000 § BINS FOLEWANCEOLAGCIND: cemiaelsceiseletsten cision sees 2 SOO Meee 
20,000 sf Matera ls DVACii eres iissiesc <a eaacete roomie h bie 


Shearing. 


9000 pounds... Pins;and T1Vets oe yeas coer a ceiac eee hese 7,500 pounds, 
Hand-driven rivets 20% less unit stresses. For 
bracing increase unit stresses 50%. 
6,000 pounds. Webs of plate girders.........-e+00. e saelene) 5.000 polnsis. 


‘ Bearing. 
16,000 pounds. Projection semi-intrados pins and rivets.... 12,000 pounds. 
Hand-driven rivets 20% less unit stresses. For 
bracing increase unit stresses 50%. 


Compression. 


Lengths less than forty times the least radius of gyration, Ppreviously 
found. See Tension. 

Lengths more than forty times the least radius of gyration, P reduced by 
following formule: 


For both ends fixed, b= 
1+ 


2 sus) 
36,000 2 
For one end hinged, ies ell ° 

1-+- Panel an 
24,0007 
For both ends hinged, 6= pane Ayn ty 


1 BME ote 
as 18,000 12 

P= permissible stress previously found (see Tension); 6 = allowable 
working stress per square inch; J = length of member in inches; 7 = least 
radius of gyration vf section in inches. No compression memoer, how: 
ever, shall have a length exceeding 45 times its least width. 


964 STRENGTH OF MATERIALS, 


Pounds per 


sq. in. 
In counter web members. SCCH SCOTS SCHSSHSSSHSSSSS*SSESSSEC SSS HFES* HES 10, 500 
In long Verticals........seeccseorsescsescces cess ssccecsececseces 10, 000 
In all main-web and lower-chord eye- DATS 55 ab vaaciivics clgdiews oe mi 3,200 
In plate hangers (neb section) .... 0.6... cece csccecece Ddseates 9.000 
In tension members of lateral and transverse bracing. 3.5 cs 19,000 
In steel-angle lateral ties (net section).... ... ... .-..seee-ss. 15,000 


For spans over 200 feet in length the greatest allowed working Stresses 
per square inch, in lower-chord and end main-web eye-bars, shall be taken at 


10,000( 1 aN 


whenever this quantity exceeds 13,200. 

The greatest allowable stress in ‘the main-web eye-bars nearest the centre 
of such spans shall be taken at 13,200 pounds per square inch ; and those 
for the intermediate eye-bars shall be found by direct interpolation between 
the preceding values. 

The greatest allowable working stresses in steel plate and lattice girders 
and rolled beams shall be taken as follows : 


min. total eo) 
max. total stress 


Pounds per 
sq. in. 
Upper flange of plate girders (gross section)...... seracodu gates 10,000 
Lower flange of plate girders (net section)...........6. se.ee0- 10,000 


In counters and long verticals of lattice girders (net section).. 9,000 
In lower chords and main HAS Cae of lattice girders (net 


SOCLION Ae ca tese etre seis eelals'e e ctoletece a aisislereei isis SaASnE HE Aocous 10,000 
In bottom flanges of rolled beams. Blais a{is a ae.eie eisio.ela clea cielo oot sitet Un GUG 
In'topiflanges of rolled DEANISs« <o sc cet.s05 c.0 816 ce msieciesiee « reroiehes 10,000 
i RESISTANCE OF HOLLOW CYLINDERS TO 
COLLAPSE. 


Fairbairn’s empirical formula (Phil. Trans. 1858) is 





p= > tess cee s oe Geb. © e - (1) 


where p = pressure in Ibs. per square inch, t = thickness of cylinder, d = 
diameter, and / = length, all in inches ; or, 


p = 806,200 ——., if Lis in feet. C1: bebe ie - (2) 


He recommends the simpler formula 


p = 9,675,600 7. ° 6 6. © © se Jes - (8) 


as sufficiently accurate for practical purposes, for tubes of considerable 
diameter and length. 

The diameters of Fairbairn’s experimental tubes were 4/’, 6’’, 8’’, 10’, and 
12’’, and their lengths, between the cast-iron ends, ranged between 19 inches 
and 60 inches. 

His formula (3) has been generally accepted as the basis of rules for 
ascertaining the strength of boiler-filues. In some cases, however, limits are 
fixed to its application by a supplementary formula, 

Lloyd’s Register contains the following formula for the strength of circular 
boiler-flues, viz., 
89,600é2 


Ld ° o-e@ ©. 6 © 4 €)Jemre qe) o - (4) 


The English Board of Trade prescribes the following formula for circular 
flues, when the longitudinal joints are welded, or made with riveted butt- 


straps, VizZ., 90,000¢2 


Prag tt ee eles eet &) 


For Tpuclsrts and for inferior Nit ol ieee the numerical factor may be 
reduced as low as 60,000, 


12s 





RESISTANCE OF HOLLOW CYLINDERS TO COLLAPSE. 265 


The rules of Lloyd’s Register, as well as those of the Board of Trade, pre- 
scribe further, that in no case the value of P must exceed the amount given 
py the following equation, viz.; 


In formule (4), (5), (6) P is the highest working pressure in pounds per 
square inch, ¢ and d are the thickness and diameter in inches, L is the 
length of the flue in feet measured between the strengthening rings, in case 
it is fitted with such. Formula (4) is the same as formula (8), with a factor 
of safety of 9. In formula (5) the length Z is increased by 1; the influence 
which this addition has on the value of P is, of course, greater for short 
tubes than for long ones. 

Nystrom has deduced from Fairbairn’s experiments the following formula 
for the collapsing strength of flues : 


_ 47 fi 
AMET GED Tossa Baar Bee 


where p, f, and d have the same meaning as in formula (1), Z is the length in 
feet, and T is the tensile strength of the metal in pounds per square inch. 

If we assign to T the value 50,000, and express the length of the flue in 
inches, equation (7) assumes the following form, viz., 


2 
Pp = 692,800 nae e «@ is ee e@ oo © @e (8) 


‘Nystrom considers a factor of safety of 4 sufficient in applying his formula, 
(See ‘‘ A New Treatise on Steam Engineering,’’ by J. W. Nystrom, p. 106.) 

Formula (1), (4), and (8) have the common defect thay they make the 
collapsing pressure decrease indefinitely with increase of length, and vice 
versa. M. Love has deduced from Fairbairn’s experiments an equation of 
a different form, which, reduced to English measures, is as follows, viz., 


{2 {2 t 
p = 5,308,150 = 441,906 5+ 18835, . 2+. + @ 


where the notation is the same as in formula (1). 

D. K. Clark, in his ‘‘ Manual of Rules,”’ etc., p. 696, gives the dimensions of 
six flues, selected from the reports of the Manchester Steam-Users Associa- 
tion, 1862-69, which collapsed while in actual use in boilers. These flues 
varied from 24 to 60 inches in diameter, and from 3-16 to 3 inch in thickness, 
They consisted of rings of plates riveted together, with one or two longitud- 
inal seams, but all of them unfortified by intermediate flanges or strength- 
ening rings. At thecollapsing pressures the flues experienced compressions 
ranging from 1.53 to 2.17 tons, or a mean compression of 1,82 tons per square 
inch of section. From these data Clark deduced the following formula 
“for the average resisting force of common boiler-flues,”’ viz., 


p = tt (220% _ 500), Pa Meltes th Sovadesvra az (40) 


where p is the collapsing pressure in pounds per square inch, and d and t 
are the diameter and thickness expressed in inches. 

QO. R. Roelker, in Van Nostrand’s Magazine, March, 1881, discussing the 
above and other formnle, shows that experimental data are as yet insuffi- 
cient to determine the value of any of the formule. He says that Nystrom’s 
formula, (8), gives a closer agreement of the calculated with the actual col- 
Japsing pressures in experiments on flues of every description than any of 
the other formule. 


Collapsing Pressure of Plain Iron Tubes or Flues, 


(Clark, S. E., vol. i. p. 648,) 


The resistance to collapse of plain-riveted flues is directly as the square of 
the thickness of the plate, and inversely as the square of the diameter. The 
support of the two ends of the flue does not practically extend over a length 
of tube greater than twice or three times the diameter. The collapsing 
pressure of long tubes is therefore practically independent of the length 


266 STRENGTH OF MATERIALS, 


Instances of collapsed flues of Cornish and Lancashire boilers collated by 
Clark, showed that the resistance to collapse of dues of 3¢-inch plates, 18 to 
43 feet long, and 80 to 50 inches diameter, varied as the 1.75 power of the 
diameter. Thus, 


TOUGIATHOLErS OL wa), see sere snes eng esc 380 85 40 45 50 inches, 

the collapsing pressures were......... 46 58 45 37 380 Ibs. per sq. in; 
for 7-16-inch plates the collapsing 

pressures were.......... shal, i | ahaa ed dh Ria DAB Py tear ory Be 


For collapsing pressures of plain iron flue-tubes of Cornish and Lanca 
shire steam-boilers, Clark gives: 


200,000¢2 
Fagen 
Ff = collapsing pressure, in pounds per square inch; 

t = thickness of the plates of the furnace tube, in inches, 
d = internal diameter of the furnace tube, in inches. 


For short lengths the longitudinal tensile resistance may be effective in 
augmenting the resistance to collapse. Flues efficiently fortified by flange. 
joints or hoops at intervals of 8 feet may be enabled to resist from 50 lbs. 
to 60 lbs. or 70 Ibs. pressure per square inch more than plain tubes, accord- 
ing to the thickness of the plates. 

Strength of Smali Wubes.—The collapsing resistance of solid. 
drawn tubes of small diameter, and from .134 inch to .109 inch in thickness, 
fas been tested experimentally by Messrs. J. Russell & Sons. The results 
tor wrought-iron tubes varied from 14.33 to 20.07 tons per square-inch sec- 
tion of the metal, averaging 18.20 tons, as against 17.57 to 24.28 tons, averag- 
ing 22.40 tons, for the bursting pressure. 

(For strength of Segmental Crowns of Furnaces and Cylinders see Clark, 
S. E., vol. i, pp. 649-651 and pp. 627, 628.) 

Formula for Corrugated Furnaces (Hng’g, July 24, 1891. p. 
102).— As the result of a series cf experiments on the resistance to collapse 
of Fox’s corrugated furnaces, the Board of Trade and Lloyd’s Registry 
altered their formule for these furnaces in 1891 as follows: 

Board of Trade formula is altered from 


12,500 x 7 14,000 x T 
D D 

T = thickness in inches; 

D = mean diameter of furnace; 


WP = working pressure in pounds per square inch. 
Lloyd’s formula is altered from 


1000 x (T—2) _ a 1°84 x (T.=.2) 
TS SWE to > 


T = thickness in sixteenths of an inch; 
D = greatest diameter of furnace; 
WP = working pressure in pounds per square inch, 


= WP to = WP, 


= WP: 


TRANSVERSE STRENGTH, 


In transverse tests the strength of bars of rectangular section is found to 
vary directly as the breadth of the specimen tested, as the square of its 
depth, and inversely as its length. The deflection under any load varies as 
the cube of the length, and inversely as the breadth and as the cube of the 
depth. Represented algebraically, if S = the strength and D the deflection, 
tthe length, b the breadth, and d the depth, 


‘ bd? “ 13 
S varies as aia and D varies as bas" 


For the purpose of reducing the strength of pieces of various sizes to 
a common standard, the term modulus of rupture (represented by R) is 
used. Its vatue is obtained by experiment on a bar of rectangular section 


TRANSVERSE STRENGTH. - 267 


supported at the ends and loaded in the middle and substituting numerical 
values in the following formula : 


3 Pl 
R= 3 bam 
in which P = the breaking load in pounds, / = the length in inches, b the 
breadth, and d the depth. 

The modulus of rupture is sometimes defined as the strain at the instant 
of rupture apon a unit of the section which is most remote from the neutral 
axis on the side which first ruptures. This definition, however, is based 
upon a theory which is yet in dispute among authorities, and it is better to 
define it as a numerical value, or experimental constant, found by the ap- 
plication of the formula above given. 

From the above formula, making / 12 inches, and b and d each 1 inch, it 
follows that the modulus of rupture is 18 times the load required to break a, 
bar oneinch square, supported at two points one foot apart, the load being 
applied in the middle. 
span in feet X load at middle in lbs, 


Coefficient of transverse strength = breadth in inches X (depth in inches)®. 


P =;th of the modulus of rupture. 


Fundamental Formulz for Flexure of Beams (Merriman). 

Resisting shear = vertical shear; 

Resisting moment = bending moment; 

Sum of tensile stresses = sum of compressive stresses; 

Resisting shear = algebraic sum of all the vertical components of the in- 
ternal stresses at any section of the beam. 

Tf A be the area of the section and Ss the shearing unit stress, then resist- 
ing shear = ASs; and if the vertical shear = V, then V = ASs, ' 

The vertical shear is the algebraic sum of all the external vertical forces 
on one side of the section considered. It is equal to the reaction of one sup- 
port, considered as a force acting upward, minus the sum of all the vertical 
downward forces acting between the support ard the section. 

The resisting moment = algebraic sum of all the moments of the inter- 
nal horizontal stresses at any section with reference to a point in that sec- 


: 8 Se : ; ? : : 
tion, = = in which S = the horizontal unit stress, tensile or compressive 


as the case may be, upon the fibre most remote from the neutral axis, c = 
the shortest distance from that fibre to said axis, and J = the moment of 
inertia of the cross-section with reference to that axis. 

The bending moment M is the algebraic sum of the moment of the ex- 
ternal forces on one side of the section with reference to a point in that sec- 
tion = moment of the reaction of one support minus sum of moments of 
loads between the support and the section considered. 


The bending moment is a compound quantity = product of a force by the 
distance of its point of application from the section considered, the distance| 
being measured on a line drawn from the section perpendicular to the 
direction of the action of the force. 

Concerning the above formula, Prof. Merriman, Hng. News, July 21, 1894, 
says: The formula just quoted is true when the unit-stress S on the part of 
the beam farthest from the neutral axis is within the elastic limit of the 
material. It isnot true when this limit is exceeded, because then the neutral 
axis does not pass through the centre of gravity of the cross-section, and 
because also the different longitudinal stresses are not proportional to their 
distances from that axis, these two requirements being involved in the de- 
duction of the formula, But in all cases of design the permissible unit- 
stresses should not exceed the elastic limit, and hence the formula applies 
rationally, without regarding the ultimate strength of the material or any 
of the circumstances regarding rupture. Indeed so great reliance is placed 
upon this formula that the practice of testing beams by rupture has been 
almost entirely abandoned, and the allowable unit-stresses are mainly de- 
rived from tensile and compressive tests. 


— ——————eEeE~= rll lOO ae 


STRENGTH OF MATERIALS. 


268 








*(AJaBeUu) 
























































eee 3 eae 7 eA EAS gaa hee eg biconkuetere 
s1A1 8F90 ePAd P : 

am | 2 leu mee) ae 
el d Id = € sld SPIL pe} Pp 28 poxlq 
ta 39 4 = me Bees ah. ae, ‘G+ sonserensedoencted Copied Seley me 
a + id? mah = iar tereerer-siTQUILIOdx gy S,Mopieg ‘eulBg 
1a a = ee 1a sis = ee =q ¢++ee*-QIppIur UI popvoy ‘spua T30q 4B PextT 
GCoba)e| fe | aaCatety [HCHt) | Gh teates} Longe eet 
oe ie 2 oe aie a are ah see seeeveereeraerer eee: KTUTIOTIIN PapBo] OWLY 
ne = = = 1d? se = : = 7 seeeeereerorppltl Ul pepsBo] ‘spus 4¥v pojzoddng 
an : = = at a : : oh = : e "seresers KTULIOTIUN POINGHISIP PBOT PLAk OUIBY 
Ee : ai ee oe al ae : = seeeceeroreraI1O OY] 4B PRO ‘pUe CUO 4e POXIY 

rnuee 1220. bate acen| coed | 01 aves at 
*"NOLEOUS | 


“SSOU0 WHOAING 10 SUVA 10 HLDNAUMLS ASHUASNVAL HOT WTIAWHOA TVAANAS 


APPROXIMATE SAFE LOADS IN LBS, ON STEEL BEAMS, 269 


Formule for Transverse Strength of Beams,.—Referring to 
table on preceding page, : 

P = load at middle; 

W= total load, distributed uniformly; 

= length, b = breadth, d = depth, in inches; 

E = modulus of elasticity; 

R = modulus of rupture, or stress per square inch of extreme fibres 

JI = moment of inertia; 

c = distance between neutral axis and extreme fibre, 


For breaking load of circular section, replace bd? by 0.59d8. 

For good wrought iron the value of R is about 80,000, for steel about 120,000, 
the percentage of carbon apparently having no influence. (Thurston, Iron 
and Steel, p. 491). 

For cast iron the value of R varies greatly according to quality. Thurston 
found 45,740 and 67,980 in No. 2 and No. 4 cast iron, respectively. 

- For beams fixed at both ends and loaded in the middle, Barlow, Oy othe 
Pl, the 


APPROXIMATE GREATEST SAFE LOADS IN LBS, ON 
STEEL BEAMS, (Pencoyd Iron Works.) 


' Based on fibre strains of 16,000 lbs. for steel. (For iron the loads should be 
one-eighth less, corresponding to a fibre strain of 14,000]bs. per square inch.) 
L = length in feet between supports; a@ = interior area in square 


A = sectional area of beam in square 
inches; 
D = depth of beam in inches. 























Shape of 
presen: Load in Load Load in Load 
Middle. Distributed. Middle. Distributed. 
Solid Rect- 890.4AD 1780 AD wLs wL3 
angle. L ia 32.4 D2 524 D2 
HollowRect-| 890(4D-—ad) | 1780(AD—ad) ws wLs 
angle. DL L 32(4D2—ad?) | 52(4D?—ad?) 
Solid Cylin- 667 AD 13834 D — wLs ws 
der. L L 24.4 D? 88.4 D2 
Hollow 667(4D—ad) | 1333(AD—ad) wLs wLs 
Cylinder. G is 24(4D?—ad2) | 38(AD?—ad®) 
Even-legged 885.4 D 1770 4D wL3 wl 
Angle or Sans 
Tee. L L 32.4 D2 524D 
Channel or 1525.4 D 8050.4 D wLs wLs 
Z bar. ns 7 53.4 D2 85.A D2 
13804 D 2760.4 D ws wLs 
Deck Beam. é ake 50AD2 80AD2 
‘| 16954D 3390.4 D wLs wLs 
I Beam ay, a Py JOS 58.4 D? 98.4 D? 














Greatest Safe Load in Pounds. 

















oy 


d 


inches; 


= interior depth in inches, 
w = working load in net tons. 





Deflection in Inches. 

























































































270 STRENGTH OF MATERIALS, 


The above formule for the strength and stiffness of rolled beams of vs- 
rious sections are intended for convenient application in cases where 
strict accuracy is not required. 

The rules for rectangular and circular sections are correct, while those for 
the flanged sections are approximate, and limited in their application to the 
standard shapes as given in the Pencoyd tables. When the section of any 
beam is increased above the standard minimum dimensions, the flanges re- 
maining unaltered, and the web alone being thickened, the tendency will be 
for the load as found by the rules to be in excess of the actual; but within 
the limits that it is possible to vary any section in the rolling, the rules 
will apply without any serious inaccuracy. 

The calculated safe loads will Le approximately one half of loads that 
would injure the elasticity of the materials. 

The rules for defiection apply to any load below the elastic limit, or less 
than double the greatest safe load by the rules. 

If the beams are long without lateral support, reduce the loads for the 
ratios of width to span as follows: 

Proportion of Calculated Load 


Length of Beam. forming Greatest Safe Load. 
20 times flange width. Whole calculated load. 
30 66 66 66 i 66 ob 
40 66 66 66 8-10 66 G6 
50 = 66 66 7-10 “cc 66 
60 «6 (Ys 66 6-10 “ 66 
70 oe 66 66 5-10 a“ 66 


These rules apply to beams supported at each end. For beams supported 
otherwise, alter the coefficients of the table as described below, referring to 
the respective columns indicated by number. 


Changes of Coefficients for Special Forms of Beams. 





* Coefficient for Safe Coefficient for Defiec- 
Kind of Beam. Toad toh. 








Fixed at one end, loaded|One fourth of the coeffi- |One sixteenth of the co- 
at the other, cient, col. IT. efficient of col. IV. 


Fixed at one end, load |One fourth of the coeffi- |Five forty-eighths of the 
evenly distributed. cient of col. II. coefficient of coi. V. 





Both ends rigidly fixed, |Twice the coefficient of |Four times the coeffi- 
or a continuous beam, | col. II. cient of col. IV. 
with a load in middle. 





Both ends rigidly fixed, |One and one-half times |Five times the coefficient 
or a continuous beam, | the coefficient of col.| of col. V. 
with load evenly dis-| III. 
tributed. 


ELASTIC RESILIENCE. 


In a rectangular beam tested by transverse stress, supported at the ends 
and loaded in the middle, 


in which, if P is the load in pounds at the elastic limit, R = the modulus of 
transverse strength, or the strain on the extreme fibre, at the elastic limit, 
E = modulus of elasticity, A = deflection, 1, b, andd= length, breadth, and 
depth in inches, Substituting for P in (2) its value in (1), we have 

i 1 Riz 


4=6 Ga 


BEAMS OF UNIFORM STRENGTH THROUGHOUT LENGTH. 24% 


The elastic resilience = half the product of the load and deflection = 4PA 
and the elastic resilience per cubic inch 


Pe 
~ 2 lbd 
Substituting the values of P and A, this reduces to elastic resilience per 


Lays § per Be See ve ‘ : 
eubic inch = wT which is independent of the dimensions; and therefore 
10 
the elastic resilience per cubic inch for transverse strain may be used as @ 
modulus expressing one valuable quality of a material. 
Similarly for tension: 
Let P = tensile stress in pounds per square inch at the elastic limit; 
e = elongation per unit of length at the elastic limit; 
E£ = modulus of elasticity = P + e; whence e = P+ E. 


‘ ‘ 2 
Then elastic resilience per cubic inch = 14Pe = — 


BEAMS OF UNIFORM STRENGTH THROUGHOUT 
THEIR LENGTH. 


The section is supposed in all cases to be rectangular throughout. The 
beams shown in plan are of uniform depth throughout. Those shown in 
elevation are of uniform breadth throughout. 

B = breadth of beam. D= depth of beam. 


ELEVATION. y, Fixed at one end, loaded at the other; 
curve parabola, vertex at loaded end; BD? 
proportional to distance from loaded end. 
The beam may be reversed, so that the up- 
per edge is parabolic, or both edges may be 
parabolic. 


Fixed at one end, loaded at the other; 
triangle, apex at loaded end; BD? vropor- 
tional to the distance from the loaded end. 


Fixed at one end; load distributed; tri- 
angle, apex at unsupported end; BD? pro- 
portional to square of distance from unsup- 
ported end. 


Fixed at one end; load distributed; curves 
two parabolas, vertices touching each other 
at unsupported end; BD? proportional to 
distance from unsupported end. 


Supported at both ends; load at any one 
point; two parabolas, vertices at the points 
of support, bases at point loaded; BD? pro- 
portional to distance from nearest point of 
support. The upper edge or both edges 
may also be parabolic. 


Supported at both ends; Joad at any one 
point; two triangles, apices at points of sup- 
port, bases at poiut loaded; BD? propor- 
tional to distance from the nearest point of 
support. 


PLAN. * Supported at Doth ends; load Gist 

ne PARABOLA curves two parabolas, vertices at the middle 
20000000 of the Heat: bases centre line of beam; BD? 
proportional to product of distances from 
points of support. 















ATION, 
aad Supported at both ends; load distributed; 
curve semi-ellipse; BD? proportional to the 
product of the distances from the points of 
support, 


~ 


272 STRENGTH OF MATERIALS. 


PROPERTIES OF ROLLED STRUCTURAL STEEL. 


Explanation of Tables of the Properties of I Beams, 
Channels, Angles, Deck-Beams, Bulb Angles, Z Bars, 
Tees, Trough and Corrugated Plates, 


(Tae Carnegie Steel Co., Limited.) 


The tables for I beams and channels are calculated for all standard 
weights to which each pattern is rolled. The tables for deck-beams and 
angles are calculated for the minimum and maximum weights of the 
various shapes, while the properties of Z bars are given for thicknesses 
differing by 1/16 inch. 

For tees, each shape can be rolled to one weight only. 

Column 12 in the tables for I beams and channels, and column 9 for 
deck-beams, give coefficients by the help of which the safe, uniformly 
distributed load may be readily determined. To do this, divide the coeffi- 
cient given by the span or distance between supports in feet. If the weight 
of the deck-beams is intermediate between the minimum and maximum 
weights given, add to the coefficient for the minimum weight the value given 
for one pound increase of weight multiplied by the number of pounds 
the section is heavier than the minimum. 

If a section is to be selected (as will usually be the case), intended to carry 
a certain load for a length of span already determined on, ascertain the 
coefficient which this load and span will require, and refer to the table for a 
section having a coefficient of this value. The coefficient is obtained by mul- 
tiplying the load, in pounds uniformly distributed, by the span length in feet. 

In case the load is not uniformly distributed, but is concentrated at the 
middle of the span, multiply the load by 2, and then consider it as uniformly 
distributed. The deflection will be 8/10 of the deflection for the latter load. 

For other cases of loading obtain the bending moment in ft.-lbs,; this 
multiplied by 8 will give the coefficient required. 

If the loads are quiescent, the coefficients for a fibre stress of 16,000 Ibs. 
per square inch for steel may be used; but if moving loads are to be pro- 
vided for, a coefficient of 12,500 lbs. should be taken. Inasmuch as the effects 
of impact may be very considerable (the stresses produced in an unyielding 
inelastic material by a load suddenly applied being double those produced 
by the same load in a quiescent state), it will sometimes be advisable to use 
still smaller fibre stresses than those given in the tables. In such cases the 
coefficients may be determined by proportion. Thus, for a fibre stress of 
8,000 lbs. per square inch the coefficient will equal the coefficient for 16,000 
Ibs. fibre stress, from the table, divided by 2. 

The section moduli, column 11, are used te determine the fibre stress per 
square inchin a beam, or other shape, subjected to bending or transverse 
stresses, by simply dividing the bending moment expressed in inch-pounds 
by the section modulus. 

In the case of T shapes with the neutral axis parallel to the flange, there 
will be two section moduli, and the smaller is given. The fibre stress cal- 
culated from it will, therefore, give the larger of the two stresses in the 
extreme fibres, since these stresses are equal to the bending moment divided 
by the section modulus of the section. 

For Z bars the coefficients (C) may be applied for cases where the bars are 
subjected to transverse loading, as in the case of roof-purlins. 

For angles, there will be two section moduli for each position of the neutral 
axis, since the distance between the neutral axis and the extreme fibres has 
a different value on one side of the axis from what it has on the other. The 
section modulus given in the table is the smaller of these two values. 

Column 12 in the table of the properties of standard channels, giving the 
distance of the center of gravity of channel from the outside of web, is used 
to obtain the radius of gyration for columns or struts consisting of two 
channels latticed, for the case of the neutral axis passing through the centre 
of the cross-section parallel to the webs of the channels. This radius of 
gyration is equal to the distance between the centre of gravity of the chan- 
nel and the centre of the section, i.e., neglecting the moments of inertia of 
the channels around their own axes, thereby introducing a slight error on 
the side of safety. 

(For much other important information concerning rolled structural 
shapes, see the ‘‘ Pocket Companion” of The Carnegie Steel Co., Limited, 
Pittsburg, Pa., price $2.) . 


PROPERTIES OF ROLLED STRUCTURAL SHAPES, 9%3 


Properties of Carnegie Standard I Beams-Steel. 








| 












































1/2) 8 +4 5 | 6 pd 8 9 10 11 12 
gs3 |ge& |gt3 j2ef |882 | Ses 
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nial FE] 4/8/F |S = a 6S D -) 
in.} Ibs, |sq. in.| in. |_in. if IR? r yt S C 
Bi {24/100 |29.41,0.75)7.25) 2380.3 48.56 9.00 1.28 198.4 2115800 
1S) 95 127.94,0.69|7.19) 2309.6 | 47.10] 9.09 1.80 | 192.5 | 2052900 
6 )5 90 126.47\/0.63)7.13] 2239.1 | 45.70 | 9.20 1.31 | 186.6 | 1990300 
SPOT) Qe | 42 .00 0.57 7.07] 2168.6 44.35 9.31 1.33 180.7 1927600 
“1°80 128.32)/0.50)7.00) 2087.9 | 42.86 9.46 1.36 174.0 1855900 
B3 [20] 7 22.06 0.65 6.40 1268.9 80.25 7.58 yk aly. 126.9 1353500 
ee 1) 70 120.59 0.57/6.32) 1219.9 29.04 7.70 1.19 122.0 1301200 
ee 1! 65 119.08/0.50/6.25) 1169.6 | 27.86 7.83 1.21 117.0 1247600 
B80 |18} 7 20.59.9.72)6.26! 921.3 24.62 6.69 1.09 .} 102.4 1091900 
 ) *) 65. 119.12,0.64|6.18]** 881.5 23.47 6.79 1.11 97.9 1044800 
« 1"! 60) 117.65)0.55/6.09) 841.8 22.38 6.91 1.13 93.5 997700 
PORE | 6.2115 93 0.46 6.00) 795.6 21.19 7.07 1.15 88.4 943000 
7 115) 55. |16.18/0.66)5.75) 511.0 17.06 5.23 0.95 68.1 726800 
1! 5O 114.71/0.56)5.65) 483.4 16.04 5.73 1.04 64.5 687500 
se 1) 45 118.24)0.46)5.55) 455.8 15.09 5.87 1.07 60.8 648200 
“s 1) 42. 112.48)0.41/5.50) 441.7 14.62 5.95 1.08 58.9 628300 
BS {12} 25 /10.29/0.44|5.09} 228.3 10.07 4.71 0.99 38.0 405800 
PF) 31 BP 9. 26)0585)5.001 | 215.8 9.50 4.83 1.01 36.0 383700 
Bi11 |10| 40 |11.760.75)5.10) 158.7 9.50 8.67 0.90 31.7 838500 
“ ) 1 35 110.29/0.60)4.95) 146.4 8.52 3.77 0.91 29.3 812400 
coe slen hi OO 8.82,0.45)/4.80) 134.2 7.65 3.90 0.93 26.8 286300 
ie rilee | 2 7.387/0.31/4.66} 122.1 6.89 4.07 0.97 24.4 260500 
B13 | 9} 35 |10.29'0.73)4.77) 111.8 7.31 3.29 0.84 24.8 265000 
gees ast 8.82,0.57/4.61; 101.9 6.42 3.40 0,85 22.6 241500 
Sehr s| 2D 7.35 0.41)4.45 91.9 5.65 3.54 0.88 20.4 217900 
heh OT 6.31/0.29)4.33 84.9 5.16 3.67 0.90 18.9 201300 
B15] 8} 25.5) 7.50,0.54)4.27 68.4 4.75 3.02 0.80 ile yl 182500 
So ar bea 6.76,0.45)4.18 64.5 4.39 3.09 0.81 BG 172000 
se) St 20.5] 6.03,0.36)4.09 60.6 4.07 3.17 0.82 15.1 161600 
foe ets Lo 5.33 0.27/4.00 56.9 3.78 3.27 0.84 14.2 151700 
B17 | 7| 20 5 88,0.46)\3.87 42.2 3.24 2.68 0.74 12.1 128600 
eS) 17.5) 5.15.0.35.3.76 39.2 2.94 2.76 0.76 11.2 119400 
“* 1°) 15 | 4.42:0.25/3.66 36.2 2.67 2.86 0.78 10.4 110400 
B19| 6) 1744) 5.07/0.48/3.58 26.2 2.36 Pe 0.68 8.7 93100 
* | 1 1484) 4.84,0.35)3.45 24.0 2.09 2.35 0.69 8.0 85300 
“© 1) 1214) 3,61)0,23,3.33 21.8 1.85 2.46 0.72 7.3 77500 
B21 | 5) 1434) 4.34,0.50.3.29 15.2 1.70 1.87 0.63 6.1 64600 
se |S) 4214) 38.60,0.36)3.15 13.6 1.45 1.94 0.63 5.4 58160 
se] 4 934) 2.87)0.21/38,00 12.1 1:23 2.05 0.65 4.8 51600 
B23] 4] 10.5) 3,09 0.41)2.88 coe 1.01 1.52 0.57 3.6 38100 
1 1 9.5} 2.79,0.8412.80 Giz 0.93 hb) 0:58 3.4 86000 
“wy “| 8,5) -2.50.0,26)2.73 6.4 0.85 1 59) 0.58 3.2 33900 
ath iar lia te (fi)! 2.21'0.19'2.66 6.0 0.7 1.64 0.59 3.0 81800 
B77 |. 3] .7.5) 2.21,0.386)2.52 2.9 0.60 a ben ts 0.52 1.9 20700 
ss | 1 6.5] 1.91/0.26/2.42 PSE 0.53 1.19 0.52 1.8 19100 
sf let) 5 Bd 1.638.0.1712.38 PAS) 0.46 1.238 0.53 5 er 17600 





I = safe loads in lbs., uniformly distributed; 1 = span in feet; 
M = moment of forces in ft.-lbs.; C = coefficient given above. 
L 


: M=-—; C= Li = 8M = 2, f= fibre stress, 


9V4 STRENGTH OF MATERIALS. Tox 


Properties of Special I Beams—Steel, 












































ak SP 3 4,516 7 8 9 10 11 12 
dio |gt2 lese |eae lage | ses 
EY Sos oe Sos eae Te ee 
: o| [ESF [ESS (BSP [S88 [azo | deo 
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Mole! o=4 ‘ lems ee CS Org soe ai a, 
olD = Mw | Sindh , ets ps a a tel S 
TS 1M 5 2 - f& |° = 2)9 Ee gS wiles Se 5 ne ola 
Els] &B| A) Blo |. FEz| Ss .e/CSeSlo Sus leke | 2S 
ee 3 Sn Nats Olas e cigitena loom o tea =o 
Saree Oo} BLA jos sold aoe Ss seoja so lloauss.| 3. S 
213i ©] sisi] s |sSss|sosklec tris sus|seago| Gye 
29 |e] © PLE] |S4es/o4 on saealg4on/Psss| S25 
nial el] a/a\|F a fa x wD 5 
in.| Ibs, |sq.in.| in. | in uf I’ r a S C 
B2 }20] 100 |29.41]0.88]7.28} 1655.8 | 52.65 |} 7.50 pe! 165.6 | 1766100 
re yes) 95 127.94)0281|7.21) 1606 8 50.78 (sats; 1.35 160.7 | 17138900 
7 8h OD 126.47/0.74/7.14| 1557.8 48.98 7.67 1.36 155.8 | 1661500 
se) ) 85 :125.00]0.66{7.06] 1508.7 47.25 Reed 1.37 150.9 | 1609300 
se 1) 680 [23.73/0.60/7.00] 1466.5 | 45.81 | 7.86 1.39 146.7 | 1564300 
B4 |15} 100 |29.41'1.18/6.771 900.5 50.98 5.53 1.31 120.1 | 1280700 
Peel 9D 122.04) be0S|6.07 (iy oreeo I 46 ton BlmOnno 1,32 116.4 | 1241500 
, “| 90 |26.47/0.99/6.58} 845.4 45.91 5.65 1.32 112.7 | 1202300 
“e | s) 685 125.00/0.89/6.48] 817.8 43.57 5i%2 1.82 109.0 | 1163000 
se}! 80 (23.81/0.81)6.40} 795.5 41.76 ek 1.32 106.1 | 1131300 
B5 {15} 75 |22.06)0.88/6.29| 691.2 30.68 5.60 1.18 92.2 983000 
‘ |‘ 70 |20.59/0.78|6.19) 663.6 29.00 5.68 1.19 88.5 943800 
e ) cl 65 119.1210.69/6.10] 636.0 | 27.42 | 5 77 1.20 84.8 | 904600 
ve 1 sl 60 6(117.67/0.59/6.00} 609.0 25.96 5.87 1.21 81.2 866100 
BS /12} 55 |16.18]0.82/5.61] 3821.0 17.46 4.45 1.04 63:5 570600 
“ey 50 114.71/0.70/5.49) 303.38} 16.12 | 4.54 1.05 50.6 | 539200 
“) 9) 46 113.24/0.5815.37| 285.7 14.89 4.65 1.06 47.6 507900 
se 1) 40 111.84/0.46/5.25] 268.9 13.81 ap ape 1.08 44.8 478100 
Properties of Carnegie Trough Plates—Steel,. 
Noes of Raatas 
: a ot. nertia, Section a 
Section] Sizes | Weight] ‘Area | Thick: | Neutral |afoaulus, GY" 
IndeX-| Inches. | Foot. | tion. | Inches. | pavaitel to! before: ‘before 
Length. SAEs 
lbs sq. in I S r 
M10 | 916x334 | 16.32 4.8 % 3.68 lapis 0.91 
Mi1 | 916x334 | 18.02 5.3 9/16 4.13 1.57 0.91 
M12 | 916x334 | 19.72 5.8 Bg 4.57 tert 0.90 
M13 | 936x834 | 21.42 6.3 11/16 5.02 1.96 0.90 
M14 914 x 334 23.15 6.8 34 5.46 2.15 0.90 








Properties of Carnegie Corrugated Plates—Steel, 


—____— 

















aes of : Radius 
Size, |Weight| Area| Thick- | inertia. | Section [ray ig 
Tipe ‘n per lof Sec-| ness in ata: pee a tion, 
“* | Inches. Foot. | tion. | Inches. Parallel'to| “before: Axis as 
Length. before. 
Grit) % ~ ‘Tbs. §q. in. ve S ta 
M30 | 83% x1%4| 8.06] 2.4 0.64 0.80 | 0.52 
M31 834 x14) 10.10 8.0 5/16 0.95 1.13 0.57 
M32 | 834 x1%4| 12.04] 3.5 4 1.25 1.42 0.62 
M33 «4/12 8/16x 284; 17.75 | 5.2 3 4.7 3.33 0.96 
M34 |12 3/16 x 234; 20.71 | 6.1 7/16 5.81 3.90 0.98 
M35: /12 3/16x 234! 23.67' 70 6.82 4.46 0.99 





219 


PROPERTIES OF ROLLED STRUCTURAL STEEL. 





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PROPERTIES OF ROLLED STRUCTURAL STEEL, 277 


Properties of Standard Channels—Steel, 



























































1; 2 8] 4) 5 6 7 8 9 10 1i 12 
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in.| lbs. | sq.in.) in. | in Z Ts r A S C x 

15] 55. |16.18/0.82/3.82} 430.2 12.19 5.16 868 57.4 | 611900 823 

“) BO. |14.71/0.72/3.7 402.7 11.22 5.23 87% 53.7 72700 803 

*) 45. |18:24|0.62)3.62! 3875.1 LOSo Web ooe .882 50.0 | 533500 788 

**) 40. 111.76]0.52/8.52} 347.5 9.39 5.43 893 46.3 | 494200 783 

**) 85. |10.29/0.43/3.43] 320.0 8.48 5.58 908 42.7 | 455000 789 

“1 33. | 9.90)0.40/3.40} 312.6 8.25 5.62 912 41.7 | 444500 794 

12] 40. |11.76)0.76/3.42| 197.0 6.63 4.09 «(ol 82.8 | 350200 722 

* 85. |10.29/0.64/3.30} 179.3 590 61417 (57 | 29.9 | 318800 | .694 

** 30. | 8.82/0.51/38.17} 161.7 521 4.28 . 768 26.9 | 287400 677 

**) 25. | 7.85/0.39 3.05) 144.0 4.53 | 4.43 .785 | 24.0 | 256100 | .67 

**) 20.5) 6 03/0.28)2.94) 128.1 3.91 4.61 805 21.4 | 227800 704 

10] 35. |10.29/0.82/3.18} 115.5 4.66 | 3.35 67% 23.1 | 246400 | .695 

“1 30. | 8.82/0.683.04) 103.2 3.99 3.42 672 20.6 | 220300 651 

) 25. |, 7.8510.538 2.891), 91.0 SOM eis. .680 | 18.2 | 194100 | .620 

1 20. | 5.88/0.388.2.74| 78.7 2.85 | 3.66 .696 | 15.7 | 168000 | .609 

**) 15. | 4.46/0.24'2.60] 66.9 BOO Ll wOae -718 | 13.4 | 142700 | .689 

9} 25. | 7.35)0.61/2.81 70.7 2.98 3.10 637 15.7 | 167600 615 

“| 20, | 5.88/0.45 2.65 60.8 2.45 3.21 .646 13.5 | 144100 585 

Cat Hs 4.41|0.29;2.49 50.9 ils 3.40 - 665 11.3 | 120500 590 

**! 1314] 3.89 0.23 2.43 47.3 130% 3.49 674 10.5 | 112200 607 

8} 2114] 6.25)0.58 2.62 47.8 2.25 2.00 .600 11.9 | 127400 587 

**) 1834] 5.51/0.49/2.53 43.8 2.01 2.82 .603 11.0 | 116900 567 

**! 1614) 4.78)0.40/2.44 39.9 1.78 2.89 .610 10.0 | 106400 556 

**) 1334} 4.04/0.31/2.35 36.0 1.55 2.98 .619 9.0 96000 557 

641114] 3,35/0.22/2.26] 32.3 Use Sa 630 8.1 | 86100 | .576 

7 1934) 5.81/0.68 2.51 33.2 1.85 2.39 -565 9.5 | 101100 583 

“) 1714) 5.07/0.53/2.41 80.2 1.62 2.44 564 8.6 92000 555 

**) 1434) 4.34)0.42/2.30 Vice 1.40 2,50 .568 7.8 82800 533 

1 1214) 3.60)0.82/2.20 24.2 1.19 2.59 575 6.9 73700 528 

“)  934| 2.85/0.21/2.09] 21.1 0.98 | 2.72 .586 6.0 | 66800 | .546 

6} 15.5) 4.56/0.56)/2.28 19.5 1,28 2.07 .529 6.5 69500 546 

*) 13. | 3.82/0.44/2.16 17.3 1.07 2.18 -029 5.8 61600 517 

©) 10.5] 3.09)0.382)2.04 aed 0.88 2.21 .034 5.0 53800 503 

sl 8. 1 2.38/0.20)1.92 13.0 0.70 2.84 .542 4.3 46200 517 

5} 11.5) 8.38/0.48)2.04; 10.4 Or325 Lae 493 4.2 | 44400 | .508 

‘1 9. | 2.65/0.33)1.89 8.9 0.64! 1,88 493 8.5 | 87900 | .481 

Pleo ole O10. 1911 Je 7.4 0.48 1.9) 498 8.0 31600 489 

4\ 714| 2.138/0.32/1.72 4.6 0.44 1.46 «455 2.3 24400 | .463 

‘| 614] 1.84/0.25)1.65 4.2 0.38 4.51 454 aoik 22300 458 

| 514) 1.55/0.18)1.58 3.8 0.32 1.56 .453 1.9 20200 464 

3] 6. | 1.76/0.36/1.60 2.1 0.31 | 1.08 421 1.4} 14700 | .459 

ss) 5. | 1.47/0.26/1.50 1.8 0.25 1.12 415 1.2 13100 443 

“) 4, | 1.19]0,17/1.41 1.6 On20e) I 1d .409 1.1 | 11600 | .443 

L = safe load in lbs., uniformly distributed; 7 = span in feet; 

M = moment of forces in ft.-lbs.; C = coefficient given above. 
C CA 8fS, =o filbrelatre 

L=73 M=-; C= Ll =8M=-—73 igs re stress, 











Carnegie Deck-beams., 





278 PROPERTIES OF ROLLED STRUCTURAL STEEL. 








































































































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ao pete toe Ae ; 
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BN lh So SSD I eget ecicieae 52 a Ne 
a | 0} Iv[No1pusc ny 2D 99 19 OP 19 1 WHO TBSLIRS S e8uvlq 09 Jorreavg 
-1dq SIXV [B1jNON ns ose ak He = =, ~™) 9) 22] 9 Jo *O Uno sIxy 
“el41ou] JO JUSTO] aS 3) [eaqnoN ‘vIyZEUT Jo “UO 
rs C1n0~eHOSSOrM®D Sars INIIID DO OSid =a, = 
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Ye) esuela JO WIPIM | At. Apion Oe tI OO OD OF 69 OD OD 6D CR = : Nu Renee =a OR ee iA 
1G1D.1D Wi IGA Wwe ET WOTZ 4) JO “D FO VOUBISIGT) FS SSC OOH ee HT HOOS 
3 1 Go Otte o at OO Otnt+onor— : Ss se 
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2 7 *‘UOL 00: a Wee gt ie ee ET Sr ee ee ee 
| paenDoRaOaoate HS (SHSeueetas = 1008 J V | Gisd 6 ot od aR GR ios Od Sod aE 
(fet ot) A ms Se OES C= [OT SHSOSGS Rn Beton 
Be oy ae PRA O PSE. | NS gmk Seti ed oleae hE Beate eg eT cy eee yy | eee el ee CRON OT wR 7S TLR Soe ec oy 
| R 1S on | 900} 10d FUSIOM | Sa5 Sin DOD OIONHHMOAD 
| aSes looses SeeaaRtssh |= ae 
| . i+? ha wD OD NNN 
ery “300M Tod UBIOM | OO en koa locetceeete Sener kd ee gee 
| i—-Siesraanrtes is Sate eee ; : (09 BPSD 69 60 FR 10 SHH HO RL 
ee ee ee =&§ rx| “woag £q oBuepd +9218 | EX KX XXX KXXXXXXXX 
was “awe 70 Widog "| -gooo PR MrEpS |S Ge lowe wei! = | TNS ae 
aeer 2 AD AD SHS SHS SRN Sh SHH SH tt St 





STRENGTH OF MATERIALS. 


Carnegie T Shapes—(Continued). 














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a 

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a Joos WFPM |B Gr SPATASASOMMSAOAWHSSLHOGESHOSHOSC HOGAN AFT GTNMAAIARADNA ANAS 

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279a 


STRENGTH OF MATERTALS, 


Properties of Standard and Special Angles of Minimum 


. 


Dimensions. 


Six 
#234 x 234 


214 x24 
246 x26 
#214 x 214 
#214 x 214 
pen ay 
Qinsce 


134 x 134 
134 x 134 


144x114 


*ilgxllg 
*1Uex ile 
lee 1 





Gravity from Back of 


Flange. 
tral Axis through Cen- 


tre of Gravity Parallel 


Moment of Inertia, Neu: 
to Flange. 
Section Modulus, 


Thickness, 

Weight per Foot. 

Area of Section. 
Distance of Centre of 





omic ctor 
l 
| 

ree 00 

a OT Co CO QW -2-F 


Ke ee Re 
ete ap 


OMe tS 


Coro 
mweew ewe wero WAITS 


Co Op & =F 
 ietaJ 


7 WO OF 
rt > O09 
o ocoooo odo re 


HwHo 
COCO COOSo SCHOH 


St ded 


MROWS BSmoHw ODA 


Dooor SorYFory 


and Maximum Thicknesses and Weights. 


ANGLES WITH EQUAL LEGS. 


ee ee ee ee ee ee eee 


oa 
| 


=) 
(©) 


68 


- Angles marked * are special, 


Neu- 


tral Axis through Cen- 
tre of Gravity Parallel 


to Flange. 
Radius of Gyration, Neu- 
tre of Gravity Parallel 


to Flange. 
Least Radius of Gyration, 


tral Axis through Cen- 





| 
| 
| 
| 
| 
| 


R 


vO OT & =F 


mt 0 et 9 


ao ooo ss: oc coo) OD or 
lo sie sie) 
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Cot GO DO ows. Ororos or loror Ewes 
rt He 09 


Mm 09 25 WO 
ie OUR orgor) 


9 


gh 
at 


Centre of Gravity : 
Angle of 45° to Flanges. 


‘ = Neutral Axis throu 
@o 09 0 oc & tw a OTe Ororas or iO WO Coon e 
lor) dante} lorie shank ie) or OO oOonwo womwort 


@ 
ROW, DOO 


Sesso eoseso esco ecco scecoma coooo ceooo 9CoCorrF 
0 Ww 9% 


ba eh ek Re 
C-2O co 





PROPERTIES OF ROLLED STRUCTURAL STEEL. 2/98 


Properties of Standard an@ Special Angles of Minimum 
and Maximum Thickness and Weights, 


ANGLES WITH UNEQUAL LEGS. 








1 eulesale diate bar dade ht Goalies 9 | 10 | 41 


Moments of} Section 


Inertia. tate ae Radii of Gyration. 
I ; 





Peasy bel i 
8| § 
mn . as) ita ‘ a] ' ‘ . 
= B 8 152 185 jee |80 | SB 3 0 te, 
s 218) a ee ee de ge (de jhe | sz 
g ay Ce no nO Iw nor] ma no 2S 
® 9141 2 he ee eS THA 1S Ka = Bp 
& 21] 8 Hegltoditeciesl Mos |tog| 38 
a a 2 = a bela > otis S Bola > bo gr w | grou cot 
SO s|SSa|bSS/STS| 558 | SSE | oe 
Samia cm|Saml\5em| Sam |] Sam | Sa 
Z ic’ Zz A A 4 
inches, | inch. |Ibs. |sq.in. 
*Y x34] 1 [32 8] 9.50 | 7.53 [45.87 | 2.96 10.58 | 0.89 | 2.19 | .88 
#7 X3l6 | 7/16 |15.0| 4.40 | 3.95 [22.56 | 1.47] 5.01] 0.95 | 2.2 .89 
6 x4 7% (27.2| 7.99 | 9.75 [27.73 | 3.39 | 7.15 | 1.11 1.86 | .88 
6 x4 84 112.3] 8.61 | 4.90 |13.47 | 1.60 | 3.32 | 1.17 | 1.98 | .88 
6 X34} 4% [25.7] 7.55 | 6.55 |26.38 | 2.59 | 6.98] 0.93 | 1.87 | .7 
6 x3i4| 36 |11.7] 3.42 | 3.34 112.86 | 1.23 | 3.25] 0.99. | 1.94 | 77 
#5 x4 7 |24.2| 7.11 | 9.28 [16.42 | 3.31 | 4.99 | 1.14 | 1.52 | .88 
5 x4 34 111.0] 3.23 | 4.67 | 8.14 | 1.57 | 2.84 | 1.20 | 1.59 | .86 
5 x34 | % |22.7] 6.67 | 6.21 [15.67 | 2.52] 4.88] 0.96 | 1.58 | .77 
5 x3% | 8 (10.4 3.05 | 3.18 | 7.78 | 1.21 | 2.29] 1.02 | 1.60 | .%6 
5 X83 {13/16 |19.9] 5.84 | 3.71 [18.98 | 1.74] 4.45 | 0.80 | 1.55 | .66 
5 x3 | 5/16 | 8.2] 2.40 | 1.75 | 6.26 | 0.75 | 1.89] 0.85 | 1.61 | .66 
*414x3 {13/16 |18.5| 5.43 | 3.60 ]10.88 | 1.71 | 3.62 | 0.81 1.88 | .67 
*414X3 34 | 9.1] 2.67 | 1.98 | 5.50 | 0.88 | 1.83] 0.86 | 1.44 | .66 
#4° "314 (13/16 |18.5| 5.43 | 5.49 | 7.77 | 2.30 | 2.92 | 1,01 | 1.19 | .74 
*4 316 | 36 | 9.1] 2.67 | 2.99 | 4.18 | 1.18] 1.50] 1.06 | 1.25 | .% 
4 x3 {13/16 117.1] 5.08 | 3.47 | 7.84 | 1.68 | 2.87] 0.83 | 1.21 | .66° 
4 x3 | 5/16 | 7.1] 2.09 | 1.65 | 3.88 | 0.74 | 1.23 | 0.89 | 1.27 | .65 
346X383 [13/16 |15.7] 4.62 | 3.33 | 4.98 | 1.65 } 2.20] 0.85 | 1.04 | .65 
316X383 | 5/16 | 6.6] 1.938 | 1.58 | 2.33 | 0.72 | 0.96 | 0.90 | 1.10 } .63 
B44 x24 111/16 |12.4] 3.65 | 1.72 | 4.13 | 0.99 | 1.85] 0.67 | 1.06 | .58 
314x214 | 14 | 4.9] 1.44 | 0.78] 1.80] 0.41] 0.75] 0.74 | 1.12 | .55 
#3142” | 9/16 | 9.0] 2.64 | 0.75 | 2.64 | 0.53 | 1.30] 0.53 | 1.00 | .45 
#314 2 14 | 4,8| 1.25 | 0.40 | 1.86 | 0.26 | 0.63 | 0.57 | 1.04 | .44 
3 x26 | 9/16 | 9.5] 2.78 | 1.42 | 2.28 | 0.82] 1.15] 0.72 | 0.91 | .54 
3 x26] 4 | 4.5] 1.81 | 0.74] 1.17} 0.40 | 0.56 | 0.75 | 0.95 | .53 
3 x2 4 | 7.7] 2.95 | 0.67 | 1.92 | 0.47 | 1.00] 0.55 | 0.92 | .47 
*3 x2 14 | 4.0] 1.19 | 0.89 ] 1.09 | 0.25 | 0.54 | 0.56 | 0.95 | .46 
24xe2 6.8| 2.00 | 0.64 | 1.14 | 0.46 | 0.70 | 0.56 | 0.75 | .44 
914x2 | 8/16 | 2.8] 0.81 | 0.29 | 0.51 | 0.20, 0.29 | 0.60. | 0.7% .43 
#217114 | 16 | 5.5] 1.63 | 0.26 | 0.82 | 0.26 1 0.59 | 0.40 | 0.71 | .39 
*214 144 | 3/16 | 2.3] 0.67 | 0.12 | 0.84 | 0.11 | 0.23 | 0.43 | 0.72 | .40 
*2 x186| 1% | 2.7] 0.78 | 0.12 | 0.87 | 0.12 | 0.23 | 0.89 | 0.68 | .30 
*2 x13¢ | 8/16 | 2.1] 0.60 | 0 09 | 9.24 | 0.09 | 0.18 | 0.40 | 0.63 | .29 
#134X1 1% | 1.8) 0.53 | 0.04 | 0.09 | 0.05 | 0.09 | 0.27 | 0.41 | .25 
1.0) 0.28 | 0.02 | 0.05 | 0.03 | 0.06 | 0.29 | 0.44 | .22 








*138xX1 1g 





Angles marked * are special, 


250 





1 


td N Section Index. 


. 
- 


ces 
oo 


« 
ele 


« 
on 


ets 
a 


-N 
+ Ot 


n 
. 


-N 
“O 


ee 


Zi1 
oe 
ZAR 





2 


| 


dae, 


12. 


14. 


| Weight per Foot. 








Area of Section. 





ce OY t) 


we Ooo oF, 








STRENGTH OF MATERIALS, 


Properties of Carnegie Z Bars. 


(For dimensions see table on page 178.) 


| 
| 
| 


of Gr. 


Perpendicular to Web. 


Mom. of Inertia. Neutral 
Axis through C. 


if 
25.32 
29.80 
34.36 


34.64 
38.86 
43.18 














ertia. Neutral 
ugh C. of Gr. 


Aa 


Coincident with Web, 


Mom. of 
Axis th 








6 





is 


Neutral 


Axis through C. of 
Perpendicular to Web. 


Section Modulus. 





we 








7 





of Gr. 


Coincident with Web. 


Radii of 


Neutral 


Section Modulus. 
Axis through C. 





wo SOR RHR wr 


a. 
\ 


wz 


co 0 co 


mee Be Co 


WR Be Se Bw wer 
a, em igh —ipd ir oie Mee eae Bier, marae ar al 





8 





Neut. 
of Gr. 


tyration. 
Perpendicular to Web. 


Axis through C. 





1.91 


cS) 


Rom © 
Dew Gane 


So SD 


wm 2 fe OCroror 


Se gee Se Se eS eee (eS See ee 
ace ovis et ear atm ZN dep so * 6 
20 we COOM CTU 


— ee 
oe 
et Rr 


02 0O 








Neut. 
of Gr. 


Radii of Gyration. 
Axis through C. 
Coincident with Web. 





Le ne ee ee ee ee ee ee ee ee ee ae ae 
ep are Celene eee ge SSE OE oe eRe ee ee ar SS Me PU ee eee eee Se a” rere EY Nee ne a 








10 





Least 
Axis 


Neutral 


Diagonal. 


Radii of Gyration. 
Radius, 





~ 


ISI OCODm OBMOO COD 
“1D WHR RW LHW 


~J-0-5 
SOT ee 


=? 


s 
—_ 


| 
| 


| 
| 


for 


Strength 
Fibre Stress of 16,000 Ibs. 
per sq. in,, Axis Perpen- 
dicular to Web at Centre, 


Coeff. of 


| 
| 


C 
90,000 
104,800 
119,700 


123,200 
136,700 
150,400 


149,800 
162.3800 
174,900 


57,009 
68,200 
79,400 


81.900 
91,900 
102,100 


101.000 
110,300 
119,500 


33,500 
41,700 
49,800 
51,500 


58,700 
65,900 
64,500 
70,900 
77,400 
20 500 
25,400 
27,400 
31,800 


32,600. 
36,600 





12 


for 
€ Axis Perpen- 
dicular to Web at Centre, 


Fibre Stress of 12.000 bs. 


Coeff. of Strength 
per sq--in.. 


| 
| 


Cc’ 
67,500 
78,600 
89,800 


92,400 
102,600 
112,800 


112,800 
121,800 
131,200 


42,700 
51,100 
59,500 


61,400 
69.000 
76,600 
"5,800 
82.700 
89,600 


25,100 
31,800 
37,400 


38,600 
44,006 
49,400 
48,400 
53,200 
58, 100 
15,400 
19,000 
20,600 
23,800 - 


24,500 
2" 400 





Dimensions of lightest weight bars of each size: Z1, Z2, and Z3, depth of 
web 6 in., width of flange 3% in., thickness of metal respectively 3¢, 9/16. 
: ZA, Z5, Z6, 5 & 814 x 5/16, %, and 11/16 in.; Z7, Z8, Z9, 4 x 3 1/16 
Z10, Z11, Zi2, 3 X 211/16 x 4, 3%, and \% in. Each 


and 34 in. 


x \, 7/16, and %& in. : 


dimension is increased 1/16 in. in the next heavier weight. 


TORSIONAL STRENGTH. 281 


FLOORING MATERIAL. 


For fire-proof flooring, the space between the floor-beams may be spanned 
with brick arches, or with hollow brick made especially for the purpose, the 
latter being much lighter than ordinary brick. 

Arches 4inches deep of solid brick weigh about 70 lbs. per square foot, 
including the concrete levelling material, and substantial floors are thus 
made up to 6 feet span of arch, or much greater span if the skew backs at 
the springing of the arch are made deeper, the rise of the arch being prefer- 
ably not less than 1/10 of the span. Hollow brick for floors are usually in 
depth about 4g of the span, and are used up to, and even exceeding, spans 
of 10 feet. The weight of the latter material will vary from 20 lbs. per 
square foot for 3-foot spans up to 60 lbs. per square foot for spans of 10 feet. 
Full particulars of this construction are given by the manufacturers. For 
supporting brick floors the beams should be securely tied with rods to resist 
the lateral pressure. 

In the following cases the loads, in addition to the weight of the floor 
itself, may be assumed as: 


For street bridges for general public traffic........ 80 lbs. per sq. ft. 
Horfloorsof dwellings iii2% 98.9222 lit te at 40983 SATE 
For churches, theatres, and ball-rooms............ 80 Tbs. hr eas 
Hor nay lafis i, Bsr es, SUID! I, SPE IS EEE SO TOS, PEST es 
HOmsStorarerol STAM lor teas cee k. sane ten Le 100 Ths eS Bee? 
For warehouses and general merchandise......... 250 Ibs. Seng 8 
HOrdtacluOriesy hy. cee «koe Sill cele ate watt oatets dete: 200 to 400-lbs. ‘“* * 
For snow thirty inches deep........... 0.2.06... 16, LoS Ree anes 
For maximum pressure of wind .................. 50 Ibs. ec oga 
ONE IIC KeWallsiter, ccc 582 sapae oot Se leain una ieee ets 112 lbs. per cu. ft. 
HMOMMASONTY, WAUSHs Ss ss ates de Sakis calor e seus 116-144 lbs. “* * 


Roofs, allowing thirty pounds per square foot for wind and snow: 


For corrugated iron laid directly on the purlins... 37 lbs. per sq. ft. 
For corrugated iron laid on boards...............4 40 lbs, <- Shbe 
Horislate nailedstoathse. f.si0st ee ee ae 43: DST Drs ta: 
For slate nailed on boards...................s0000- 4Gil DS Sail Ces 


If plastered below the rafters, the weight will be about ten pounds per 
square foot additional. 


TEIE-RODS FOR SIEGE SUPPORTING BRICK 





CHES. 
The horizontal thrust of brick arches is as follows: 
2 
ase = pressure in pounds. per lineal foot of arch: 


W = load in pounds. per square foot; 
S = span of arch in feet; 
R = rise in inches. 


Place the tie-rods as low through the webs of the beams as possible and 
spaced so that the pressure of arches as obtained above will not produce a 
greater stress than 15,000 lbs. per square inch of the least section of the bolt, 


TORSIONAL STRENGTH. 


Let a horizontal shaft of diameter = d be fixed at one end, and at the 
other or free end, at a distance = / from the fixed end, let there be fixed a 
horizontal lever arm with a weight = P acting at a distance = a from the 
axis of the shaft so as to twist it; then Pa = moment of the applied force. 


os it SJ , ; : ; 
Resisting moment = twisting moment = oe? in which S= unit shearing 


resistance, J = polar moment of inertia of the section with respezt to the 
axis, and c = distance of the most remote fibre from the axis, in @ cross- 
section. Fora circle with diameter d, 


J = —-; c= léd; 


py Pye 
J  7ndS dS _ ‘ng iil Nee 
| —— = eee ev oee oy g 





282 STRENGTH OF MATERIALS. 


For hollow shafts of external diameter d and internal diameter @4, 





4 _ q,4 sii bahar 
Re seh he as ad ena ee oe 
‘i 1 air S 
(1 ae) 
For a square whose side = d, 
d* yy, SI a3g 
Seas = ; —_ = = = 3 
J= Butte d V4; , Pa 7.9196 0.23638. 
For a rectangle whose sides are b and d, 
bd3 b3d ——> ST (bd3 + b3d)S 
= ere = 2 Pik — «= at, eee aed ec mee 
J 2 ne a c= l4 Vb? + d?; ; Pa Pgiriiaiica 


The above formule are based on the supposition that the shearing resist- 
ance at any point of the cross-section is proportional to its distance from the 
axis; but this is true only within the elastic limit. In materials capable of 
flow, while the particles near the axis are strained within the elastic limit 
those at some distance within the circumference may be strained nearly to 
the ultimate resistance, so that the total resistance is something greater 
than that calculated by the formulae. (See Thurston, ‘“ Matls. of Eng.,’’ Part 
iI. p. 527.) Saint Venant finds for square shafts Pa = 0.208d8S (Cotterill. 
“Applied Mechanics,’ pp. 348, 355). For working strength, however, the 
formule may ve used, with S taken at the safe working unit resistance. 

For a rectangle, sides b dGonger) and d (shorter) and area A, 

A 2 
+ = 35 41.80" 

The ultimate torsional shearing resistance S is about the same as the di- 
rect shearing resistance. and may be taken at 20,000 to 25,000 lbs. per square 
inch for cast iron, 45,000 lbs. for wrought iron, and 50,000 to 150,000 Ibs. for 
steel, according to its carbon and temper. Large factors of safety should 
be taken, especially when the direction of stress is reversed, as in reversing 
engines, and when the torsional stress is combined with other stresses, as is 
usual in shafting. (See “Shafting.’’) 

Elastic Hesistance to Torsion.—Let. / = length of bar being 
twisted, d = diameter, P= force applied at the extremity of a lever arm 
of length = a, Pa = twisting moment, G = torsional modulus of elasticity, 
6 = angle through which the free end of the shaft is twisted, measured in - 
are of radius = 1. 

For a cylindrical shaft 


4 9 39 
If a = angle of torsion in degrees, 
Bgl al papper Aho 180 X 82Pal y 583.6 Pal 
180 ” 7 72d4#G d4G ° 


The value of G is given by different authorities as from 1 to 2/5 of E, the 
modulus of elasticity for tension. 


COMBINED STRESSES. 


(From Merriman’s ‘‘ Strength of Materials.’’) 


Combined Tension and HMlexure.—Let 4 =the area of a bar 
subjected to both tension and flexure, P= tensile stress applied at the ends, 
P+ A= unit tensile stress, S = unit stress at the fibre on the tensile side most 
remote from the neutral axis, due to flexure alone, then maximum tensile 
unit stress = (P+ A)+ S. A beam to resist combined tension and flexure 
should be designed so that (P- A) + S shall not exceed the proper allow- 
able working unit stress. : 

Combined Compression and Flexure.—If P+ A= unit stress 
due to compression alone, and S = unit compressive stress at fibre most 
remote from neutral axis, due to flexure alone, then maximum compressive 
unit stress = (P+ A)+ 8S. 

Combined Tension (or Compression) and Shear.—lIf ap« 


STRENGTH OF FLAT PLATES. 2838 


plied tension (or compression) unit stress = p, applied shearing unit stress 
= v, then from the combined action of the two forces 


Max. S= + Vv? +14p2, Maximum shearing unit stress; 
Max. t= p+ Vv? + 14p?, Maximum tensile (or compressive) unit stress. 


Combined Flexure and Torsion.—If S = greatest unit stress 
due to flexure alone, and Ss = greatest torsional shearing unit stress due to 
torsion alone, then for the combined stresses 


Max. tension or compression unit stress t = 4S + 4/Ss? + 145?; 
Max. shear s = + VSs? + 1482. 


Formula for diameter of a round shaft subjected to transverse load while 
transmitting a given horse-power (see also Shafts of Engines): 


eyes 16M a 16 M2 402,500,000.H2 
ke t 12 n2 


at 





? 


where M = maximum bending moment of the transverse forces in pound- 
inches, H = horse-power transmitted, n = No. of revs. per minute, and t = 
the safe allowable tensile or compressive working strength of the material. 

Combined Compression and Torsion.—For a vertical round 
shaft carrying a load and also transmitting a given horse-power, the result- 
ant maximum compressive unit stress 


4P publ) here 
t=—, + 4/221 0002 ieanae 





~~ wd? 


in which Pis the load. From this the diameter d may be found when ¢ and 
the other data are given. 

Stress due to Temperature.—Let / = length of a bar, A = its sec- 
tional area, c = coefficient of linear expansion for one degree, t = rise or 
fall in temperature in degrees, # = modulus of elasticity, A the change of 
length due to the rise or fall ¢; if the bar is free to expand or contract, A = 
Gu: 

If the bar is held so as to prevent its expansion or contraction the stress 
produced by the change of temperature = S= ActH. The following are 
average values of the coefficients of linear expansion for a change in temper- 
ature of one degree Fahrenheit: 


For brick and stone....a@ = 0.0000050, 
Honcast irons. vances: a = 0.0000062, 
For wrought iron.......@ = 0.0000067, 
HE ORIST ECCI 5.215 dstesre ne a = 0.0000065. 


The stress due to temperature should be added to or subtracted from the 
stress caused by other external forces according as it acts to increase or to 
relieve the existing stress. 

What stress will be caused in a steel bar 1 inch square in area by a change 
of temperature of 100° F.? S = ActH =1 X .0000065 x 100 x 30,000,000 = 
19,400 Ibs. Suppose the bar is under tension of 19,500 Ibs. between rigid abut- 
ments before the change in temperature takes place, a cooling of 100° F. 
will double the tension, and a heating of 100° will reduce the tension to zero. 


STRENGTH OF FLAT PLATES. 
For a circular plate supported at the edge, uniformly loaded, according to 


Grashof, 
Bae | ese, Sep , a Ore 
f= 6p? ta 4/ EPs Y ory 5,2" 
For a circular plate fixed at the edge, uniformly loaded, 
2 72 2 r2p aft? 
eg a= sD ee lhe pe Se 
S=3 Pi 4/5 P= 9,2? 


in which f denotes the working stress; r, the radius in inches; t, the thick 
ness in inches; and p, the pressure in pounds per square inch. 


284 STRENGTH OF MATERIALS. © 


For mathematical discussion, see Lanza, ‘‘ Applied Mechanics,’ p. 900, etc. 
Lanza gives the following table, using a factor of safety of 8, with tensile 
strength of cast iron 20,000, of wrought iron 40,000, and of steel 80,000 : 


Supported. Fixed. 
Cast (TON.oe 4 tae sh = .0182570r Vp t = .0163300r Vp 
Wrought iron........ t = .0117850r 4/p t = .0105410r 4/p 
Steel sisc ciate cesses ae t = .00912877r 4/p t = .00816497 4/p 


For a circular plate supported at the edge, and loaded with a concen- 
trated load P applied at a circumference the radius of which is r9: 


4 r ie dP 
he & log = +3} nt? “nt? 
for WEL SLOT BOR" © 30 DH 40g ar Bo: 
To 
c= 4.07 5.00 5.53 5.92 6,22; 
cP . _ tf 
sa Muley te geal UT 


The above formule are deduced from theoretical considerations, and give 
thicknesses much greater than are generally used in steam-engine cylinder- 
heads. (See empirical formule under Dimensions of Parts of Engines.) The 
theoretical formule seem to be based on incorrect or incomplete hypoth- 
eses, but they err in the direction of safety. 

The Strength of Unstayed Flat Surfaces.—Robert Wilson 
(Eng’g, Sept. 24, 1877) draws attention to the apparent discrepancy between 
the results of theoretical investigations and of actual experiments on the 
strength of unstayed flat surfaces of boiler-plate, such as the unstayed flat 
crowns of domes and of vertical boilers. 

Rankine’s ‘*‘ Civil Engineering” gives the following rules for the strength 
of a circular plate supported all round the edge, prefaced by the remark 
that ‘‘ the formula is founded on a theory which is only approximately true, 
but which nevertheless may be considered to involve no error of practical 
importance:”’ 


Wb Pb 
Ep abe eons 
Here 
M = greatest bending moment ; 
2 
W = total load uniformly distributed = us ; 


6 = diameter of plate in inches ; 
P = bursting pressure in pounds per square inch. 


Calling ¢ the thickness in inches, for a plate supported round the edges, 


1 Pb? 
aes 2. vee gets aay MES 
M 7 42,000b¢?; 24 70004 


For a plate fixed round the edges, 


2 Pb? t? < 63,000 
eee = DEI" ee SRE neta be hobs 
ia = 000¢2; whence P= 72 ’ 


where 7 = radius of the plate. 
Dr. Grashof gives a formula from which we have the following rule: 


_ t2 x 72,000 
= , ae 


This formula of Grashof’s has been adopted by Professor Unwin in his 
‘*Blements of Machine Design.” These formule by Rankine and Grashof 
may be regarded as being practically the same. 

On trying to make the rules given by these authorities agree with the 
results of his experience of the strength of unstayed flat ends of cylindrical 
boilers and domes that had given way after long use, Mr. Wilson was led to 
believe that the above rules give the breaking strength much lower than it 


Ng 


STRENGTH OF FLAT PLATES, 285 


actually is. He describes a number of experiments made by Mr. Nichols of 
Kirkstall, which gave results varying widely from each other, as the method 
of supporting the edges of the plate was varied, and also varying widely 
from the calculated bursting pressures, the actual results being in all cases 
very much the higher. Some vouclusions drawn from these results are: 

1. Although the bursting pressure has been found to be so high, boiler- 
makers tnust be warned against attaching any importance to this, since the 
plates deflected almost as soon as any pressure was put upon them and 
sprang back again on the pressure being taken off. This springing of the 
plate in the course of time inevitably results in grooving or channelling, 
which, especially when aided by the action of the corrosive acids in the 
water or steam, will in time reduce the thickness of the plate, and bring 
about the destruction of an unstayed surface at a very low pressure. 

2. Since flat plates commence to deflect at very low pressures, they should 
never be used without stays; but it is better to dish the plates when they are 
not stayed by flues, tubes, ete. 

3. Against the commonly accepted opinion that the limit of elasticity 
should never be reached in testing a boiler or other structure, these experi- 
ments show that an exception should. be made in the case of an unstayed 
flat end-plate of a boiler, which will be safer when it has assumed a perma- 
nent set that will prevent its becoming grooved by the continual variation 
of pressure in working: The hydraulic pressure in this case simply does 
what should have been done before the plate was fixed, that is, dishes it. 

4. These experiments appear to show that the mode of attaching by flange 
or by an inside or outside angle-iron exerts an important influence on the 
manner in which the plate is strained by the pressure. 

When the plate is secured to an angle-iron, the stretching under pressure is, 
to a certain extent, concentrated at the line of rivet-holes, and the plate par- 
takes rather of a beam supported than fixed round the edge. Instead of the 
strength increasing as the square of the thickness, when the plate is attached 
by an angle-iron, it is probable that the strength does not increase even 
directly as the thickness, since the plate gives way simply by stretching at 
the rivet-holes, and the thicker the plate, the less uniformly is the strain 
borne by the different layers of which the plate may be considered to be 
made up. When the plate is flanged, the flange becomes compressed by the 
pressure against the body of the plate, and near the rim, as shown by the 
coutrary flexure, the inside of the plate is stretched more than the outside, 
and it may be by a kind of shearing action that the plate gives way along 
the line where the crushing and stretching meet. 

5. These tests appear to show that the rules deduced from the theoreticat 
investigations of Lamé, Rankine, and Grashof are not confirmed by experi- 
ment, and are therefore not trustworthy. 
ee ee of Lamé, ete., apply only within the elastic limit. (Hng’g, Dec. 

Unbraced Wrought-iron Heads of Boilers, ete, (The Loco- 
motive, heb. 1890).—Few experiments have been made ou the strength of 
tlat heads, and our knowledge of them comes largely from theory. Experi- 
ments have been made on small plates 1-16 of an inch thick, yet the data so 
obtained cannot be considered satisfactory when we consider the far thicker 
neids that are used in practice, although the results agreed well with Ran- 
kine’s formula. Mr. Nichols has made experiments on larger heads, and 
from them he has deduced the following rule: *t To find the proper thick- 
ness for a flat unstayed head, multiply the area of the head by the pressure 
per square inch that it is to bear safely, and multiply this by the desired 
factor of safety (say 8); then divide the product by ten times the tensile 
strength of the material used for the head.”? Hisrule for finding the burst- 
ing pressure when the dimensions of the head are given is: ‘‘ Multiply the 
thickness of the end-plate in inches by ten times the tensile strength of the 
material used, and divide the product by the area of the head in inches.” 

In Mr. Nichols’s experiments the average tensile strength of the iron used 
for the heads was 44;800 pounds. The results he obtained are given below, 
with the calculated pressure, by his rule, for comparison. 

1, An unstayed flat boiler-head is 34144 inches in diameter and 9-16 inch 
thick. What is its bursting pressure? The area of a circle 341% inches in 
diameter is 935 square inches; then 9-16 x 44.800 * 16 = 252,000, and 252,000 + 
935 = 270 pounds, the calculated bursting pressure, The head actually burst 
at 280 pounds. 

2. Head 3414 inches in diameter and % inch thick. The area = 935 
square inches; then, 3g x 44,800 x 10 = 168,000, and 168,000 -- 935 = 180 pounds, 
calculated bursting pressure. This head actually burst at 200 pounds. 


236 STRENGTH OF MATERIALS. 


3. Head 2614 inches in diameter, and 3g inch thick. The area 541 square 
inches. Then, 3¢ X 44,800 x 10 = 168,000, and 168,000 + 541 = 311 pounds, 
This head burst at 370 pounds. 

4. Head 2844 inches in diameter and % inch thick. The area = 638 
square inches; then, 3g « 44,800 x 10 = 168,000, and 168,000 + 638 = 263 
pounds. The actual bursting pressure was 300 pounds. 

_ In the third experiment, the amount the plate bulged under different 
pressures was as follows: 


At pounds per sq. in.... 10 20 40 80 120 140 170 200 
Plate bulged. ... ....5., 1/32 1/16 % 14 36 4% 56 34 


The pressure was now reduced to zero, ‘‘ and the end sprang back 3-16 
inch, leaving it with a permanent set of 9-16 inch. The pressure of 200 Ibs. 
_ was again applied on 86 separate occasions during an interval of five days, 

the bulging and permanent set being noted on each occasion, but without 
any appreciable difference from that noted above. 

The experiments described were confined to plates not widely different in 
their dimensions, so that Mr. Nichols’s rule cannot be relied upon for heads 
that depart much from the proportions given in the examples. 

Whickness of Flat Cast-iron Plates to resist Bursting 
Pressures,—Capt. John Ericsson (Church’s Life of Ericsson) gave the 
following rules: The proper thickness of a square cast-iron plate will be ob- 
tained by the following: Multiply the side in feet (or decimals of a.foot) by 
14 of the pressure in pounds and divide by 850 times the side in inches; the 
quotient is the square of the thickness in inches. P 

For a circular plate, multiply 11-14 of the diameter in feet by 4 of the 
pressure on the plate in pounds. Divide by 850 times 11-14 of the diameter 
ininches. [Extract the square root. ] 

Prof. Wm. Harkness, Hng’g News, Sept. 5, 1895, shows that these rules can 
be put in a more convenient form, thus: 


For square plates 7’ = 0.004958 /p, 
and 


For circular plates T = 0.00439D 4p, 


where T = thickness of plate, S = side of the square, D = diameter of the 
circle, and p = pressure in lbs. per sq. in. Professor Harkness, however, 
doubts the value of the rules, and says that no satisfactory theoretical solu- 
tion has yet been obtained. 

Strength of Stayed Surfaces.—A flat plate of thickness ¢ is sup- 
orted uniformly by stays whose distance from centre to centre is a, uniform 
oad p lbs. per square inch, Each stay supports pa? lbs. The greatest 

stress on the plate is 


2a? ; 
f= 9 qa: (Unwin). 
SPHERICAL SHELLS AND DOMED BOILER-HEADS. 


To find the Thickness of a Spherical Shell to resist a 
given Pressure.—Let d = diameter in inches, and p the internal press-° 
ure per square inch. The total pressure which tends to produce rupture 
around the great circle will be 447d*p. Let S = safe tensile stress per 
square inch, and ¢ the thickness of metalin inches; then the resistance to the 
pressure will be wdtS. Since the resistance must be equal to the pressure. 


\nd%p = ndtS. Whence t = — 

The same rule is used for finding the thickness of a hemispherical head 
to a cylinder, as of a cylindrical boiler, 

Thickness of a Domed Head of a boiler,—If S = safe tensile 
stress per square inch, d = diameter of the shell in inches, and ¢ = thickness 
of the shell, t = pd + 2S; but the thickness of a kemispherical head of the 
same diameter ist = pd+4S. Hence if we make the radius of curvature 
of a domed head equal to the diameter of the boiler, we shall have ¢ = 
ve = Be or the thickness of such a domed head will be equal to the thick- 
ness of the shell. 


THICK CYLINDERS UNDER TENSION. 287 


Stresses in Steel Plating due to Water-pressure, as in 
plating of vessels and bulkheads (Hngineering, May 22, 1891, page 629). 

Mr. J. A. Yates has made calculations of the stresses to which steel plates 
are subjected by external water-pressure, and arrives at the following con- 
clusions : 

Assume 2a inches to be the distance between the frames or other rigid 
supports, and let d represent the depth in feet, below the surface of the 
water, of the plate under consideration, ¢ = thickness of plate in inches, 
D the deflection from a straight line under pressure in inches, and P= stress 
per square inch of section. 


For outer bottom and ballast tank plating, a = 4205, D should not ke 
greater than .05 a and < not greater than 2 to 8 tons ; while for bulkheads, 


2a 

2° and P not greater than 
7tons. To illustrate the application of these formule the following cases 
have been taken: 


ete., @ = 2352 a D should not be greater than .1 











For Outer Bottom, etc. For Bulkheads, ete. 
Thick- Depth Spacing of Thick- Maximum Space: 
ness of | below Frames should | ness of ete ing of Rigid 
Plating. | Water. not exceed Plating Stiffeners. 

in ft in. in. ft ft in 
4% 20 About 21 1% 20 9 10 
10 ee he 36 20 Wid 
$2 18 She 18 3% 10 14 8 
8 9 Ss (86 4 20 4 10 
4 10 Shae O0) 4 10 9 8 
14 5 $64 4440 4 10 4 10 





It would appear that the course which should be followed in stiffening 
bulkheads is to fit substantially rigid stiffening frames at comparatively 
wide intervals, and only work such light angles between as are necessary 
for making a fair job of the bulkhead, 


THICK HOLLOW CYLINDERS UNDER TENSION. 


Burr, “ Elasticity and Resistance of Materials,”’ p. 36, gives 
; t = thickness; r = interior radius ; 
: h-+ Diy 1 h = maximum allowable hoop tension at the 
ee = 4 
h—p 





interior of the cylinder; 
p = intensity of interior pressure. 
Merriman gives 
$s = unit stress at inner edge of the annulus; 


y = interior radius ; t = thickness ; 
l = length. 


re 
The total stress over the area 2¢1 = 2sl1 ——,. . . «1. 6 «© ew © ws (1) 


r+t 
The total interior pressure which mae to rupture the cylinder is 2rl xp: 
If p be the unit pressure, then p = rar from which one of the quantities 
s, p, r, or t can be found when the other three are given. 
_ pr+t), _ S- pit, a ee 
o t ? Oe Dp ’ WS 5 ae Pp 


288 STRENGTH OF MATERIALS. 


In eq. (1), if t be neglected in comparison with r, it reduces to 2slt, which 
is the same as the formula for thin cylinders. If t = r, it becomes sit, or 
only half the resistance of the thin cylinder. ‘ , 

The formule given by Burr and by Merriman are quite different, as will 
be.seen by the following example : Let maximum unit stress at the inner 
edge of the annulus = 8000 lbs. per square inch, radius of cylinder = 4 inches, 
interior pressure = 4000 lbs. per square inch. Required the thickness. 


_,§ (8000 +4000)? 4 _ arya SER ee 

By Burr, te 4) Ee —4000 1 \ = 4(V3 — 1) = 2.928 inches. 
4x 4000 __,. 

By Merriman, ¢ = 8000 — 4000 = 4 inches. 


Limit to Useful Thickness of Hollow Cylinders (Eng’9, 
Jan. 4, 1884).—Professor Barlow lays down the law of the resisting powers 
of thick cylinders as follows : : 

‘‘In a homogeneous cylinder, if the metal is incompressible, the tension 
on every concentric layer, caused by an internal pressure, varies inversely 
as the square of its distance from the centre.” 

Suppose a twelve-inch gun to have walls 15 inches thick. 


Pressure on exterior 6? _ 1: 12.25 
Pressure on interior” 212 7° °°’ 
So that if the stress on the interior is 12144 tons per square inch, the stress 
on the exterior is only 1 ton. 
Let s = the stress on the inner layer, and s, that at adistance x from the 
axis ; r = internal radius, R = external radius. 
72 
42° 


$28 78 524, Or 88 


The whole stress on a section 1 inch long, extending from the interior to 
; ; -?r 
the exterior surface, is S= sr X op tt 
In a 12-inch gun, let s = 40 tons, r = 6 in., R = 21 in. 


s= 40x 6x = = 172 tons. 
Suppose now we go on adding metal to the gun outside: then R will be- 
come so large compared with r, that R — r will approach the value R, so 


that the fraction ~~ becomes nearly unity. 


Hence for an infinitely thick cylinder the useful strength could never 
exceed Sr (in this case 240 tons). 


Barlow’s formula agrees with the one given by Merriman. 
Another statement of the gun problem is as follows: Using the formula 


a werat 
Ply 





40 X 15 


. 


s = 40tons, t= 15in., r = 6in., p = 





= 28% tons per sq. in., 284 x 


radius = 172 tons, the pressure to be resisted by a section 1 inch long of the 

thickness of Roy oa one side. Suppose thickness were doubled, making 
: x : 

t= 30 ins p= was = 331% tons, or an increase of only 16 per cent. 


For short cast-iron cylinders, such as are used in hydraulic presses, it is 
doubtful if the above formule hold true, since the strength of the cylindri- 
cal portion is reinforced by the end. In that case the bursting strength 
would be higher than that calculated by the formula. A rule used in 
practice for such presses is to make the thickness = 1/10 of the inner cir- 
cumference, for pressures of 3000 to 4000 lbs. per square inch. The latter 
pressure would bring a stress upon the inner layer of 10,350 lbs. per square 
inch, as calculated by the formula; which would necessitate the use of the 
best charcoal-iron to make the press reasonably safe. ; 


HOLDING-POWER OF NAILS, SPIKES, AND SCREWS. 289 


THIN CYLINDERS UNDER TENSION. 


Let p = safe working pressure in lbs. per sq. in.; 
d = diameter in inches; 
T = tensile strength of the material, lbs. per sq. in.; 
t = thickness in inches; 
Jf = factor of safety; { 
c = ratio of strength of riveted joint to strength of solid plate. 


Ne cr ed 
{pd =2Tic; p= af? t= ote 
If T= 50000, f=5, and c= 0.7; then 
_ 14000¢, ,_s_ dp 
ea Sgn? Se T4000" 


The above represents the strength resisting rupture along a longitudinal 
seam. For resistance to rupture in a circumferential seam, due to pressure 
pid? _ Ttrdc, 
an fiw 

4Ttc 

af” 
Or the strength to resist rupture around a circumference is twice as great 
as that to resist rupture longitudinally ; hence boilers are commonly single- 
riveted in the circumferential seams and double-riveted in the longitudinal 
seams. 





on the ends of the cylinder, we have 


whence p = 


HOLLOW COPPER BALLS. 


Hollow copper balls are used as floats in boilers or tanks, to control feed 
and discharge valves, and regulate the water-level. 

They are spun up in halves from sheet copper, and a rib is formed on one 
half. Into this rib the other half fits, and the two are then soldered or 
brazed together. In order to facilitate the brazing, a hole is left on one side 
of the ball, to allow air to pass freely in or out; and this hole is made use of 
afterwards to secure the float to its stem. The original thickness of the 
metal may be anything up to about 1-16 of an inch, if the spinning is done 
on a hand lathe, though thicker metal may be used when special machinery 
is provided for forming it. In the process of spinning, the metal is thinned 
down in places by stretching; but the thinnest place is neither at the equator 
of the ball (i.e., along the rib) nor at the poles. The thinnest points lie along 
two circles, passing around the ball parallel to the rib, one on each side of it, 
from a third to a half of the way tothe poles. Along these lines the thick- 
ness may be 10, 15, or 20 per cent less than elsewhere, the reduction depend 
ing somewhat on the skill of the workman. 

The Locomotive for October, 1891, gives two empirical rules for determin- 
ing the thickness of a copper ball which is to work under an external 
pressure, as follows: 
diameter in inches X pressure in pounds per sq. in. 


16,000 


2. Thickness = diameter x _//pressure , 
1240 
These rules give the same result for a pressure of 166 lbs. only. Example: 
Required the thickness of a 5-inch copper ball to sustain 


Pressures of....... eae 50 100 150 166 200 250 Ibs. per sg. in. 
Answer by first rule... .0156 .0312 .0469 .0519 .0625 .0781 inch. 
Answer by second rule .0285 .0403 .0494 .0518 .0570 .0637 ‘* 


HOLDING-POWER OF NAILS, SPIKES, AND 
SCREWS. 
(A. W. Wright, Western Society of Engineers, 1881.) 
Spikes.—Spikes driven into dry cedar (cut 18 months): 


1. Thickness = 


Size Of@SpIeS: .......5 . este renee e+ ee 5X 4in. sq. 6X MEX WS xX % 
Lengthidniven ins. .j. 2.56 eames: tees 414 in. 5in, 5in. 44% iy 
Pounds resistance to drawing. Av’ge, lbs. 857 821 1691 1202 

Max.uy 1159 928 2129 1556 


From 6 to 9 tests each......... Min. “ "66 "66 1120 687 


290 STRENGTH OF MATERIALS, 


A. M. Wellington found the force required to draw spikes 9/16 x 9/16 in., 
driven 414 inches into seasoned oak, to be 4281 ]bs.; same spikes, etc., in un. 
seasoned oak, 6528 lbs. 

‘*Professor W. R. Johnson found that a plain spike 8 inch square 
driven 33g inches into seasoned Jersey yellow pine or unseasoned chestnut 
required about 2000 lbs. force to extract it; from seasoned white oak about 
4000 and from well-seasoned locust 6000 Ibs.” 

Experiments in Germany, by Funk, give from 2465 to 3940 Ibs. (mean of 
many experiments about 3000 lbs.) as the force necessary to extract a plain 
1-inch square iron spike 6 inches long, wedge-pointed for one inch and 
driven 41% inches into white or yellow pine. When driven 5 inches the force 
required was about 1/10 part greater. Similar spikes 9/16 inches square, 7 
inches long, driven 6 inches deep, required from 3700 to 6745 lbs. to extract 
them from pine; the mean of the results being 4873 Ibs. In all cases about 
twice as much force was required to extract them from oak. The spikes 
were all driven across the grain of the wood, When driven with the grain, 
spikes:or nails do not hold with more than half as much force. 

Boards of oak or pine nailed together by from 4 to 16 tenpenny common cut 
nails and then pulled apart in a direction lengthwise of the boards, and 
across the nails, tending to break the latter in two by a shearing action, 
averaged about 300 to 400 lbs. per nail to separate them, as the result of 
many trials, 

Resistance of Drift-bolts in Timber.—Tests made by Rust and 
Coolidge, in 1878. 


Pounds, 
Ist Test. 1 in. square iron drove 380 in. in white pine, 15/16-in. hole..... 26,400 
Pda een TOUNGS as Se | awe Oben ee ie we de/l6-ins Sc... 16,800 
3d “ iin. square ‘‘ mame wove. si St etl 5/1G-1N Sencile. eine 14,600 
4th ‘> ):lins round ~ ‘ Ho nseennt # SN HIB /16-In ths oe 13,200 
PUD ede es ID TOuUNnG aan s€ 4 84): St Norw*y pine;13/16-in. o£ 3.2. 18,720 
6th ‘* lin. square ‘‘ ss BOR Eo Es sé 4999 15/18-in.) 1 820,219,200 
fth “lin. square $$ rer PLB ESS i S89 6 /1G6-in 8. OIE). 15,600 
8th “* . lin, round ‘ SSirje LSBs Hance $7 thd SPS003 7116-in Meson at 14,400 


Notz.—In test No. 6 drift-bolts were not driven properly, holes not being 
in line, and a piece of timber split out in driving. 
Woree required to draw Screws out of Norway Pine. 


diam. drive screw 4 in. in wood. Power required, average 2424 Ibs. 
f ‘¢ 4 threads per in. 5 in. in wood. S$ A $8 2743 SS 
3 “  D’ble thr’d, 3 per in., 4 in. in “ 8 ss sf 2780 ‘ 
Fé “  Lag-screw, 7 perin., 114 ‘* ‘“ $s st “$ 1465 * 
66 é 66 66 6 66 bb 244 66 66 66 ee 66 2026 iT 3 
inch R:R: spike ses) Be SURNEE Se s 4s ps 2191 ‘ 


Force required to draw Wood Screws out of Dry Wood, 
—Tests made by Mr. Bevan. The screws were about two inches in length, 
.22 diameter at the exterior of the threads, .15 diameter at the bottom, the 
depth of the worm or thread being .035 and the number of threads in one 
inch equal 12. They were passed through pieces of wood half an inch in 
thickness and drawn out by the weights stated: Beech, 460 lbs.: ash, 790 
lbs.; oak, 760 lbs.; mahogany, 770 Ibs.; elm, 665 lbs.; sycamore, 880 Ibs. 

Tests of Lag-screws in Various Woods were made by A. J. 
Cox, University of Iowa, 1891: 


. “Size Max. 
: Size Length ‘ 
Kind of Wood. Screw. sa in Tie. pee: Tests 
Seasoned white oak............... 5éin. Win. 44%in. 8037 8 
i S ih Mees ne sles e's are oe ie "5 ¥ i, $f orn ] 
‘ oe ie A‘ 4144 “ 8780 2 
Yellow-pine stick... ........, EY Re ge “4 38008 
White cedar, unseasoned.......... 5g * ws 4 “ 3405 2 


In figuring area for lag-screws, the surface of a cylinder whose diameter is 
equal to that of the screw was taken. The length of the screw part in each 
case was 4 inches.—Enqgineering News, 1891. 

Cut versus Wire Nails.—Experiments were made at the Watertown 
Arsenal in 1893 on the comparative direct tensile adhesion, in pine and 
ese of cut aud wire nails. The results are stated by Prof. W. H. Burr 
as follows: 


HOLDING-POWER OF NAILS, SPIKES, AND SCREWS. 291 


There were 58 series of tests, ten pairs of nails (a cut and a wire nail in each) 
being used, making a total of 1160 nails drawn. The tests were made in 
spruce wood in most instances, but some extra ones were made in white 
pine, with ‘‘ box nails.” The nails were of all sizes, varying from 11 inches to 
6 inches in length. In every case the cut nails showed the superior holdiug 
strength by a large percentage. In spruce, in nine different sizes of nails, 
both standard and light weight, the ratio of tenacity of cut to wire nail 
was about 3 to 2, or, as he terms it, ‘‘a superiority of 47.45% of the former.” 
With the “ finishing’ nails the ratio was roughly 3.5 to 2; superiority 722%. 
With box nails (114 to 4 inches long) the ratio was roughly 8 to 2; superiority 
51%. The mean superiority in spruce wood was 61%. In white pine, cut nails, 
driven with taper along the grain, showed a superiority of 100%, and with 
taper across the grain of 135%. Also when the nails were driven in the end 
of the stick, i.e., along the grain, the superiority of cut nails was 100%, or the 
ratio of cut to wire was2to1. The total of the results showed the ratio of 
tenacity to be about 3.2 to 2 for the harder wood, and about 2to1 for the 
softer, and for the whole taken together the ratio was 3.5 to 2. We are 
led to conclude that under these circumstances the cut nail is superior to 
the wire nail in direct tensile holding-power by 72.74% 


Nail-holding Power of Various Woods, 


(Watertown Experiments.) 
Holding-power per square inch of 














Kind of Wood. Biba otewal, ; aur Purtage ta Wood. gos aee 
Wire Nail. Cut Nail. Mean. 
8d 450 
i 455 
. . 20 ‘ 407 
WIC, DINGY ol cece ess 50 “4 167 347 405 
863 
60 ‘‘ 340 J 
pte (pees 
i ee 55 
Yellow pine.............. ep j aU danas A i 662 
60 ‘* l 604 
Bie 1340 l 
WIG Oki. fo dc) omisau,cje's 20 ‘* 940 1292 1216 
60 ‘* 1018 ) 
50‘ 664 
Chestnut 2 ek eo ; ae os t 683 
gre = 1179 
Laurel set. exoehaend 48h Ai beatgyencn eit sige OBlon. bel aaay 9 ie pst 1800 
Nail-holding Power of Various Woods. 
(F. W. Clay’s Experiments. Hng’g News, Jan. 11, 1894.) : 
Wood -————Tenacity of 6d nails———~ 
Plain, Barbed. Blued. Mean, 
White pines#/siigt: eek. La, at 106 94 135 111 
Yellow pines: 2.22.0... Wola siate tic teed heey ees 190 130 270 196 
Basswood Sie sae Tae ad 78 132 219 143 
White oak........ SL RLG.AN PONG. ae ah OS } 226 300 555 860 
HE MIOCIE NS HARES GIRS, was Slochtertia gd Ae the nha eek 141 201 319 220 


Tests made at the University of Illinois gave the resistance of a 1-in. round 
rod in a 15/16-inch hole perpendicular to the grain, as 6000 lbs. per lin. ft. in 
pine and 15,600 lbs. in oak, Experiments made at the East River Bridge 
gave resistances of 12,000 and 15,000 lbs. per lin. ft. for a 1-in. round rod in 
holes 15/16-in. and 14/16-in. diameter, respectively, in Georgia pine. 


Hiolding-power of Bolts in White Pine, 
(Hng’g News, September 26, 1891.) 


Round. Square. 
Lbs. Lbs. 
Average of all plain 1-in, bolts.................. 2. 8224 8200 
Average of all plain bolts, 54 to 14gin.............. 7805 8110 
Averagreror tall: bolts). Haan .teetadie. weed sled 8383 ~ 8598 


Round drift-bolts should be driven in holes 13/16 of their diameter, and 
square drift-bolts in holes whose diameter is 14/16 of the side of the square, 


292 STRENGTH OF MATERIALS. 


STRENGTH OF WROUGHT IRON BOLTS. 
(Computed by A. F. Nagle.) 


Stress upon Bolt upon Basis of 

















dH w GH 8 a yg ay m 
PhO Wore oat weer (PS ne ape oat [a yee etaey oped he Umm ae 
SE meth |) chris | epeas ily a! Seg Wr uo aH] -d |ag 
O02} oe /PES|mos aes aS) AG) oO Pas: oRoie 
S| 2218 Sao |e ja Sain) oS Selo. dees ene 
Baa |S eo) PEt Rolo ve en tet! amt eel al coe Leona I) See ane ied 
26/5" |$a2}3u8| 82 | $2) SF | SF | 8e laa 
AR Q ra a a oD x Yo) ~ - 
lbs. lbs. Ibs. lbs. lbs. Ibs. 
14) 13 38 12 350 460 580 810 1160 5800 
9-16} 12 44 15 450 600 750 1050 1500 7506 
5g} 11 49 19 560 750 930 1310 1870 9000 
34| 10 60 28 85 1130 1410 1980 <830 14000 
%l 9 G1 39 1180 157 197 2760 3940 19000 
1 8 81 52 1550 207 2600 36380 5180 25000 
1% (eo 91 65 1950 2600 8250 4560 6510 80000 
14 fi 1.04 84 2520 3360 4200 5900 8410 39000 
13g 6 Ler 24 00 3000 4000 5000 7000 10000 46000 
14% 6 13254-1223 38680 4910 6140 8600 12280 56000 
15g 54 | 1.35 | 1.44 4300 5740 7180 10000 14360 65000 
134 5 1.45 | 1.65 4950 6600 8250 11560 16510 74000 
1% ‘a9 115%.11.95 5840 7800 9800 13640 19500 85000 
2 416 | 1.66 | 2.18 6540 8720 10900 15260 21800 95000 
214 4% | 1.92 | 2.88 8650 11530 14400 20180 28800 | 125000 
216 4 Pasay Sistas 10640 14200 17730 24830 85500 | 150000 
234 4 220 | 4,43 18290 17720 22150 31000 44300 |-186000 
3 3144 | 2.57 | 5.20 15580 2077 26000 36360 52000 | 218000 
34 344 | 3.04 | 7.25 21760 29000 36260 50760 72500 | 290000 
4 3 3.50 | 9.62 28860 88500 48100 7350 96200 | 385000 


When it is known what load is to be put upon a bolt, and the judgment oi 
the engineer has determined what stress is safe to put upon the iron, look 
down in the proper column of said stress until the required load is found. 
The area at the bottom of the thread will give the equivalent area of a flat 
bar to that of the bolt. 

Effect of Initial Strain in Bolts.—Suppose that bolts are used 
to connect two parts of a machine and that they are screwed up tightly be- 
fore the effective load comes on the connected parts. Let P,; =-the initial 

’ tension on a bolt due to screwing up, and P, = the load afterwards added. , 
The greatest load may vary but little from P, or P,, according as the 
former or the latter is greater, or it may approach the value P, + Pg, de- 
pending upon the relative rigidity of the bolts and of the parts connected. 
Where rigid flanges are bolted together, metal to metal, it is probable that 
the extension of the bolts with any additional tension relieves the initial 
tension, and that the total tension is P, or Py, but in cases where elastic 
packing, as india rubber, is interposed, the extension of the bolts may very 
little affect the initial tension, and the total strain may be nearly P, + Pg. 
Since the latter assumption is more unfavorable .to the resistance of the 
bolt, this contingency should usually be provided for. (See Unwin, ‘‘ Ele- 
ments of Machine Design ’’ for demonstration.) 


' STAND-PIPES AND THEIR DESIGN. 


(Freeman C. Coffin, New England Water Works Assoc., Eng. News, March 
16, 1893.) See also papers by A. H. Howlaud, Eng. Club of Phil. 1887; B. F. 
Stephens, Amer, Water Works Assoc., Eng. News, Oct. 6 and 13, 1888; W. 
Kiersted, Rensselaer Soe. of Civil Eng., Hng’g Record, April 25 and May 2, 
1891, and W. D. Pence, Eng. News, April and May, 1894. 

The question of diameter is almost entirely independent of that of height. 
The efficient capacity must be measured by the length from the high-water 
line to a point below which itis undesirable to draw the water on account of 
loss of pressure for fire-supply, whether that point is the actual bottom of 
the stand-pipe or above it. This allowable fluctuation ought not to exceed 
50 ft., in most cases. This makes the diameter dependent upon two condi 


STAND-PIPES AND THEIR DESIGN. 293 


tions, the first of which is the amount of the consumption during the ordi- 
nary interval between the stopping and starting of thepumps. This should 
never draw the water below a point that will give a good fire stream and 
leave a margin for still further draught for fires. The second condition is 
the maximum number of fire streams and their size which it is considered 
necessary to provide for, and the maximum length of time which they are 
liable to have to run before the pumps can be relied upon to reinforce 
them. ; 

Another reason for making the diameter large is to provide for stability 
against wind-pressure when empty. 

The following table gives the height of stand-pipes beyond which they are 
not safe against wind-pressures of 40 and 50 lbs. per square foot. The area 
of surface taken is the height multiplied by one half the diameter. 


Heights of Stand-pipe that will Resist Wind-pressure 
by its Weight alone, when Empty. 


Diameter, Wind, 40 lbs. Wind, 50 lbs, 
feet. per sq. ft. per sq. ft. 
ROIS BO 45 85 
ADEN GAQB RR ACICON Ie pee nas 70 55 
OO Zone cfovcitccisas vemcea sss oie 150 80 
OO MEL eine ts Tas celncecs sees e 160 


To have the above degree of stability the stand-pipes must be designed 
with the outside angle-iron at the bottom connection. 

Any form of anchorage that depends upon connections with the side 
plates near the bottom is unsafe. By suitable guys the wind-pressure is re- 
sisted by tension in the guys, and the stand-pipe is relieved from wind 
strains that tend to overthrow it. The guys should be attached to a band 
of angle or other shaped iron that completely encircles the tank, and rests 
upon some sort of bracket or projection, and not be riveted to the tank 
They should be anchored at a distance from the base equal to the height of 
the point at which they are attached, if possible. 

The best plan is to build the stand-pipe of such diameter that it will resist 
the wind by its own stability. 


Whickness of the Side Plates. 


The pressure on the sides is outward, and due alone to the weight of the 
water, or pressure per square inch, and increases in direct ratio to the 
height, and also to the diameter. The strain upon a section 1 inch in height 
at any point is the total strain at that point divided by two—for each side is 
supposed to bear the strain equally. The total pressure at any point is 
equal to the diameter in inches, multiplied by the pressure per square inch, 
due to the height at that point. It may be expressed as follows: 


H = height in feet, and f = factor of safety; 
d = diameter in inches; 
p = pressure in lbs. per square inch; 
.4384 = p for 1 ft. in height; 
s = tensile strength of material per square inch; 
T = thickness of plate. 


Then the total strain on each side per vertical inch 
_ 434Hd _ pd, T= .434Hdf _ pdf 


Oe Gly Be 2s 2s 
Mr, Coffin takes f = 5, not counting reduction of strength of joint, equiv- 
alent to an actual factor of safety of 3 if the strength of the riveted joint is 
taken as 60 per cent of that of the plate. 
The amount of the wind strain per square inch of metal at any joint can 
be found by the following formula, in which 


H = height of stand-pipe in feet above joint; 

T = thickness of plate in inches; 

p = wind-pressure per square foot: 

W = wind-pressure per foot in height above joint; 

W = Dp where D is the diameter in feet; 

m = average leverage or movement about neutral axis 
mo or. central pojnts in the circumference; or, 

m = sine of 45°, or ,707 times the radius in feet. 


294 ' STRENGTH OF MATERIALS, 


Then the strain per square inch of plate 
} H 
(Hw)-> 


~ ‘cire. in ft. X mr 


Mr. Coffin gives a number of diagrams useful in the design of stand-pipes, 
together with.a number of instances of failures, with discussion of their 
probable causes. 
Mr. Kiersted’s paper contains the following : Among the most prominent 
strains a stand-pipe has to bear are: that due to the static pressure of the 
‘water, that due to the overturning effect of the wind on an empty stand- 
pipe, and that due to the collapsing effect, on the upper rings, of violent 
wind storms. . oe 
For the thickness of metal to withstand safely the static pressure of 
water, let i i 
‘¢ = thickness of the plate iron in inches; 
H = height of stand-pipe in feet; 
D = diameter of stand-pipe in feet. 


Then, assuming a tensile strength of 48,000 lbs. per square inch, a factor 
of safety of 4, and efficiency of double-riveted lap-joint equalling 0.6 of the 
strength of the solid plate, j 

10,000¢ 


which will give safe heights for thicknesses up to 5¢ to 34 of aninch. The 
same formula may also apply for greater heights and thicknesses within 
practical limits, if the joint efficiency be increased by triple riveting. , 

The conditions for the severest overturning wind strains exist when the 
stand-pipe is empty. 

Formula for wind-pressure of 50 pounds per square foot, when 


d = diameter of stand-pipe in inches; 
«& = any unknown height cf stand-pipe; 


x= V80ndt = 15.85 at. 


The following table is calculated by these formule. The stand-pipe is 
intended to be self-sustaining; that is, without guys or stiffeners. 


Heights of Stand-pipes for Various Diameters an 
Thicknesses of Plates. ‘ 




















Thickness of Diameters in Feet. 

PlatesinsMrac- ls |. one 

tions of an Inch. | 5 6 ih 8 9 |} 10° | 12 | 14 |} 15 |-16 | 18 | 20 | 25: 
Salis “See AMEN 50 |.55 | 60 | 65 55) 50] 35 

MEO oat os ete rs Se BO okie eee ee Goie60ll V50V. 40\> 240i eiiecek beset 
Sl Gree. ces 60 | 65 | 70 | 75 ole. 55] 50}; 45) 40) 35) 85) 25 
BolGm Mere s rahe a 75 | 80 | 85 90} 85} 70} 60] 55) 50) 45) 40! 35 
75 LT Beatin See 75 | 80 | 90 |} 95 | 100} 100) 85) 75) 70) 65) 55) 50} 40 
VAIO ar ctr atc eces @ 80 | 90 | 95 |100 | 110} 115] 100) 85} 80) 75} 65) 60) 45 
BG as celeste oo. | 85 .| 95. 1100: 1110:) 115) 120) 115) 100} 90; 85) 75| 70) 55 
QL1G% ree ee tie oe] die ds 115 | 125] 130] 180) 116} 100) 95} 85} 80} 60 
LOR 160 see OE rhe leds silts bcke [io bes 130] 135} 145} 120) 115) 105} 95) 85] 65 
Fe BESS WTR seg esas cee. dtae hs Cae Rr hla ee Me 145} 155} 1385) 125) 120) 105! 95) 75 
HORT Ghc cm Lene meets ce loesele cet 150} 165} 145) 135) 180) 115) 105) 80 
TSG as aad lls Uhl el a (CPE | He 160} 150} 140) 125) 110) 90 
TAATG eee y RT ee ce toes PS UN, Pace aa ere Men ee 160) 150} 185) 120} 95 
Sas Tapani ieee 408 Ol. cl icinotl Repeal Hecate WEEE tse ied ese ail ta Shodl[iA e 160} 145) 130] 105 
OHI oe SR gel see hairs a] PER EE ee oll be ERC .. | 155!.140] 110 








Heights to nearest 5 feet. Rings are to build 5 feet vertically. 


Failures of Stand-pipes have been numerous in recent years. A 
list showing 23 iniportant failures inside of nine years is given in a paper by 
Prof. W. D. Pence, Eng’g. News, April 5, 12, 19 and 26, May 3, 10 and 24, and 
June 7, 1894. His discussion of the probable causes of the failures is most 
valuable, Le 


WROUGHT-IRON AND STEEL WATER-PIPES.  %95 


Kenneth Allen, Engineers Club of Philadelphia, 1886, gives the following 
rules for thickness of plates for stand pipes. 

Assume: Wrought iron plate T. S. 48,000 pounds in direction of fibre, and 
T. S. 45,000 pounds across the fibre. Strength of single riveted joint .4 that 
of the plate, and of double riveted joint, .7 that of the plate ; wind pressure 
= 50 pounds per square foot ; safety factor = 3. 

Let h = total height in feet ; r = outer radius in feet ; r’ = inner radius 
in feet ; p = pressure per square inch ; ¢ = thickness in inches ; d = outer 
diameter in feet. 

Then for pipe filled and longitudinal seams double riveted 


pcziic PTX 12 Caste. 
~ 48,000 x .7 x 1% ~ +4801’ 


and for pipe empty and lateral seams, single riveted, we have by equating 
moments : 


h 7854 h2 72 
or — j2 — 1 4 0 -4 A4 4 tho — 
50 X 27 (5) = 144 x 6000 (@ 73) * , whence 7 We= Fray 


Table showing required Thickness of Bottom Plate. 




















Height in Diameter. 
Feet. Eee MCE LRT L A. BEER MORO ER Bn BaD AN RARER 
5 feet. 10 feet. | 15 feet. | 20 feet. | 25 feet. | 30 feet. 
4, at th ay a) ” 
50 + 7-64* 1 * 11-64* 15-64 19-64 23-64 
60 +11-64* 9-64* %—32 9-32) | * 23-64 27-64 
70 + 7-82 11-64* 4 21-64 13-32 31-64 
*80 +19-64 3216 9-32 34 15-32 9-16 
90 t 3% 7-32 5-16 27-64 17-32 54 
100 +29-64 | +15-64 23-64 1532 37-64 45-64 
125 +23-64 7-16 7-64 47-64 % 
150 +33-64 17-32 45-64 % 1 3-64 
175 +11-16 89-64 13-16 dyis32 gee 
200 +29-32 45-64 15-16 1 11-64 1 25-64 





* The minimum thickness should = 3-16’, - 
N.B.—Dimensions marked + determined by wind-pressure. 


Water Tower at Yonkers, N. W.—This tower, with a pipe 122 feet 
high and 20 feet diameter, is described in Hngineering News, May 18, 1892. 

The thickness of the lower rings is 11-16 of an inch, based on a tensile 
strength of 60,000 lbs. per square inch of metal, allowing 65% for the strength 
of riveted joints, using a factor of safety of 34% and adding a constant of 
lg inch. The plates diminish in thickness by 1-16 inch to the last four 
plates at the top, which are 14 inch thick. 

The contract for steel requires an elastic limit of at least 33,000 lbs. per 
square inch ; an ultimate tensile strength of from 56,000 to 66,000 lbs. per 
square inch ; an elongation in 8 inches of at least 20%, and a reduction of 
area of at least 45%. The inspection of the work was made by the Pittsburgh 
Testing Laboratory. According to their report the actual conditions de- 
veloped were as follows: Elastic limit from 34,020 to 39,420; the tensile 
strength from 58,330 to 65,390 ; the elongation in 8 inches from 224 to 32% ; 
reduction in area from 52.72 to 71.82% ; 17 plates out of 141 were rejected in 
the inspection. 


WROUGHT-IRON AND STEEL WATER-PIPES, 


Riveted Steel Water=-pipes (Engineering News, Oct. 11, 1890, and 
Aug. 1, 1891.)—The use of riveted wrought-iron pipe has been common in 
the Pacifie States for many years, the largest being a 44-inch conduit in 
connection with the works of the Spring Valley Water Co., which supplies 
San Francisco. The use of wrought iron and steel pipe has been neces- 
sary in the West, owing to the extremely high pressures to be withstood 
and the difficulties of transportation. As an example: In connection with 


296 STRENGTH OF MATERIALS. 


the water supply of Virginia City and Gold Hill, Nev., there was laid in 
1872 an 1114-inch riveted wrought-iron pipe, a part of which is under a head 
of 1720 feet. 

In the East, the most important example of the use of riveted steel water 
pipe is that of the East Jersey Water Co., which supplies the city of Newark, 
The contract provided for a maximum high service supply of 25,000,000 gal- 
lons daily. In this case 21 mules of 48-inch pipe was laid, some of it under 340 
feet head. The plates from which the pipe is made are about 138 feet long 
by 7 feet wide, open-hearth steel. Four plates are used to make one section 
of pipe about 27 feet long. The pipe is riveted longitudinally with a double 
row, and at the end joints with a single row of rivets of varying diameter, 
corresponding to the thickness of the steel plates. Before being rolled into 
the trench, two of the 27-feet lengths are riveted together, thus diminishing 
still further the number of joints to be made in the trench and the extra 
excavation to give room for jointing. All changes in the grade of the pipe- 
line are made by 10° curves and all changes in line by 2, 5, 7% and 10° 
curves. To lay on curved lines a standard bevel was used, and the different 
curves are *secured by varying the number of beveled joints used on a 
certain length of pipe. 

The thickness of the plates varies with the pressure, but only three thick- 
nesses are used, 14, 5-16, and 3g inches, the pipe made of these thicknesses 
having a weight of 160, 185, and 225 Ibs. per foot, respectively. At the works 
all the pipe was tested to pressure 114 times that to which it is to be sub- 
jected when in place. 

Mannesmann Tubes for High Pressures.—At the Mannes- 
inann Works at Komotau. Hungary, more than 600 tons or 25 miles of 3-inch 
and 4-inch tubes averaging 144 inch in thickness have been successfully 
tested to a pressure of 2000 Ibs. per square inch. These tubes were intended 
for a high-pressure water-main in a Chilian nitrate district. 

This great tensile strength is probably due to the fact that, in addition to 
being much more worked than most metal, the fibres of the metal run 
spirally, as has been proved by microscopic examination. While cast-iron 
tubes will hardly stand more than 200 lbs. per square inch, and welded tubes 
are not safe above 1000 lbs. per square inch, the Mannesmann tube easilv 
withstands 2000 Ibs. per square inch. The length up to which they can 
be readily made is shown by the fact that a coil of 3-inch tube 70 feet long 
was made recently. 

For description of the process of making Mannesmann tubes see Trans, 
A.I. M. E, vol. xix., 384, 


STRENGTH OF VARIOUS MATERIALS. EXTRACTS 
FROM KIRKALDY’S TESTS. 


The recent publication, in a book by W. G. Kirkaldy, of the results of many 
thousand tests made during a quarter of a century by his father, David Kir- 
kaldy, has made an important contribution to our knowledge coucerning 
the range of variation in strength of numerous materials. A condensed — 
abstract of these results was published inithe American Muchinist, May 11 
ang 18, 1893, from which the following still further condensed extracts are 
taken: 

The figures for tensile and compressive strength, or, as Kirkaldy calls 
them, pulling and thrusting stress, are given in pounds per square inch of 
original section, and for bending strength in pounds of actual stress or 
pounds per BD? (breadth X square ef depth) for length of 36 inches between 
supports. The contraction of area is given as a percentage of the original 
area, and the extension as a percentage in a length of 10 inches, except when 
otherwise stated. The abbreviations T. S., E. l., Contr., and Ext. are used 
for the sake of brevity, to represent tensile strength, elastic limit, and per- 
centages of contraction of area, and elongation, respectively. 

Cast Tron.—44 tests: T. 8. 15,468 to 28,740 pounds; 17 of these were un- 
sound, the strength ranging from 15,468 to. 24,357 pounds. Average of all, 
23,805 pounds. 

Thrusting stress, specimens 2 inches long, 1.34 to 1.5 in. diameter: 43 tests, 
all sound, 94,352 to 131,912; one, unsound, 93,759; average of all, 113,825. 

Bending stress, bars about 1 in. wide by 2 in deep, cast on edge. Ulti- 
mate stress 2876 to 3854; stress per BD? = 725 to 892; average, 820. Average 
modulus of rupture, R, = 3/2 stress per BD? x length, = 44,280. Ultimate 
deflection, .29 to .40 in.; average, .34 inch. 

Other tests of cast iron, 460 tests, 16 lots from various sources, gave re- 


EXTRACTS FROM KIRKALDY’S TESTS. 207 


sults with total range as follows: Pulling stress, 12,688 to 38.616 pounds; 
thrusting stress, 66,363 to 175,950 pounds; bending stress, per BD?, 505 to 
1128 pounds; modulus of rupture, R, 27,270 to 61,912. Ultimate deflection, 
-21 to .45 inch. 

The specimen which was the highest in thrusting stress was also the high- 
est in bending, and showed the greatest deflection, but its tensile strength 
was only 26,502. 

The specimen with the highest tensile strength had a thrusting stress of 
143,939, and a bending strength, per BD?, of 979 pounds with 0.41 deflection. 
The specimen lowest in T. 8. was also lowest in thrusting and bending, but 
gave .38 deflection. The specimen which gave.21 deflection had T.S., 19,188: 
thrusting. 104.281; and bending, 561. 

Kron Castings.—69 tests; tensile strength, 10,416 to 31,652; thrusting 
stress, ultimate per square inch, 53,502 to 132,031. 

Channel Krons.—Tests of 18 pieces cut from channel irons. T. S. 
40,693 to 53,141 pounds per square inch; contr. of area from 3.9 to 32.5 2%. 
Ext. in 10 in. from 2.1 to 22.5 2 The fractures ranged all the way from 100% 
fibrous to 100% crystalline. The highest T. S., 53,141, with 8.1 % contr. and 
5.8 % ext., was 100 % crystalline; the lowest T. S., 40,6938, with 3.9 contr. and 
2.1% ext., was 75% crystalline. All the fibrous irons showed from 12.2 to 
22.5% ext., 17.3 to 32.5 contr., and T. S. from 48,426 to 49,615. The fibrous 
irons are therefore of medium tensile strength and high ductility. The 
crystalline irons are of variable T. S., highest to lowest, and low ductility. 

Lowmoor Iron Bars.—Three rolled bars 214 inches diameter; ten- 
sile tests: elastic, 23,200 to 24,200; ultimate, 50.875 to 51,905; contraction, 44.4 
to 42.5; extension, 29.2 to 24.3. Three hammered bars, 4% inches diameter, 
elastic 25,100 to 24,200; ultimate, 46,810 to 49,223; contraction, 20.7 to 46.5; 
extension, 10.8 to 31.6. Fractures of all, 100 per cent fibrous. In the ham- 
mered bars the lowest T. S. was accompanied by lowest ductility. 

Iron Bars, Various, —Of a lot of 80 bars of various sizes. some rolled 
and some hammered (the above Lowmoor bars included) the lowest T.S. 
(except one) 40,808 pounds per square inch, was shown by the Swedish 
“hoop L” bar 344 inches diameter, rolled. Its elastic limit was 19,150 
pounds; contraction 68.7% and extension 37.7% in 10 inches. It was also 
the most ductile of all the bars tested, and was 100% fibrous. The highest 
T. S., 60,780 pounds, with elastic limit, 29,400; contr., 36.6; and ext., 24.3 4, 
was shown by a “ Farnley ” 2-inch bar, rolled. It was also 100% fibrous, 
The lowest ductility 2.6% contr., and 4.1% ext., was shown by a 3384-inch 
hammered bar, without brand. It also had the lowest T.S., 40,278 pounds, 
but rather high elastic limit, 25,700 pounds. Its fracture was 95% crystal- 
line. Thus of the two bars showing the lowest T. S., one was the most duc- 
tile and the other the least ductile in the whole series of 80 bars. 

Generally, high ductility is accompanied by low tensile strength, as in the 
Swedish bars, but the Farnley bars showed a combination of high ductility 
and high tensile strength. 

Locomotive Forgings, Iron.—1’ tests: average, E. L., 30,420; T.S., 
50.521; contr., 36.5: ext. in 10 inches, 23.8. 

Broken Anchor Forgings, Kron,—4 tests: average, E, L., 23,825; 
T.S., 40,083; contr., 3.0; ext. in 10 inches, 3.8. 

Kirkaldy places these two irons in contrast to show the difference between 
good and bad work. The broken- anchor material, he says, is of a most 
treacherous character. and a disgrace to any manufacturer, 

Iron Plate Girder.—Tensile tests of pieces cut from a riveted iron 
girder after twenty years’ service in a railway bridge. Top plate, average 
of 3 tests, H. L., 26,600; T. S., 40,806; contr. 161; ext. in 10 inches, 7 8. 
Bottom plate, average of 3 tests, E. L., 31,200; T.S., 44,288; contr , 13.3; ext. 
in 10 inches, 6.8. Web-plate, average of 3 tests, E. L., 28,000; T. S , 45.902; 
contr., 15 9; ext. in 10 inches, 8.9. Fractures all fibrous. The results of 30 
+ests from different parts of the girder prove that the iron has undergone 
no change during twenty years of use. ; 

Steel Plates,.—Six plates 100 inches long, 2 inches wide, thickness vari- 
ous, .36to .97inch T.S., 55,485 to 60,805; E. L , 29,600 to 33,200; contr., 52.9 
to 59.5; ext.. 17.05 to 18.57. 

Steel Bridge Links,—40 links from Hammersmith Bridge, 1886. 


298 STRENGTH OF MATERIALS. 











[| Fracture. 
[<2 
fas) rs 
a, tw 
: =| & 
° fy sey 
ws 4 — 3 s 5 
r . to) 4 = fos] 
ist & OD ical n os 
Average of all............. 67.294 | 38,294 | 34.5% | 14.117 
Lowest ls Sivec246 eee see 60,753 | 86,080 | 30.1 15.51 80% 70% 
Highest T.S. and E. L..... 75,986 | 44,166 | 31.2 12.42 15 
MO WES bubie lat lopuelils ques 64,044 | 32,441 34.7 13.43 80 70 
Greatest Contraction.....| 68.745 | 388,118 52.8 15.46 100 0 
Greatest Extension....... 65,980 | 86,792 | 40.8 17.78 85 65 
Least Contr. and Ext...... 63,980 | 39,017 6.0 6.62 0 100 





The ratio of elastic to ultimate strength ranged from 50.6 to 65.2 per cent; 
average, 56.9 per cent. 

Extension in lengths of !00 inches. At 10,000 lbs. per sq. in., .018 to .024; 
mean, .020 inch; at 20.(00 Ibs. per sq. in. .049 to .063; mean, .055 inch; at 
30,000 lbs. per sq. in., .083 to.100; mean, .090; set at 30,000 pounds per sq. in., 
0 to .002; mean. 0. 

The mean extension between 10,000 to 30,000 lbs. per sq. in. increased regu- 
larly at the rate of .007 inch for each 2000 lbs. per sq. in. increment of strain. 
This corresponds to a modulus of elasticity of 28,571,429. The least increase 
of extension for an increase of load of 20,000 lbs. per sq. in., .065 inch, cor- 
responds to a modulus of elasticity of 30,769,231, and the greatest, .076 inch, 
to a modnlus of 26,315,789. 

Steel Rails.— Bending tests, 5 feet between supports, 11 tests of flange 
rails 72 pounds per yard, 4.63 inches high. 


Elastic stress, Ultimate stress. Deflection at 50,000 Ultimate 


Pounds. Pounds. Pounds. Deflection. 
Hardest.... 84,200 60,960 3.24 ins, 8 ins. 
Softest .... 32,000 56,740 oem Sst 
Meat ss 32,763 59,209 Boos Bt 


All uncracked at 8 inches deflection. 
Pulling tests of pieces cut from same rails. Mean results. 


Elastic Ultimate Contraction of 
Stress. Pounds. area of frac- Extension 
persq.in. per sq. in. ture. in 10 ins, 
TOOL TANS WI os .5 3 44,200 83,110 19.9% 13.5% 
Botton of rails. ..... 40,900 77,820 80.9% 22.8% 


Steel Tires,—Tensile tests of specimens cut from steel tires, 


Krupp STEEL.—262 Tests. 


Ext. in 

E. L. Ts 83 Contr. 5 inches. 
Highest........ 69,250 119,079 31.9 18.1 
Mean te. cc.. 52,869 104,112 29.5 19.7 
Lowest ...... Ht 41,700 90,523 45.5 23.4 

VickERS, Sons & Co.—%70 Tests. 

Ext. in 

EB. L. Te Contr. 5 inches, 
Highest........ 58,600 120,789 11.8 8.4 
IMG AE SIR s s.ccr ee 51,066 101,264 17.6 12.4 
Lowest........ 43,700 ' 87,697 24.7 16.0 


Note the correspondence between Krupp’s and Vickers’ steels as to tem 
sile strength and elastic limit, and their great difference in contraction and 
elongation. The fractures of the Krupp steel averaged 22 per cent silky, 
2 per cent granular; of the Vicker steel, 7 per cent silky, 93 per cent granu- 
ar. 


EXTRACTS FROM KIRKALDY’S TESTS. 299 


Steel Axles.—Tensile tests of specimens cut from steel axles. 
PATENT SHAFT AND AXLE TREE Co.—157 Tests. 


Ext. in 

Heeb. T.S. Contr. 5 inches. 
Highest.. ..... 49,800 99,009 21.1 16.0 
Meiners Sofas 36,267 72,099 83,0 23.6 
Lowest. ...... 31,800 61,382 34.8 25.3 

VICKERS, Sons & Co.—125 Tests. 

Ext. m 

Welt THs: Contr. 5 inches. 
Highest....... : 42,600 83,701 18.9 13.2 
WACESZ Cie en eer Ta 37,618 70,57. 41.6 27.5 
ISG WeSt... fuse 80,250 56,388: 49.0 37.2 


The average fracture of Patent Shaft and Axle Tree Co. steel was 33 per 
cent silky, 67 per cent granular. 

The average fracture of Vickers’ steel was 88 per cent silky, 12 per cent 
granular. 

Tensile tests of specimens cut from locomotive crank axles, 


ViIcKERS’.—82 Tests, 1879. 


Ext. in 

E. L. EPA Sy Contr. 5 inches. 
ighestiy <..scas 26,700 68,057 28.3 18.4 
Meanie se oo 24,146 57,922 2.9 24.0 
Lowest ........ 21,700 50,195 52.7 86.2 

VickeEerRS’.—%8 Tests, 1884. 

Ext. in 

E. L. TS: Contr. 5 inches. 
Highest........ 27,600 64,873 27.0 20.8 
Mean SF4.02 23,578 56,207 Bont 25.9 
Lowest........ 17,600 47,695 85.0 27.2 

FRIED. Krupp.—43 Tests, 1889. 

Ext. in 

BH. .L. Se Contr. 5 inches. 
EI ehestan css 31,650 66,868 48.6 85.6 
NG AN AiseeG 22). 29,491 61,774 pole yity 32.3 
Lowest ........ 21,950 55,172 55.3 85.6 


Steel Propeller Shafts,—Tensile tests of pieces cut from two shafts, 
mean of four tests each. Hollow shaft, Whitworth, T. §., 61,290; E. L., 
80,575; contr., 52.8; ext. in 10 inches, 28.6. Solid Shaft, Vickers’, T. S., 
46,870; E. L. 20,425; contr., 44.4; ext. in 10 inches, 30.7. 

Thrusting tests, Whitworth, ultimate, 56,201; elastic, 29,300; set at 30,000 
Ibs., 0.18 per cent; set at 40,000 lbs., 2.04 per cent; set at 50,000 lbs., 3.82 per 
cent. 

Thrusting tests, Vickers’, ultimate, 44,602; elastic, 22,250; set at 30,000 lbs., 
2.29 per cent; set at 40,000 Ibs., 4.69 per cent. 

. Shearing strength of the Whitworth shaft, mean of four tests, was 40,654 
lbs. per square inch, or 66.3 per cent of the pulling stress. Specific gravity 
of the Whitworth steel, 7.867: of the Vickers’, 7.856. 

Spring Steel.—Untempered, 6 tests, average, E. L., 67,916: T. S., 
115,668; contr., 37.8; ext. in 10 inches, 16.6. Spring steel untempered, 15 
tests, average, E. L., 38,785; T. S., 69,496; contr., 19.1; ext. in 10 inches, 29.8. 
These two lots were shipped for the same purpose, viz., railway carriage 
leaf springs. 

Steel Castings,.—44 tests, E. L., 31,816 to 35,567; T. S., 54,928 to 63,840; 
contr., 1.67 to 15.8; ext., 1.45 to 15.1. Note the great variation in ductility. 
The steel of the highest strength was also the most ductile. 


Riveted Joints, Pulling Tests of Riveted Steel Plates, 
Triple Riveted Lap Joints, Machine Riveted, 
Holes Drilled. 

Plates, width and thickn ss, inches : 
13.50 X .25 13.00 X .51.. 11.75 x .78 12.25 X 1.01 14.00 X .77 
Plates, gross sectional area square inches : 
B75 .63 9.165 12.372 10.780 
Stress, total, pounds: 
199,320 332,640 423,180 528,000 455,210 . 


~ 


300 STRENGTH OF MATERIALS, 


Stress per square inch of gross area, joint: 


59,058 50,172 46,173 . 42,696 42,227 
Stress per ae inch of 'plates, solid : 
4,050 62,280 68,045 
Ratio of Seas of joint to solid plate : 
83.46 76.83 72.09 68.05 62.06 
Ratio net area of plate to gross: 
73.4 65.5 62. 64.7 72.9 
Where fr, actured : 
plate at plate at plate at plate at rivets 
holes. holes. holes. holes. sheared. 


Rivets, diameter, area and number 
-45, .159, 24 64, 3821, 21 “95, - 708, 12 1.08, .916, 12 «95, .708, 123 


Rivets, total area $ 
3.816 741 8.496 10.992 8.496 
Strength of Welds.—Tensile tests to determine ratio of strength of 
weld to solid bar. 
Iron TiE Bars.—28 Tests. 
Strength of solid bars varied from........ .......-+0.--- 48,201 to 57,065 Ibs. 
Strenth of welded bars varied from........0-.2.+-+-00--++ 17,816 to 44,586 lbs, 


Ratio of weld to solid varied from....... .......- eslesio ee 37.0 to 79.1% 
Iron PLATES.—? Tests. 
Strength of solid plate from....... ue stehee's scesctecscealoeen 44,001 LO4(4elplbae 
Strength of welded plate from.. sajsesiviseeessectesies ee 0,440 LOoo,UolsLbse 
Ratio of weld to solid................ siceeciele wedi iesseals ole 57.7 to 83.9% 
Hate ey —216 Tests. 
Strength of solid bar from.. ofS cs cereus oe seh ekige G0; Lee CO Dl goter see 
Strength of welded bar from.. dessa sereletie cote sic oma'e f «e+ » 39,575 to 48,824 lbs. 
Ratio of weld to solid.. seat Baidle Sees Cac ec a emiets G2.1 to 95.4% 
Iron BARS. erica Sa Electric Machine Welded. 

32 tests, solid iron, average...........0..020. Ssgtieteeteatals e's 52,444 

If as jeléctric welded, AVETAZEC. 000 see seeesserereere ost 405 836 ratio 89.1% 
p RE ee SATO pyc h eYe Moun amr oo il a ER DR de eA Len ei Ret oi 0! : 46, 899 “ 89.3% 

STEEL BARS AND PLATES.—14 Tests. 

Strength of solid Wak. Sse. coc cweecetoe te won Fret GHA 54,226 to 64,580 
Strength of weld.. L Xareisrsiciote visteteeteioiin sibcieenie a's oj ates 4 28,558 to 46,019 
Ratio weld to solid........... AAS tee I eT oe 52.6 to 82. 1% 


The ratio of weld to solid in ali the feats eaaainie from 87.0 to 95.4 is proof 
of the great variation of workmanship in weldin 

led Pia toa tests, average, HE. L., 5900; '., S., 24,7815 contr., 24.5; 
ext 

Copper Plates.—As rolled, 22 tests, .26 to .75 in. thick; E. L., 9766 to 
18,650; T. S., 30,993 to 34,281; contr., 31.1 to 57.6; ext., 39.9 to 52.2. The va- : 
riation in elastic limit is due to difference in the heat at which the plates 
were finished. Annealing reduces the T. S. only about 1000 pounds, but oe 
E. L. from 3000 to 7000 pounds. 

- Another series, .38 to .52 thick; 148 tests, T. S., 29,099 to 31,924; contr., 28.7 
to 56. ati ext. i» 10 inches, 28. 1 to 41.8. | Note the uniformity in tensils 
strengt 

Drawn Copper.—‘4 tests (0.88 to 1.08 inch diameter); T. S., 31,634 to 
40,557; contr., 37.5 to 64.1; ext. in 10 inches, 5.8 to 48.2. 

Bronze from a Propeller Hlade.—Means of two tests each from 
centre and edge. Central portion (sp. gr. 8.320). E. L., 7550; T. S., 26,312; 
contr., 25.4; ext. in 10 inches, 32.8. Edge ope (sp. gr. ” $550). E. Ls 8950; 
AT ie 35, 960; contr., 37.8; ext. in 10 fnches, 47.9. 

Cast German Silver.—10 tests: E. L., 13, 400 to 29,100; T. S., 23,714 to 
46,510; contr., 3.2 to 21.5; ext. in 10 inches, 0. 6 to 10.2. 


Thin Sheet Metal.—Tensile Strength. 


Germon silver, 2 lots.-...°........... Stee AGhetaticr Sherri. 75,816 to 87,129 
Bronze, 4 lots;..... cles. Bictee's orsic'e-< eres ces ec cccce cesses oMmnrcoU to 92,086 
Brass, 2 lots ...... odo DR INeiis cie\c,05elns'es ecleeatts cine Peg eee bet .. 44,398 to 58,188 
Copper, 9 lots eeeeereeoes SOs SCOVtttwseereaSeeeeeseoeroes eee eeeeeeeeeeee 30,476 to 48,450 


Tron, 13 lots, lengthway.....sececcssss coccccccce. ccsccsececs 44,331 to 59,484 
Iron, 13 lots, CVOSSWAY sceeibtar dees nace «cacovccescackene asehaseemrincos LO Di,au0 
Steel, 6 lots. ee see eee Fee SSSSeeeSFeeeSeSeoeeeSeeser eosegeeee 49,253 to 78,251 
Steel, 6 lots, Crossway... QOO8 CCH BEG KEHHSHHSSOHEETSHHAOHHHEED 55,948 to 80,799 


EXTRACTS FROM KIRKALDY’S TESTS, $01 


Wire.—Tensile Strength. 


German silver, 5 lots........- Calewisieh Mea's ess 4 ee ols we vebaet sig os OL, (OO) LO Ueaee 
Bronze, 1 lot eee eeee eo 8 @ @rxeeee eee oceee see 08888288 2OGSFOGHESH>+ 28 78,049 

Brass, as drawn, 4 lots thee. @eeeeseeeecooe SOO, O88 8080808 © 2 * 8008 81,114 to 98,578 
Copper, aS drawn, 3 lOtS......ccecccccccccccscce-cocvesreoreeee 31,007 to 46,494 
Copper annealed, 'S l0tss. .v... cece ceccscdccccetcscanccon aces 4,900 60 45,210 
Copper (another lot), 4 lots .......ce0s.cevccesscoccccsssesese O0,002 tO 62,190 
Copper (extension 36.4 to 0.6%). 


Iron, 8 lots ee e+e @eee ee ee ee eereoe eree2 8028008008 02888 8888 ~ OG Ge ae 59,246 to 97,908 
Iron (extension 15.1 to 0.72). 
Steel, 8lots............ fences erections SUSI c ees on tid censc tees Ll UOsol a tO OLe.neo 


The Steel of 318,823 T.S. was .047 inch diam., and had an extension of only 
0.3 per cent; that of 103,272 T. S, was .107 inch diam. and had an extension 
of 2.2 per cent. One lot of .044 inch diam. had 267,114 T. S., and 5.2 per cent 
extension. 


Wire Ropes. 
Selected Tests Showing Range of Variation, 




















SS) :  |Strands.| » ¥ z 

=| ®O e sS oa 

Cg} ag uo 2S 

p TROD ee ei eee eee @ 80° 
Description. a3 as ihe 2 oe Hemp Core. gas 

5.8 | 38 |oa| oz 2 as 

a” |e WalZe Se an 

den MD 

Wwe Re ——e ee ee Oe 

Galvanized.......] 7.70 | 53.00) 6 19 | .1563 Main 339,780 
Ungalvanized....| 7.00 | 53.10} 7 19 |.1495| Main and Strands {| 314,860 
Ungalvanized....| 6.38 | 42.50) 7 19 | .1347 Wire Core 295,920 
Galvanized....... 7.10 | 87.57| 6 30 }.1004] Main and Strands | 272,750 
Ungalvanized....| 6.18 { 40.46] 7 19 | .1302 Wire Core 268,470 
Ungalvanized....} 6.19 | 40.33] 7 19 |.1316 Wire Core 221,820 
Galvanized....... 4.92 | 20.86] 6 30 |.0728 | Main and Strands | 190,890 
Galvanized.......] 5.36 | 18.94] 6 12 |.1104] Main and Strands | 136,550 
Galvanized.......] 4.82 } 21.50] 6 @ 1.1693 Main 129,710 
Ungalvanized....) 3.65 } 12.21] 6 19 | .0755 Main 110,180 
Ungalvanized....| 3.50 | 12.65] 7 e122 Wire Core 101,440 
Ungalvanized....] 3.82 | 14.12) 6 7 1.185 Main 98,670 
Galvanized...... 4.11 § 11.35! 6 12 '.080 ! Main and Strands 75,110 
Galvanized.......| 8.31 | 7.27] 6 12 |.068 } Main and Strands 55,095 | 
Ungalvanized....| 3.02 | 8.62] 6 @ | 105 Main 49,555 
Ungalvanized....| 2.68 | 6.26| 6 6 | .0963 | Main and Strands 41,205 
Galvanized.......| 2.87 | 5.43| 6 12 | .0560] Main and Strands 38,555 
Galvanized....... 2.46 | 3.85] 6 12 | .0472 | Main and Strands 28,075 
Ungalvanized....| 1.75 | 2.80] 6 7 1.0619 Main 24,554 
Galvanized.......| 2.04 | 2.72] 6 12 | .0878{ Main and Strands 20,418 
Galvanized.......| 1.76 | 1.85] 6 12 | .03805 Main 14,634 








Hemp Ropes, Untarred.—15 tests of ropes from 1.53 to 6.90 inches 
circumference, weighing 0.42 to 7.77 pounds per fathom, showed an ultim- 
ate strength of from 1670 to 33,808 pounds, the strength per fathom weight 
varying from 2872 to 5534 pounds. : 

Hemp Ropes, Tarred. --15 tests of ropes from 1.44 to 7.12 inches 
circumference, weighing from 0.38 to 10.39 pounds per fathom, showed an 
ultimate strength of from 1046 to 31,549 pounds, the strength per fathom 
weight varying from 1767 to 5149 pounds. 

Cotton Ropes.— ropes, 2.48 to 6.51 inches circumference, 1.08 to 8.17 
pounds per fathom. Strength 3089 to 23,258 pounds, or 2474 to 3346 pounds 
per fathom weight. 

Manila BRopes.—35 tests: 1.19 to 8.90 inches circumference, 0.20 to 
11.40 pounds per fathom. Strength 1280 to 65,550 pounds, or 38003 to 7394 
pounds per fathom weight. Fe 


302 STRENGTH OF MATERIALS, 


Belting. 

No. of Tensile strength 
lots. per square inch. 
11 Leather, single, ordinary tanned ..........5. ccccceseccce cece 3248 to 4824 
4 Leather, single, Helvetia ....... elidel gece Nels mene Deja oe eiaeie rene 5631 to 5944 
% Leather, double, ordinary tanned............... dalejae ote ohucitiarehs 2160 to 3572 
8 Leather, double Helvetia........ 2. ..cccecee Eeaiatsl ae twsiaate einasiane 4078 to 5412 
GC COtton, SOG WOVE ie. cs Sac aco cteteeticns ocve cutie ebunate ciate ciate 5648 to 8869 
ICottonafolded, Stitched > vi... s0s scncccms oa fawer tcc cineee stele - 4570 to 7750 

1 Flax, solid, woven............ Sinainhe srcke sot 0 ss crete sist ania everest 9946 

ipl lax. folded, Stitched... 23.0.5. 00 cecccessscseecen in ate ma sails Pa 6389 
OULLAIGNSONG, WOVEN, -.shioccises secwswees doereseces sce ce chides. teemmOUdT COM Oo 
2 Rubber, solid, woven.... ... a sta'd) ladies delete cag a eee ee 4271 to 4343 


Canvas.—35 lots: Strength, lengthwise, 113 to 408 pounds per inch; 
crossways, 191 to 468 pounds per inch. 

The grades are numbered 1 to 6, but the weights are not given. The 
strengths vary considerably, even in the same number. 

Marbles,—Crushing strength of various marbles. 88 tests, 8 kinds. 
Specimens were 6-inch cubes, or columns 4 to 6 inches diameter, and 6 and 
12 inches high. Range 7542 to 13,720 pounds per square inch. 

Granite.—Crusbhing strength, 17 tests; square columns 4 X 4 and 6X 4, 
4 to 24 inches high, 3 kinds. Crushing strength ranges 10,026 to 13,271 
pounds per square inch. (Very uniform.) 

Stones.—(Probably sandstone, local names only given.) 11 kinds, 42 
tests, 6 x 6, columns 12, 18 and 24 inches high. Crushing strength ranges 
from 2105 to 12,122. The strength of the column 24 inches long is generally 
from 10 to 20 per cent less than that of the 6-inch cube. 

Stones.—(Probably sandstone) tested for London & Northwestern Rail- 
way. 16 lots, 3to6 tests in alot. Mean results of each lot ranged from 
3785 to 11,956 pounds. The variation is chiefly due to the stones being from 
different lots. The different specimens in each lot gave results which gen- 
erally agreed within 30 per cent. 

Bricks.—Crushing strength, 8 lots; 6 tests in each lot; mean results 
ranged from 1835 to 9209 pounds per square inch. The maximum variation 
in the specimens of one lot was over 100 per cent of the lowest. In the most 
uniform lot the variation was less than 20 per cent. 


Wood.—Transverse and Thrusting Tests. 





bs Thrust- 
2 | Sizes abt. in } Span, | Ultimate es ere 
n 4 ; a ae: Lw Stress 
2 square, inches.} Stress. Ebr | per sa. 
in. 


ee ee ny 








Pitch pine........./ 10 | 11144 to 12 144 to to to 
P ” (: 80,52 1403 5438 
37,948 6357 2478 
Dantzic fir........] 12 | 12 .to13 144 to to to 
54,152 790 8423 
* 82,856 1505 2473 
English oak....... 3 444 X 12 120 to to to 
39,084 1779 4437 
American white |, 23,624 1190 2656 
OOK avs cle Peaea pro 416 XK 12 120 to to to 
26,952 137: 3899 
Demerara greenheart, 9 tests (thrusting)............0...-eeseee 8169 to 10,785 
Orevon pine, STGHES Meek ss. ose. + oldie ele Maelo bt CHAR ObOtab so 50c . 5888 and 7284 
Honduras mahogany, 1 test............... oie 0) »1elec$ elas fo'er je faiade SeMees Agssietae 100 
Tobasco mahogany, 1 test....... 5 baie tehd Ablalele fa epanter ts Es. s afabeemebetets ayfots eh dW9a 5978 
INOGWAYASPLUCE) SO SbOmne die cirial=.>.6013.06 5 - cece clewe cemhineres o eeeeee, 5209 and 5494 
American yellow pine, 2 tests..... Sh Q3 oP aceon se b ewatttideesee o01D).and'3993 
English asin; l, testing, fae 268d Wisde dbo jejelswinlan + olslslaeeiines Safe die vit sible et POULD 


Portland Cement,—(Austrian.) Cross-sections of specimens 2 x 214 
inches for pulling tests only; cubes, 3 x 3 inches for thrusting tests; weight, 


MISCELLANEOUS TESTS OF MATERIALS, 303 


98.8 pounds per imperial bushel; residue, 0.7 per cent with sieve 2500 meshes 
per square inch; 38.8 per cent by volume of water required for mixing; time 
of setting, 7 days; 10 tests to each lot. The mean results in lbs. per sq. in. 
were as follows: 


Cement Cement 1Cement, 1Cement, 1 Cement, 
alone, alone, 2. Sand, 3 Sand, 4 Sand, 
Age. Pulling. Thrusting, Thrusting. Thrusting. Thrusting. 
10 days 376 2910 893 407 228 
20 days 420 8342 1023 494 275 
30 days 451 3724 1172 594 338 


Portland Cement.—Various samples pulling tests, 2x 214 inches 
cross-section, all aged 10 days, 180 tests; ranges 87 to 643 pounds per square 


inch, 
TENSILE STRENGTH OF WIRE. 
(From J. Buckuall Smith’s Treatise on Wire.) 
Tons per sq. Pounds per 
in. sectional sq. in. sec- 
area. tional area. 
Black or annealed iron Wire........sceceseceseee 25 56,000 
Bright hard draw... :s.cenues- cece ut As'es steer et 35 78,400 
Bessemer, steel Wire... 0.6 ii c cee cece cee cer scen 40 89,600 
Mild Siemens-Martin steel wire............ wae 60 134,000 
High‘carbon ditto (or ‘‘ improved’)... ... .... 80 179,200 
Crucible cast-steel ‘‘improved ”’ wire... ........ 100 224,000 
‘Improved.’ cast-steel ‘‘ plough”’.............. 120 268,800 
Special qualities of tempered and improved cast- 
SLCC] WATE WIA Yy ULLAL, Go .jcres0, cisco chia c ceed 150 to 170 336,000 to 380,806 


MISCELLANEOUS TESTS OF MATERIALS, 
Reports of Work of the Watertown Testing-machine in 


1883. 
TESTS OF RIVETED JOINTS, IRON AND STEEL PLATES. 














: PA - ; Bas ao = 
= ys i: of |, | # [Haas | eS] 8 
= A site ie = a Sele aust Ov rey 
mH | Bg | ges | ge | S| £2 |s8aee) 223 | 38 
D2 BS ava ~ 1 MA |RoeRos| MES, pO 
0) vO oo as ala NN B= ane iS 
a O48 Sas = © | So [2rugsl ear! 3h 
p--) oe rt =e fo) Orn ous = © o 
° A Ag 6 |\4|l = Saem | 249] -om 
a o 5 a a Sso® | Fa8 2 
B | A a ess [am | & 
# | 3¢ 11-16 34 1044 16 | 134 | 389,800 | 47,180 | 47.0 + 
* | 32 11-16 34 Giolsskadbe 1,000 | 47,180 | 49.0 + 
* 1A 34 13-16 5 2 35,650 44,615 | 45.6 t 
# % 4 13-16 10 5 2 35,150 44,615 | 44.9 f 
* 34 11-16 34 10 5 2 46,360 47,180 | 59.9 § 
* | 38 11-16 34 10 5 2 46.87: 47,180 | 60.5 § 
* 4% 34 13-16 10 5 2 46,400 44,615 | 59.4 § 
* re 34 13-16 10 5 2 46,140 | 44,615 | 59.2 § 
* 74 ‘i 1 1-16 10144 4 254 44,260 44,635 | 57.2 § 
* Be 1 1 1-16 1014 4 254 42,350 44,635 | 54.9 § 
* 34 144 1 3-16 Hie9 4 2.9 42,310 46,590 | 52.1 § 
* | 34 14 1 3-16 £1,950) 4 2.9 41,920 | 46,590 | 51.7 § 
«| 2 34 13-1 10i4 6) |. 134 61,270 | 53.330 | 59.5 ¢ 
+| 3% 34 13-16 | 1016 |6 | 134 60,830 | 53,330 | 59.1 + 
+ by 15-16 10 5 2 47,5380 57,215 | 40.2 f 
+ % 15-16 1 10 5 2 49,840 ST 215) (4 onan 
+ | 38 11-16 34 10 5 2 62,77 53,330 | 71.7 § 
+ 3% 11-16 4, 10 5 2 61,210 53,330 | 69.8 § 
+ 6 15-16 a 10 5 2 68,920 5,215 || 5721 § 
wi % 15-16 1 10 5 2 66,710 | 57,215 | 55.0 § 
+ | 5% 1 11-16 | 914 |4 | 236 | 62180 | 52,445 | 68.4 § 
+ | 5% 1 11-16 | 916 |4 | 284 | 62.590 | 52,445 | 68.8 § 
+| %&% 1% 13-16 | 10 4 | 24 54,650 | 51,545 -| 54.08 
t+! 34 1lg 1 3-16 10 4 246 54,200 | 51,545 | 53.4 § 
* Iron. t Steel. } Lap-joint, § Butt-joint. 


304 STRENGTH OF MATERIALS. 


The efficiency of the joints fs found by dividing the maximum tensile 
ahi gon the gross sectional area of plate by the tensile strength of the 
material. 


COMPRESSION TESTS OF 3x38 INCH WROUGHT-IRON BARS. 








Tested with Two Pin Ends, Pins 
14% inch in Diameter. Tested with One 
Flat and One Pin 
End, Ultimate 





Length, inches. Ultimate Com- nt ate Compressive 
pressive Strength Waatedlantiresaine Strength, pounds 
pounds per square Strength Boab dg | Per square inch. 

igs per square inch. 
RSIZGO ee SH eeaekeeate oe eee ate © alee ate AA nSGOS seus 
BO te crecieesee. 431990 «difibew avin oh abe dart gn] need ae aan 
26,310 eee ee @-eeeoerveee ee eel rseee @eeeeveees e@eor-eecee 
60... .0.0ee eee. ; DEBA0 ationes| tuccarsasqahowte suas xs |e aed 
90 ‘ 24,030 { 26,780 25,120 
bald acto gat wk 25,380 25,580 25,190 
120 j 20,660 j 23.010 22,450 
ies eae her Wee 22,450 21,870 
150.20. dazesa: ptel tent letesbvisaceat lia enrtUAuup Raoae 
( 13,010 eee teeeeee e@coce . eee eerece 
er ay ‘ {15,700 pias ak A i ia a tcek 
Diameter ~ ‘Ult. Comp. Str., 
Tested with two pin- of Pins. per aq: in., lbs. 
ends. Lena of bars 1%8 Hct capiasatt atte con 4 cen 
120 ine es. in se eeeseee cee recseeeses:e % 
Pon SIN Pile) SOREN AMR erced sy Fh 
IAP “Eo at ba see eecnks ae cues ton ten BeeeeIO 


TENSILE TEST OF SIX STEEL EYE-BARS. 
COMPARED WITH SMALL TEST INGOTS. 


The steel was made by the Cambria Iron Company, and the eye-bar heads 
made by Keystone Bridge Company by upsetting and hammering. All the 
bars were made from one ingot. Two test pieces, 34-inch round. rolled from 
a test-ingot, gave elastic limit 48,040 and 42.210 pounds; tensile strength, 
73,150 and 69,470 pounds, and elongation in 8 inches, 22.4 and 25.6 per cent. 
respectively. The ingot from which the eye-bars were made was 14 inches 
square, rolled to billet, 7 x 6 inches. The eye-bars were rolled to 6144 x 1 inch, 
Pear gave carbon .27 to .30; manganese, .64 to .73; phosphorus, 
074 to .098. 


Gauged Elastic Tensile Elongation 
Length, limit, Ibs. strength per per cent, in 
inches, per sq. in. sq. in., lbs. Gauged Length, 

160 37,480 67,800 15.8 

160 36,650 64,000 6.96 

if) 0" Oe 71,560 8.6 

200 37,600 68,720 12.3 

200 35,810 65,850 12.0 

200 33,230 64,410 16.4 

200 37,640 68,290 13.9 


The average tensile strength of the 34-inch test pieces was 71,310 lbs., that 
of the eye-bars 67,230 lbs., a decrease of 5.7%. The average elastic limit of 
the test pieces was 45,150 lbs., that of the eye-bars 36,402 lbs., a decrease of 
19.4%. The elastic limit of the test pieces was 63.3% of the ultimate strength, 
that of the eye-bars 54.2% of the ultimate strength. 


MISCELLANEOUS TESTS OF MATERIALS. 305 


COMPRESSION OF WROUGUT-IRON COLUMNS, LATTICED BOX 
AND SOLID WEB. 


ALL TESTED WITH PIN ENDS. 








: ol » = 

wey o » ei wn 

2 bic me, | 8d, 

q dEs Coa 2 

Columns made of ae ati ie age Bete 

Ms oz; ouels 

an oa SOe 22 SO 

a Ss Bay mi posa 
4 82 18° aa 

rere Leg) eee er es yy eee 
6.inch channel, solid web...............: 10.0 | 9.881 432 | 230,220 
6." ie s, ALT 5 5, oiled dee es 15.0 9.977 592 21,050 
6 “* Si “ Sa Tanta e cts eisiere ately 20.0 9.762 T55 16,220 
Set < be 37: 2 NR OM Mogi 20.0 16.281 1,290 22,540 
8“ “ OF" Oa eS ne RS 26.8 | 16.141 | 1,645 | 17,570 

8-inch channels, with 5-16-in. continuous 

lates! Ah. bs Pca kh ogi AMOS sites Sy 26.8 | 19.417 | 1,940 25,290 


5-16-inch continuous plates and angles, 
Width of plates, 12in., 1 in. and 7.85in.| 26.8 | 16.168 | 1,765 28,020 
7-16-inch continuous plates and angles. 


IPIAtES 123in SWiCege.t. tic cc eide oe « slereiane.« 26.8 20.954 2,242 25,770 
8-inch channels, latticed.................- 13.3 7.628 679 38,910 
Bist $f So Th Molle etal stacy gave 20.0 7.621 924 34.120 
8x4 KA OF SSR RE, tvPht ee Par scares ete 26.8 67 iecoo 29.870 
8-inch channels, latticed, swelled sides..| 13 4 7.624 684 83,530 
Sues He as ‘s ait al REMEBER D) aBDANG: 921 33,890 
8. % sf Ue ss ai Ba 61s eth 1,280 30,770 
10 “* iy Ee See 16.8 11.944 1,470 33.740 
10 “ ss Ce Ges San cea eee 25.0 12.175 1,926 32,440 


10-inch channels, latticed, swelled sides. 16.7 | 12.366 1,549 31,130 
fut: ry ce ‘s oe) aly 25.0 ee 111932". 1.962 32,740 
* 10-inch channels, latticed one side; con- 


tinuous plate one side ......... ....... 25.0 | 17.622 | 1,848 26,190 
+10 inch channels, latiged © one aides con- 
tinuous plate one side.. 25.0 G21 1,827 17,270 


* Pins in centre of gravity of channel bars and continuous plate, 1.63 
inches from centre line of channel bars. 
+ Pins placed in centre of gravity of channel bars. 


EFFECT OF COLD-DRAWING ON STEEL 


Three pieces cut from the same bar of hot-rolled steel: 


1. Original bar, 2.03 in. diam.. gauged length 30 in., tensile strength 55,400 
lbs. per square in.; elongation 23.9%. 
2. Diameter reduced in compression dies (one pass) .094 in.; T. S. 70,420; el. 
2.7% in 20 in, 
3° 66 be be bs 66 46 6e oe in. ik Ss. 81, 890; el. 
0.075% in 20 in. 


Compression test of cold-drawn bar (same as No. 3), length 4 in., diam. 
1.808 in.: Compressive strength per sq. in., 75,000 lbs.; amount of compres- 
sion .057 in.; set .04 in. Diameter increased by compression to 1.821 in. in 
the middle; *to 1.813 in. at the ends. 

Tests of Cold-rolled and Cold-drawn Steel, made by the 
Cambria Iron Co. in 1897, gave the following results (aver ages of 12 tests of 
each): 


Before cold- rolling, E. L. 35,390 T.S. 59,980 El. in 8 i in, 28. He Red. 58.5% 
After 72530 ‘+ 79 133 0 9.6 34.9** 
After cold- drawing, o 76, 350; 83, 860 BO BO i cise Da aba c er rg 


The original bars were 2 in. and % in. diameter. The test pieces cut from 
the bars were 34 in. diam., 18 in. long. he reduction in diameter from the 
bot-rolled to the cold- rolled or cold-drawn bar was 1/16 in, in each case. 


306 STRENGTH OF MATERIALS. 


TE»is OF AMERICAN WOODS. (See also page 30u.y 


In all cases a large number of tests were made of each wood. Minimum 
and maximum results only are given. All of the test specimens had a sec. 
tional area of 1.575 x 1.575 inches. The transverse test specimens were 89.37 
inches between supports, and the compressive test specimens were 12.60 


inches long. Modulus of rupture calculated from formula R = Sa cs 
load in pounds at the middle, 7 = length in inches, b = breadth, d = depth; 




















Compression 
eee ae Parallel to 
odulus o “as 
Name of Wood. Rupture. RPE ETS 
Min. Max. Min. Max. 
Cucumber tree (Magnolia acuminata)..| 7,440 | 12,050 4,560 7,410 
Yellow poplar white wood (Lirioden- 

LVOM LULLDUL ETO) eamelble cae «sor aint 6,560 | 11,756 4,150 5,790 
White wood, Basswood (Tilia Ameri- 

CURD) ALO ratte SAAR RRte setae wo lea oars 6,720 | 11,580 8,810 6,480 
Sugar-maple, Rock-maple (Acer sac- 

CROUTIMUND sate die Re teal tas es aS Netgh ohehe 9,680 | 20,130 7,460 9,940 
Red maple (Acerrubrum) .. ...........| 8,610 | 13,450 6,010 7,500 
Locust (Robinia psewdacacia).... ..... 12,200 | 21,780 8,330 11,940 
Wild cherry (Prunus serotina).......... 8,310 | 16,800 5,830 9,120 
Sweet gum (Liquidambar styraciflua)..| 7,47 11,130 5,630 7,620 
Dogwood (Cornus florida).......... ....| 10,190 14,560 6,250 9,400 
Sour gum, Pepperidge (Nyssa sylvatica).| 9,830 14,300 6,240 7,480 
Persimmon (Diospyros Virginiana). ...| 10,290 | 18,500 6,650 8,080 
White ash (FPraxunis Americana).......| 5,950 15,800 4,520 8,830 
Sassafras (Sassafras officinale)....., 2.0. 5,180 | 10,150 4,050 5,970 
Slippery elm (Ulmus fulva). ...... .... 10,220 | 138,952 6,980 8,790 
White elm (Ulmus Americana)..........| 8,250 | 15,070 4,960 8,040 


Sycamore; Buttonwood (Platanus occi- 
OR ADAGE EA BOcin COI COCs Ibm AG cae eh gale Ob 
Butternut; white walnut (Juglans ci- 





WLCTE CL) oo dcr ins Se ween: se muce ON 4,700 | 11,740 5,480 6,810 
Black walnut (Juglans nigrd)........... 8,400 | 16,320 6,940 8,850 
Shellbark hickory (Carya alba). ........| 14,870 | 20,710 7,650 10,280 
Eiguus (COTY PONCING) Ke menu seene suet 11,560 | 19,430 7,460 8,470 
White oak (Quercis Wlba).........0-20.--| 7,010 18,360 5,810 9,07 
Red oak (Quercus rwbra). ....ce- cece 9,760 18,370 4,960 8,970 
Black oak (Quercus tinctoria).........6. 7,900 18,420 4,540 8,550: 
Chestnut (Castanea vulgaris). .......... 5,950 | 12,870 3,680 6,650 
Beech (Fagus ferrugined)...... Ba tee AS 13,850 | 18,840 5,770 7,840 
Canoe-birech, paper-birch (Betula papy- 

PACED) mere ales. Pe RAY Kea MERE RELLY 11,710 | 17,610 5,770 8,590 
Cottonwood (Populus monilifera)....... 8,290 | 13,430 3,790 6,510 
White cedar (Thuja occidentalis)....... 6,310 9,530 2,660 5,819 
Red cedar (Juniperus Virginiana).....] 5,640 | 15,100 4,400 7,040 
Cypress (Saxodiwne Distichwnr)..........} 9,580 | 10,030 5,060 7.140 
White pine (Pinus strobus).......e0..0e- 5,610 | 11,580 3,750 5.600 
Spruce pine (Pinus glabra).........+.... 38,780 | 10,980 2,580 4,680 
Long-leaved pine, Southern pine (Pinus . 

PLAST ELA) WE, DIR 976 5's) aye 6 bien Soles -{ 9,220 | 21,060 4,010 | 10,600 
White spruce (Picea alb@)...... ....e.0s 9,900 11,650 4,150 5,300 
Hemlock (Tsuga Canadensis)........... 7,590 | 14,680 4,500 7,420 
Red fir, yellow fir (Pseudotsuga Doug-| — 

LASTL VIO. TUG eee PaP ee nAG Wk..  UIS 8,220 | 17,920 4,880 9,800 
Tamarack (Larix Americana) ......... 10,080 | 16,770 6,810 | 10,700 


SHEARING STRENGTH OF IRON AND STEEL. 


H. V. Loss in American Engineer and Railroad Journal, March and April, 
1893, describes an extensive series of experiments on the shearing of iron 
and steel bars in shearing machines. Some of his results are: 


: CHAINS. 807 


Depth of penetration at point of maximum resistance for soft steel bars 
is independent of the width, but varies with the thickness. If d = depth of 
penetration and ¢t = thickness, d = .3¢ for a flat knife, d = .25 ¢ for a 4° bevel 


knife, and d = .16 //#3 for an 8° bevel knife. The ultimate pressure per inch 
of width in flat steel bars is approximately 50,000 lbs. x t. The energy con- 
sumed in foot pounds per inch width of steel bars is, approximately: Ae 
thick, 1300 ft.-lbs.; 114’’, 2500; 134’’, 3700; 1%%’’, 4500; the energy increasing 
at a slower rate than the square of the thickness. Jron angles require more 
energy than steel angles of the same size; steel breaks while iron has ta be 
cut off. For hot-rolled steel the resistance per square inch for rectan- 
swat sections varies from 4400 lbs, to 20,500 Ibs., depending partly upon its 
hardness and partly upon the size of its cross-area, which latter element 
indirectly but greatly indicates the temperature, as the smaller dimensions 
require a considerably longer time to reduce them down to size, which time 
again means loss of heat. 

It is not probable that the resistance in practice can be brought very 
much below the lowest figures here given—viz., 4400 lbs. per square inch— 
as a decrease of 1000 lbs. will henceforth mean a considerable increase in 
cross-section and temperature. 


HOLDING-POWER OF BOILER-TUBES EXPANDED 
INTO TUBE-SHEETS. 


Experiments by Chief Engineer W. H. Shock, U.S. N., on brass tubes, 244 
inches diameter, expanded into plates 34-inch thick, gave results ranging 
from 5850 to 46,000 lbs. Out of 48 tests 5 gave figures under 10,000 lbs., 12 
between 10,000 and 20,000 Ibs., 18 between 20,000 and 30,000 lbs., 10 between 
30,000 and 40,000 lbs., and 3 over 40,000 lbs. 

Experiments by Yarrow & Co., on steel tubes, 2 to 244 inches diameter, 
gave results similarly varying, ranging from 7900 to 41,715 lbs., the majority 
ranging from 20,600 to 30,000 Ibs. In 15 experiments on 4 and 5 inch tubes 
the strain ranged from 20,720 to 68,040 lbs. Beading the tube does not neces- 
sarily give increased resistance, as some of the lower figures were obtained 
with beaded tubes. (See paper on Rules Governing the Construction of 
Steam Boilers, Trans, Engineering Congress, Section G, Chicago, 1893.) 


CHAINS. 
Weight per Foot, Proof Test and Breaking Weight. 
(Pennsylvania Railroad Specifications, 1899.) 





Nominal Maximum 





: 4 -| Weight | Proof |Breaking 
et ey Description. — Rees per Foot.| Test. Weight. 
Inches. Inches. 5. Lbs. Lbs. 
5/32 |Twisted chain............ 103.1 0.20 
3/16 oa Fie Bina esate botene 96.2 0.35 
3/16 |Perfection twisted chain.} 151.25 0.266 
14 Straight link chain....... 102.0 0.7 1,500 8,000 
5/16 ss “ sen 114.7 1.10 3,000 5,500 
34 (Sor fn Siar Cora 114.7 1.50 3,500 7,000 
36 Crane chaintwcert: cress 113.6 1.50 4,000 7,500 
7/16 |\Straight-link chain.......| 127.5 1.90 5,000 9,500 
7/16 Crane Chain....cc0% dasa 126.3 1.90 5,500 10,000 
% Straight-link chain...... 153.0 2.50 7,000 12,500 
re Crane chain.............. 138.9 2.50 7,500 13,000 
5% Straight-link chain..... EAP ces) 4.00 11,000 20,000 
58 Grane, chain: -inc. aaeasnan 176.7 4.00 11,000 20,C00 
34 Straight-link chain....... 204.0 5.50 16,000 29,000 
34 Crane chain..... «0. neces 202.0 5.50 16,000 29,000 
% + MMM docinwas td 252.5 7.40 22,000 40,000 
es tar Ir cy tei te HELM 9 50 30,000 55,000 
1% 48 EEE rioicisis of 303.0 12.00 40,000 66,000 
144 = FS oo cearetnee Eee 353.5 15.00 50,000 82,000 
1% st aM Acris citi oer 416.6 21.00 70,000 | 116,000 





Elongation of all sizes,10 per cent. All chain must stand the proof test 
without deformation. A piece 2 ft. long out of each 200ft.is tested to 
destruction, 


808 STRENGTH OF MATERIALS. 


British Admiralty Proving Tests of Chain Cables.—Stud. 
links. Minimum size in inches and 16ths. Proving test in tons of 2240 lbs. 
Mio. Size: 3% 48 480 O68 O38) 1 ee lee lye lie lie IY lye. 
Test, tons: 83§ 103%; 1138 13833 1533 18 208 223 ely 28y% 31 34 375%. 
Min. Size: 18 LPR LO Pl SL Tee oa | Peete ee ee oe 
Test, tons: 4039 4348 4739 515, 5533 593 6325 6733 72 7635 812% 912%. 

Wrought-iron Chain Cables.—The strength of a chain link is 
léss than twice that of a straight bar of a sectional area equal to that of one 
side of the link. A weld exists at one end and a bend at the other, each re- 
quiring at least one heat, which produces a decrease in the strength. The 
report of the committee of the U. S. Testing Board, on tests of wrought-iron 
and chain cables contains the following conclusions. That beyond doubt, 
when made of American bar iron, with cast-iron studs, the studded link is 
inferior in strength to the unstudded one. 

‘‘That when proper care is exercised in the selection of material, a varia- 
tion of 5 to 17 per cent of the strongest may be expected in the resistance 
of cables. Without this care, the variation may rise to 25 per cent. 

‘That with proper material and construction the ultimate resistance of 
the chain may be expected to vary from 155 to 170 per cent of that of the 
bar used in making the links, and show an average of about 163 per cent. 

“ That the proof test of a chain cable should be about 50 per cent of the 
ultimate resistance of the weakest link.” 

The decrease of the resistance of the studded below the unstudded cable 
is probably due to the fact that in the former the sides of the link do not 
remain parallel to each other up to failure, as they do in the latter, The re- 
sult is an increase of stress in the studded link over the unstudded in the 
proportion of unity, to the secant of half the inclination of the sides of the 
former to each other. 

From a great number of tests of bars and unfinished cables, the commit- 
tee considered that the average ultimate resistance, and proof tests of chain 
cables made of the bars, whose diameters are given, should be such as are 
shown in the accompanying table. 


ULTIMATE RESISTANCE AND PROOF TESTS OF CHAIN CABLES. 


Diam. 


‘ Diam : 
Average resist. * [Average resist.! ,., 
oe = 163% of Bar. Proof Test. of = 1634 of Bar. Proof Test. 

Inches. Pounds. Pounds. Inches. Pounds. Pounds. 
1 1/16 W112 33,840 1 9/16 162,283 97,159 
1 1,16 79,544 37,820 156 174,475 82,956 
1144 88,445 42,053 1 11/16 187,075 88,947 
1 3/16 97,731 46,468 134 200,074. 95,128 
114 107,440 51,084 1 13/16 213,475 101,499 
1 5/16 W17.577 55,903 1% Q7QTh : 108,058 
134 128,129 60,920 1 15/16 241,463 _ 114,806 
1 7/16 139,103 66,138 2 256,040 121,737 
1 150,485 71,550 





STRENGTH OF GLASS, 
(Fairbairn’s “‘ Useful Information for Engineers,’ Second Series.) 


_ Best Common Extra White 
Flint Glass, Green Glass. Crown Glass. 


Mean specific gravity ...............scee ees 3.078 2.528 ., 2.450 
Mean tensile strength, lbs. per sq.in., bars.. 2,413 2,896 2,546 
do thin plates. 4,200 4,800 6,000 


Mean crush’g strength, lbs. p. sq. in., cyl’drs. 27,582 39,876 31,003 
do. cubes. 18,1380 20,206 21,867 
The bars in tensile tests were about 44 inch diameter. The crushing tests 
were made on cylinders about 34 inch diameter and from 1 to 2 inches high, 
and on cubes approximately 1 inch on a side. The mean transverse strength 
of glass, as calculated by Fairbairn from a mean tensile strength of 2560 
{bs. and a mean compressive strength of 30,150 lbs. per sq. in., is, for a bar 
supported at the ends and loaded in the middle, 


2 
w= s140e, 


STRENGTH OF TIMBER. 309 


in which w = breaking weight in lbs., b = breadth, d = depth, and 2 = length, 
in inches. Actual tests will probably show wide variations in both direc- 
tions from the mean calculated strength. 


STRENGTH OF COPPER AT HIGH TEMPERATURES, 


The British Admiralty conducted some experiments at Portsmouth Dock- 
yard in 1877, on the effect of increase of temperature on the tensile strength 
of copper and various bronzes. The copper experimented upon was in rods 
.72-in, diameter. 

The following table shows some of the results: : 








Temperature | Tensile Strength Temperature | Tensile Strength 
Fahr. in lbs. per sq. in. Fahr. in lbs. per sq. in. 
Atmospheric. 23,115 300° 21,607 
100° 23,366 400° 21,105 
200° 22,110 500° 19,597 





Up to a temperature of 400° F. the loss of strength was only about 10 per 
cent, and at 500° F. the loss was 16 per cent. The temperature of steam at 
200 lbs. pressure is 382° F., so that according to these experiments the loss 
of strength at this point would not be a serious matter, Above a tempera- 
ture of 500° the strength is seriously affected. 


STRENGTH OF TIMBER. 


Strength of Long-leaf Pine (Yellow Pine, Pinus Palustris) from 
Alabama (Bulletin No. 8, Forestry Div., Dept. of Agriculture, 1893. Tests 
by Prof. J. B. Johnson.) 

The following is a condensed table of the range of results of mechanical 
tests of over 2000 specimens, from 26 trees from four different sites in 
Alabama ; reduced to 15 per cent moisture : 





: Av’g of 

Butt Logs. |Middle Logs.| Top Logs. |all Butt 
Logs. 
Specific gravity .........- 0.449 to 1.039 |0.575 to 0.859 |0.484 to 0.907 | 0.767 
Transversestrength,5 +> 4,762 to 16,200|7,610 te 17,128 4,268 to 15,554] 12,614 
do do. at elast. limit |4,930 to 13,110/5,540 to 11,790 2,553 to 11,950! 9,460 
Mod. of elast., thous. Ibs.|1,119 to 3,117)1,1386 to 2,982) 842 to 2,697) 1,926 


Relative elast. resilience, 
inch-pounds per cub. in.| 0.23 to 4.69 | 1.34 to 4.21 0.09 to 4.65 2.98 
Crushing endwise, str. per 
sqadn.-lbaije: saeatetc..t 4,781 to 9,850/5,030 to 9,800)4,587 to 9,100 | 7,452 
Crushing across grain, 
strength per sq. in.,lbs.| 675 to 2,094) 656 to 1,445) 584 to 1,766 1,598 
Tensile strength per sq.in.|8,600 to 31,890)6,830 to 29,500/4,170 to 23,280} 17,359 
Shearing strength (with 
grain), mean per sq.in.| 464 to 1,299] 589 to 1,230; 484 to 1156 866 








Some of the deductions from the tests were as follows : 

1. With the exception of tensile strength a reduction of moisture is ac- 
companied by an increase in strength, stiffness, and toughness. 

2. Variation in strength goes generally hand-in-hand with specific gravity. 

3. In the first 20 or 30 feet in height the values remair constant ; then 
occurs a decrease of strength which amounts at 70 feet to 20 to 40 per cent 
of that of the butt-log. 

4. In shearing parallel with the grain and crushing across and parallel 
with the grain, practically no difference was found. 

5. Large beams appear 10 to 20 per cent weaker than small pieces. 

6. Compression tests endwise seem to furnish the best average statement 
of the value of wood. and if one test only can be made, this is the safest, as 
was also recognized by Bauschinger. 

%. Bled timber is in no respect inferior to unbled timber. 


510 STRENGTH OF MATERIALS. 


The figures for crushing across the grain represent the load required te 
cause a compression of 15 per cent. The relative elastic resilience, in inch- 
pounds per cubic inch of the material, is obtained by measuring the area 
of the piotted-strain diagram of the transverse test from the origin to thé 
point in the curve at which the rate of deflection is 50 per cent greater than 
the rate in the earlier part of the test where the diagram is a straight line. 
This point is arbitrarily chosen. since there is no definite ‘‘ elastic limit”? in 
timber as there is in iron. The *‘strength at the elastic limit’’ is the 
strength taken at this same point. Timber is not perfectly elastic for any 
load if left on any great length of time. 

The long-leaf pine is found in all the Southern coast states from North 
Carolina to Texas. Prof. Johnson says it is probably the strongest timber 
in large sizes to be had in the United States. In small selected specimens, 
other species, as oak and hickory, may exceed itin strength and tough- 
ness, The other Southern yellow pines, viz., the Cuban, short-leaf and 
the lobiolly pines are inferior to the long-leaf about in the ratios of their 
specific gravities; the long-leaf being the heaviest of all the pines. It 
averages (kiln-dried) 48 pounds per cubic foot, the Cuban 47, the short-leaf 
40, and the loblolly 34 pounds. 

Strength of Spruce Timber.—The modulus of rupture of spruce 
is given as follows by different authors: Hatfield, 9900 lbs. per square inch ; 
Rankine, 11,100; Laslett, 9045; Trautwine, 8100; Rodman, 6168. Traut- 
wine advises for use to deduct one-third in the case of knotty and poor 
timber, 

Prof. Lanza, in 25 tests of large spruce beams, found a modulus of 
rupture from 2995 to 5666 lbs.; the average being 4613 lbs. These were 
average beams, ordered. from dealers of good repute. Two beams of 
selected stock, seasoned four years, gave 7562 and 8748 Ibs. The modulus 
of elasticity ranged from 897,000 to 1,588,000, averaging 1,294,000. 

Time tests show much smaller values for both modulus of rupture and 
modulus of elasticity. A beam tested to 5800 lbs. ina screw machine was 
left over night, and the resistance was found next morning to have dropped 
to about 3000, and it broke at 3500. 

Prof. Lanza remarks that while it was necessary to use larger factors of 
safety, when the moduli of rupture were determined from tests with smaller 
pieces, it will be sufficient for most timber constructions, except in factories, 
to use afactor of four. For breaking strains of beams, he states that it is 
better engineering to determine asthe safe load of a timber beam the load 
that will not deflect it more than a certain fraction of its span, say about 
1/300 to 1/400 of its length. 


Properties of Timber, 
(N. J. Steel & Iron Co.’s Book.) 











A Relative |Shearing 

* heciae A Sie oh ee ae ene Strength 

Pedi. : trengt rength per |for Cross} with the 

Description. ae per sq. inch, | sq.inch, |Breaking.| Grain, 

ibe in lbs. in lbs. White lbs, per 

Pine = 100.| sq. inch 

ASN |.) ceulh « 5% 43 to 55.8/11,000 to 17,207] 4,400 to 9,363) 130 to 180 | 458 to 700 
Beech.....+ «+. (43 to 53.4/11,500 to 18,000] 5,800 to 9,363] 100 to 144]........ 5 
Cedars. c.2-b ie 50 to 56.8/10,200 to 11,400] 5,600 to 6,000} 55 to 63 |........ bs 
HOrnry eee eee deo ce, 3.6. b alee sotilienea tle pecan 130 oestigiaion 5 
Chestnut..... ae 33 10,500 5,350 to 5,600) 96 to 123}........ BG 
Blin) hh eecnetes 34 to 36.7/13,400 to 13,489] 6,831 to 10,331 OOS, wae. aieee 
Hemlock... cei Suseienice.e 8,700 5,700 ote 6) 6d Wa es Se 
Hickory......+.|..--.--- -|12,800 to 18,000 8,925 JOO BO wlO Ns 0. Rees 
Locust....6.<0. 44 20,500 to 24,800} 9,113 to 11,700) 182 to 227).......... 
Maple ......... 49 10,500 to 10,584 8,150 122 to 220 | 367 to 647 
Oak, White..../45 to 54.5/10,253 to 19,500] 4,654 to 9,509) 180 to 177 | 752 to 966 
Oak, Live...... OMe 6,850 155't6 189) 2.28. 
Pine, White.... 30 10,000 to 12,000] 5,000 to 6,650 100 225 to 423 
Pine, Yellow...|28.8 to 33/12,600 to 19,200] 5,400 to 9,500] 98 to 170 | 286 to 415 


DPluces<.accces lo. s eee 10,000 to 19,500] 5,050 to 7,850] 86 to 110 | 253 to 874 
alnut, Black. 42 . 9,286 to 16,000 COOO FM antec cet 2. || SRE 


STRENGTH OF TIMBER. 311 


The above table should be taken with caution. The range ox variation in 
the species is apt to be much greater than the figures indicate. See Johnson’s 
tests on long-leaf pine, and Lanza’s on spruce, above. The weight of yellow 
pine in the table is much less than that given by Johnson. (W. K.) 

Compressive Strengths of American Woods, when slowly 
and carefully seasoned.—Approximate averages, deduced from many exper- 
iments made.with the U. S. Government testing-machine at Watertown, 
Mass., by Mr. S. P. Sharpless, for the Census of 1880. Seasoned woods resist 
crushing much better than green ones; in many cases, twice as well. Differ- 
ent specimens of the same wood vary greatly. The strengths may readily 
vary as much as one-third part more or less from the average. 














End- Side- End- Side- 
wise,* | _wise,t wise,* | wise,t 
Ibs. per] lbs. per Ibs. per|lbs. per 
sq.in. | sq. In. sq. in. | Sq. in. 
(Op is yeesal OV 
Ash, red and white} 6800 {1300} 3000 { Maple: 
LASPEIER Were emitters 4400 | 800] 1400 sugar and black..} 8000 ‘|1900\4300 
IBCO CH 60; sssje sie a) 2)> 5/5 7000 |1100| 1900 white and red....} 6800 1300/2900 
BEMGh wdiekus avaiiena 000 |1300| 2600 {Oak : | 
BUCKEY CS . aes vee slew 4400 | 600} 1400 white, post (or 
PUCLOTTNIUE claare ar'e 5400 | 700} 1600 iron), swamp 
Buttonwood white, red, and 
(syeamore)| 6000 {1300} 2600 blacks. saasae ar 7000 {1600/4000 
Cedar, rede)... .,i6+- 6000 | 700} 1000 — scrub and basket.| 6000 {1700/4200 
Cedar, white (arbor- chestnut and live} 7500 |1600 4500 
VIVE) ee ree sien 44001). 500) 2 900: ae Pith sasha tate wee egnes 6500 41300/3000 
Catalpa (Ind.bean)}| 5000 | 700} 1800 § Pine : 
Cherry, wild....... 8000 1700} 2600 # white............. 5400 8600/1200 
CRESURU Ge sere sys: 53800 | 900} 1600 red or Norway....| 63800 | 600)1400 
Coffee-tree, Ky....| 5200 |1300) 2600 §. pitch and Jersey 
Cypress, bald...... 6000 500| 1200 SCTUD.s.p 6 ene 58 5000 |1000}2000 
Elm, Am, or white} 6800 {1300} 2600 GEOL 1A eine 1. stale} 8500 |1300/2600 
‘Siu YOO seeees dee) £7700), 11300); 2600: B Pop tarts cs icchioye sro 0's 5000 600/1100 
Hemlock. ncn scncnk 5300 | 600} 1100 fSassafras........... 5000 |1300}2100 
FLICK ONY parece 8000 |2000} 4000 BSpruce, black.......| 5700 | 700/1300 
Lignum-vitee ..... 10000 |1600)13000 tf white....... 4500 | 6001200 
Linden, American.| 5000 | 500} 900 {Sycamore (button- 
Locust: WOOO)? sovisen unite: 6000 |1800)2600 
black and yellow.| 9800 , |1900} 4460 | Walnut: 
Hhoneyess th oar 7000 |1600| 2600 f black............. 8000 |1300\2600 
Mahogany.........| 9000 |1700} 5300 # white (butternut).} 5400 | 700|/1600 
Willow ...+.0+-+.-+| 4400 | 700/1400 





aple: 
broad-leafed, Ore.} 5300 |1400} 2600 





* Specimens 1.57 ins. square X 12.6 ins. long. : 

+ Specimens 1.57 ins. square X 6.3ins. long. Pressure applied at mid-length 
by a punch covering one-fourth of the length. The first column gives the 
loads producing an indentation of .01 inch, the second those producing an 
indentation of 1 inch. (See also page 306). 


Expansion of Timber Due to the Absorption of Water, 


(De Volson Wood, A. 8S. M. E., vol. x.) 


Pieces 36 X 5in., of pine, oak, and chestnut, were dried thoroughly, and 
then immersed in water for 37 days. 
The mean per cent of elongation and lateral expansion were: 


Pine. Oak. Chestnut, 
Elongation, per cent............ 0.065 0.085 0.165 
Lateral expansion, per cent.... 2.6 3.5 3.65 


Expansion of Wood by Heat.—Trautwine gives for the expansion 
of white pine for 1 degree Fahr. 1 part in 440,530, or for 180 degrees 1 part in 
2437. or about one-third of the expansion of iron, 


812 STRENGTH OF MATERIALS, 


Shearing Strength of American Woods, adapted for 
Pins or Treenails, 


J. C. Trautwine (Jour. Franklin Inst.). (Shearing across the grain.) 





per sq. in. er sq. in. 

Ash “see C88 eeeeetee--8eeeee-@ ee 6280 FiGKOrys dadcescleccdecee eae er 
Beech.... eeeesreeseeeeeeeeseeteeee 5223 fe eeee eee C8 et - Cee steeeeeee F285 
Birch sees eeeoee @reeeos @eeeeseeeece 5595 Maplemicsises keto a eeeeerser 6355 
Cedar (white)........ AA ee 1312 Ble Oak seas tae cSdc (bideo swan tee es veenateD 
2 AS) drains @ Vieeksdese! 1519 Vin Oaks (ive) ev steaeee eee & S400 
Cedar (Central American)...... 3410 | Pine (white)....... Ses are SS 2480 
OLD eo eee ererarnoe bees oeg4D Pine (Northern yellow.......... 4340 
HeStHUG 2) bee <ccces s Satante Meet el OOD Pine (Southern yellow) .... ... 5785 
DOF WOOd is. svocecct as. siecwahess seu COLO Pine (very resinous yellow)..... 5053 
Ebony..... UT Sfeaielec cams scihkceiaste T7150 Poplar? Shee ccs telitic ewes Coe oale 
Gum Ess 2.2 BEL C wale an wie cle eae OOOO Sprucesane Res. sinlaic detec < eum coe 
HHeMIOCK. oe ost cketasscict conescesy St00 Walnut (black)c.c & ee eee eee 
Locust . 3.3 sae de saekeccusm closes 6150 Walnut (common)....... ..-... 2830 


THE STRENGTH OF BRICK, STONE, ETC. 


A great advance has recently been made in the manufacture of brick, in 
the direction of increasing their strength. Chas. P. Chase, in Engineering 
News, says: ‘‘ Taking the tests as given in standard engineering books eight 
or ten years ago, we find in Trautwine the strength of brick given as 500 to 
4200 lbs. per sq. in. Now, taking recent tests in experiments made at 
Watertown Arsenal, the strength ran from 5000 to 22,000 Ibs. persq.in. In 
the tests on Illinois paving-brick, by Prof. I. O. Baker, we find an average 
strength in hard paving brick of over 5000 lbs. per squareinch. Theaverage 
crushing strength of ten varieties of paving-brick much used in the West, I 
find to be 7150 Ibs. to the square inch.”’ 

A recent test of brick made by the dry-clay process at Watertown Arsenal, 
according to Paving, showed an average compressive strength of 8972 lbs, 
per sq.in. In one instance it reach d 4973 lbs. per sq. in. A test was made 
at the same place on a *‘fancy pressed brick.”’ The first crack developed 
at a pressure of 305.4000 lbs., and the Frick crushed at 364,300 Ibs., or 11,130 
Ibs. per sq. in. This indicates almost as great compressive strength as 
granite paving-blocks, which is from 12,000 to 20,000 Ibs. per sq. in. 

R mre following notes on bricks are from Trautwine’s Engineer’s Pocket- 
ook: 

Strength of Brick.—40 to 300 tons per sq. ft., 622 to 4668 Ibs. per sq. in, 
A soft brick will crush under 450 to 600 lbs. per sg. in., or 80 to 40 tons per 
square foot, but a first-rate machine-pressed brick will stand 200 to 400 tons 
per sq. ft. (3112 to 6224 Ibs. per sq. in.). 

Weight of Bricks,.—Per cubic foot, best pressed brick, 150 lbs.; good 
pressed brick, 131 lbs.; common hard brick, 125 lbs.; good common brick, 
118 lbs.; soft inferior brick, 100 lbs. 

Absorption of Water.—aA brick will in a few minutes absorb 4 to 
34 lb. of water, the last being 1/7 of the weight of a hand-moulded one, or 14 
of its bulk. 

Tests of Bricks, full size, on flat side. (Tests made at Water 
town Arsenal in 1883.)—The bricks were tested betwen flat steel buttresses. 
Compressed surfaces (the largest surface) ground approximately flat. The 
bricks were all about 2 to 2.1 inches thick, 7.5 to 8.1 inches long, and 3.5 ta 
3.76 inches wide. Crushing strength per square inch: One lot ranged from 
11,056 to 16,734 lbs.; a second, 12,995 to 22,351; a third, 10,390 to 12,709. Other 
tests gave results from 5960 to 10.250 lbs. per sq. in. 

Crushing Strength of Masonry Materials. (From Howe's 
* Retaining-Walls.’’) 


tons per sq. ft. tons per sq. ft. 
Brick, best pressed... 40to 300 Limestones and marbles. 250 to 1000 
Chaike tides -.. aca 20to 380 #Sandstone........... epee 200 (09 550 
Granite i... 00d... am 800 to 1200 Soapstone........60-- ---. 400 to 800 


Strength of Granite.—The crushing strength of granite is commonly 
rated at 12,000 to 15,060 lbs. per sq. in. when tested in two-inch cubes, and 
only the hardest and toughest of the commonly used varieties reach a 
strength above 20,000 Ibs. Samples of granite from a quarry on the Con- 


STRENGTH OF LIME AND CEMENT MORTAR. 313 


necticut River, tested at the Watertown Arsenal, have shown a strength of 
85,965 Ibs. per sq. in. (Engineering News, Jan. 12, 1893 ). 

Strength of Avondale, Pa., Limestone—(. Engineering News, 
Feb. 9, 1893).—Crushing strength of 2-in, cubes: light stone 12,112, gray stone 
18,040, Ibs. per sq. in. 

Transverse test of lintels, tool-dr essed, 42 in. between knife-edge bear: 
ings, load with knife-edge brought upon the middle between bearings: 
Gray stone, section 6 in. wide X 10 in. high, broke under a load of S 950 Ibs, 

Modulus of EUIPOUT Coe ce enon Miss aren wat ces enens fs seb gece® Adi Ver tt 

Light stone, section 844 in. wide X 10 in. high, broke under........ ia (20 ia 
Modultig of ruptures f5< side ce else cele ooh slaleiataleleteleists ela'e's's/e/<tcitin Le 170 * 
Absorption.—Gray stone. . +O OS COS SFOSEH SOSH SES ESE OOH OTOH ESSE OEOE .051 of 1% 
TASH SON O sjacctess svs'delsse sc cles eoseresceoerveeeeses oe ee .052 of 1% 


Transverse Strength of Flagging. 
(N. J. Steel & Iron Co.’s Book.) 
EXPERIMENTS MADE BY R. G. HATFIELD AND OTHERS. 


b = width of the stone in inches; d = its thickness in inches; / = distance 
between bearings in inches 

The breaking loads in cone of 2000 Ibs., for a BMRA placed at the centre 
of the space, will be as follows: 





bd2 bd? 

kere x Ta ’. 
Bluestone flagging.............. .744 Dorchester freestone...........  .264 
Quincy granite...) 5..00....-.. .624 Aubigny-freestone.........c.s65 -216 
Little Falls freestone...... aeoae cL Ole Onen ELreeSLONe aa san tele sc aceen 144 
Belleville, N. J., freestone...... 480 Glass..c+.... Goede deapases seanen 1.000 
Granite (another quarry)....... .482 Slate....... woes ss Reset at send e020) 
Connecticut freestone...... AGae AB 


Thus a block of Quincy granite 80 inches wide and 6 inches thick, resting 
on beams 86 inches in the clear, would be broken by a load resting midway 


between the beams = 20 * bd X .624 = 49.92 tons. 





STRENGTH OF aes AND CEMENT MORTAR, 
(Engineering, October 2, 1891.) 


Tests made at the University of Illinois on the effects of adding cement to 
lime mortar. In all the tests a good quality of ordinary fat lime was used, 
slaked for two days in an earthenware jar, adding two parts by weight of 
water to one of lime, the loss by evaporation being made up by fresh addi- 
tions of water. The cemeuts used were a German Portland, Black Diamond 
(Louisville), and Rosendale. As regards fineness of gr inding, 85 per cent of 
the Portland passed through a No, 100 sieve, as did 72 per cent of the Rosen- 
dale. A fairly sharp sand, thoroughly washed and dried, passing through @ 
No. 18 sieve and caught on a No. 30, was used. The mortar in all cases con- 
sisted. of two volumes of sand to one of lime paste. The following results 
were obtained on adding various percentages of cement to the mortar: 


Tensile Strength, pounds per square inch. 





Ne, 4 7 14 21 28 50 84 

Bosses sere Dave. Days.| Days. | Days. Days. Days. Days. 
* Limo mortar® .-.. Stats siete 4 8 10 13 18 21 26 
20 per cent Rosendale..| 5 84 914 12 17 17 18 
2 Portland.. 5 8144] 14 20 25 24 26 
30 ** * Rosendale..{ 7 11 13 1814 21 2216 | 23 
30 as i, sharers a - 16 18 22 25 5 27 
40 ‘ osendale.. 0 12 161 21 2244 | 2 36 
40° “D) sa Portland Ss. ise 39 38° ia 47 59 57 
60." See osendales: 9 13 20 16 22 2214 23 
60. “© fee Portland...;)ai45 58 55 68 7 102 78 
80 “ **  Rosendale..| 12 1814 | 2214 27 29 31144 | 33 
80 ‘ GeieePortland....) 987 91 103 124 94 210 145 
100 *“ ‘ Rosendale..} 18 23 26 31 34 46 48 


100 * ‘ Portland....| 90 1120 | 146 152 181 205 1 202 





$14 : STRENGTH OF MATERIALS. * 


MODULI OF ELASTICITY OF VARIOUS MATERIALS, 

The modulus of elasticity determined from a tensile test of a bar of any 
material is the quotient obtained by dividing the tensile stress in pounds per 
square inch at any point of the test by the elongation per inch of length 
produced by that stress ; or if P = pounds of stress applied, K = the sec- 
tional area, 1 = length of the portion of the bar in which the measure- 
ment is made, and A ae the elongation in that length, the modulus of 


elasticity # =F sitet The modulus is generally measured within the 


elastic limit only, in materials that have a well-defined elastic limit, such as 
iron and steel, and when not otherwise stated the modulus is understood to 
be the modulus within the elastic limit. Within this limit, for such materials 
the modulus is practically constant for any given bar, the elongation being 
directly proportional to the stress. In other materials, such as cast iron, 
which have no well-defined elastic limit, the elongations from the beginning 
of a test increase in a greater ratio than the stresses, and the modulus is 
therefore at its maximum near the beginning of the test, and continually 
decreases. The moduli of elasticity of various materials have already been 
given above in treating of these materials, but the following table gives 
some additional values selected from different sources : 


BYassCastyoa yee wu cesie series 9,170,000 

Fora WAL Os cree o@ sl heehesers ares 14,230,000 
Copperisoniicenes nunc eelen een 15,000,000 to 18,000,000 
head sie Wi ae Py a aE -»- 1,000,000 
in Caste) jaleies esas seniaa’s 4,600,000 
Trompecastie,'s.. 3. csesseas Sahar 3c 12.000,000 to 27,000,000 (?) 
[rOn;  WrOUCHE, «2... save eases 22,000,000 to 29,000,000 (?) 
Steeles. ssa. Ioawwekenen 28,000.000 to 32,000,000 (see below) 
Mea rites as eee ote totes 25,000,000 
DIB tO weed cise siuislecieare ceccles s0 14,500,000 
Glass....... Ue a Nooectics Dearate hg 8,000,000 
TA eee ee oles Dec aeeiatee 1,600,000 
Beeches Poe cs « SEA SHAS AAS 1,300,000 
Birch...) ccc ates ea cictecaste ? (,200,000<to, 1,500,000 
BAL OR Fy Ook A Sa ral Setecee eae 869,000 to 2,191,000 
Oakanede ey k shicleuin cus waebesies 974,000 to 2,288,000 
USTs ees oy Sea alge Pn reg epee ae ‘42. 2,414,000 
Walnut. 29... Sn eee 306,000 


Pine, long-leaf (butt-logs)... 1,119,000 to 3,117,000 Avge. 1,926,000 

The maximum figures given by many writers for iron and steel, viz., 
40,000,000 and 42,000,000, are undoubtedly erroneous. The modulus of elas- 
ticity of steel (within the elastic limit) isremarkably constant, notwithstand- 
ing great variations in chemical analysis, temper, ete. It rarely is found 
below 29,000,000 or above 31,000,000. It is generally taken at 30,000,000 in 
engineering calculations. Prof. J. B. Johnson, in his report on Long-leaf 
Pine, £893, says: *‘The modulus of elasticity is the most constant and reliable 


property of all engineering materials. The wide range of value of the | 


modulus of elasticity of the various metals found in public records must be 
explained by erroneous methods of testing.” 

In a.tensile test of cast iron by the author (Van Nostrand’s Science Series, 
No. 41, page 45), in which the ultimate strength was 23,285 lbs. per sq. in., 
the measurements of elongation were made to .0001 inch, and the modulus 
of elasticity was found to decrease from the beginning of the test, as 
follows: At 1000 Ibs. per sq. in., 25,000,000; at 2000 lbs., 16,666,000; at 4000 
Ibs., 15,384,000 ; at 6000 Ibs., 13,636,000 ; at 8000 lbs., 12,500,000 ; at 12,000 lbs., 
i ygeaae at 15,000 Ibs., 10,000,000; at 20,000 lbs., 8,000,000 ; at 23,000 lbs., 

FACTORS OF SAFETY. 

A factor of safety is the ratio in which the load that is just sufficient to 
overcome instantly the strength of a piece of material is greater than the 
greatest safe ordinary working load. (Rankine.) 

Rankine gives the following ‘‘examples of the values of those factors 
which occur in machines”’: : 

Deadilpad.. Live Load, Live Load, 


Greatest. ~ Mean, 
Iron and steel........ 3 6 ' from 6 to 40 
Timber. i...) «cabanas 4to5 8 to 10 Rete 
Masonry........seee- 4 8 = Bema 4 ) 


° 


FACTORS OF SAFETY. 315 


The great factor of safety, 40, is for shafts in millwork which transmit 
yery variable efforts. 

Unwin gives the following ‘‘ factors of safety which have been.adopted in 
certain cases for different materials.’? They “include an allowance for 
ordinary contingencies.” 

Dead § So ive Load. my 
Load, 22 Temporary In Permanent In Structures 
* Structures. Structures. subj. Seats 





Wrought ironandsteel. 3 4 4to5 

Castdron ..icccccacsGece, 7) Oo 4 5 mlO 
Timber. e2eereee 08088 20988 C8098 4 10 eeoee 
ISTICIGWOVKcaroic aac ecamentes¢ scare 6 AGCE 
DLAGOIN Venegas cows scnces,  eU S006 20 to 30 sade 


Unwin says says that *‘ these numbers fairly represent practice based on 
experience in many actual cases, but they are not very trustworthy.” 

Prof. Wood in his ‘‘ Resistance of Materials’? says: ‘‘In regard to the 
margin that should be left for safety, much depends upon the character of 
the loading. If the load is simply a dead weight, the margin may be com- 
paratively small; but if the structure is to be subjected to percussive forces 
or shocks, the margin should be comparatively large on account of the 
indeterminate effect produced by the force. In machines which are sub- 
jected to a constant jar while in use, it is very difficult to determine the 
proper margin which is consistent with economy and safety. Indeed, in 
such cases, economy as well as safety generally consists in making them 
excessively strong, as a single breakage may cost much more than the extra 
material necessary to fully insure safety.” 

For discussion of the resistance of materials to repeated stresses and 
shocks, see pages 238 to 240. 

Instead of using factors of safety it is becoming customary in designing 
to fix a certain number of pounds per square inch as the maximum stress 
which will be allowed on a piece. Thus, in designing a boiler, instead of 
naming a factor of safety of 6 for the plates and 10 for the stay-bolts, the 
ultimate tensile strength of the steel being from 50,000 to 60,000 lbs. per sq. in., 
an allowable working stress of 10,000 lbs. per sq, in. on the plates and 6600 
lbs. per sq. in. on the stay-bolts may be specified instead. So also in 
Merriman’s formula for columns (see page 260) the dimensions of a column 
are calculated after assuming a maximum allowable compressive stress per 
square inch on the concave side or the column. 

The factors for masonry under dead load as given by Rankine and by Unwin, 
viz., 4 and 20, show aremarkable difference, which may possibly be explained 
as follows: If the actual crushing strength of a pier of masonry is known 
from direct experiment, then a factor of safety of 4 is sufficient fora pier of 
the same size and quality under a steady load; but if the crushing strength 
is merely assumed from figures given by the authorities (such as the crush- 
ing strength of pressed brick, quoted above from Howe’s Retaining Walls, 40 
to 300 tons per square foot, average 170 tons), then a factor of safety of 20 
may be none too great. In this case the factor cf safety is really a ‘‘ factor 
of ignorance.”? 

The selection of the proper factor of safety or the proper maximum unit 
stress for any given case is a matter to be largely determined by the judg- 
ment of the engineer and by experience. No definite rules can be given. 
The customary or advisable factors in many particular cases will be found 
where these cases are considered throughout this book. In general the 
following circumstances are to be taken into account in the selection of 
a factor: 

1. When the ultimate strength of the material is known within narrow 
limits, asin the case of structurai steel when tests of samples have been 
made, when the load is entirely a steady one of a known amount, and there 
is no reason to fear the deterioration of the metal by corrosion, the lowest 
factor that should be adopted is 3. 

2, When the circumstances of 1 are modified by a portion of the load being 
variable, as in floors of warehouses, the factor should be not less than 4, 

3. When the whole load, or nearly the whole, is apt to be alternately out 
on and taken off, as in suspension rods of floors of bridges, the factor should 
be 5 or 6. : 

4, When the stresses are reversed in direction from tension to compres- 
sion, as in some bridge diagonals and parts of machines, the factor should 
be not less than 6, 


816 STRENGTH GF MATERIALS. 


5. When the piece is subjected to repeated shocks, the factor should be 
not less than 10, 

6. When the piece is subject to deterioration from corrosion the section 
should be sufficiently increased to allow for a definite amount of corrosion 
before the piece be so far weakened by it as to require removal. 

7%. When the strength of the material. or the amount of the load, or both 
are uncertain, the factor should be increased by an allowance sufficient te 
cover the amount of the uncertainty. 

8. When the strains are of a complex character and of uncertain amount, 
such as those in the crank-shaft of a reversing engine, a very high factor is 


necessary, possibly even as high as 40, the figure given by Rankine for shafts 
in millwork. 


THE MECHANICAL PROPERTIES OF CORK, 


Cork possesses qualities which distinguish it from all otuer solid or liquid 
bodies, namely, its power of altering its volume in a very marked degree in 
consequence of change of pressure. It consists, practically, of an aggrega- 
tion of minute air-vessels, having thin, water-tight, and very strong walls, 
and hence, if compressed, the resistance to compression rises in a manner 
more like the resistance of gases than the resistance of an elastie solid such 
as a spring. In a spring the pressure increases in proportion to the dis- 
tance to which the spring is compressed, but with gases the pressure in- 
creases in amuch more rapid manner; that is, inversely as the volume 
which the gasis made to occupy. But from the permeability of cork to 
air, it is evident that, if subjected to pressure in one direction only, it will 
gradually part with its occluded air by effusion, that is, by its passage 
through the porous walls of the cells in which it is contained. The gaseous 
part of cork constitutes 58% of its bulk. Its elasticity has not only a very 
considerable range, but it is very persistent. Thus in the better kind of corks 
used in bottling the corks expand the instant they escape from the bottles. 
This expansion may amount to an increase of voluine of 75%, even after the 
corks have heen kept in a state of compression in the bottles for ten years. 
If the cork be steeped in hot water, the volume continues to increase till 
it attains nearly three times that which it occupied in the neck of the bottle. 

When cork is subjected to pressure a certain amount of permanent defor- 
mation or ‘‘permanent set’’'takes place very quickly. This property is 
common to all solid elastic substances when strained beyond their elastic 
limits, but with cork the limits are comparatively low. Besides the perma- 
nent set, there is a certain amount of sluggish elasticity—that is, cork on 
veing released from pressure springs back a certain amount at once, but 
the complete recovery takes an appreciable time. 

Cork which had been compressed and released in water many thousand 
times had not changed its molecular structure in the least, and had contin- 
ued perfectly serviceable. Cork which has been kept under a pressure of 
three atmospheres for many weeks appears to have shrunk to from 80% to 
85% of its original volume.—Van Nostrand’s Eng’g Mag. 1886, xxxv. 307, 


TESTS OF VULCANIZED INDIA-RUBBER. 


Lieutenant L. Viadomiroff, a Russian naval officer, has recently carried 
out a series of tests at the St. Petersburg Technical Institute with a view to 
establishing rules for estimating the quality of vulcanized india-rubber. 
The following, in brief, are the conclusions arrived at, recourse being had 
to physical properties, since chemical analysis did not give any reliable re- 
sult: 1. India-rubber should not give the least sign of superficial cracking 
when bent to an angle of 180 degrees after five hours of exposure ina closed 
air-bath to a temperature of 125° C. The test-pieces should be 2.4 inches 
thick. 2. Rubber that does not contain more than half its weight of metal- 
lic oxides should stretch to five times its length without breaking. 38. Rub- 
ber free from all foreign matter, except the sulphur used in vulcanizing it, 
should stretch to at least seven times its length without rupture. 4. The 
extension measured immediately after rupture should not exceed 12% of the 
original length, with given dimensions. 5. Suppleness may be determined 
by measuring the percentage of ash formed in incineration. This may form 
the basis for deciding between different grades of rubber for certain pur- 

oses. 6. Vulcanized rubber should not harden under cold. These rules 
bas been adopted for the Russian navy.—Jron Age, June 15, 1893. 


XYLOLITH,; OR WOODSTONE 


is a material invented in 1883, but only lately introduced to the trade by 
Otto Serrig & Co., of Pottschappel, near Dresden, It is made of magnesia 


ALUMINUM—ITS PROPERTIES AND USES. ola 


cement, or calcined magnesite, mixed with sawdust and saturated with a 
solution of chloride of caleium. This pasty mass is spread out into sheets 
and submitted to a pressure of about 1000 lbs. to the square inch, and then 
simply dried in the air. Specific gravity 1.5538. The fractured surface shows 
a uniform close grain of a yellow color, It has a tensional resistance when 
dry of 100 lbs. per square inch, and when wet about 66 lbs. When immersed 
Lake for 12 hours it takes up 2.1% of its weight, and 3.8% when imimersed 
216 hours. 

When treated for several days with hydrochloric acid it loses 2.3% in 
weight, and shows no loss of weight under boiling in water, brine, soda-lye, 
and solution of sulphates of iron, of copper, and of ammonium. In hardness 
the material stands between feldspar and quartz, and as a non-conductor of 
heat it ranks between asbestos and cork. 

It stands fire well, and at a red heat it is rendered brittle and crumbles at 
the edges, but retains its general form and cohesion. This xylolith is sup- 
plied in sheets from in. to 1% in. thick, and up to one metre square. It 
is extensively used in Germany for floors in railway stations, hospitals. etc., 
and for decks of vessels. It can be sawed, bored, and shaped with ordinary 
woodworking tools. Putty in the joints and a good coat of paint make it 
entirely water-proof. It is sold in Germany for flooring at about 7 cents per 
square foot, and the cost of laying adds about 4 cents more.—Eng’g News, 
July 28, 1892, and July 27, 1893. 


ALUMINUM—iITS PROPERTIES AND USES. 
(By Alfred E, Hunt, Pres’t of the Pittsburgh Reduction Co.) 


The specific gravity of pure aluminum in acast state is 2.58; in rolled 
bars of large section it is 26; in very thin sheets subjected to high com- 
pression under chilled rolls, itis as much as 2.7. Taking the weight of a 
given bulk of cast aluminum as 1, wrought iron is 2.90 times heavier 3; struc- 
tural steel, 2.95 times ; copper, 3.60 3; ordinary high brass, 3.45. Most wood 
suitable for use in structures has about one third the weight of aluminum, 
which weighs 0.092 lb. to the cubic inch. 

Pure aluminum is practically not acted upon by boiling water or steam. 
Carbonic oxide or hydrogen sulphide does not act upon it at any tempera- 
ture under 600° F. It is not acted upon by most organic secretions. 

Hydrochloric acid is the best solvent for aluminum, and strong solutions 
of caustic alkalies readily dissolve it. Ammonia has a slight solvent action, 
and concentrated sulphuric acid dissolves aluminum upon heating, with 
evolution of sulphurous acid gas. Dilute sulphuric acid acts but slowly on 
the metal, though the presence of any chlorides in the solution allow rapid 
decomposition. Nitric acid, either concentrated or dilute, has very little 
action upon the metal, and sulphur has no action unless the metal is at ‘a red 
heat. Sea-water has very little effect on aluminum. Strips of the metal 
placed on the sides of a wooden ship corroded less than 1/1000 inch after six 
months’ exposure to sea-water, corroding less than copper sheets similarly 

laced. 

4 In malleability pure aluminum is only exceeded by gold and silver. In 
ductility it stands seventh in the series, being exceeded by gold, silver, 
platinum, iron, very soft steel, and copper. Sheets of aluminum have been 
rolled down toa thickness of 0.0005 inch, and beaten into leaf nearly as 
thin as gold leaf. The metal is most malleable at atemperature of between 
400° and 600° F., and at this temperature it can be drawn down between 
rolls with nearly as much draught upon it as with heated steel. It has also 
been drawn down into the very finest wire. By the Mannesmann process 
aluminum tubes have been made in Germany. 

Aluminum stands very high in the series as an electro-positive metal, ang 
ee with other metals should be avoided, as it would establish a galvanic 
couple. 

The electrical conductivity of aluminum is only surpassed by pure copper, 
silver, and gold. With silver taken at 100 the electrical conductivity of 
aluminum is 54.20; that of gold on the same scale is 78; zinc is 29.90; iron is 
only 16, and platinum 10.60. Pure aluminum has no polarity, and the 
metal in the market is absolutely non-magnetic. 

Sound castings can be made of aluminum in either dry or ‘‘ green ”’ sand 
moulds, or in metal ‘‘chills.”> It must not be heated much beyond its 
melting-point, and must be poured with care, owing to the ready absorption 
of occluded gases and air. The shrinkage in cooling is 17/64 inch per foot, 
or a little more than ordinary brass. It should be melted in plumbayo 
crucibles, and the metal becomes molten at a temperature of 1120° F. ac- 
cording to Professor Roberts-Austen, or at 1:300° I’. according to Richards, 


318 : STRENGTH OF MATERIALS, 


The coefficient of linear expansion, as tested on 83-inch round aluminungy 
rods, is 0.00002295 per degree centigrade between the freezing and boiling 
point of water. The mean specific heat of aluminum is higher than that of 
any other metal, excepting only magnesium and the alkali metals. From 
zero to the melting-point it is 0.2185; water being taken as 1, and the latent 
heat of fusion at 28.5 heat units. The coefficient of thermal conductivity of 
unannealed aluminum is 87.96; of annealed aluminum, 38.37. As a conductor 
of heat aluminum ranks fourth, being exceeded only by silver, copper, and 

old. 

‘ Aluminum. under tension, and section for section, is about as strong as 
cast iron. The tensile strength of aluminum is increased by cold rolling or 
cold forging, and there are alloys which add considerably to the tensile 
strength without increasing the specific gravity to over 3 or 3.25. 

The strength of commercial aluminum is given in the following table as 
the result of many tests : 


Elastic Limit Ultimate Strength Percentage 
per sq. in. in per sq. in. in of Reduct’n 
Form. Tension, Tension, of Area in 
Ibs. lbs. Tension. 
Castings ....25 cescsecs 6,500 15,000 15 
DMCC tesick Gale wielere wlercie 12,000 24,000 85 
Wire. .....20e.00+e008 16,000-30,000 80,000-65,000 60 
TABR Wo lsiiasois es stele ele 4,000 28,000 40 


The elastic limit per square inch under compression in cylinders, with 
length twice the diameter, is 3500. The ultimate strength per square inch 
under, compression in cylinders of same form is 12,000. The modulus of 
elasticity of cast aluminum is about 11,000,000. It is rather an open metal in 
its texture, and for cylinders to stand pressure an increase in thickness must 
be given to allow for this porosity. Its maximum shearing stress in castings 
is about 12,000, and in forgings about 16,000, or about that of pure copper. 

Pure aluminum is too soft and lacking in tensile strength and rigidity for 
many purposes. Valuable alloys are now being made which seem to give 
great promisefor thefuture, They are alloys containing from 2% to 7% or 8% 
of copper, manganese, iron, and nickel. As nickel is one of the principal. 
constituents, these alloys have the trade name of ‘‘ Nickel-aluminum.”’ 

Plates and bars of this nickel alloy have a tensile strength of from 40,000 to 
50,000 pounds per square inch, an elastic limit of 55% to 60% of the ultimate ten- 
sile strength, an elongation of 20% in 2 inches, and a reduction of area of 252. 

This metal is especially capable of withstanding the punishment and 
distortion to which structural material is ordinarily subjected. Nickel-— 
aluminum alloys have as much resilience and spring as the very hardest of 
hard-drawn brass. 

Their specific gravity is about 2.80 to 2.85, where pure aluminum has a 
specific gravity of 2.72. 

In castings, more of the hardening elements are necessary in order to give 
the maximum stiffness and rigidity, together with the strength and ductility 
of the metal; the favorite alloy material being zine, iron, manganese, and 
copper. Tin added to the alloy reduces the shrinkage, and alloys of alumi- 
num and tin can be made which have less shrinkage than east iron. 

The tensile strength of hardened aluminum-alloy castings is from 20,000 
to 25,000 pounds per square inch. 

Alloys of aluminum and copper form two series, both valuable. The 
first is aluminum-bronze, containing from 5% to 1114% of aluminum; and the 
second is copper-hardened aluminum, containing from 2% to 15% of copper. 
Aluminum-bronze is a very dense, fine-grained, and strong alloy, having goud 
ductility as compared with tensile strength. The 10% bronze in forged bars 
will give 100,000 lbs. tensile strength per square inch, with 60,000 lbs. elastic 
limit per square inch, and 10% elongation in 8inches. The 5% to 714% bronze 
has a specific gravity of 8 to 8.30, as compared with 7.50 for the 10% to 1114% 
bronze, a tensile strength of 70,000 to 80.000 lbs., an elastic limit of 40,000 
lbs. per square inch, and an elongation of 30% in 8 inches. 

Aluminum is used by steel manufacturers to prevent the retention of the 
occluded gases in the steel, and thereby produce a solid ingot. The propor: 
tions of the dose range from 4% lb. to several pounds of aluminum per ton of 
steel. Aluminum is also used in giving extra fluidity to steel used in castings, 
making them sharper and sounder. Added to east iron, aluminum causes 
the iron to be softer, free from shrinkage, and lessens the tendency to “ chill.” 

With theexception of lead and mercury, aluminum unites with all metals, 


ALLOYS. 319 


though {it unites with antimony with great difficulty. A small percentage 
of silver whitens and bardens the metal, and gives it added strength; and 
this alloy is especially applicable to the manufacture of fine instruments 
and apparatus. The fcllowing alloys have been found recently to be useful 
in the arts: Nickel-aluminum, composed of 20 parts nickel to 80 of aluminum; 
rosine, made of 40 parts nickel, 10 parts silver, 30 parts aluminum, and 20 
parts tin, for jewellers’ work; mettaline, made of 35 parts cobalt, 25 parts 
aluminum, 10 parts iron, and 30 parts copper. The aluminum-bourbounz 
metal. shown at the Paris Exposition of i889, has a specific gravity of 2.9 to 
2.96, and can be cast in very solid shapes, as it has very little shrinkage. 
From analysis the following composition is deduced: Aluminum, 85.74%; tin, 
12.94%; silicon, 1.82%; iron, none. 

The metal can be readily electrically welded, but soldering is still not sat- 
isfactory. The high heat conductivity of the aluminum withdraws the heat 
of the molten solder so rapidly that it ‘‘ freezes’ before it can flow suffi- 
ciently. A German solder said to give good results is made of 80% tin to 20% 
zine, using a flux composed of 80 parts stearic acid, 10 parts chloride of 
zinc, and 10 parts of chloride of tin. Pure tin, fusing at 250° C., has also 
been used as a solder. The use of chloride of silver as a fiux has been 
patented, and used with ordinary soft solder has given some success. A 
pure nickel soldering-bit should be used, as it does not discolor aluminum 


as copper bits do. 
ALLOYS. 


ALLOYS OF COPPER AND TIN. 
(Extract from Report of U. S. Test Board.*) 

















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26 | 0. 100. 3, 005s see eemhnoor pl 3.740] $* 6,400° 12 J 557 


* The tests of the alloys of copper and tin and of copper and zine, the re- 
sults of which are published in the Report of the U. S. Board appointed te 
test Iron, Steel, and other Metals, Vols. T and II, 1879 and 1881, were made 
by the author under direction of Prof. R. H. Thurston, chairman of the 
Committee on Alloys. See preface to the report of the Committee, in Val. J. 


320 ALLOYS. 


Nos. 1a and 2 were full of biow-holes. 

Tests Nos. 1 and 1@ show the variation in cast copper due to varying cor- 
ditions of casting. In the crushing tests Nos. 12 to 20, inclusive, crushed and 
broke under the strain, but all the others bulged and flattened out. In these 
gases the crushing strength is taken to be that which caused a decrease of 
10% in the length. The test-pieces were 2 in. long and 54 in. diameter. The 
torsional tests were made in Thurston’s torsion-machine, on pieces 9% in. 
diameter and 1 in. long between heads. 

Specific Gravity of the Copper-tin Alloys.—The specific 
gravity of copper, as found in these tests, is 8.874 (tested in turnings from 
the ingot, and reduced to 39.1° F.). The alloy of maximum sp. gr. 8.956 
contained 62.42 copper, 37.48 tin, and all the alloys containing less than 387% 
tin varied irregularly in sp. gr. between 8.65 and 8.93, the density depending 
not on the composition, but on the porosity of the casting. It is probable 
that the actual sp. gr. of all these alloys containing less than 87% tin is about 
8.95, and any smaller figure indicates porosity in the specimen. 

From 37% to 100% tin, the sp. gr. decreases regularly from the maximum of 
8.956 to that of pure tin, 7.293. 


Note on the Strength of the Copper-tin Alloys. 


The bars containing from 2% to 24% tin, inclusive, have considerable 
strength, and all the rest are practically worthless for purposes in which 
strength is required. The dividing line between the strong and brittle alloys 
is precisely that at which the color changes from golden yellow to silvere 
white, viz., at acomposition containing between 24% and 30% of tin. 

It appears that the tensile and compressive strengths of these alloys are 
in no way related to each other, that the torsional strength is closely pro- 
portional to the tensile strength, and that the transverse strength may de- 
pend in some degree upon the compressive strength, but it is much more 
nearly related to the tensile strength. The modulus of rupture, as obtained 
by the transverse tests, is, in general, a figure between those of tensile and 
compressive strengths per square inch, but there area few exceptions in 
which it is larger than either. 

The strengths of the alloys at the copper end of the series increase rapidly 
with the addition of tin till about 4% of tin is reached, The transverse 
strength continues regularly to increase to the maximum, till the alloy con: 
taining about 1714% of tin is reached, while the tensile and torsiona! 
strengths also increase, but irregularly, to thesame point. This irregularity 
is probably due to porosity of the metal, and might possibly be removed by. 
any means which would make the castings more compact. The maximum 
is reached at the alloy containing 82.70 copper, 17.34 tin, the transverse 
strength, however, being very much greater at this point than the tensile 
or torsional strength. From the point of maximum strength the figures 
drop rapidly to the alloys containing about 27.5% of tin, and then more slowly 
to 37.5%, at which point the minimum (or nearly the minimum) strength, by 
all three methods of test, is reached. The alloys of minimum strength are 
ce from 37.5% tin to 52.5% tin. The absolute minimum is probably about 
45% 0 tin. 

From 52.5% of tin to about 77.5% tin there is a rather slow and irregular in. 
crease in strength. From ‘7.5% tin to the end of the series, or all tin, the 
strengths slowly and somewhat irregularly decrease. 

The results of these tests do not seem to corroborate the theory given by 
some writers, that peculiar properties are possessed by the alloys which 
are compounded of simple multiples of their atomic weights or chemical 
equivalents, and that these properties are lost as the compositions vary 
more or less from this definite Constitution. It does appear that a certain 
percentage composition gives a maximum strength and another certain 
percentage a minimum, but neither of these compositions is represented by 
simple multiples of the atomic weights. 

There appears to be a regular law of decrease from the maximum to the 
minimum strength which does not seem to have any relation to the atomic 
proportions, but only to the percentage compositions. 

Hardmness.—tThe pieces containing less than 24% of tin were turned in 
the lathe without difficulty, a gradually increasing hardness being noticed, 
ue Jest eed giving a very short chip, and requiring frequent sharpening 
of the tool. 

With the most brittle alloys it was found impossible to turn the test-pieces 
in the lathe to a smooth surface. No. 13 to No. 17 (26.85 to 84.47 tin) could 
not be cut with a tool at all, Chips would fly off in advance of the too! and 


ALLOYS OF COPPER AND ZINC. 321 


beneath it, leaving a rough surface; or the tool would sometimes, apparently, 
crush off portions of the metal, grinding it to powder. Beyond 40% tin the 
hardness decreased so that the bars could be easily turned. 


ALLOYS OF COPPER AND ZINC, (U.S. Test Board). 


Elastic} xs Torsional 


j geome ;| Trans- |S 
Mean Com- Limit | ¢ ¥ ms ; Tests. 
position by| Tensile | % of 24 Tost ak F Wee % ea a 
} 7 =, » Ge 
No. Analysis. Strength, Preak a5 Modu! 3 ao Str’gth Ke E of 38 
q. to: Toad) sc lus of 2 Stee ae ea ae to 
pa Zine Ibs. per|—"" eas Bs in., Ibs. eae cas 
sq. in . 
MEO TAOO] Mite Ool et elect) 6l casts sclipctnl aes cic arasteotiess Se Lon eson 
2 | 82.93] 16.98] 382,600 201s NW2Gecb i eogkoe Went aoeess came oo 829 
3 | 81.91] 17.99) 32,670 80.6 |31.4) 21,198 Ly meaiees 166 345 
4 | 77.39] 22.45) 35,630 20.0 135.5] 25,3874 28 ee LOO 811 
5 | 76.65] 28.08) 30,520 24.6 135.8) 22,825 *e 42,000 | 165 267 
6 | 73.20) 26.47) 31,580 23.7 138.5} 25,894 $8 st Be toes Sor 68 293 
% | 71.20] 28.541 30,510 | 29.5 [29.2] 24.468 | * vesee| 164 | 269 
8 | 69.74] 80.06) 28,120 28.7% 20.7] 26,980 34 avete ete 143 202 
9 | 66.27] 83.50) 37,800 25.1 137.7] 28,459 st oe tee Vee ao 257 
10 | 63.44] 36.36) 48,800 82.8 {31.7| 43,216 Se PTE 202 230 
<1 | 60.94] 88.65} 41,065 40.j |2u.%| 38,968 sé 45,000 | 194 202 
13 | 58.49] 41.10) 50,450 64.4 110.1] 63,804 SP ay | eh ee 227 93 
13 | 55.15] 44.44) 44,280 44.0 |15.c} 42,463 ef 78,000 | 209 109 
14 | 54.86] 44.78] 46,400 53.9 8.0} 47,955 oe ee ere Pa: 23 G2 
15 | 49.66} 50.14] 30,990 54.5 5.0] 83,467 | 1.26 | 117,400] 172 38 
16 | 48.99} 50.82) 26,050 100. O18) 440.1898 2026 oe). eck 176 16 
17 | 47.56{ 52.28] 24,150 100 0.8; 48,471 | 1.17 | 121,000) 155 13 
18 | 43.86) 56.22 9,170 |} 100. SVEN GOI OS OM ES ouiR 88 2 
19 | 41.80) 58.12 8,727 100. Weies Wee Ole | OSO42 lam we oct 18 2 
20 | 32.94) 66.23 1,774 100. sooo} 8,296 | 0.04 mae’ 29 1 
21 | 29.20) 70.17 6,414 100. eeee} 16,579 | 0.04 Aarti 40 2 
22 | 20.81) 77.63 9,000 100. 0.2] 22,972 | 0.18 | 52,152 65 1 
93 | 12.12} 86.67) 12,4138 100. 02415 35;026 | O81 te. se. 82 3 
4 4.35] 94.59] 18,065 100. O25 2651627 | O46h ee eee 81 22 
25 | Cast!Zine. 5.400 CDi 0.71 7,589 ! 0.12 | 22,000 37 142 


Variation in Strength of Gun-bronze, and Means of 
Improving the Strength.—tThe figures obtained for alloys of from 
7.8% to 12.7% tin, viz., from 26,869 to 29,430 pounds, are much less than are 
usually given as the strength of gun-metal. Bronze guns are usually cast 
under the pressure of a head of metal, which tends to increase the strength 
and density. Thestrength of the upper part of a gun casting, or sinking 
head, is not greater than that of the small bars which have been tested in 
these experiments. The following is an extract from the report of Major 
Wade concerning the strength and density of gun-bronze (1850):—HKxtreme 
variation of six samples from different parts of the same gun (a 32-pounder 
howitzer): Specific gravity, 8.48% to 8.835; tenacity, 26,428 to 52,192, Extreme 
variation of all the samples tested: Specific gravity, 8.308 to 8.850; tenacity, 
23,108 to 54,531. Extreme variation of all the samples from the gun heads: 
Specific gravity, 8.308 to 8.756; tenacity, 23,529 to 35,484, 

Major Wade says: The general results on the quality of bronze as it is 
found in guns are mostly of a negative character, They expose defects in 
density and strength, develop the heterogeneous texture of the metal in dif- 
ferent parts of the same gun, and show the irregularity and uncertainty of 
quality which attend the casting of all guns, although made from s.milar 
inaterials, treated in like manner. 

Navy ordnance bronze containing 9 parts copper and 1 part tin, tested at 
Washington, D.C.,in 1875-6, showed a variation in tensile strength from 
29.800 to 51,400 lbs. per square inch, in elongation frcm 8% to 58%, and in spe- 
cifie gravity from 8.39 to 8.88, 

That a great improvement may be made in the density and tenacity of 
gun-vronze by compression has been shown by the experiments of Mr.58. B. 
Dean in Boston, Mass., in 13869, and by those of General Uchatius in Austria 
in 1873. The former increased the density of the metal next the bore of the 
gun from 8.321 to 8.875, and the tenacity from 27,238 to 41,471 pounds per 


S22 


ALLOYS. 


square inch. The latter, by a similar process, obtained the following figures 


for tenacity: 


Pounds per sq. in, 


Bronze with 10¢ tints. .pecrass oeaccewslectc oo te el ee 
Bronze, WALLIS LIM cceniee close lele cs eeistiaeemiiele e- 73,958 
Bronze with 6% tin,..acse) cccececrsse.crscccces $4,000 


ALLOYS OF COPPER, TIN, AND ZINC. 
(Report of U. S. Test Board, Vol. II, 1881.) 














Analysis, 
No. Original Mixture, 
in ee a 
Report. 
Cu. | Sn, | Zn. 

G2 90 5 

5 88.14); 1.86) 10 
"0 85 5 10 
71 85 10 5 
89 85 1250 2.5 
88 82.5) 112.5 5 
C7 82200 lo 2.5 
67 80 5 15 
68 80 10 10 
69 80 15 5 
86 77.5 1) 10 12.5 
87 Wied, \eleeaal 0 
63 is) 5 20 
85 5 G51 17.5 
64 5 10 15 
65 "5 15 10 
66 vis) 20 5 
83 (285 Ws 20 
84 72.5) 10 V5 
59 70 5 25 
8&2 40 7.5 | 22.5 
60 70 10 20 
61 ri 15 15 
62 vi 20 10 
81 67.5 |} 2.5 [7380 
74 67.5 5 AY bef3) 
vis) 67.5 7.5 1 25 
80 65 2.5 | 32.5 
55 65 5 30 
56 65 10 25 
57 65 15 20 
58 65 20 15 
79 62.5 2.5 | 385 

4 60 2.0 Meo 
52 60 5 35 
53 60 10 30 
54 60 15 25 
12 58.22} 2.30) 39.48 

3 58.7 8.45| 82.5 

4 OCsD jaeleecolmel eo 
73 ys) eoriEda > 
50 55 5 40 
51 55 10 35 
49 50 5 45 


Transverse 
Strength. 
Modulus] Deflec- 

of ion, 
Rupture} jns. 
41,334 | 2.68 
31,986 3 67 
44,457 | 2.85 
62,47 2.56 
62,405 | 2.83 
6°,960 | 1.61 
69,045 1.09 
42,618 | 38.88 
67,117 2.45 
54,476 44 
63,849 | 1.19 
67,705 B71 
55,300 2.91 
62,607 | 1.39 
58,345 Bie} 
51,109 sol 
40,235 wel 
51,839 | 2.86 
53,230 74 
57,349 | 1.37 
48,836 .36 
36,520 | .18 
387,924 20 
15,126 .08 
58,343 | 2.91 
55,976 49 
46,875 232 
56,049 2.36 
51,369 56 
27,075 14 
18,591 07 
11,932 | 05 
69,255 | 2.34 
69,508 | 1.46 
46,076 .28 
24,699 nel 
18,248 -09 
95,623 | 1.99 
30,752 .18 
2,752 .02 
72.308 | $8.05 
88,174 128 
28,258 .14 
20,814 11 








Tensile Elongation 
Strength per per cent in 
square inch. 5 inches. 

A, yep A, B, 
23,660 | 80,740 | 2.34 9.68 
82,000 | 83,000 | 17.6 19.5 
28,840 | 28,560 | 6.80 5.28 
35,680 | 86,000 | 2.51 2°25 
34,500 | 82,800 | 1.29 2°99 
86,000 | 34,000 .86 .92 
83.600) 983,800) a sneees 68 
87,560 | 32,300 } 11.6 3.59 
82,830 | 81,950 | 1.57 1.67 
82,350 | 380;760 s DG 44 
35,500 | 36,000 | 1.00 1.00 
36,000 | 32,500 503 .59 
33,140 | 34,960 | 2.50 | 3.19 
33,700 | 39,300 | 1.56 1.53 
35,320 | 34,000 | 1.18 | 1.25 
35,440 | 28,000 59 54 
23,140 | 27,660 “4570 BS Pa 
82,700 | 84,800 | 38.7! 3.7 
80,000 | 30,000 -48 .49 
38,000 | 82,940 | 2.06 .99 
38,000 | 22,400] 84 .40 
83,140 | 26,300 oH bat IACI oA 
33,440 | 27,800 P26 Sasa a 
17,000 | 12,900} .08 |....... , 
34,720 | 45.850 | 7.27 3.09 
84,000 | 34,460 1.06 243 
29,500 | 30.000 .36 .26 
41,350 | 38,800 | 8.26 38.02 
87,140 | 86,000 | 1.21 61 
25.720 | 22,500 015 19 

6,820 4,231 snipiece.e | metete ete - 
3,765 2, G60") aesiee Pe eae oe 
44,400 | 45,000 | 2.15 2.19 
57,400 | 52,900 | 4.87 8.02 
41,160 | 38,330 .39 46 
21,780 | 21,240 015 copter 
185020 "| 124005 | ete ieee : 
66,500 | 67,600 3.13 3.15 
Broke Bee tiest; ver|y brittle 
725 B00) || Paawemee ties tet 
68,900 | 68,900 | 9.48 2.88 
27,400 | 30,500 46 .43 
25,460 | 18,500 29 -10 
23,000 | 31,800 -66 45 





The transverse tests were made in bars 1 in. square, 22 in. between sup. 


ports. The tensile tests were made on bars 0.798 in. diam. turned from the 


two halves of the trans 


other B. 


verse-test bar, one half being marked «4 and the 


ee | 


ALLOYS OF COPPER, TIN, AND ZINC. 323 


Ancient Bronzes.—The usual composition of ancient bronze was the 
same as that of modern gun-metal—90 copper, 10 tin; but the proportion of 
tin varies from 5% to 15%, and in some cases lead has been found. Some ane 
cient Egyptian tools contained 88 copper, 12 tin. 

Strength of the Copper-zine Alloys.—the alloys containing less 
than 15% of*zine by original mixture were generally defective. The bars 
were full of blow-holes, and the metal showed signs of oxidation. To insure 
(phn it appears that copper-zine alloys should contain more than 

of zinc. 

From No. 2 to No. 8 inclusive, 16.98 to 80.06% zine the bars show a remark- 
able similarity in all their properties. They have all nearly the same 
strength and ductility, the latter decreasing slightly as zinc increases, and 
are nearly alike in color and appearance. Between Nos. 8 and 10, 30.06 and 
36.36% zine, the strength by all methods of test rapidly increases. Between 
No. 10 and No, 15, 36.36 and 50.14% zinc, there is another group, distinguished 
by high strength and diminished ductility. The alloy of maximum tensile, 
transverse and torsional strength ec Untains about 41% of zine. 

The alloys containing less than 55% of zinc are all yellow metals. Beyond 
55% the color changes to white, and the alloy becomes weak and brittle. Be- 
tween 70% and Bre zinc the color is bluish gray, the brittJeness decreases 
and the strength increases, but not to such a degree as to make them useful 
for constructive purposes. 

Difference between Composition by Mixture and by 
Analysis,—There is in every case a smaller percentage of zine in the 
average analysis than in the original mixture, and a Jarger percentage of 
copper. The loss of zinc is variable, but in guneral averages from 1 to 2%. 

Liquation or Separation of the Metals.—In several of the 
bars a considerable amount of liquation took place, analysis showing a 
difference in composition of the two ends of the bar. In such cases the 
change in composition was gradual from one end of the bar to the other, 
the upper end in general containing the higher percentage of copper. A 
notable instance was bar No. 13, in the above table, turnings from the upper 
end containing 40.36% of zinc, and from the lower end 48.522. 

Specific Gravity.—The specific gravity follows a definite law. varying 
with the composition, and decreasing with the addition of zinc. From the 
plotted curve of specific gravities the following mean values are taken: 


Percent zinc....es00e O 10 20 380 40 50 60 %0 80 90 100, 
Specific gravity....... 8.80 8.72 8.60 8.40 8.36 8.20 8.00 7.72 7.40 7.20 7.14. 


Graphic Representation of the Law of Variation of 
Strength of Copper=-Tin-Zine Alloys.—In an equilateral triangle 
the sum of the perpendicular distances from any point within it to the three 
sides is equal to the altitude. Such a triangle can therefore be used to 
show graphically the percentage composition of any compound of three 
parts, such as a triple alloy. Let one side represent O copper, a second 
0 tin, and the third 0 zinc, the vertex opposite each of these sides repre- 
senting 100 of each element respectively. On points in a triangle of wood 
representing different alloys tested, wires were erected of lengths propor- 
tional to the tensile strengths, and the triangle then built up with plaster te 
the height of the wires. The surface thus formed has a characteristic 
topography representing the variations of strength with variations of 
composition. The cut shows the surface thus made. The vertical section 
to the left represents the Jaw of tensile strength of the copper-tin alloys, 
the one to the right that of tin-zinc alloys, and the one at the rear that of 
the copper-zine alloys. The high point represents the strongest possible 
alloys of the three metals, Its composition is copper 55, zinc 43, tin 2, and its 
strength about 70,000 lbs. The high ridge from this point to the point of 
maximum height of the section on the left is the line of the strongest alloys, 
represented by the formula zine + (8 X tin) = 55. 

All alloys lying to the rear of the ridge, containing more copper and less 
tin or zine are alloys of greater ductility than those on the line of maximum 
strength, and are the valuable commercial alloys; those in front on the decliv- 
ity toward the central valley are brittle, and those in the valley are both brit- 
tle and weak. Passing from the valley toward the section at the right the 
alloys lose their brittheness and become soft, the maximum softness being 
at tin = 100, but they remain weak, as is shown by the low elevation of the 
surface. This model was planned and constructed by Prof. Thurston in 
1877. (See Trans. A. £. C. E. 1881 Report of the U. S. Board appointed to 


324 ALLOYS. 


test Tron, Steel, ete., vol. if., Washington, 1881, and Thurston’s Materiats 
of Engineering, vol. fii.) : 

The best alloy obtained in Thurston's research for the U. S. Testing Board 
has the composition, Copper 55, Tin 0.5, Zine 44.5. The tensile strength in a 
cast bar was 68,900 lbs. per sq. in., two specimens giving the same result; the 
elongation was 47 to 51 per cent in S5inches, Thurston’s formula for copper- 
tin-zinc alloys of maximum strength (Trans. A. S. C. K.. 1881) is ¢-+ 3¢ = 55, 






Me DZ 


Fic. %7. 


in which z is the percentage of zinc and ¢ that of tin. Alloys proportioned 
according to this formula should have a strength of about 40,000 Ibs. 
per sq. in. +500z. The formula fails with alloys containing less than 1 per 
cent of tin. 

The following would be the percentage composition of a number of alloys 
ale according to this formula, and their corresponding tensile strength in 
castings $ 


Tongue ar eeeue 
Tin, Zine. Copper. ae ee Tin. Zinc, Copper. he bee 

sq. in. sq. in. 
1 52 47 66,000 s 31 61 55,500 
2 49 49 64,500 9 28 63 54,000 
3 46 61 63,000 10 25 65 52,500 
4 43 53 61,500 12 19 69 49,500 
5 40 55 60,000 14 13 3 46,500 
6 87 57 58,500 16 v4 G7 43,500 
7 84 59 57,000 18 1 81 40,506 


These alloys. while possessing maximum tensile strength, would in general 
be too hard for easy working by machine tools. Another series made on 
the formula z 4+-4 ¢ = 50 would have greater ductility, together with con- 
siderable strength, as follows, the strength being calculated as before, 
fanativ strength in lbs, per sq, in, s 40,000 |- 600g, 


ALLOYS OF COPPER, TIN, AND ZING B25 


arene. Tensile 
Tin, Zinc. Copper. Re aS Tin. Zinc. Copper. Neer eee 

Sq. in. sq. in, 

1 46 53 63,000 ? 22 71 51,000 

2 42 56 61,000 8 18 %4 49,000 

3 38 59 59,000 9 14 Yee 47,000 
4 384 62 57,000 10 10 80 45,000 
5 380 65 55,000 11 6 83 45,000 
6 26 68 53,000 12 2 86 41,000 


Composition of Alloys in Every-day Use in Brass 
Foundries. (American Machinist.) (See also p. 203.) 








per. Zine.| Tin. |Lead. 


.j———} ————— —— | —___—— |... 





Admiralty metal. .} 87% 5 8 |......jFor parts of engines on board 


naval vessels. 
Bell metal.........} 16 |......] 4  |......|Bells for ships and factories. 


Brass (yellow).....| 16 oma Beseisety avs For plumbers, ship and house 
brass work. 
Bush metal......] 64 8 4 4 |For bearing bushesfor shafting. 
Gun metal......... 82 1 3 |......|For pumpsand other hydraulic 
purposes. 
Steam metal.......[ 20 1 1144} 1 |Castings subjected to steam 
pressure. 
Hard gun metal...} 16 |...... 214 |......|For heavy bearings. 
Muntz metal....... 60 GOs Pome sacl oes see Metal from which bolts and nuts 
are forged,valve spindles, etc. 
Phosphor bronze..| 92 {......| 8 phos. tinjFor Me Mie pumps and general 
work. 
“* o 4.1 90 }.. ...]10 * ‘|For cog and worm wheels, 


bushes, axle bearings, slide 
valves, etc. 
Brazing Pep eate Fat 016 8 j......]......|Flanges for copper pipes. 
Pe esolders. 50 BOY) Peas peeicae Solder for the above flanges. 


Gurley’s Bronze.—16 parts copper, 1 tin, 1 zine, 4 lead, used by 
W.& L. KE. Gurley of Troy for the framework of their engineer’s transits, 
Tensile strength 41,114 lbs, per sq. in., elongation 27% in 1 inch, sp. gr. 8.696, 
(W. J. Keep, Trans. A. 1. M. E. 1890.) 

Useful Alloys of Copper, Tin, and Zinc. 
(Selected from numerous sources.) 
Copper. Tin, Zine, 





U. S. Navy Depts journal poneete =| 6 1 14 parts. 

ANG Ulde-C1Setiee cece cies 82.8 13.8 8.4 per cent, 
Tobin bronze....-... Dee c ese tes Ce ROO eonem eo DOMOoL4Oe eo) ass 
Naval brass.. . Mbaceerinbhase Wz 1 37 “ 
Composition, US. ‘Navy.. aomodadodoo: tals) 7 2 Sh Te Ne 
Brass bearings (J. Rose)...secccccess ier 11.0 1 3 rere 
Gun mie talanches chet cant eceoneee nae 92.5 

he os ee ecereoveeeocsest® eeeeeeee | 91 v¢ of de Le 
. ee eee ° ereeeeee  ee280088 8088 87.75 9.75 2.5 #6 ne 
.* se REE WGA ee ey. eee 85 5 10 Ge < 
ba das Si 3 fa fe cere S15 
P 1 2 arts, 
Tough brass for engines.....cc.cesce 113 5 ig 11.7 Hee cent. 
Bronze for rod-boxes (Lafond).,..... 82 16 2 slightly malleable, 
te 06 pieces ei to shock.. 83 15 1.50 0.50 lead. 
Redtbrassied. 502s. Oe eee _ parts 20 1 1 1 WV 
a SGPEe at Sh Sees per cent 87 4.4 SS dD ee 
Bronze for pump casings (Lafond)... 88 10 2 
“  ** eccentric straps. “ 84 14 4 A 
«shrill whistles....... 80 18 vese a4 antimony, 


ae low-toned whistles....... 81 1? soe’ Ry 


326 ALLOYS. 


Copper. Tin, Zine. 

Art bronze, dull red fracture..ccosss. 97 2 1 

Gold DGONZENetas acuietee sites te ceeee'e 89.5 2.1 5.6 2.8 lead. , 
Bearing metal ......eesescceeeeeerees 89 3 ’ 


8 
ceeh cbaagteuedcepeh ssl 00 Memes PEE ole 


he sé eecerceeeoeeoeeeeeeeeee608 4 ereuw 
$ “ @eeeeeeeoeorveeeeee +++ 2008 8514 1234 2 
i ee @eeeseeoeeeeegoaeeeeerv ese 80° ae av, 141 ad 
C eres eee- ee ee eeeee ee ee. ea ° 
etter ETS RES eg GOMGe Chae © lead 
English brass of a.p, 1504............ 64 8 2914 314 lead. 


Tobin Bronze.—This alloy is practically a sterro or delta metal with 
the addition of a small amount of lead, which tends to render copper softer 
and more ductile. (F. L. Garrison, J. #’. J., 1891.) 

The following analyses of Tobin bronze were made by Dr. Chas. B, Dudley: 


Pig Metal, Test Bar (Rolled). 





per cent. per cent. 
WOPPELEesiescioecites seciees ce cees eoccee 59.00 61.20 
PAIN seo COC CHOCO HOSS CORSO OLOSCES SF eS2808 88.40 87.14 
Wie aeAae CO COHOKRT OHS ECEHEHTTLEHS LEH LOO OES 16 0.90 
Tron.... PeCSSe SECO OOS SEES SESS s Bee F822 OEE 0.12 0.18 
TCA vcsc. ci edccecccsccscetsce cee ceca 0.31 0.35 


Dr Dudley writes, ‘‘ We tested the test bars and found 78,500 tensile 
strength with 15% elongation in two inches, and 4014% in eight inches. This 
high tensile strength can only be obtained when the metal is manipulated. 
Such high results could hardly be expected with cast metal.” 

The original Tobin bronze in 1875, as described by Thurston, Trans. 
A. S. C. E 1881, had, composition of copper 58,22, tin 2.380, zinc 3948. As 
cast it had a tenacity of 66,000 lbs. per sq. in., and as rolled 79,000 Ibs.; cold 
rolled it gave 104,000 Ibs. 

A circular of Ansonia Brass & Copper Co. gives the following :—The tensile 
strength of six Tobin bronze one-inch round rolled rods, turned down to a 
diameter of 5g of an inch, tested by Fairbanks, averaged 79,600 lbs. per sq. 
in., and the elastic limit obtained on three specimens averaged 54,257 lbs. per 
sq. in. 

At acherry-red heat Tobin bronze can be forged and stamped as readi!y 
as steel. Bolts and nuts can be forged from it, either by hand or by ma-~ 
chinery, with a marked degree of economy. Its great tensile strength, and 
resistance to the corrosive action of sea-water, render it a most suitable 
metal for condenser ee steam-launch shafting, ship sheathing and | 
fastenings, nails, hull plates for steam yachts, torpedo and life boats, and 
ship deck fittings. 

The Navy Department has specified its use for certain purposes in the 
machinery of the new cruisers. Its specific gravity is 8.071. The weight of 
a cubic inch is .291 lb. : 


Special Alloys. (Engineer, March 24, 1893.) 
JAPANESE ALLoys for art work: 


Copper. | Silver. Gold. Lead. Zine. Iron. 























ee | 








—a22 


Shaku-do...... 94.50 1.55 3.73 0.11 trace. trace. 
Shibu-ichi. .... 67.31 82.07 traces. Roe 


GILBERT’s ALLoy for cera-perduta process, for casting in plaster-of-paris. 
Copper 91.4 ‘Vin 5.7 Lead 2.9 Very fusible. 


COPPER-ZiINC-IRON ALLOYS. 
(F. L. Garrison, Jour. Frank. Inst., June and July, 1891.) 


Delta Metal.—This alloy, which was formerly known as sterro-metal, 
is composed of about 60 copper, from 34 to 44 zinc, 2 to 4 iron, and 1 'to 2 tin. 

The peculiarity of all these alloys is the content of iron, which appears to 
have the property of increasing their strength to an unusual degree. In 
making delta metal the iron is previously alloyed with zinc in known and 
definite proportions. When ordinary wrought-iron is introduced into 
molten zinc, the latter readily dissolves or absorbs the former, aud will take 


PHOSPUOR-BRONZE AND OTHER SPECIAL BRONZES, 327 


it up.to the extent of about &% or more. By adding the zinc-iron alloy thus 
obtained to the requisite amount of copper, it is possible to introduce any 
definite quantity of iron up to 5% into the copper alloy. Garrison gives the 
following as the range of composition of copper-zinc-iron, and copper-zine- 
tin-iron alloys: 


: Il, 
Per cent. Per cent: 
POM srescicelas sacs ects ave.’ 0.1 to5 NOM Socsie: oa he ee eo Be 0.1 to 5 
TODD CL leg. o.a.ce sue steele s 50 to 65 UT Tiare ore ra atvie etels (ajereye ole Bate 0.1 to 10 
NOP ok pees Tease cts ns tose LOU VANE Sea tay ME ee OO Or: 1.8 to 45 
COP PEMicgis stay dite sicjeheisies 98 to 40 


The advantages claimed for delta metal are great strength and toughness. 
It produces sound castings of close grain. It can be rolled and forged hot, 
and can stand a certain amount of drawing and hammering when cold. It 
panes a high polish, and when exposed to the atmosphere tarnishes less than 

rass. 

When cast in sand delta metal has a tensile strength of about 45,000 pounds 
per square inch, and about 10% elongation ; when rolled, tensile strength of 
60,000 to 75,000 pounds per square inch, elongation from 9% to 17% on bars 1.128 
inch in diameter and 1 inch area. 

Wallace gives the ultimate tensile strength 33,600 to 51,520 pounds per 
square inch, with from 10% to 20% elongation, 

Delta metal can be forged, stamped and rolled hot. It must be forged at 
ries cherry-red heat, and care taken to avoid striking when ata black 

eat. 

According to Lloyd's Proving House tests, made at Cardiff, December 20, 
1887, a half-inch delta metal-rolled bar gave a tensile strength of 88,400 
pounds per square inch, with an elongation of 80% in three inches. 

PHOSPHOR-BRONZE AND OTHER SPECIAL 
BRONZES. 

Phosphor-bromze.—in the year 1868, Montefiore & Kunzel of Liége, 
Belgium, found by adding small proportions of phosphorus or ‘‘ phosphoret 
of tin or copper’’ to copper that the oxides of that metal, nearly always 
present as an impurity, more or less, were deoxidized and the copper much 
improved in strength and ductility, the grain of the fracture became finer, 
the color brighter, and a greater fluidity was attained. 

Three samples of phosphor-bronze tested by Kirkaldy gave: 


Elastic limit, Ibs. per sq. in ....... 23,800 24,700 16,100 
Tensile strength, lbs. persq. in.... 52,625 46,100 44.448 
Hlongation, per cent........<..... - 8.40 1.50 83.40 


The strength of phosphor-bronze varies like that of ordinary bronze 
according to the percentages of copper, tin, zine, lead, ete., in the alloy. 

Weoxidized Bronze.—tThis alloy reseinbles phosphor bronze some- 
what in composition and also delta metal, in containing zinc and iron. The 


Coppers... 2.4% er auea ee ObN ELON E tsBil va a ets'sae. cue Cur iid 
Pint hires obdaAcoo lonsdabse eee, DIVE saree he we ecess 1 0.00 
ZINC ies ot elton ce elecse cere 3.23 Phosphorus......... 0.005 
Lead Simemeee sr ccitcss cscs cole 





100.615 


Comparison of Copper, Silicon-bronze, and Phosphore 
bronze Wires. (Higineering, Nov. 23, 1833.) 














Description of Wire. Tensile Strength. (Relative Conductivity. 
PureiCOPPOLr. nus eaceiatnsis steters 39,827 lbs. per sq. in. 100 per cent. Fs" 
Silicon bronze (telegraph)..... 41-G9GueS Sony) bon 1S 96) So tes 

ee ‘* (telephone)..... 1OSS0 80m re tie ess oy $ 34, Sees 
Phosphor bronze (telephone)... }102,390 “ “% “ + 2OVes: “° 








Penn. 'R. R. Co.’s Specifications for Phosphor-Bronze 
(1902).—The metal desired is homogeneous‘alloy of copper, 79.70: tin. 10.003 
Jead, 9.50; phosphorus, 0.80. Lots will not be accepted if samples do not 
show tin, between 9 and 11%; lead, between 8 and 11%; phosphorus, between 
9.7 and 1%; nor if the metal contains a sum total of other substances than 
oes BL} lead, and phosphorus in greater quantity than 0,50 per cent. (Sea 

SO p, d3¢, 


~ 


328 ALLOYS. 


Silicon Bronze. (Aluminum World, May, 1897.) 


The most useful of the silicon bronzes are the 3% (97% eopper, 3% silicon’ 
and the 5% (95% copper, 5% silicon), although the hardness and strength of 
the alloy can be increased or decreased at will by increasing or decreasing 
silicon. <A 8% silicon bronze has a tensile strength, in a casting, of about 
55,000 lbs. per sq. in., and from 50% to 60% elongation. The 5% bronze has a 
tensile strength of about 75,000 lbs. and about 8% elongation. More than 5% 
or 54% of silicon in copper makes a brittle alloy. In using silicon, either as 
a flux or for making silicon bronze, the rich alloy of silicon and copper 
which is now on the market should be used. It should be free from iron 
and other metals if the best results are to be obtained. Ferro-silicon is not 
suitable for use in copper or bronze mixtures. 


ALUMINUM ALLOYS, 
Aluminum Bronze. (Cowles Electric Smelting and Al. Co.’s circular.) 

The standard A. No, 2 grade of aluminum bronze, containing 10% of alumi- 
num and 90% of copper, has many remarkable characteristics which dis- 
tinguish it from all other metals. 

The tenacity of castings of A No. 2 grade metal varies between 75,000 and 
90,000 lbs. to the square inch, with from 4% to 14% elongation. 

Increasing the proportion of aluminum in bronze beyond 11% produces a 
brittle alloy; therefore nothing higher than the A No. 1, which contains 11%, 
is made, 

The B, C, D, and E grades, containing 714%, 5%, 2l4z%, and 114% of alumirum, 
respectively, decrease in tenacity in the order named, that of the former 
being about 65,000 pounds, while the latter is 25,000 pounds. While there is 
also a proportionate decrease in transverse and torsional strengths, elastic 
limit, and resistance to compression as the percentage of aluminum is low- 
ered and that of copper raised, the ductility on the other hand increases in 
the same proportion. The specific gravity of the A No. 1 grade is 7.56. 

Bell Bros., Newcastle, gave the specific gravity of the aluminum bronzes 


as follows: 
8%, 8.691; 4%, 8.6213 5%, 8.369; 10%, 7.689, 
Tests of Aluminum Bronzes, 
(By John H. J. Dagger, in a paper read before the British Association, 1889.) 
Tensile Strength, 





Per cent Elonga- : 
SIMCOE PTE TTT) ERBGDRTTET DLS : Specific 
Al of Tons per Pounds per tion, Gravity. 
‘pete square inch.| squareinch, | Per cent. 
Deve esc gecee cen eat 40 to 45 89,600 to 100,800 8 7.23 
LO Saisie oie waedicrecnte 33 ** 40 73,920 ** 89,600 14 7.69 
WG vorechelels cveiste sue cits 25 ** 30 56,000 ** 67,200 40 8.00 
5-545..... Anddnaddicas LOeSE1S 33,600 ** 40,320 40 8.37 
rey eKare'eh oie alo lives pea ts) 29,120 ** 33,600 50 8.69 
VS ea 11°13 = | 24.640 “ 29-120 55 A 





Both physical and chemical tests made of samples cut from various sec - 
tions of 214%, 5%, 714%, or 10% aluminized copper castings tend to prove that 
the aluminum unites itself with each particle of copper witb uniform pro- 
portion in each case, so that we have a product that is free from liquation 
and highly homogeneous. (R. C. Cole, Iron Age, Jan. 16, 1890.) 

Casting.—The melting point of aluminum bronze varies slightly with 
the amount of aluminum contained, the higher grades melting at a some- 
what lower temperature than the lower grades. The A No. 1 grades melt 
at about 1700° F., a little higher than ordinary bronze or brass. 

Aluminum bronze shrinks more than ordinary brass. As the metal solidi- 
fies rapidly it is necessary to pour it quickly and to make the feeders amply 
large, so that there will be no ‘freezing’ in them before the casting is 
properly fed. Baked-sand moulds are preferable to green sand, except for 
small castings, and when fine skin colors are desired in the castings. (See 
paper by Thos. D. West, Trans. A. S. M. E. 1886, vol. viii.) 

All grades of aluminum bronze can be rolled, swedged, spun, or drawn 
cold except Aland A2, They can all be worked at a bright red heat. 

In rolling, swedging, or spinning cold, it should be annealed very often, and | 
at a brighter red heat than is used for annealing brass. 

Brazing.—Aluminum bronze will braze as well as any other metal, 
using one quarter brass solder (zinc 500, copper 500 (and three quarters 
borax, or, better, three quarters cryolite. 


ALUMINUM ALLOYS. 329 


Soldering.—To solder aluminum bronze with ordinary soft (pewter) 
solder: Cleanse well the parts to be joined free from grease and dirt. Then 
place the parts to be soldered in a strong solution of sulphate of copper and 
place in the bath a rod of soft iron touching the parts to be joined. After 
a while a coppery-like surface will be seen on the metal. Remove from 
bath, rinse quite clean, and brighten the surfaces. These surfaces can then 
be tinned by using a fluid consisting of zinc dissolved in hydrochloric acid, in 
the ordinary way, with common soft solder. 

Mierzinski recommends ordinary hard solder, and says that Hulot uses 
an alloy of the usual half-and-half lead-tin solder, with 12.5%, 25% or 50% of 
zinc amalgam. te 

Aluminum-Brass (E. H. Cowles, Trans. A. I. M. E., vol. xviiij— 
Cowles aluminum-brass is made by fusing together equal weights of A 1 
aluminum-bronze, copper, and zinc. The copper and bronze are first thor- 
oughly melted and mixed, and the zinc is finally added, The material is left 
in the furnace until small test-bars are taken from it and broken. When 
these bars show a tensile strength of 80,000 pounds or over, with 2 or 3 per 
cent ductility, the metal is ready to be poured. Tests of this brass, on small 
bars, have at times shown as high as 100,000 pounds tensile strength. 

The screw of the United States gunboat Petrel is cast from this brass, 
mixed with a trifle less zinc in order to increase its ductility. 


Tests of Aluminum-Brass, 
(Cowles E. S. & Al. Co.) 





Tensile | Elastic 





Diameter Lae . ~~ |Hlonga- 
Specimen (Castings.) | of Piece, ees pirene ly tena tion. |Remarks. 
Teh q. in.| lbs. per S. Pel! perc 
. sq. In. sq. In. 
15% A grade Bronze. 2 a0 
AE AVANICON Sat oe eter 465 .1698| 41,225 17,668 | 4114 oo oe 
68% Copper. ........+ robes 
i part A Bronze.... ) Yodo 
Tyan ZN. si pas, 465 |. 109G tue vot ae gate. 244 | $a $= 
1 part Copper.. ese aes 
1 part A Bronze.... ) ae og 
PIATRA Co ns a.s.0)5 460 S1GG]* |e saeA Gy yet h eon 244 | 828 
1 part Copper.. .. ( ae 


mmm s  0P te , Pa Dt ee I cre ee ne eee eee 

The first brass on the above list is an extremely tough metal with low 
elastic limit, made purposely so as to “ upset’’ easily. The other, which is 
called Aluminum-brass No 2, is very hard. 

We have not in this country orin England any official standard by which 
to judge of the physical characteristics of cast metals. There are two con- 
ditions that are absolutely necessary to be known before we can make a 
fair comparison of different materials: namely, whether the casting was 
made in dry or green sand orin achill, and whether it was attached toa 
larger casting or cast by itself. It has also been found that chill-castings 
give higher results than sand-castings, and that bars cast by themselves 
purposely for testing almost invariably run higher than test-bars attached 
to castings. Itisalsoa fact that bars cut out from castings are generally 
weaker than bars cast alone, (EK. H. Cowles.) 

Caution as to Reported Strength of Alloys.—The same 
variation in strength which has been found in tests of gun-metal (copper 
and tin) noted above. must be expected in tests of aluminum bronze and in 
fact of all alloys. They are exceedingly subject to variation in density and 
in grain, caused by differences in method of molding and casting, tempera- 
ture of pouring, size and shape of casting, depth of ‘*‘ sinking head,” ete, 


Aluminum Hardened by Addition of Copper. 
Rolled Sheets .04 inch thick. (The Engineer, Jan. 2, 1891.) 


Tensile Strength 


Al. Cu. Sp. Gr. Sp. Gr. in pounds per 
Per cent. Per cent. Calculated. Determined, square inch, 
100 ° idea 2.67 26.535 


330 % ALLOYS. 


Tests of Aluminum Alloys. 
(Engineer Harris, U.S. N., Trans. A. I. M. E., vol. xviii.) 





Composition. Tensile |Elastic Reduce: 
Fa pete a Strength, Hast biel tion of 
op- umi-| ass, P ‘ per sq. in.|lbs per Ae |p ATeAn 
per. | num. Silicon.| Zine. | Iron. lpg. sq. in. | Pe? ct. per et. 
91 50%) 6.50%) 1.75% |. cece. 0.25% | 60,700 | 18,000 | 28.2 30.7 
88.50 9.33 AGO Pe sotGoal| - (Ub 66,000 27,000 3.8 7.8 
91.50 6.50 SOR | ater 0.25 67,600 | 24,000} 13. 21.62 
90.00 9.00 DSOOM IP SRD Se PEE Be 72,830 | 33,000 2.40 5.7 
63.00 3.33 OVS3 2) |*832383% |e... 82,200 60,000 2.33 9.88 
63.00 3.33 Ol SO PSS. Saws Ws 70,400 | 55,000 0.4 4.33 
91.50 6.50 DECSE RUGS PU 0.25 59,100 | 19,000} 15.1 23.59 
93.00 6.50 O50 el eos ite | OL: 53,000 | 19,000 6.2 15.5 
88.50 9.33 1 OOre WS. stor 0.50 69,930 | 33,000 1.33 3.30 
92.00 6.50 GON? PMI Lee oe 46,530 | 17,000 7.8 19.19 





For comparison with the above 6 tests of ‘‘ Navy Yard Bronze,” Cu 88, 
Sn 10, Zn 2, are given in which the T.S. ranges from 18,000 to 24,590, E. L. 
from 10.000 to 18,000, El. 2.5 to 5.8%, Red. 4.7 to 10.89, 


Alloys of Aluminum, Silicon and Iron. 


M. and E. Bernard have succeeded in obtaining through electrolysis, by 
treating directly and without previous purification, the aluminum earths 
(red and white bauxites) the following : 

Alloys such asferro-aluminum, ferro-silicon-aluminum and silicon-alumi- 
num, where the proportion of silicon may exceed 10% which are employed 
in the metallurgy of iron for refining steel and cast-iron. 

Also silicon-aluminum, where the proportion of silicon does not exceed 
10%. which may be employed in mechanical constructions in a rolled or 
hammered condition, in place of steel, on account of their great resistance, 
especially where the lightness of the piece in construction constitutes one 
of the main conditions of success. 

The following analyses are given: 

1. Alloys applied to the metallurgy of iron, the refining of steel and cast 
iron: No. 1. Al, 70%; Fe, 25%; Si, 5%. No. 2. Al, 70; Fe, 20; Si, 10. No.3. Al, 
70; Fe, 15; Si, 15. No.4. Al, 70; Fe, 10; Si, 20. No.5. Al, 70; Fe, 10; Si, 10; 
Mn, 10. No. 6. Al. 70; Fe, trace; Si,+0; Mn, 10. 

2. Mechanical alloys: No. 1. Al, 92; Si, 6.75; Fe, 1.25. No.2. Al, 90; Si. 
9.25; Fe, 0.75. No. 8. Al, 90; Si, 10; Fe, trace. The best results were with 
alloys where the proportion of iron was very low, and the proportion of 
silicon in the neighborhood of 10%. Above that proportion the alloy be- , 
comes erystalline and can no longer be employed. The density of the alloys 
of silicon is approximately the same as that of aluminum.—La Metallurgie, 

92: 


Tunesten and Aluminum,.—Mr. Leinhardt Mannesmann says that 
the addition of a little tungsteiu to pure aluminum or its alloys communi- 
cates a remarkable resistance to the action of cold and hot water, salt 
water and other reagents. When the proportion of tungsten is sufficient 
the alloys offer great resistance to tensile strains. 

Aluminum, Copper, and 'Fim.—Prof. R. C. Carpenter, Trans. 
A.S.M.E., vol. xix., finds the following alloys of maximum strength ina 
series in which two of the three metals are in equal proportions: 

Al, 85; Cu, 7.5; Sn, 7.5; tensile strength, 30,000 lbs. per sq. in.; elongation 
in 6 in, 4%: sp. gr., 3.02. Al, 6.25; Cu, 87.5; Sn, 6.25; T.S., 63,000; El., 3.8; 
sp. gr., 735. Al, 5; Cu, 5: Sn, 90; T. S., 11,000; El., 10.1; sp. gr., 6.82. 

Aluminum and Zime.—Prof. Carpenter finds that the strongest 
alloy of these metais consists of two parts of aluminum and one part of zine. 
Its tensi.e strength is 24,000 t. 26,000 lbs. per sq. in.; has but little ductility, 
s readily cut with machine-tools, and is a good substitute for hard cast 

rass. 

Aluminum and Tin.—M. Bourbouze bas compounded an alloy of 
aluminum and tiv, by fusing together 100 parts of the fone with 10 parts 
of the latter. This alloy is paler than aluminum, and has a specific gravity 
of 2.85, The alloy is not as easily attacked by several reagents as alumi- 


ALLOYS OF MANGANESE AND COPPER. 331 


num is, and it can also be worked more readily, Another advantage is that 
. can be soldered as easily as bronze, without further preliminary prepara< 
ons. 

Aluminum-Antimony Alloys.—Dr. C. R. Alder Wright describes 
some aluminum-antimony alloys ina communication read before the Society 
of Chemical Industry. The results of his researches do not disclose the 
existence of a commercially useful alloy of these two metals, and have 
greater scientific than practical interest. A remarkable point is that the 
alloy with the chemical composition Al Sb has a higher melting point than 
either aluminum of antimony alone, and that when aluminum is added to 
pure antimony the melting-point goes up from that of antimony (450° C.) 
to a certain temperature rather above that of silver (1000° C.). 


ALLOYS OF MANGANESE AND COPPER, 


Various Manganese Alloys.—E. H. Cowles, in Trans. A. I. M. E., 
vol. xviii, p. 495, states that as the result of numerous experiments on 
mixtures of the several metals, copper, zinc, tin, lead, aluminum, iron, and 
manganese, and the metalloid silicon, and experiments upon the same in 
ascertaining tensile strength, ductility, color, etc., the most important 
determinations appeat to be about as follows: 

1. That pure metallic manganese exerts a bleaching effect upon copper 
more radical in its action even than nickel. In other words, it was found 
that 1814% of manganese present in copper produces as white a color in the 
resulting alloy as 25% of nickel would do, this being the amount of each 
required to remove the last trace of red. 

2. That upwards of 20% or 25% of manganese may be added to copper with- 
out reducing its ductility, although doubling its tensile strength and chang- 
ing its color. 

3. That manganese, copper, and zinc when melted together and poured 
into moulds behave very much like the most ‘ yeasty’? German silver, 
producing an ingot which is a mass of blow-holes, and which swells up 
above the mould before cooling. 

4. That the alloy of manganese and copper by itself is very easily 
oxidized. 

5. That the addition of 1.25% of aluminum to a manganese-copper alloy 
converts it from one of the most refractory of metals in the casting process 


' into a metal of superior casting qualities, and the non-corrodibility of which 


is in many instances greater than that of either German or nickel silver. 

A ‘‘silver-bronze”’ alloy especially designed for rods, sheets, and wire 
has the following composition : Manganese, 18; aluminum, 1.20; silicon, 0.5 ; 
zine, 13; and copper, 67.5%. It has a tensile strength of about 57,000 pounds 
on small bars, and 20% elongation. It has been rolled into thin plate and 
drawn into wire .008 inch in diameter. A test of the electrical conductivity 
of this wire (of size No. 82) shows its resistance to be 41.44 times that of pure 
copper. This is far lower conductivity than that of German silver. 

Wanganese Bronze. (Ff. L. Garrison, Jour. F.1., 1891.)—This alloy 
has been used extensively tor casting propeller-blades. Tests of some made 
ty B. H. Cramp & Co., of Philadelphia, gave an average elastic limit of 
80,000 pounds per square inch, tensile strength of about 60,000 pounds per 
square inch, with an elongation of 8% to 10% in sand castings. When rolled, 
the elastic limit is about 80,000 pounds per square inch, tensile strength 
95,000 to 106,000 pounds per square inch, with an elongation of 12% to 152. 

Compression tests made at United States Navy Department from the 
metal in the pouring-gate of propeller-hub of U.S. S. Maine gave in two tests 
a crushing stress of 126,450 and 135,750 lbs. per sq. in. The specimens were 
1 inch high by 0.7 X_0.7 inch in cross-section = 0.49 square inch. Both speci 
mens gave way by shearing, on a plane making an angle of nearly 45° with 
the direction of stress. 

A test on a specimen 1 X 1 X 1 inch was made from a piece of the same 

ouring-gate. Under stress of 150,000 pounds it was flattened to 0.72 inch 

igh by about 114 x 114 inches, but without rupture or any sign of distress. 

One of the great objections to the use of manganese bronze, or in fact 
any alloy except iron or steel, for the propellers of iron ships is on account 
of the galvanic action set up between the propeller and the stern-posts. 
This difficulty has in great measure been overcome by putting strips of 
rolled zine around the propeller apertures in the stern-frames. 

The following analysis of Parsons’ manganese bronze No. 2 was made 
from a chip from the propeller of Mr. W. K. Vanderbilt’s yacht Alva. 


332 TR A ALLOYS. 





CODPeh sweet seeceredeees hel ie false SAO S AHS OSr os bore ... 88.644 
ZINC ete se es Bae terctrer state aTelcte eve erthostie etctale hectare Ste aes hen 1.570 
Lilt soerecyavioleie nie Ne aioregeieva.s vk’ ob Late etiets oie eatele. sg eeerals ae 8.700 
EVOn Seca cote cents’: von bse dan take onate cheer mete ec ore 0.720 
TRC AA ctie corre siete ee Cee ree nae eRe et 0.295 
IPHOSPNOTUSE cen eee et See ie ror RAL See ceric trace 

99.929 


It will be observed there is no manganese present and the amount of zine 
is very small. 

E. H. Cowles, Trans. A. I. M. E., vol. xviii, says: Manganese bronze, so 
called, is in reality a manganese brass, for zine instead of tin is the chief 
element added to the copper. Mr. P. M. Parsons, the proprietor of this 
brand of metal, has claimed for it a tensile strength of from 24 to 28 tons on 
small bars when cast in sand. Mr. W.C. Wallace states that brass-founders 
of high repute in England will not admit that manganese bronze has more 
than from 12 to 17 tons tensile strength. Mr. Horace See found tensile 
strength of 45,000 pounds, and from 6% to 1214% elongation. 


GERMAN-SILVER AND OTHER NICKEL ALLOYS. 


German Silver.—The composition of German silver is a very uncertain 
thing and depends largely on the honesty of the manufacturer and the 
price the purchaser is willing to pay. It is composed of copper, zinc, and 
nickel in varying proportions. The best varieties contain from 18% to 25% of 
nickeland from 20% to 30% of zine, the remainder being copper. The more 
expensive nickel silver contains from 25% to 33% of nickel and from 75% to 66% 
of copper. The nickel is used as a whitening element; it also strengthens 
the alloy and renders it harder and more non-corrodible than the brass 
made without it, of copper and zine. Of all troublesome alloys to handle in 
the foundry or rolling-mill, German silver is the worst. It is unmanageable 
and refractory at every step in its transition from the crude elements into 
rods, sheets, or wire. (EK. H. Cowles, Trans. A. I. M. E., vol. xviii. p. 494.) 


Copper. Nickel. Tin. Zine. 

German’ silver... c.0 cc senesiv cle ee 51.6 25.8 22.6 ricteed 
ih: eb dversitole beatinatie nee niet. 50.2 14.8 3.1 31.9 

he Soe titties ceowacn ase cies 51.1 13.8 3.2 31.9 
he Neiidse'ss eis cece ster iices 52 to 55 18 tO 25) eee 20 to 30 
Nickel BARNA 5 aecdsn ‘oer Set bO-00 26 tO S30 ser 1. 6 enn eres 


A refined copper-nickel alloy containing 50% copper and 49% nickel, with 
very small amounts of iron, silicon and carbon, is produced direct from 
Bessemer matte in the Sudbury (Canada) Nickel Works. German silver 
manufacturers purchase a ready-made alloy, which melts at a low heat and 
requires simple addition of zinc, instead of buying the nickel and copper 
separately. This alloy, ‘‘50-50°’ as it is called, is almost indistinguishable 
from pure nickel. Its cost is less than nickel, its melting point much lower, 
it can be cast solid in any form desired, and furnishes a casting which works 
easily in the lathe or planer, yielding a silvery white surface unchanged by 
air or moisture. For bullet casings now used in various British and conti- 
nental rifles, a special alloy of 80% copper and 20% nickel is made. 


Copper. Nickel. Zine. 
@HINGSE_PACKTONS, cc cscccecce coe cene 4Uc4 31, 4 6.5 parts. 
CRMMCEULILEN Seer ts otto sisic- teers c seisuee site 8 6.5 ‘ 
GerinanesiVe eases’ «ccrces cececesenne 1 1 % 
a MMMACHOADCL).\ cc chee ones 8 2 3.5 ds 
t “ (closely resembles sil). 8 3 3.5 ee 


ALLOYS OF BISMUTH. 


By adding a small amount of bismuth to lead that metal may be hard- 
ened and toughened. An alloy consisting of three parts of lead and two of 
bismuth has ten times the hardness and twenty times the tenacity of lead. 
The alloys of bismuth with both tin and lead are extremely fusible, and 
take fine impressions of casts and moulds. An alloy of one part bismuth, 
two parts tin, and one part lead is used by pewter-workers as a soft solder, 
and by soap-makers for moulds, An alloy of five parts bismuth, two parts 
tin, and three parts lead melts at 199° F , and is somewhat used fot ster- 
eotyping, and for metallic writing-pencils. Thorpe gives the following 
proportions for the better-known fusible metalas 





vo 


BEARING-METAL ALLOYS. 339 
ve ‘ Cad- | Mer- Melting- 

Name of Alloy. Bismuth.) Lead. | Tin. | vim cury. point, 
NGWLOL Sacce ness Rates 50 BLD [alist Oltes cereal tee fee 202oe EH . 
OSE.S. jatescee SP RBG SOND 50 OBral Que ah | eis eel meseiceds OBR? «Me 
DArcet’s..... Ge op sig tis paaets 50 25.00 | 25.00 ae 201e aS 
D’Arcet’s with mercury. 50 20.00 20. 00a... aH) KO abplps te 2 Be 
WHOOUS Stace fee ecole 50 OOO tal aU] lia os) eee oral wey en 
LADO WIZ See. ee en eee 50 26.90 felseco| Loca Oawenta |e tao moe 

Guthrie's ‘‘ Entectic’’... 50 20.55 | 21.10] 14.03]......|‘* Very low.” 


The action of heat upon some of these alloys is remarkable. Thus, Lipo- 
witz’s alloy, which solidifies at 149° Fah., contracts very rapidly at first, as 
it cools from this point. As the cooling goes on the contraction becomes 
slower and slower, until the temperature falls to 101.3° Fah. From this 
point the alloy expands as it cools, until the temperature falls to about 77° 
Fah., after which it again contracts, so that at 32° F. a bar of ths alloy has 
the same length as at 115° F. ; 

Alloys of bismuth have been used for making fusible plugs for boilers, but 
it is found that they are altered by the continued action of heat, so that one 
cannot rely upon them to melt at the proper temperature. Pure Banca tin 
is used by the U. S. Government for fusible plugs. 


KFUSIBLE ALLOYS. (From various sources.) 


Sir Isaac Newton’s, bismuth 5, lead 8, tin 2, melts at................. 212° FF, 
mosewe bismuth 27lead 1; tin 1, melts atesss7 ss. om aan ne eelneee ok 200° ** 
Wood’s, cadmium 1, bismuth 4, lead 2, tin 1, melts at................. 165 “* 
Guthrie’s, cadmium 13.29, bismuth 47.38, lead 19.36, tin 19.97, melts at. 160 ‘‘ 
Lead 3, tin 5, bismuth 8, melts at........... SeaNaerarcrehiiraten wre RGA Sete 0G ee 
Lead 1, tin 3, bismuth 5, melts at..... Peta archcvaye tiers 7 aoe Ne crektens tet niente Paley 
Meadetatiie+, DISmUth:D. Melati sestreee acti alercierelerer- Be 2s Citic aero ae 240 ‘ 
Mind wisnauthy 1 MMe|lts At 17s. seca. seme nomic ce leals: rarely otalcie athe s cetceesttomoe Ouees 
Weadieutin Ss. melts at. i Vigeeste Peet sacle we rec wletsteeleteiwnctaeasistean eee tenoOdmes 
Tint Ombisimu ch: 1) MCLLS ACs sores sare Miele vteretste otaletciercialetote¥atafelsFeVal Sielsjtene eee O50 ee 
Lead Ttini2amelts: atic clic ies sss cis oie Stelerere ale lehavere cate staleletetsiereretetene cletuairee OOO nes 
Tin §, bismuth 1,-mel{s at... 5. voce ss a cecre Pee adecugcdee vse hoes cree ooetes 
(meada2ehin 1, melts ab cUe anew sen ord See devel he's creda Keema aiee Ree ata gse 
ew delenitied, MIClES AL. Aor seine seis otsie tlotetere sis wielnioreisie sisal steletarsaris aieicrsietestels 466 “ 
WGA Weeti i 35, ICIS Abie wecae seceded sisi set lelees sicecls cuisiecs sales ates Oodvie 
Linee iy Lo epaoe he We Boaale hice hint Gocied foc c UGcib OS UO DO IOAEOOHOCROR TIO Boe eee e OO oie 
Lead ti bismuth 1; melts ata. tess. Malet Sa tantevsteits oieis sleieiese ofc care cts ey 
Lead 1, Tin 1, bismuth 4, melts at...... Me islole cteie\elotatniaia oiaia ciererascicteljeve centers oO Lana 
Wend oO. tin 3. DISMULDISAMVeLtStat Artec ete ivicisicleveloicis eles ae iesacu tele oceanic ee US uy 
Poinvo. DISMUth 5, WrelGSia.bowecsats oelerce sehatelee Saharan ee icroce oer steno are oO: te 


BEARING-“METAL ALLOYS. 
(C. B. Dudley, Jour. F. I., Feb. and March, 1892.) 


Alloys are used as bearings in place of wrought iron, cast iron, or steel, 
partly because wear and friction are believed to be more rapid when two 
metals of the same kind work together, partly because the soft metals are 
more easily worked and got into proper shape, and partly because it is de- 
sirable to use a soft metal which will take the wear rather than a hard 
metal, which will wear the journal more rapidly. 

A good bearing-metal must have five characteristics: (1) It must be strong 
enough to carry the load without distortion. Pressures on car-journals are 
frequently as high as 850 to 400 Ibs. per square inch. 

(2) A good bearing-metal should not heat readily. The old copper-tin 
hearing, made of seven parts copper to one part tin, is more apt to heat 
than some other alloys. In general, research seems to show that the harder 
the bearing-metal, the more likely it is to heat. 

(8) Good bearing-metal should work well in the foundry. Oxidation while 
melting causes spongy castings. It can be prevented by a liberal use of 
powdered charcoal while melting. The addition of 1% to 2% of zincor a 
small amount of phosphorus greatly aids in the production of sound cast: 
ings. This is a principal element of value in phosphor-bronze, 


334 — ALLOYS. 


(4) Good bearing metals should show small friction. It is true that friction 
is almost wholly a question of the lubricant used; but the metal of the bear- 
ing has certainly some influence. 

re Other things being equal, the best bearing-metal is that which wears 
slowest. 

The principal constituents of bearing-metal alloys are copper, tin, lead, 
zinc, antimony, iron, and aluminum, The following table gives the constitu- 
ents of most of the prominent bearing-metals as analyzed at the Pennsyl- 
vania Railroad laboratory at Altoona, 


Analyses of Bearing-metal Alloys. 




















Cop- . : Anti- 
Metal. per. Tin. }Lead.| Zine.| ony, Iron. 
Camelia metal........ Rayboncuwee NQ.20) 1 4.25|" 1475) 10220), on oe 0.55 
Anti-friction metal...........4-. ileG0, TOS. Lolacntcalsceren Eeeeee trace 
IWiHTILGIMGUALaaseticas scree sisicieietie Iuecerisce  aacieists fei aah Mose 12-08 1] poe ee 
Car-brass lining. fe AIDA horbater arte trace] 84.87) ..... HE (Pl Pra ere, 
Salgee anti-friction............. 4.00.4 0.91). 1510) 85.0% hoa, wash eee oe 
Graphite bearing-metal..... Pet beta 14.38) 67.73) ,..... 16.73 Peres 
Antimonial lead........ Leeeeie eis il eee eco BA | wel shee SO GOs ecek 1S. Soe ene 
Carbon <bronzesccic. ces lesiss «=> (O24 [Det e|e 14.04 lias wee | tee cee ee eee (2) 
Cornish’ bronze. ai 0-60 ees sss° 77.83 | 9.60} 12.40) trace|....<... trace(3) 
Delta metal.......... Stlaresat Bieter ere) tae rl lis ots A IU) sepsis alle ny 0.07 
*Magnolia metal................ trace |...... 83.55) trace} 16.45 |trace(4) 
American anti-friction metal....|........]...... 78.44| 0.98) 19.60 | 0.65 
MNODINUDYONZEs./se:s sie sis ap slots ceteoee 59.00 | 2.16] 0.31} 88.40).......; 0.11 
Graney bronze.......... 25 Se HS 80.4) 96.9520) 6155 OG Sere elects trcees | eee 
Damascus bronze,......--.. cceee| ee tOs4l |! LO S60 MO S2 ieee nitlin eee en eee ee 
Manganese Dr0nZe@, 6. 0s0s 00550) 90.02 |. 9.58) 4in oe [ead ies] ene ye doles eeledo) 
Ajax metal... ....<% sFaGagos 5d $1524) ) 10:98) Ee TeoC lt Ea aliisete eee s pe te (6) 
ANE CtON MetalPossecccriele.seil sees ce tase. 88.32] eisnee 11,03 ae ace 
Harrington bronze.........-..6- 55.7 0597'| snub 42. OF rena ae 0.68 
Car - bax Metals .cc,c0.00.010: ».0.0/0,0,0:8iejl ee, nao | pee’ a2| 04 coal strAce!Pl4ceeamOcor 
LALA age enislcsissaiswieciniccaiesiiste senile ress 94 40}. he exe 6, 08p1% Ff. 
EbOSMNOLr-DTODZE..... wcerijeccn cecal cf Qe1s}, 20,22) . OIG sts ciel bree eae (@ 
KE MeCLAl,. .cebsccccecesensn|isnlOscO 2 O5001s25 00|h ae aaleemte a) 21h ome (8) 
Other constituents: 

(1) No graphite. (5) No manganese. 

(2) Possible trace of carbon. (6) Phosphorus or arsenic, 0,87, 

(3) Trace of phosphorus. (7) Phosphorus, 0.94. 


(4) Possible trace of bismuth. (8) Phosphorus, 0.20. 


* Dr. H. C. Torrey says this analysis is erroneous and that Magnolia 
metal always contains tin. 


As an example of the influence of minute changes in an elloy, the Har- 
rington bronze, which consists of a minute proportion of iron in a copper- 
zinc alloy, showed after rolling a tensile strength of 75,000 lbs. and 20% elon- 
gation in 2 inches. , 

In experimenting on this subject on the Pennsylvania Railroad, a certain 
number of the bearings were made of a standard bearing-metal. and the 
same number were made of the metal to be tested. These bearings were 
placed on opposite ends of the same axle, one side of the car having the 
standard bearings, the other the experimental. Before going into service 
the bearings were carefully weighed, and after a sufficient time they were 
again weighed. 

The standard bearing-metal used is the ‘‘S bearing-metal’’ of the Phos- 
phor-bronze Smelting Co. It contains about 79.70% copper, 9.50% lead, 10% 
tin, and 0.80% phosphorus, A large number of experiments haveshown that 
the loss of weight of a bearing of this metal is 1 1b. to each 18,000 to 25,000 
miles travelled. Besides the measurement of wear, observations were made 
on the frequency of ‘‘ hot boxes ’’ with the different metals. 

The results of the tests for wear, so far as given, are condensed into the 
following table ; 


BEARING-METAL ALLOYS. 335 


Composition, Rate 
Metal. ee —__-—————~ _ of 
Copper. Tin. Lead. Phos, Arsenic, Wear, 
Standard. tse ses . 79.70 10.00 9.50 0.80 melee 100 
Copper-tin.......... 87.50 12.50 Jeet icete Seace: 148 
Copper-tin, second experiment, same metal......ccccccccccesssesscseves 153 
Copper-tin, third experiment, same metal...... cep Noseeeuy 0 vdeenenos wIAEh 
Arsenic-bronze...... 89.20 10. aE Seas 0.80 142 
Arsenic-bronze... .. 79.20 10.00 7.00 ecco 0.80 115 
Arsenic-bronze...... 0G 10,00 9.50 We eie 0.80 101 
SKS bronze)sech te. 77.00 10.50 12.50 ne ow $856 
“K bronze, second experiment, Same metal....ccccccccccccceerscesees I2.0 
Alloy BP deer sg 77.00 8.00 15.00 Moers aos 86.5 


The old copper-tin alloy of 7 to 1 has repeatedly proved its inferiority to the 
phosphor-bronze metal. Many more of the copper-tin bearings heated 
than of the phosphor-bronze. The showing of these tests was so satisfac- 
tory that phosphor-bronze was adopted as the standard bearing-metal of 
the Pennsylvania R.R., and was used for a long time. 

The experiments, however, were continued. It was found that arsenic 
practically takes the place of phosphorus in a copper-tin alloy, and three 
tests were made with arsenic-bronzes as noted above. As the proportion 
to lead is increased to correspond with the standard, the durability increases 
as well, In view of these results the ‘‘K’’ bronze was tried, in which neither 
phosphorus nor arsenic were used, and in which the lead was increased 
above the proportion in the standard phosphor-bronze. The result was that 
the metal wore 7.30% slower than the phosphor-bronze. No trouble from 
heating was experienced with the ‘‘ K’’ bronze more than with the standard. 
Dr. Dudley continues: 

At about this time we began to find evidences that wear of bearing-metal 
alloys varied in accordance with the following law: “That alloy which has 
the greatest power of distortion without rupture (resilience), will best resist 
wear.”’ It was now attempted to design an alloy in accordance with this 
law, taking first the proportions of copper and tin, 9% parts copper to 1 of 
tin was settled on by experiment as the standard, although some evidence 
since that time tends to show that 12 or possibly 15 parts copper to 1 of tin 
might have been better. The influence of lead on this copper-tin alloy seems 
to be much the same as a still further diminution of tin. However, the 
tendency of the metal to yield under pressure increases as the amount of 
tin is diminished, and the amount of the lead increased, so a limit is set to 
the use of lead. A certain amount of tin is also necessary to keep the lead 
alloyed with the copper. 

Bearings were cast of the metal noted in the table as alloy ‘‘ B,”’ and it 
‘wore 13.5% slower than the standard phosphor-bronze. This metal is now 
the standard bearing-metal of the Pennsylvania Railroad, being slightly 
changed in composition to allow the use of phosphor-bronze scrap. The 
formula adopted is: Copper, 105 lbs.; phosphor-bronze, 60 Ibs,; tin, 934 Ibs. ; 
lead, 2514 lbs. By using crdinary care in the foundry, keeping the metal 
well covered with charcoal during the melting, no trouble is found in casting 
good bearings with this metal. The copper and the phosphor-bronze can be 
put in the pot before putting it in the melting-hole. The tin and lead should 
be added after the pot is taken from the fire. 

It is not known whether the use of a little zinc, or possibly some other 
combination, might not give still better results. For the present, however, 
this alloy is considered to fulfil the various conditions required for good 
bearing-metal better than any other alloy. The phosphor-bronze had an 
ultimate tensile strength of 30,000 lbs., with 6% elongation, whereas the alloy 
‘““B” had 24,000 lbs. tensile strength and 11% elongation. 

White Metal for Engine Bearings. (Report of a British Naval 
Committee, Hig’g, July 18, 1902.)—For lining bearings, crankpin bushes, and 
other parts exclusive of cross-head bushes: Tin 12, copper 1, antimony 1. 
Melt 6 tin 1 copper, and 6 tin 1 antimony separately and mix the two together. 

For cross-head bushes a harder alloy, viz., 85% tin, 5% copper, 10% antimony, 
has given good results. 


(For other bearing-metals, see Alloys containing antimony, on next page.) 


Seite ee ALLOYS, 


ALLOYS CONTAINING ANTIMONY. 
Various ANALYSES OF BABBITT METAL AND OTHER ALLOYS CONTAINING 








ANTIMONY. 
Tin.|Copper| Antimony.| Zinc. Lead. | Bismuth. 
Babbitt metal ‘ 50 1 5 Partgiy gisan's sieeve. eve saists Mal Rae 
for light duty { =89.3) 1.8 829 Per. Ctr ls |, <s:08 dole silts > use «econ Mapeetorale beets 
Harder Babbitt 96 4 8 partsh #lvccesemee . ae 
for bearings* = 869) 03.7. 54 DETIOU Crete tue edule cll ste'elarelelc'e) sa [eiionts ponies / 
Britannia.. ... SET) el 0 al 2.9 4 io Sais erased atoll tbe eres 
"4 235285 Siro een ee see 16.2 1: Dats [iat sr.c6 sees cilues £982 eee 
st Bate Steines 16, DSO Ee eaeee tees baat Bieta 
= Ss Are 70.5) 4 25,054 Bmah beeere Risa ea Lack: SPER Mee ee 
ESUEN gereactior 22 10 62. Ge tee SET 
SSeabbith ves. AD Dl ead Diey| LO. Wee Pit | etn emiersnes reAUS Oe Peas tr este 
Plate pewter... 89.3) 1.8 Fo Lee ede, Bese AEE erate 1.8 
White metal... 85 5 10. Bearings on Ger. locomotives. 





*It is mixed as follows: Twelve parts of copper are first melted and then 
36 parts of tin are added; 24 parts of antimony are put in, and then 36 parts 
of tin, the temperature being lowered as soon as the copper is melted in 
order not to oxidize the tin and antimony, the surface of the bath being 
protected from contact with the air. The alloy thus made is subsequently 
remelted in the proportion of 50 parts of alloy to 100 tin. (Joshua Rose.) 

White-metal Alloys.—The following alloys are used as lining metals 
by the Eastern Railroad of France (1890): 


Number. Lead, Antimony. Tin. Copper. 
BBS ACI Gp oe ite 65 25 0 10 

a AEN RRS PPI 0 11.12 83.33 5.55 
Oreck acto CO 20° 10 0 
ci Piscrestrice 80 8 12 0 


No. 1 is used for lining cross-head slides, rod-brasses and axle-bearings: 
No. 2 for lining axle-bearings and connecting-rod brasses of heavy engines; 
No. 3 for lining eccentrie straps and for bronze slide-valves; and No. 4 for 
metallic rod-packing. 

Some of the best-known white-metal alloys are the following (Circular 
of Hoveler & Dieckhaus, London, 1893): 


Tin. Antimony. Lead. Copper. Zinc. 
1 2 2 


Nee AESONS ay nies chess ete eee 86 27 
Qa Richards ......: Soticasuc 70 15 1014 416 0 
OAOOULUS seekers ce eelaciers 55 18 2314 316 0 
AMRENCONS heise cceeca 16 0 0 5 79 
5.) French Navy...........,  % 0 fi a 8714 
6. German Navy........... 85 vers 0 1% 0 


‘“*There are engineers who object: to white metal containing lead or zinc. 
This is, however, a prejudice quite unfounded, inasmuch as lead and zinc 
often have properties of great use in white allovs.”’ 

It is a further fact that an ‘‘ easy liquid’ alloy must not contain more 
than 18% of antimony, which is an invaluable ingredient of white metal for 
improving its hardness; but in no case must it exceed that margin, as this 
would reduce the plasticity of the compound and make it brittle. 

Hardest alloy of tin and lead: 6 tin, 4 lead. Hardest of all tin alloys (?): 74 
tin, 18 antimony, 8 copper. 

Alloy for thin open-work, ornamental castings: Lead 2, antimony 1. 
White metal for patterns: Lead 10, bismuth 6, antimony 2, common brass 8, 
tin 10. 

Type-metal is made of various proportions of lead and antimony, from 
17% to 20% antimony according to the hardness desired. . 


Babbitt Metals. (C. R. Tompkins, Mechanical News, Jan. 1891.) 


The practice of lining journal-boxes with a metal that is sufficiently fusi- 
ble to be melted in a common ladle is not always so much for the purpose 
of securing anti-friction properties as for the convenience and cheapness of 
forming a perfect bearing in line with the shaft without the necessity of 


ALLOYS CONTAINING ANTIMONY. 837 


yoring them, Boxes that are bored, no matter how accurate, require great 
sare in fitting and attaching them to the frame or other parts of a machine. 

It is not good practice, however, to use the shaft for the purpose of cast- 
ing the bearings, especially if the shaft be steel, for the reason that the hot 
metal is apt to spring it; the better plan is to use a mandrel of the same 
size or a trifle larger for this purpose. For slow-running journals, where 
the load is moderate, almost any metal that may be conveniently melted 
and will run free will answer the purpose. For wearing properties, with a 
moderate speed, there is probably nothing superior to pure zine, but when 
not combined with some other metal it shrinks so much in cooling that it 
cannot be held firmly in the recess, and soon works loose; and it lacks those 
anti-friction properties which are necessary in order to stand high speed. 

For line-shafting, and all work where the speed is not over 300 or 400 7. p. 
m., au alloy of 8 parts zine and 2 parts block-tin will not only wear longer 
than any composition of this class, but will successfully resist the force of 
a heavy load. The tin counteracts the shrinkage, so that the metal, if not 
overheated, will firmly adhere to the box until it is worn out. But this 
mixture does not possess sufficient anti-friction properties to warrant its use 
in fast-running journals. 

Among all the soft metals in use there are none that possess greater anti- 
friction properties than pure lead; but lead alone is impracticable, for it isso 
soft that it cannot be retained in the recess. But when by any process lead 
can be sufficiently hardened to be retained in the boxes without materially 
injuring its anti-friction properties, there is no metal that will wear longer 
in light fast-running journals. With most of the best and most populaL 
anti-friction metals in use and sold under the name of the Babbitt metal, 
the basis is lead. , 

Lead and antimony have the property of combining with each other in 
all proportions without impairing the anti-friction properties of either. The 
antimony hardens the lead, and when mixed in the proportion of 80 parts 
lead by weight with 20 parts antimony, no other known composition of 
metals possesses greater anti-friction or wearing properties, or will stand a 
higher speed without heat or abrasion. It runs free in its melted state, has 
no shrinkage, and is better adapted to light high-speeded machinery than 
any other known metal. Care, however, should be manifested in using it, 
and it poe never be heated beyond a temperature that will scorch a dry 

ine stick. 

4 Many different compositions are sold under the name of Babbitt metal. 
Some are good, but more are worthless; while but very little genuine Babbitt 
metal is sold that is made strictly according to the original formula. Most 
of the metals sold under that name are the refuse of type-foundries and 
other smelting-works, melted and cast into fancy ingots with special brands, 
and sold under the name of Babbitt metal. 

It is difficuit at the present time to determine the exact formulas used by 
the original Babbitt, the inventor of the recessed box, as a number of differ. 
ent formulas are given for that composition. Tin, copper, and antimony 
were the ingredients, and from the best sources of information the original 
proportions were as follows : 

Another writer gives: 


50 parts! tiny. cv csectccccigeccecdioccces S37 00-.00 83.38% 
2 parts copper..... elo Sails cinieiste airetet == OU) 8.3% 
4 parts ANTIMONY ore -wuslees.ccieemeean si 161% 8.3% 


The copper was first melted, and the antimony added first and then about 
ten or fifteen pounds of tin, the whole kept at a dull-red heat and constantly 
stirred until the metals were thoroughly incorporated, after which the 
balance of the tin was added, and after being thoroughly stirred again it 
was then cast into ingots. When the copper is thoroughly melted, and 
before the antimony is added, a handful of powdered charcoal should be 
thrown into the crucible to form a flux, in order to exclude the air and pre- 
vent the antimony from vaporizing; otherwise much of it will escape in the 
form of a vapor and consequently be wasted. This metal, when carefully 
prepared, is probably one of the best metals in use for lining boxes that are 
subjected to a heavy weight and wear; but for light fast-running journals 
the copper renders it more susceptible to friction, and it is more liable to 
heat than the metal composed of lead and antimony in the proportions just 
given. 


338 STRENGTH OF MATERIALS. 
SOLDERS. 


Common solders, equal parts tin and lead; fine solder, 2 tin to 1 kad; cheap 
solder, 2 lead, i tin. 
Fusing-point of tin-lead alloys: 


Tin 1 to lead 25......558° F. Tin Vs to lead 1 Bp oe 
wy 90... BA {. oP 340 

chs beneath Peeves | co 3 e687 OE Signe 

ds Syne ait tek 482 beige) ts) cer tT ges 

ssp y) STM Og. i ads 462 BS: Atom ei ghana 278 

Sails (ehh rivee et g DHE: 37 “#6 % 6 4 1381 


Common pewter contains 4 lead to 1 tin. 
Gold solder: 14 parts gold, 6 silver, 4 copper. Gold solder for 14-carat 
gold: 25 parts dois 25 silver, 12144 brass, 1 zine. 
Silver solder: Yellow brass %0 parts, zinc 7, tin 1114, Another: Silver 145 
parts, brass (3 copper, 1 zinc) 73, zine 4. 
German-silver solder: Copper 88, zine 54, nickel 8. 
Novel’s solders for aluminum: 
Tin a parts, lead 5; melts at 536° to 572° F. 
eZine: ds gs 536 to 612 
Ss 4000 “ copper 10 to 153 St 662 to 842 
* 1000 ‘* nickel 10 to 15; sf 662 to 842 
Novel’s solder for aluminum bronze: Tin 900 parts, copper 100, bismuth 2 
to 3. It is claimed that this solder is also suitable for joining aluminum to 
copper, brass, zinc, iron, or nickel. 


ROPES AND CABLES. 


STRENGTH OF ROPES, 


(A S. Newell & Co., Birkenhead. Klein’s Translation of Weisbach, vol. iii, 
part 1, sec. 2.) 








Hemp. Tron. Steel. 
MeSeT Ty tis ica Tere | Tensile 
Weight Weight Weight Strength. 
Girth. per Girth. per Girth. per ele 
Fathom. Fathom. Fathom. 





ee ee | a | af 





— | 


Inches. bounds eae Pounds. | Inches, | Pounds. Gross tons, 
‘ 1 


234 2 
114 114 1 1 3 

8% : 3 O14 1% 1% 5 

9 

414 5 1% 3° i 6 
Q BU 156 7 

B14 7 a1 4 154 aug 8 
214 41 9 

6 9 

614 10 

7 12 

iM 4 

8 16 

814 18 

9 22 

10° 26 

11 30 

12 34 








STRENGTH OF ROPES, 832 


Flat Ropes. 











Hemp. Iron, Steel. 
Traye een =T~| Tensile 
Weight Weight. Weight | Strength. 
Girth, per Girth. per Girth. per 
Fathom. Fathom, Fathom, 











—== <== 








Inches, } Pounds. Inches. {| Pounds. | Inches. | Pounds. | Gross tons, 
4 1 20 1 20 


x aie 1 
B x14} 24 a4 xiZ 18 23 
Bg x I 26 287 x 54 15 27 
934 x 1 28 8 x5 16 2 x 10 28 

x 1441 30 34 x54 18 QV «le 11 32 
7 xe 36 314 x 54 20 214 x 16 12 36 
814 x 24] 40 384x11/16] 22 2 x14 1B 40 
814 x 2 45 4 xJ1/16 25 234 x 38 15 45 
9 x Wel 50 4, x 34 28 x 16 50 
94% x 234] BD 414 x 34 32 314 x 36 18 56 
10 x Bel 60 456 x 34 - 34 314 x 36 20 60 


Working Load, Diameter, and Weight of Ropes and 
Chains, (Klein’s Weisbach, vol. iii, part 1, sec. 2, p. 561.) 


Hemp ropes: d= diam. of rope. Wire rope: d=diam. of wire, n= 
number of wires, G = weight per running foot, k= permissible load in 
ponnds per square inch of section, P= permissible load on rope or chain, 

Oval chains: d = diam. of iron used ; inside dimensions of oval 1.5d and 
2.6d. Hach link is a piece of chain 2.6d long. G9 = weight of a single link = 
2.10d3 lbs.; G = weight per running foot = 9.73d? lbs. 





Hempen Rope. 








peed Me Mie ae 2 RE Pee Lan Wire Rope. 
Dry and Untarred. | Wet or Tarred. 
k (1bs.) = 1420 1160 17000 
r oat P 
d (ins.) = 0.03 VP 0.033 /P 0.0087 = 
P(lbs.) = | 1120d? = 2855G 916d2 = 1975G 13350nd? = 45904 
Gilbs)) == 1,28d? = 0.00035P 1.54d2 = 0.0005P 2.91nd? =0.000218P 
Open-link Chain, Stud-link Chain. 
k (Ibs.) = 8500 11400 
d (ins.) = 0.0087 /P 0.0076 4/P 
P (lbs) = 13350d2 = 1360G 17800d2 = 1660G 
G (Ibs.) = 9.73d?2 = 0.000737P 10.65d2 = 0.0006P 





Stud shains 4/3 times as strong as open-link variety. [This is contrary to 
the statements of Capt. Beardslee, U. S. N., in the report of the U. S. Test 
Lia asi Be holds that the open link is stronger than the studded link. See 
p. antel, f 


340 


STRENGTH OF MATERIALS. 


STRENGTH AND WEIGHT OF WIRE ROPE, HEMPEN ROPE, AND 


CHAIN CABLES. 


(Klein’s Weisbach.) 








Breaking Load Ginhpt Wire Reve)" Weimneor One 
in tons of Kind of Cable. Dlamet Sear I OPe! Foot In length. 
2240 Ibs. Sr Ra a Pounds. 
of Chain, inches. 
Wire Rope 1.0 0.125 
1 Ton............|4 Hemp Rope 2.0 0.177 
Chain A 0.500 
Wire Rope 2.0 0.438 
8 Tons........../4 Hemp Rope 5.0 0.978 
: Chain 18 2.667 
Wire Rope 2.5 0.753 
12 Tons......... .|4 Hemp Rope 7.0 2.036 
Chain 11/16 4.502 
Wire Rope ©.0 1.1386 
16 Tons......3-.«.}4 Hemp Rope 8.0 2.365 
Chain 13/16 6.169 
Wire Rope 3.5 1.546 
20 Tons... ... ..-|~ Hemp Rope 9.0 8.225 
Chain 29/82 7.674 
Wire Rope 4.0 2.043 
24 Tons.........-.|4 Hemp Rope 10.0 4.166 
Chain 31/32 8.836 
Wire Rope 4.5 725 
30 Tons..... - --|{ Hemp Rope 11.0 5.000 
Chain 1.1/16 10.335 
Wire Rope 5.0 3.723 
86 Tons..... ie Hemp Rope 12.5 5.940 
Chain 1.3/16 13.01 
Wire Rope Dew 4.50 
44 TOnSS i eses e's Hemp Rope 14.9 6.94 
Chain 1.5/16 16.00 
Wire Rope 6.0 5.67 
54 Tons..... Stee } Hemp Rope NAO 7.92 
Chain 1.7/16 19.16 
Length sufficient to provide the maximum working stress: 
Hempen rope, dry and untarred...........-.-0.-- 2855 feet. 
a $$ WetiOrn tarred she .2h .Soneee en eee ieee 
NVNTO:POPels ck acdevseere ames cies aie os Meseeioins Boroke Riera io REUR Ae 
Open-link Chain. (.02v.| oseseauees cee ecuees Se Ee 1360 ‘* 
Stud chain...... a8 ATE Seis, Rata, ad ema ae 7, 1660 ‘*° 


Sometimes, when the depths are very great, ropes are given approximately 
the form of a body of uniform strength, by making them of separate pieces, 
whose diameters diminish towards the lower end: It is evident that by this 
means the tensions in the fibres caused by the rope’s own weight can be 
considerably diminished. 

Rope for Hoisting or Transmission. Manila Rope 
(C. W. Hunt Company, New York.)—Rope used for hoisting or for treus- 
mission of power is subjected to a very severe test. Ordinary rope chafes 
and grinds to powder in the centre, while the exterior may look as though 
it was little worn. 

In bending a rope over a sheave, the strands and the yarns of these strands 
slide a ea distance upon each other, causing friction, and wear the rope 
internally. . 

The ‘‘Stevedore’’ rope used by the C. W. Hunt Co. is made by lubricating 
the fibres with plumbago, mixed with sufficient tallow to hold it in position. 
This lubricates the yarns of the rope, and prevents internal chafing and 
wear. After running a short time the exterior of the rope gets compressed 
and coated with the lubricant. 

In manufacturing rope, the fibres are first spun into a yarn, this varn 
being twisted in a direction called ‘‘right hand.’? From 20 to 80 of these 
yarns, depending on the size of the rope, are then put, together and twisted 
in the opposite direction, or ‘left hand,” into a strand. Three of these 


‘STRENGTH OF ROPES. ; 341 


strands, for’a 3-strand, or four for a-4-strand rope, are then. twisted 
together, the twist being again in the “right hand” direction. When the 
strand is twisted, it untwists each of the threads, and when the three 
strands are twisted together into rope, it untwists the strands, but again 
twists up the threads. It is this opposite twist that keeps the rope in its 
proper form. When a weight is hung on the end of arope, the tendency is 
for the rope to untwist, and become longer. In untwisting the rope, it 
would twist the threads up, and the weight will revolve until the strain of 
the untwisting strands just equals the strain of the threads being twisted 
tighter. In making a rope it is impossible to make these strains exactly — 
balance each other. It is this fact that makes it necessary to take out the 
““turns’’ in a new rope, that is, untwist it when it‘is put at work. The 
proper twist that should be put in the threads has been ascertained approx- 
imately by experience. 

The amount of work that the rope will do varies greatly. It depends not 
only on the quality of the fibre and the method of laying up the rope, but 
also on the kind of weather when the rope is used, the blocks or sheaves 
over which it is run, and the strain in proportion to the strain put upon the 
rope. The principal wear comes in practice from defective or badly set 
sheaves, from excess of load and exposure to storms. 

The loads put upon the rope should not exceed those given in the tables, 
for the most economical wear. The indications of excessive load will be the 
twist coming out of the rope, or one of the strands slipping out of its proper 
position. A certain amount of twist comes out in using it the first day or 
two, but after that the rope showld remain substantially the same. If it 
does not, the load is too great for the durability of the rope. If the rope 
wears on the outside, and is good on the inside, it shows that it has been 
chafed in running over the pulleys or sheaves. If the blocks are very small, 
it will increase the sliding of the strands and threads, and result in a more 
rapid internal wear. Rope made for hoisting and for rope transmission is 
usually made with four strands, as experience has shown this to be the most 
serviceable. 

The strength and weight of ‘‘ stevedore”’ rope is estimated as follows: 


Breaking strength in pounds = 720 (circumference in inches)?; 
Weight in pounds per foot = .032 (circumference in inches)?. 


aie Technical Words relating to Cordage most frequently 
eard are: 

YaRN.—Fibres twisted together. 

THREAD.—Two or more small yarns twisted together. 

StRING:—The same as a thread but a little larger yarns, 

STRAND.—Two or more large yarius twisted together. 

Corp.—Several threads twisted together, 

Ropge.—Several strands twisted together. 

HawseEr.—A rope of three strands. 

SHRoupD-Laip.—A rope of four strands. 

CaBLE.—Three hawsers twisted together. 

YARNS are laid up left-handed into strands. 

STRANDS are laid up right-handed into rope. 

HaAwseErs are laid up left-handed into a cable. 
A rope is: 

Laip by twisting strands together in making the rope. 

SPLICED by joining to another rope by interweaving the strands. 

WHIPPED.—By winding a string around the end to prevent untwisting. 

SERVED.—When covered by. winding a yarn continuously and tightly 
around it. 

PARCELED.—By wrapping with canvas. 

SEIZED.—When two parts are bound together by a yarn, thread or string. 

PayED.— When painted, tarred or greased to resist wet. 

Havuu.—To pull on a rope. 

Taut.—Drawn tight or strained. 

Splicing of Ropes.—tThe splice in a transmission rope is not only the 
weakest part of the rope but is the first part to fail when the rope is worn 
out. If the rope is larger at the splice, the projecting part will wear on the 
pulleys and the rope fail from the cutting off of the strands. The following 
directions are given for splicing a 4-strand rope. bot dae 

The engravings show each successive operation in splicing a 134 inch 
manila rope, Each engraving was made from a full-size specimen, 


Se, 


342 


STRENGTH OF MATERIALS, 





SPLIcING oF RopEs. 


SPLICING OF ROPES. $43 


Tie a piece of twine, 9 and 10, around the rope to be spliced, about 6 feet 
from each end. Then unlay the strands of each end back to the twine. 

Butt the ropes together and twist each corresponding pair of strands 
loosely, to keep them from being tangled, as shown in F'g. 78. 

The twine 10 is now cut, and the strand 8 unlaid and strand 7 carefully laid 
in its place for a distance of four and a half feet from the junction. 
st The strand 6 is next unlaid about one and a half feet and strand 5 laid in 

s place. 

The ends of the cores are now cut off so they just meet. 

Unlay strand 1 four and a half feet, laying strand 2 in its place. 

Unlay strand 8 one and a half feet, laying in strand 4. 

Cut all the strands off to a length of about twenty inches, for convenience 
in manipulation. § 

The rope now assumes the form shown in Fig. 79 with the meeting points 
_ of the strands three feet apart. 

Each pair of strands is successively subjected to the following operation: 

From the point of meeting of the strands 8 and 7, unlay each one three 
turns; split both the strand 8 and the strand 7 in halves as far back as they 
are now unlaid and ‘‘ whip’ the end of each half strand with a small 
piece of twine. 

The half of the strand 7 is now laid in three turns and the half of 8 also 
laid in three turns. The half strands now meet and are tied in a simple 
knot, 11, Fig. 80, making the rope at this point its original size. 

The rope is now opened with a marlin spike and the half strand of 7 
worked around the half strand of 8 by passing the end cf the half strand 7 
through the rope, as shown in the engraving, drawn taut and again worked 
around this half strand until it reaches the half strand 18 that was not laid 
in. This half strand 13 is now split, and the half strand 7 drawn through 
the cyening thus made, and then tucked under the two adjacent strands, as 
shown in Fig. 81. The other half of the strand 8 is now wound around the 
other half strand 7 inthe same manner. After each pair of strands has 
been treated in this manner, the ends are cut off at 12, leaving them about 
four inches long. After a few days’ wear they will draw into the body of the 
1ope or wear off. so that the locality of the splice can scarcely be detected. 

Coal Hoisting. (C. W. Hunt Co.).—The amount of coal that can be 
loisted with a rope varies greatly. Under the ordinary conditions of use 
arope hoists from 5000 to 8000 tons. Where the circumstances are more 
favorable, the amounts run up frequently to 12,000 or 15,000 tons, occasion- 
ally to 20,000 and in one case 32,400 tons to a single fall. 

When a hoisting rope is first put in use, it is likely from the strain put upon 
it to twist up when the block is loosened from the tub. This occurs in the 
first day or two only. The rope should then be taken down and the 
“turns” taken out of the rope. When put up again the rope should give 
no further trouble until worn out. 

It is necessary that the rope should be much larger than is needed to bear 
the strain from the load. 

Practical experience for many years has substantially settled the most 
economical size of rope to be used which is given in the table below. 

Hoisting ropes are not spliced, as it is difficult to make a splice that will 
not pull out while running over the sheaves, and the increased wear to be 
obtained in this way is very small. 

Coal is usually hoisted with what is commonly called a ‘‘ double whip; ” 
that is, with a running block that is attached to the tub which reduces the 
strain on the rope to approximately one half the weight of the load hoisted. 
The following table gives the usual sizes of hoisting rope and the proper 
working strain: - 

Stevedore Hoisting-rope. 
C. W. Hunt Co. 


. Proper Working Nominal size of Approximate 
Circumference of |strain on the Rope|Coal tubs. Double| Weight of a Coil, 


the rope imans. in lbs. whip. : in lbs. 
3 350 1/6 to 1/5 tons. 360 
316 500 75% 480 
4 650 Wun, « 650 
41, 800 ig “ge 830 
5 1000 Vou gle 960 





“Hoisting rope is ordered by circumference, transmission rope by diameter, 


344 STRENGTH OF MATERIALS, 


Weight and Strength of Manila Rope. 


Spencer Miller (Hng’g News, Dec. 6, 1890) gives a table of breaking strength 
of manila rope, which he considers more reliable than the strength computed 
by Mr. Hunt’s formula: Breaking strength=720x (circumference in inches)?, 
Mr. Miller’s formulais: Breaking weight lbs.=circumference? x a coefficient 
which varies from 900 for 14’ to 700 for 2’ diameter rope, as below: 


Cirenmference .... 146 2 2% 23% 3 3% 334 444 4144 5 5% 6 
Coefficient. ........ 900 845 820 790 780 765 760 745 735 725 712 700 


The following table gives the breaking strength of manila rope as cal- 
culated by Mr. Hunt’s formula, and also by Mr. Miller’s, using in the latter 
the coefficient 9UU for sizes below 114 in. circumference and 700 for sizes above 
6in. The differences bevween the figures for any given size are probably 
not greater than the difference in actual strength of samples from different 
makers. Both sets of figures are considerably lower than those given in 
tables published by some makers of rope, but they are believed to be more 
reliable. The figures for weight per 100 ft. are from manufacturers’ tables. 











aS 2 S02 Ultimate q : Se Ultimate 
nd o My o Z 
real a= ee 2 5 Strength of ch ais Peeps ° 3 5 .| Strength of 
2o (5, 0/8™%2! Rope in lbs. © {eS 2%! Rope in Ibs 
os j=oslq “19 2 oq [Fol a "5 I : 
BO. 15 = &.| Wows Bo [Ro o|Mo, = 
B2 (23s/oS3s aa (262 "0S38 
fax) 6) = Hunt. | Miller. 6 oO = Hunt. | Miller. 
3/16| 9/16] 2 230 280 #1 5/16| 4 52 | 11,500 | 12,000 
A yl 8 400 500 #134 44%} 58 13,000 | 13.500 
Lay MUS earn 4 630 790 #16 416 65 14,600 | 14,900 
36 11g 5 900 1,140 #1 9/16) 434 7246 | 16,200 | 16,500 
G/16| 1%4 6 1,240 1,550 #15¢ 5 80 18,000 | 18,100 
6 | 116 | 7% | 1,620 | 2,090 $154 5% | 97 . | 21.800 | 21.500 
9/16] 134 8 2,050 2,480 }2 6 113 25,900 | 25,200 
% 1 2 131% | 2.880 | 3,380 F214 614, 133 | 30.400 | 29,600 
34 | 214] 16% 3,640 | 4,150 F214 7 153 35,300 | 34,300 
13/13} 216 | 20 4,500 | 5,030 fl2t4 "4 | 184 | 40,500 | 39/400 
% 234 23% 5,440 5,970 9254 8 211 46,100 | 44,800 
1 3 2814 | 6,480 | 7.020 §27% 814 | 237 | 52,000 | 50.600 
11/16) 3% | 3314 | 7,600 | 8,160 93 9 262 | 58.300 | 56,700 
14 3144 | 38 8.820 | 9.370 931% 914 | 293 | 65,000 | 63.200 
14% 334 45 10,120 | 10,690 9314 10 325 72,000 | 70,000 


For rope-driving Mr. Hunt recommends that the working strain should . 
not exceed 1/20 of the ultimate breaking strain. For further data on ropes 
see ‘‘ Rope-driving.”’ 

Knots.--A great number of knots have been devised of which a few 
only are illustrated, but those selected are the most frequently used. In 
the cuts, Fig. 82. they are shown open, or before being drawn taut, in order 
to show the position of the parts. The names usually given to them are: 


Bight of a rope. Flemish loop. 

Simple or Overhand knot. Chain knot with toggle. 
Figure 8 knot. Half-hitch. 

Double knot. Timber-hitch. 

Boat knot. Clove hitch. 

Bowline, first step. Rolling-hitch. 

Bowline, second step. Timber-hiteh and half-hitch. 
Bowline completed. . Blackwall-hitch. 

Square or reef knot. Fisherman’s bend. 

Sheet bend or weaver’s knot. Round turn and half-hitch. 
Sheet bend with a toggle. Wall knot commenced. 


CHP NM dcimnot 


Carrick bend. A ‘* - completed. 
Stevedore knot completed. B Wall knot crown commenced. 
Stevedore knot commenced. Cc as = completed 


Slip knot. 


“OZEMASM ROA BbOM> 


KNOTS. 345 


J . 


The principle of a knot is that no two parts, which would move ir the 
same direction if the rope were to slip, should lay along side of and touch- 
ing each other. 

The bowline is one of the most useful knots, it will not slip, and after 

being strained is easily untied. Commence by making a bight in the rope, 
then put the end through the bight and under the standing part as shown in 
G, then pass the end again through the bight. and haul tight. 
The square or reef knot must not-be mistaken for the “ granny ”’ knot 
that slips under a strain. Knots H, K and M are easily untied after being 
under strain. The knot M is useful when the rope passes through an eye 
oak is ey by the knot, as it will not slip and is easily untied after being 
strained. “ 


\ 
SS = 













3 y 
eae Y 
Ar SSR ¥ 
Bssx is Teal sss | 


Russ 








Fie, 82.—Knorts, 

The timber hitch S looks as though it would give way, but it will not; the 
zreater the strain the tighter it will hold. The wall knot looks complicated, 
but is easily made by proceeding as follows: Form a bight with strand 1 
and pass the strand 2 around the end of it, and the strand 3 round the end 
of 2 and then through the bight of 1 as shown inthe cut Z. Haul the ends 
taut when the appearance is as shown in AA. The end of the strand 1 is 
now laid over the centre of the knot, strand 2 laid over 1 and 3 over 2, when 


the end of 3 is passed through the bight of 1 asshownin BB, Haul all the 
strands taut as shown in CC, 


346 STRENGTH OF MATERIALS. 


To Splice a Wire Rope.—The tools required will be a smal! marline 
spike, nipping cutters, and either clamps or a small hemp-rope sling with 
which to wrap around and untwist the rope. If a bench-vise is accessible 
it will be found convenient. 

In splicing rope, a certain length is used up in making the splice. An 
allowance of not less than 16 feet for 14 inch rope, and proportionately 
longer for larger sizes, must be added to the length of an endless rope in 
ordering. 

Having measured, carefully, the length the rope should be after splic- 
ing, and marked the points M and M’, Fig. 83, unlay the strands from each 
end Hand EZ’ to Mand M’ and cut off the centre at M and M’, and then: 

(1). Interlock the six unlaid strands of each end alternately and draw 
them together so that the points Mand M’ meet, as in Fig. 84. 

(2). Unlay a strand from one end, and following the unlay closely, lay into 
the seam or groove it opens, the strand opposite it belonging to the other 
end of the rope, until within a length equal to three or four times the length 
of one lay of the rope, and cut the other strand to about the same length 
from the point of meeting as at A, Fig. 85. 

(3), Unlay the adjacent strand in the opposite direction, and following the 
unlay closely, lay in its place the corresponding opposite strand, cutting the 
ends as described before at B, Fig. 85, , 

There are now four strands laid in place terminating at 4 and B, with the 
eight remaining at M M’, as in Fig. 85. 

It will be well after laying each pair of strands to tie them temporarily at 
the points A and B. 


Pursue the same course with the remaining four pairs of opposite strands, — 


Fia. 83. 








Fic. 85. 
A ‘yA “M ATUR UK Sia? eRe ae 
M KS kes. 
Fie. 86. Fie. 87. 


SPLICING WIRE RopE. 


stopping each pair about eight or ten turns of the rope short of the preced. 
ing pair, and cutting the ends as before. f ; ; 

We now have all the strands laid in their proper places with their respect- 
ive ends passing each other, as in Fig. 86. ; : é " 

All methods of rope-splicing are identical to this point: their variety con- 
sists in the method of tucking the ends. The one given below is the one 
most generally practiced. ; 

Clamp the rope either in a vise at a point to the left of A, Fig. 86, and bya 
hand-clamp applied near A, open up the rope by untwisting sufficiently to 
cut the core at A, and seizing it with the nippers. let an assistant draw it 
out slowly, you following it closely, crowding the strand in its place until it 
is all laid in. Cut the core where the strand ends, and push the end back 
into its place. Removethe clamps and let the rope close together around it. 
Draw out the core in the opposite direction and lay the other strand in the 
centre of the rope, in the same manner. Repeat the operation at the five 
remaining points, and hammer the rope lightly at the points where the ends. 
pass each other at A, A, B, B, etc.. with small wooden mallets, and the 
splice is complete, as shown in Fig. 87, f 

If a clamp and vise are not obtainable, two rope slings and short wooden 
levers may be used to untwist and open up the rope. a 

A rope spliced as above will be nearly as strong as the original rope and 
smooth everywhere. After running a few days, the splice, if well made, 
cannot be found except by close examination. i 

The above instructions have been adopted by the leading rope manufac: 
turers of America. 


HELICAL STEEL SPRINGS. 347 


SPRINGS. i 


Wefinitions.—A spiral spring is one which is wound around a fixed 
eet or centre, and continually receding from it Jike a watch spring. A 

elical spring is one which is wound around an arbor, and at the same time 
advancing like the thread of ascrew. An elliptical or laminated spring is 
made of flat bars, plates, or “leaves,” of regularly varyiig lengths, super- 
posed one upon the other. 

Laminated Steel Springs.—Clark (Rules, Tables and Data) gives 
the following from his work on Railway Machinery, 1855: 


_ 1,66L3 | ou Dim, __ 1.66L8, 
~ btn? 7 S18) & abit 


A = elasticity, or deflection, in sixteenths of an inch per ton of load, 
s = working strength, or load, in tons (2240 lbs.), 

LL = span, when loaded, in inches, 

b = breadth of plates, in inches, taken as uniform, 

t = thickness of plates, in sixteenths of an inch, 

m = number of plates. 


Rene span- and the elasticity are those due to the spring when 
weighted, 

2. When extra thick back and short plates are used, they must be replaced 
by an equivalent number of plates of the ruling thickness, prior to the em- 
ployment of the first two formule. This is found by multiplying the num- 
ber of extra thick plates by the cube of their thickness, and dividing by the 

-cube of the ruling thickness. Conversely, the number of plates of the ruling 
thickness given by the third formula, required to be deducted and replaced 
by a given number of extra thick plates, are found by the same calculation. 

3. It is assumed that the plates are similarly and regularly formed, and 
that they are of uniform breadth, and but slightly taper at the ends. 

Reuleaux’s Constructor gives for semi-elliptic springs: 

Snbh? 6 Pl 
Re Anthea Enbh3’ 


S = max. direct fibre-strain in plate; b = width of plates; 

n = number of plates in spring; h = thickness of plates; 

l = one half length of spring; F = deflection of end of spring; 
P = load on one end of spring; # = modulus of direct elasticity. 


The above formula for deflection can be relied upon where all the plates 
of the spring are regularly shortened; but in semi-elliptic springs, as used, 
there are generally several plates extending the full length of the spring, 
and the proportion of these long plates to the whole number is usually about 


5 P13 
one fourth. In such eases f = as (G. R. Henderson, Trans. A.S. M. E., 
vol. xvi.) 

In order to compare the formule of Reuleaux and Clark we may make 
the following substitutions in the latter: sin tons = Pin lbs, - 1120;.as = 
1G; = 2l: t= Asethen 

1,.66°% 812 530 P- Pw 
4096 X 1120 x none Whence f= 557733) 


which corresponds with Reuleaux’s formula for deflection if in the latter we 
take H = 33,162,800. 
ed P _ %6nbh? sh Ney Sag 12,687nbh?2 

Naps 6 P50 Pew ah Beaks Y l , 
which corresponds with Reuleaux’s formula for working load when Sin the 
latter is taken at 76,120. 
~ The value of # is usually taken at 30,000,000 and S at 80,000, in which case 
Reuleaux’s formule become 

13,3331bh2 Pls 
om i and — F= §,000,000n5n5" 

Helical Steel Springs.—Clark quotes the following from the report 

on Satety Vaives (Trans. Inst. Engrs. and Shipbuilders in Scotland, 1874-5); 


As= 16f= 


Also 


348 SPRINGS. 


E = compression or extension of one coil in inches, 

d = diameter from centre to centre of steel bar constituting the spring 
in inches, 

w = weight applied, in pounds, 

i= cana or side of the square, of the steel bar, in sixteenths of at 
inch, 

C=a constant, which may be taken as 22 for round steel and 30 .for 
square steel. 


Notr.—The deflection HZ for one coil is to be multiplied by the number of 
free coils, to obtain the total defiection for a given spring, 

The relation between the safe load, size of steel, and diameter of coil, may 
be taken for practical purposes as follows: 


3 ———— 
D= "A “ for round steel; 


. , for square steel, 


Ww 
D=4/ 735 


Rankine’s Machinery and Millwork, p. 390, gives the followings 
Wo edt oy _ -196fa8, vy wx 12:506nfr?, 
“wy ~ 64nr3° vO by eee ond) ca ys 


ma = greatest safe sudden load. 





In which dis the diameter of wire in inches; c a co-efficient of transverse 
elasticity of wire, say 10,500,000 to 12,000,000 for charcoal iron wire and steel; 
r radius to centre of wire in coil; n effective number of coils; f greatest safe 
shearing stress, say 30,000; W any load not exceeding greatest safe load; 
vy corresponding extension or compression; Wy greatest safe load; and v,; 
greatest safe steady extension or compression. 

If the wire is square, of the dimensions d x d, the load for a given deflec- 
tion is greater than for a round wire of the diameter d in the ratio of 2.81 to 
1.96 or of 1.43 to 1, or of 10 to 7, nearly. i 

Wilson Hartnell (Proc. Inst. M. E., 1882, p. 426), says: The size of a spiral 
spring may be calculated from the formula on page 304 of “ Rankine’s Use- 
ful Rules and Tables’’; but the experience with Salter’s springs has shown 
that the safe limit of stress is more than twice as great as there given, 
namely 60,000 to 70,000 lbs. per square inch of section with 34 inch wire, and 
about 50,000 with 144 inch wire. Hence the work that can be done by 
springs of wire is four or five times as great as Rankine allows. 

For 3g inch wire and under, 


: + aNg 
Maximum load in lbs. = cecal Nea ANE Ler ee 
Mean radius of springs 


180,000 x (diam.)4 
Number of coils  (rad.)*° 

The work in foot-pounds that can be stored up in a spiral spring would 
lift it above 50 ft. 

In a few rough experiments made with Salter’s springs the coefficient of 
rigidity was noticed to be 12,600,000 to 13,700,000 with 14 inch wire; 11,000,000 
for 11/32 inch; and 10,600,000 to 10,900,000 for 34 inch wire. 

Krelical Springs.—J. Begtrup, in the American Machinist of Aug. 
18, 1892, gives formulas for the deflection and carrying capacity of helical 
springs of round and square steel, as follow: 


Weight in lbs. to deflect spring 1 in, = 








W = .392720 
ee for round steel, 
pu ghD- a 
me jed4 *2 
3 
W = .471 ~ 
7m for square steel. 
iin 3 
fe 4.71202 


Edt ° 


HELICAL SPRINGS. 349. 


W = carrying capacity in pounds, 

S = greatest tensile stress per square inch of material, 
d = diameter of steel, 

D = outside diameter of coil, 

F = deflection of one coil, 

E = torsional modulus of elasticity, 

P= load in pounds. 


From these formulas the following table has been calculated by Mr. Beg- 
trup. A spring being made of an elastic material, and of such shape as te 
allow a great amount of deflection, will not be affected by sudden shocks or 
blows to the same extent as a rigid body, and a factor of safety very much 
less than for rigid constructions may be used. 


HOW TO USE THE TABLE. 


When designing a spring for continuous work, as a car spring, use a 
greater factor of safety than in the table; for intermittent working, as in 
a steam-engine governor or safety valve, use figures given in table; for 
square steel multiply line W by 1.2 and line #’ by .59. 

Example 1.—How much will a spring of 3g’ round steel and 3’’ outside 
diameter carry with safety ? In the line headed D we find 3, and right un- 
derneath 478, which is the weight it will carry with safety. How many coils 
must this spring have so as to deflect 3’ with a load of 400 pounds ? Assum- 
ing a modulus of elasticity of 12 millions we find in the centre line headed 
F the figure .0610; this is deflection of one coil for a load of 100 pounds; 
therefore .061 « 4 = .244’’ is deflection of one coil for 400 pounds load, and 3 
+ .244 = 121g is the number of coils wanted. This spring will therefore be 
434”’ loug when closed, counting working coils only, and stretch to 734”, 

Hxample 2.—A spring 314’’ outside diameter of 7/16” steel is wound close; 
-how much ean it be extended without exceeding the limit of safety? We 
find maximum safe load for this spring to be 702 pounds, and deflection of 
one coil for 100 pounds load:.0405 inches; therefore 7.02 x .0405 = .284’ is the 
greatest admissible opening between coils. We may thus, without know- 
ing the load, ascertain whether a spring is overloaded or not. 


Carrying Capacity and Deflection of Helical Springs of 
“Round Steel. 


d = diameter of steel. D = outside diameter of coil. W = safe working 
load in pounds-——tensile stress not exceeding 60,000 pounds per square inch. 
F = deflection by a load of 100 pounds of one coil, and a modulus of elasti- 
city of 10, 12 and 14 millions respectively. The ultimate carrying capacity 
will be about twice the safe load. 









































So! D| .25 | .50 | .75 | 1.00 | 1.25 | 1.50 | 1.75 | 2.00 
Srl Wi 35 1561) 9 i 5 45) 88 | 3:3 
“S 0276) .8588| 1.433] 3.562] 7.250112.88 | 20.85] 31.57 
A) 2} 30236) [3075] 1.228] 3.053] 6.214/11.04 | 17.87] 27.06 
3 "0197 .2562| 1.023] 2.544] 5.178) 9.200] 14.89) 22.55 
> | D| .50. | .% | 1.00 | 1.25 | 1.50 | 1.75 | 2.00 | 2.25 | 2.50 
S|) 407 | 6 | 46 | 36°} 29 1 95.1 22.| 19 | 17 
As .0206| .0937] .2556| .5412] .9856] 1.624) 2.492] 3.625/5.056 
LS Fr} '0176| .0804| .2191} .4639| .8448] 1.392] 2.136] 3.107/4.334 
et '0147| .0670| .182 | .3866] .7040] 1.160] 1.780] 2.589/3.612 
>| D| 7 | 1.00 | 1.25 | 1.50 | 1.75 | 2.00 | 2.25 | 2.50 | 2.75] 3.00 
S.c| wl 241] 1671 128] 104] 88 | ¢ 66} 59 |. 53.) 49 
"5 0137| .0408] .0907| .1703! .2866] .4466| .6571| .9249/1.25611.660 
es, Pi) 0118] .0350| :0778| :1460| :2457] .3828] (5689) |7928/1_0771/1.423 
is 0098/ .0292]} .0648| .1217] .2048] .3190| :4693] .6607).8975/1.186 
~ | D1 1.25 | 1.50 | 1.75 | 2.00 { 2.25 | 2.50 | 2.75 | 3.00 | 3.25] 3.50 
St | Wl 368 | 294 | 245 210 | 1841 164] 147] 134] 123 | 113 
+ .0199! .0389] .0672] .1067] .1593] .2270! .3109] .4139].5375] .6835 
F2| 20171! 10333! 10576! .0914) .1365| 11944] 2665] .3548].4607] .5859 
'0142] .0278| .0480 20762] .1137] .1610| .2221| .29571.3839] .4883 





350 


SPRINGS. 


Carrying Capacity and Deflection of Helical Springs of 
Round Steel.—(Continwed). 





: 
> D | 1.50 
© 
W | 605 
> 
| 


0136) 
F's} .0117! 








s 0120 
> | D| 2.00 
x | W| 1263 
= .0081 
r Py “0069 
<) 0058 
Se | | 1968 
a 1963 
* 0042 
Nl w2| 0036 

-0030 





Ss 
~< D | 2.50 
Xo | W7 | 3068 
x .0034 
NW } 2} 0029 
3 0024 
_ | D | 3.00 
ye| W | 8311 
cal .0043 
B=] F+| .0037 
.0030 


1.75 
500 


2.00 
426 


9.95 


We 


371 


2.50 
829 


-0242{ .0892) .0593) .0854 








0336 
.0280 
2.50 
589 
0377 
.0323 
0269 


0508 
0424 











0732 
.0610 


3.00 
473 
0711 
.0610 
0508 











2.75 | 3.00 | 3.25 | 3.50 


295 
A tes 
1012 
0853 
8.25 

433 
0985 
0801 
.0668 


3.25 
702 
0472 
0405 
03387 





267 
1588 








245 | 226 
2066} .2640 
1771 .2268 
1476) .1886 
3.75 | 4.00 
368 | 343 


.1513).1874). 


. 1297] . 1606 


1081} .1338) . 





a | eres | a | eee | | Se | | — 


ee | S| | |  — f — — — 

















0011 



































.0029 























-0051| .0061 








-0043) .0051 |. 





3.75 
209 


8312}. 
2839}. 
+2366} . 











The formule for deflection or compression given by Clark, Hartnel), and 
Begtrup, although very different in-form, show a substantial agreement 
when reduced to the same form. 
mean diameter of coil, n the number of coils, w the applied weight in 
pounds, and C a coefficient, then 


Let d = diameter of wire in inches, D, = 





1: HELICAL SPRINGS. 351 
3 
Compression or extension of one coil = wait 
: : ; Cd4 
Weight in pounds to cause comp. or ext. of lin. = iB 
1 


The coefficient C reduced from Hartnell’s formula is 8 & 180,000 = 1,440,000; 
ey xs to Clark, 164 & 22 = 1,441.792, and according to Begtrup (using 
2,000,000 for the tor ‘sional modulus of elasticity) = 12,000,000 ~ 8 = 1,500,000. 


1205; “2 
So ss ie may take 
cd 


if we use 30,000 and 12,000,000 as the values for f 


Rankine’s formula for greatest safe extension, v¥, = 


-7854n D2 


the form v, = 100d 
and c respectively. 
The several formule for safe load given above may be thus compared, 
letting d = diameter of rie and Dy = mean diameter of coil, Rankine, 


16)8 .38927Sda8 





3 
= se Clark, W = ; Begtrup, W = 3; Hartnell, 
ae : D, D, 
a= fs ae . Substituting for f the value 30,000 given by Rankine, and for 


8 
S, 60,000 as given by Begtrup, we have W = 11,760 zeae Rankine ; 12,288 — 
1 1 


Clark; 23,562 + Begtrup; 24,000 < Hartnell. 


Taking from ‘the Peonsylviinia 1 Railroad specifications the capacity when 
closed of the following springs, in which d = diameter of wire, D diameter 
outside of coil. D, = D— d,c capacity, H height when free, and h height 
when closed, all in inches. 


No. T. d=\% D=1% D,=1% c=40 H=9 h=6 
Ss. 94 3 Qe 1,900 Bi Liga 
K. 34 534 5 2100 Cf 414 
D. 1 5 4 8,100 1dig 78 
pe 114 8 634 10.000 9 534 
a 1% 4%, 334 16,000 486 - 1386 


3 
and substituting the values of c in the formulac = W = ae we find a, the 
3 1 


: 3 
coefficient of ais to be respectively 32,000; 38,000; 32,400; 24,888; 34,560; 
42,140, average 34,000. ‘ 

Taking 12,900 as the coefficient of + according to Rankine and Clark for 


1 
safe load, and 24,000 as the coefficient according to Begtrup and Hartnell, 
we have for the safe load on these springs, as we take one or the other co- 


efficient, 

dy. S. K. 12 TE: G3 
Rankine and Clark........ eet OU 600 1,012 3,000 £750 5.400 Ibs. 
Hartnell. ..... eee U0 selte00 weet Oe te G000) 07,5007) 10.800 are 


Capacity when closed, ‘asabove 400 1,900 2.100 8,100 10,000 16,000 * 
J. W. Cloud (Trans. A. S. M. E., v. 173) gives the following: 


Smd3 32 PR2 
ie. ne ee 


P = load on spring; 
pas = maximum shearing fibre-strain in bar; 
= diameter of steel of which spring is made; 
oe = radius of centre of coil; 
l = length of bar before coiling; 
G = modulus of shearing elasticity; 
f = deflection of spring under load. 
Mr. Cloud takes S = 80,000 and G = 12,600,000. 
The stress in a helical spring is almost wholly one of torsion. For method 
of deriving the formule for springs from torsional formula see Mr. Cloud’s 
paper, above quoted. 


(P= 





352 , SPRINGS. 


ELLIPTICAL SPRINGS, SIZES, AND PROOF TESTS. 
Pennsylvania Railroad Specifications, 1890. 


- 4 











[= ie oe 
Bg|S Tests. 
eae 
i“ SalFS! piates. - 
nar. as 33 No. Size, in. : ; 
toe (35.2 Tns, i. high... lbsajInsor bse 
§ 3/5 j@) — @) Ww) En 
= = 
ee toe oe 
F1,Triple..... 40 |1184/ 5 3x 11/22 | 334 93 4800 |3 55001 2 
E 2, Quadruple! 40 |1514| 5 8x3 334 934 6650 {3 8000; 2 
ES ETO Ones ac 36 }1134| 6 3x 11/32 4 954 6000 3 8000 | — 
EH 4, Singlet...} 40 | — | 8 sé Da — free 3 2350 | — 
£5, Bee (40a eno oe 1$,* —_ 3000 0 4970 | — 
FECES See. go elOg aie ae) aL ewte es 4375 |0 6350 | — 
E7, Triple..... 36 |1134) 8 8x 11/32 | 244 9% 11,800-}]—- — | — 
£8, Doubie....| 32 | 714) 6 3x3¢ 3 9 8000 — — — 
EY ‘  ....1 36} 9144] 5 4x11/32] 31 6% 5400 |8 6000] — 
£10,Quadruple| 40 |1514| 5 3x 3% 4 10 8000 3 10,000 | 2 
| bs ns atl oie 0 | 1546] 5 8x 3g 334 934 10,600 Si te: 200s here 
#12, * . 5.6]: B4j 15g) 5 8x 86 334 934 13,100 | 8 15,780 | 2 
E 13, Double...} 30 | 944] 5 4x34 334 9 5600 2 10,600 | — 
la] ie Ose -+»| 40 | 944) 6 4x11/82 338 9 6840 4 8600 | — 
£15,Quadruple} 36 |15136} 6 8x 11/32 | 33% 934 11,820 | 214 14,870 | 2 
#16, Olese 6 |80 Hole l6 MS 44 104g 8000 234 15,500 | — 
E17, Double...| 36 | 914] 5 4x34 234 «8 8070 | 2 = 9540 | — 
H'18, Single t..| 42 |— | 9 3144x34 1* — 5250 | 0 7300 | — 
E19, Double...| 22 |1014) 6 41411/32 | 13/16 67, 13,800 |— — |— 
EF 20, PEE sisi okell| eeu etied: - 13/16 7g 15,600 — — — 
EF 21, cr 24 11014) 7 4146 x 3g 1 7144 = 15,750 0 28,800 | -— 
Ff 22, oF .| 24 ]1044| 8 oh 1 814 18.000 0 32,930 | — 
EF 23, Wiese cl co: (10) a) ond x36 214 8 8750. | 114 10,750 | — 
E 24, etesa co. hLOL geo os 214 8 7500 | 144 9500 | — 





(a) Between bands ; (/)) over all ; a.p.t., auxiliary plates touching. 
* Between bottom of eye and top of leaf. + semi-elliptical. 
Tracings are furnished for each class of spring. 


PHOSPHOR-BRONZE SPRINGS. 

Wilfred Lewis (Zngineers’ Club, Philadelphia, 1887) made some tests with 
phosphor-bronze wire, .12 in. diaineter, coiled in the form of a spiral spring, 
114 in. diameter from centre to centre, making 52 coils. 

Such a spring cf steel, according to the practice of the P. R. R., might be 
used for 40 Ibs. A load of 80 lbs. gradually applied gave a permanent set. ' 
With a load of 21 lbs. in 80 hours the spriug sengthened from 205 inches to 
2144 inches, and in 200 hours to 214% inches. It was concluded that 21 lbs. was 
too great for durability. For a given load the extension of the bronze spring 
was just double the extension of a similar steel spring, that is, for the sama 
extension the steel spring is twice as strong. 


SPRINGS TO RESIST TORSIONAL FORCE, 
(Reuleaux’s Constructor.) 





: ‘ ; bh? PlR? 
lat ] helical spring... P= = —-; = = pee, 
Flat spiral or he pring 6p? fp SRY 12 Rohs 
: : Sr d3 64 Pl R2 
helical spring .......... =o Se = ge petiel ES 
Round elical spring P aati f= Rd a Bae 
; ; Sr a3 382 P R21 
Round bar, in eg CE Je ee Te B f=akRt= = uere 
2h2 2 2 2 
Flat, bar;in torsion?s.ses2..:-. P= zl sone aula =R3= pik Lb? hi ; 
3h),3 
38h 4/2 + fi G bh 


P = force applied at end of radius or lever-arm R; % = angular motion at 
end of radius &; S = permissible maximum stress, = 4/5 of permissible 
stress in flexure; # = modulus of elasticity in tension; G = torsional modu. 
lus, = 2/5 H; 1 = developed length of spiral, or length of bar; d = diameter 
of wire; b = breadth of flat bar; h = thickness. 


HELICAL SPRINGS—SIZES AND CAPACITIES. 


003 


HELICAL SPRINGS—SIZES AND CAPACITIES, 


P, R: BR. Cos 
Class. 





On oad 


- 


Se BD 2 O32 OT OT 09 2 OT | 
i] 


WwWwooDme@®M 


GS? Ol ap 
oni a) 
RS dee 


fnefsefou}ss[os}onise}axioniseionies|ss|ssissinz}=0)<2) 
2 


09 vo 
o & 


Ww OO 
= to 


oe 
ry 


je 


cS) 
==) 


anjasjsejasjeniec|seicsiesjaciaejusisegee)sejesissiaricn) 
See re ord ap Sic Oe OO ees ICO 


ZOwWw 
— 


ins. 


Normal Weight. 


| Diam. of Bar, ins 
Length of Bar, 
Tapered to ins. 


| 
| 











ee pp 


ome 


Outside Diam. of 








(Selected from Specifications of Penna. R. R. Co., 1899.) 


Test. Height and Loads. 


DH nH 
q As) 
oO oO 
Eanes 
oa oD) 
534 3 
8 5 
416 | 375 
39 2216 
1ig | 18a 
5g 88% 
241 1% 
23 13 
191g) 13 
9 5 
S54 6 
18 11,% 
818 534 
15g | 556 
16144 | 1214 
816 | 514 
138 056 
8 1% 
1334 | 7% 
9g} 5% 
§ 536 
844 Ts 
18 11l?zs 
Ts 6 
534 | 4y¥ 
10% 634 
16 738 
G 556 
914 6 
10% | 84 
bie | 6}% 
1214 194 
fy | 534 
536 
456 | 33% 
8 5 
816 6 
B58 256 
10% 814 
1334 i 
4lg 834 
big | 344 
914 | 516 
8144 | oP 
8) 534 
TPs 6 
914 6 
8 616 
814 534 
R36 656 
Big | 534 


Load of lbs. 











> =F = 


= 
aN 


Capacity of Single 
Coil, lbs.2 ss 














* The subscript 1 means the outside coil of a concentric group or Cluster; 


@ and 3 are inner coils. 


354 RIVETED JOINTS. 


RIVETED JOINTS. 


Fairbairn’s &xperiments. (From Report of Committee on 
Riveted Joiuts, Kroc. Inst. M. £., April, 1881.) 


The earliest published experiments on riveted joints are contained in the 
memoir by Sir W. Fairbairn in the Transactions of the Royal Society. 
Making certain empirical allowances, he adopted the following ratios as ex- 
pressing the relative strength of riveted joints: 


Solid plate scsi we at racists cote < epartne, aa 100 
Double-riveted joint, ............0.... 70 
Single-riveted joint......... jhe iets hays od 56 


These well-known ratios are quoted in most treatises on riveting, and are 
still sometimes referred to as having a considerable authority. It is singular, 
however, that Sir W. Fairbairn does not appear to have been aware that the 
proportion of metal punched out in the line of fracture ought to be different 
in properly designed double and single riveted joints. These celebrated 
ratios would therefore appear to rest on a very unsatisfactory analysis of 
the experiments on which they were based. 

Loss of Strength in Punched Plates.—A report by Mr. W. 
Parker and Mr. John, made in 1878 to Lloyd’s Committee, on the effect of 
punching and drilling, showed that thin steel plates lost comparatively little 
from punching, but that in thick plates the loss was very considerable. 
The folleane table gives the results for plates punched and not annealed 
or reamed : 


Thickness of Material of Loss of Tenacity, 
Plates. Plates. per cent. 
y% Steel 8 
86 oe 18 
% 66 ‘ °6 
4 ee 33 
84 Tron 18 to 23 


The effect of increasing the size of the hole in the die-block is shown in 
the following table: 


Total Taper of Hole Material of Loss of Tenacity due to 
in Plate, inches. Plates. Punching, per cent. 
1-16 Steel 17.8 
1% 0 12.3 
4 ee (Hole ragged) 24,5 


The plates were from 0.675 to 0.712 inch thick. When %-in. punched holes 
were reamed out to 11g in. diameter, the loss of tenacity disappeared, and 
the plates carried as high a stress as drilled plates. Annealing also restores 
to punched plates their original tenacity. , 


Strength of Perforated Plates, 
(P. D. Bennett, Eng’g, Feb. 12, 1886, p. 155.) 


Tests were made to determine the relative effect produced upon tensile 
strength of a flat bar of iron or steel: 1. By a 34-inch hole drilled to the re- 
quired size ; 2. by a hole punched 1g inch smaller and then drilled to the 
size of the first hole ; and, 3, by a hole punched in the bar to the size of the 
drilled bar. The relative results in strength per square inch of original area 
were as follows: 


Ie Re 3 4 


Tron. Iron. Steel. Steel. 

Unperforated bar..............-. oes 1.000 1.000 1.000 1.000 
Perforated by drilling................ 1.029 1.012 . 1.068 1.103 
a ** punching and drilling. 1.030 1.008 1.059 1.110 

oe ‘© punching only......... 0.795 0.894 0.935 0.927 


In tests 2 and 4 the holes were filled with rivets driven by hydraulic pres- 
sure. The increase of strength per square inch caused by drilling is a phe- 
nomenon of similar nature to that of the increased strength of a grooved bar 
over that of a straight bar of sectional area equal to the smallest section of 
the grooved bar. Mr, Bennett’s tests on an iron bar 0,84 in. diameter, 10 in. 


EFFICIENCY OF RIVETING BY DIFFERENT METHODS. 355 


long, and a similar bar turned to (0.81in. diameter at one point only, showed 
that the relative strength of the latter to the former was 1.323 to 1.000, 


Riveted Joints.—Drilling versus Punching of Holes, 


The Report of the Research Committee of the Institution of Mechanical 
Engineers, on Riveted Joints (1881), and records of investigations by Prof. 
A.B. W. Kennedy (1881, 1882, and 1885), summarize the existing information 
regarding the comparative effects of punching and drilling upon iron and 
steel plates. From an examination of the voluminous tables given in Pro- 
fessor Unwin’s Report, the results of the greatest number of the experi- 
ments made on iron and steel plates lead to the general conclusion that, 
while thin plates, even of steel, do not suffer very much from punching, yet : 
in those of 14-inch thickness and upwards the loss of tenacity due to punch- 
ing ranges from 10% to 234 in iron plates, and from 11% to 33% in the case of 
mild steel. In drilled plates there is no appreciable loss of strength. It is 
possible to remove the bad effects of punching by subsequent reaming or 
annealing; but the speed at which work is turned out in these days is not 
favorable to multiplied operations, and such additional treatment is seldom 
practised. The introduction of a practicable method of drilling the plating 
of ships and other structures, after it has been bent and shaped, is a matter 
of great importance. If even a portion of the deterioration of tenacity can 
be prevented, a much stronger structure results from the same material and 
the same scantling. This has been fully recognized in the modern English 

ractice (1887) of the construction of steam-boilers with steel plates; punch- 
ing in such cases being almost entirely abolished, and all rivet-holes being 
drilled after the plates have been bent to the desired form. 


Comparative Efficiency of Riveting done by Different 
Methods, 


The Reports of Professors Unwin and Kennedy to the Institution of Me- 
chanical Engineers (Proc. 1881, 1882, and 1885) tend to establish the four fol- 
lowing points: 

1. That tiie shearing resistance of rivets is not highest in joints riveted by 
means of the greatest pressure; 

2. That the ultimate strength of joints is not affected to an appreciable 
extent by the mode of riveting; and, therefore, 

3. That very great pressure upon the rivets in riveting is not the indispen- 
sable requirement that it has been sometimes supposed to be; 

4, That the most serious defect of hand-riveted as compared with machine- 
riveted work consists in the fact that in hand-riveted joints visible slip 
commences at. a comparatively small load, thus giving such joints a low 
value as regards tightness, and possibly also rendering them liable to failure 
under sudden strains after slip has once commenced. 

The following figures of mean results, taken from Prof. Kennedy’s tables 
(Proceedings 1885, pp. 218-225), give a comparative view of hand and hy- 
draulic riveting, as regards their ultimate strengths in joints, and the periods 
at which in both cases visible slip commenced. 











Total Breaking Load. Load at which Visible Slip began. 

Puch Hydraulic Rivet- cere Hydraulic Rivet- 
Hand-riveting. ing. Hand-riveting. ing, 

Tons. Tons. Tons. Tons. 

86.01 85.75 21.7 47.5 
Pir 77.00 a Big 85.0 
82.16 82.70 25.0 53.7 
Se “ 78.58 ss 54.0 
149.2 145.5 81.7 49.7 
saePh< 140.2 Pets 46.7 
193.5 183.1 25.0 . 56.0 
eee \ 183.7 Beis Bane 





In these figures hand-riveting appears to be rather better than hydraulic 
riveting, as far as regards ultimate strength of joint; but is very much in- 
ferior to hydraulic work, in view of the small proportion of load borne by 
it before visible slip commenced, 


356 RIVETED JOINTS. 


Some of the Conclusions of the Committee of Research 
on Riveted Joints, 
(Proc. Inst. M. E., Apl. 1885.) 

The conclusions all refer to joints made in soft steel plate with steel 
rivets, the holes ail drilled, and the plates in their natural state (unannealed). 
In every case the rivet or shearing area has been assumed to be that of the 
holes, not the nominal (or real) airea of the rivets themselves. Also, the 
strength of the metal in the joint has been compared with that of strips 
cut from the same plates, and not merely with nominally similar material. 

The metal between the rivet-holes has a considerably greater tensile re- 
sistance per square inch than the unperforated metal. This excess tenacity 
amounted to more than 20%, both in 83-inch and 34-inch plates, when the 
pitch of the rivet was about 1.9 diameters. In other cases 3g-inch plate gave. 
an excess of 15% at fracture with a pitch of 2 diameters, of 10% with a pitch 
of 3.6 diameters, and of 6.6%, with a pitch of 3.9 diameters; and 34-inch plate 
gave 7.8% excess with a pitch of 2.8 diameters. : 

In single-riveted joints it may be taken that about 22 tons per square inch 
is the shearing resistance of rivet steel, when the pressure on the rivets does 
not exceed about 40 tons per square inch. In double-riveted joints, with 
rivets of about 34 inch diameter, most of the experiments gave about 24 tons 
per square inch as the shearing resistance, but the joints in one Series went 
at 22 tons. 

The ratio of shearing resistance to tenacity is not constant, but diminishes 
very markedly and not very irregularly as the tenacity increases. 

The size of the rivet heads and ends plays a most important part in the 
strength of the joints—at any rate in the case of single-riveted joints. An 
increase of about one third in the weight of the rivets (all this increase, of 
course, going to the heads and ends) was found to add about 814% to the 
resistance of the joint, the plates remaining unbroken at the full shearing 
resistance of 22 tons per square inch, instead of tearing at a shearing stress 
of only a little over 20 tons. The additional strength is probably due to the 
prevention of the distortion of the plates by the great tensile stress in the 
rivets. 

The intensity of bearing pressure on the rivet exercises, with joints propor- 
tioned in the ordinary way, a very important influence on their strength. 
So long as it does not exceed 40 tons per square inch (measured on the pro- 
jected area of the rivets), it does not seem to affect their strength ; but pres- 
sures of 50 to 55 tons per square inch seem to cause the rivets to shear in 
most cases at stresses varying from 16 to 18 tons per. square inch. For or- 
dinary joints, which are to be made equally strong in plate and in rivets, 
the bearing pressure should therefore probably not exceed 42 or 43 tons per 
square inch. For double-riveted butt-joints perhaps, as will be noted later 
a higher pressure may be allowed, as the shearing stress may probably not 
be more than 16 or 18 tons per square inch when the plate tears. 

A margin (or net distance from outside of holes to edge of plate) equa! to the 
diameter of the drilled hole has been found sufficient in all cases hitherto tried. | 

To attain the maximum strength of a joint, the breadth of lap must be 
such as to prevent it from breaking zigzag. It has been found that the net: 
metal measured zigzag should be from 80% to 85% in excess of that measured 
straight across, in order to insure a straight fracture. This corresponds tc 
a diagonal pitch of 2/3 p + d/8, if p be the straight pitch and d the diam- 
eter of the rivet-hole. 

Visible slip or ‘‘give”’ occurs always in a riveted joint at a point very 
much below its breaking load, and by no means proportional to that load. 
A collation of the results obtained in measuring the slip indicates that it de- 
pends upon the number and size of the rivets in the joint, rather than upon 
anything else ; and that it is tolerably constant for a given size of rivet ina 
given type of joint. The loads per rivet at which a joint will commence to 
slip visibly are approximately as follows: 








; ; Ps A ie Slipping Load per 
Diameter of Rivet.| Type of Joint. Riveting. Rivet: 
34 inch Single-riveted Hand 2.5 tons 
YP Double-riveted Hand 3.0 to 3.5 tons 
ears Double-riveted Machine 7 tons 
1inch Single-riveted Hand 3.2 tons 
ris Double-riveted Hand 4.3 tons 
t 


1 Double-riveted | Machine 8 to 10 tons 


DOUBLE-RIVETED LAP-JOINTS, 357 


To find the probable load at which a joint of any breadth will commence 
to slip, multiply the number of rivets in the given breadth by the proper 
fizure taken from the last column of the table above. It will be understood 
that the above figures are not given as exact; but they represent very weli 
the results of the experiments. 

The experiments point to simple rules for the proportioning of joints of 
maximum strength. Assuming that a bearing pressure of 43 tons per square 
inch may be allowed on the rivet, and that the excess tenacity of the plate 
is 10% of its original strength, the following table gives the values of the ratios 
of diameter d of hole to thickness t of plate (d + t), and of pitch p to diam- 
eter of hole (p ~ d) in joints of maximum strength in 3g-inch plate, 


For Single-riveted Plates, 





Original Tenacity of |Shearing Resistance of 








A ti . 
ate pies Ratio. | Ratio. |p) aa nm 
Fhe is SRE | diate) preted lee ere ee 
Tons per| Lbs. per | Tons per | Lbs. per Rivet Area 
sq. in. sq. in. sq. in. sq. in. 
30 67,200 22 49,200 2.48 2.30 0.667 
28 62,720 Sa2e 49,200 2.48 2.40 0.785 
30 67,200 24 53,760 2.28 2.26 0.713 
28 62,720 24 53,160 2.28 2.36 0.690 





_ This table shows that the diameter of the hole (not the diameter. of the 
rivet) should be 214 times the thickness of the plate, and the pitch of the 
rivets 234 times the diameter of the hole. Also, it makes the mean plate area 
71% of the rivet area. 

If a smaller rivet be used than that here specified, the joint will not be of 
aniform, and therefore not of maximum, strength; but with any other size 
of rivet the best result will be got by use of the pitch obtained from the 
simple formula 


d? 
p=a-> +d, 


where, as before, d is the diameter of the hole. 
The value of the constant a in this equation isas follows: 


For 30-ton plate and 22-ton rivets, a = 0.524 
ee 98 46 99 ee 6s 


0.558 
eas 0) of 24 ce "0.570 
6 28 66 9. 66 t) 0. 606 


P | 
Or, in the mean, the pitch p = 0.56 umf 


It should be noticed that with too small rivets this gives pitches often con- 
siderablv smallerin proportion than 23g times the diameter. 

For double-riveted lap=joints a similar caloulation to that given 
above, but: with a somewhat smaller allowance for excess tenacity, on 
account of the large distance between the rivet-holes, shows that for joints 
of maximum strength the ratio of diameter to thickness should remain pre- 
cisely as in single-riveted joints; while the ratio of pitch to diameter of hole 
should be 3.64 for 30-ton plates and 22 or 24 ton rivets, and 3.82 for 28-ton 
plates with the same rivets. 

Here, still niore than in the former case, it is likely that the prescribed 
size of rivet may often be Inconveniently large. In this case the diameter 
of rivet should be taken as large as possible; and the strongest joint for a 
given thickness of plate and diameter of hole can then be obtained by using 
the pitch given by the equation 


2 
_ paaSta, 


where the values of the constant a for different strengths of plates and 
rivets may be taken as follows: z 


358 RIVETED JOINTS. 


Table of Proportions of Double-riveted Lap-joints, 
2 
in which p = aS +d. 


4 


Original tenacity Shearing Resist- Value of Con- 


Thickness of of Plate, ance of Rivets. stant. 

Plate. Tons per sq. in. ‘Tons per sq. in. a 

36 incr 30 24 1515 
3g SE 28 24 1.22 
3g SS 30 22 1.05 
3B «CSS 28 22 1.12 
Bh 30 24 bale 
OHS ie 28 24 1.25 
34 «CS 30 22 1.07 
Ba 28 2 1.14 


Practically, having assumed the rivet diameter as large as possible, we 
can fix the pitch as follows. for any thickness of plate from 3 to 34 inch; 


i ‘ 94. i a? 

For He ton plate and a ton au p = 1.16 = 1 d: 
d? 

SV a Poe es ere ae) | i == 1G F +d; 


se OQ 46 66 & 94 66 “6 p= 124 +d, 


in double-riveted butt-joints it is impossible to develop the full 
shearing resistance of the joint without getting excessive bearing pressure, 
because the shearing area is doubled without increasing the area on whick 
the pressure acts. Considering only the plate resistance and the bearing 
pressure, and taking this. latter as 45 tons per square inch, the best pitch 
would be about 4 times the diameter of the hole. We may probably say 
with some certainty that a pressure of from 45 to 50 tons per square inch on 
the rivets will cause shearing to take place at from 16 to 18 tons per square 
inch. Working out the equations as before, but allowing excess strength of 
only 5% on account of the large pitch, we find that the proportions of double- 
riveted butt-joints of maximum strength, under given conditions, are those 
ot the foHowing table: : 


Double-riveted Butt-joints, 


Original Ten- Shearing Re- Bearing 
acity sistance Pres- Ratio 


of Plate, of Rivets, sure, d Ratio 
Tons per Tons per Tons per — ie 
sq. in. sq. in, sq. in. t d 

30 16 45 1.80 3.85 

28 16 45 1.80 4.06 

30 18 48 1.70 4.03 

28 18 48 1.70 4.27 

30 16 50 2.00 4.20 

28 16 50 2.00 4.42 


Practically, therefore, it may be said that we get a double-riveted butt-joint 
of maximum strength by making the diameter of hole about 1.8 times the 
See of the plate, and making the pitch 4.1 times the diameter of the 

ole. 

The proportions just given belong to joints of maximum strength. But in 
a boiler the one part of the joint, the plate, is much more affected by time 
than the other part, the rivets. It is therefore not unreasonable to estimate 
the percentage by which the plates might be weakened by corrosion, etc., 
before the boiler would be unfit for use at its proper steam-pressure, and to 
add correspondingly to the plate area. Probably the best thing to do in this 
ease is to proportion the joint, not for the actual thickness of plate, but for 
a nominal thickness less than the actual by the assumed percentage. In 
this case the joint will be approximately one of uniform strength by the 
time it has reached its final workable condition; up to which time the joint 
as a whole will not really have been weakened, the corrosion only gradually 
bringing the strength of the plates down to that of rivets. 


RIVETED JOINTS. 259 


-Efficiencies of Joints. 


The average results of experiments by the committee gave: For double- 
riveted lap-joints in 3¢-inch plates, efficiencies ranging from 67.1% to 81.2%. 
For double-riveted brtt-joints. (in double shear) 61.4% to 71.3%. These low re- 
sults were probably due to the use of very soft steel in the rivets. For single- 
riveted lap-joints of various dimensions the efficiencies varied frum 54.8% to 

. O- 

The experiments showed that the shearing resistauce of steel did not in- 
erease nearly so fast as its tensile resistance. With very soft steel, for 
instance, of only 26 tons tenacity, the shearing resistance was about 80% of 
the tensile resistance, whereas with very hard steel of 52 tons tenacity the 
shearing resistance was only somewhere about 65% of the tensile resistance. 


Proportions of Pitch and Overlap of Plates to Diameter 
of Rivet-Hoie and Thickness of Plate. 


(Prof. A. B, W. Kennedy, Proc. Inst. M. E., April, 1885.) 


t = thickness of plate; 
d = diameter of rivet (actual) in parallel hole; 
p = pitch of rivets, centre to centre; 
S = space between lines of rivets; 
= overlap of plate. 


The pitch is as wide as is allowable without imparing the tightness of the 
joint under steam. : 
For single-riveted Jap-joints in the circular seams of boilers which have 
double-riveted longitudinal lap-joints, 
G=t x 2.25; 
p = ax 2.25= 1 x 5 (nearly); 
= USE 
For double-riveted lap-joints: 











ez 2 2563 
$= 4.5f; 
U=10dE: 
Single-riveted Joints. Double-riveted Joints. 
t d p d t d p Pee ey 
3-16 7-16 | 15-16 1% 3-16 | 7-16 1144 % 2 
YY 9-16 }114 1% Yy 9-16 2 ] 3-16 234 
5-16 11-16 |1 9-16 1% 5-16 11-16 214 1% 334 
34 13-16 11% 214 38 13--16 3 134 4 
7-16 1 2 3-16 254 7-16 |1 34 2 454 
1) 1g 214 3 le 11% 4 214 514 
9-16 {144 2 13-16 336 9-16 |114 4146 | 24 5% 








With these proportions and good workmanship there necd be no fear of 
leakage of steam through the riveted joint. : 

The net diagonal area, or area of plate, along a zigzag line of fracture 
should not be less than 80% in excess of the net area straight across the 
joint, and 352 is better. j 

Mr. Theodore Cooper (R. R. Gazette, Aug. 22, 1890) referring to Prof, Ken- 
nedy’s statement quoted above, gives as a sufficiently approximate rule for 
the proper pitch between the rows in staggerei riveting, one half of the 
pitch of the rivets in a row plus one quarter the diameter of a rivet-hole. 


Apparent Excess in Strength of Perforated over Unper= 
forated Plates, (Proc. Inst. M. E., October, 1588.) 


The metal between the rivet-holes has a considerably greater tensile re- 
sistance per square inch than the unperforated metal. This excess tenacity 
amounted to more than 20%, both in 3¢-inch and 34-inch plates, when che 
pitch of the rivets was about 1.9 diameters. In other cases 3-inch plate 
gave an excess of 15% at fracture with a pitch of 2 diameters, of 10% with a 
pitch of 3.6 diameters, and of 6.6% with a pitch of 3.9 diameters; and 34-inch 
plate gave 7,8% excess with a pitch of 2.8 diameters. 


360 RIVETED JOINTS. 


(1) The ‘‘excess strength due to perforation ” is increased by anything 
which tends to make the stress in the plate uniform, and to diminish the 
effect of the narrow strip of metal at the edge of the specimen. 

(2) It is diminished by increase in the ratio of p/d, of pitch to diameter of 
hole, so that in this respect it becomes less as the efficiency of the joint 
increases. 

(3) It is diminished by any increase in hardness of the plate. 

(4) For a given ratio p/d, of pitch to diameter of hole, it is also apparently 
diminished as the thickness of the plate is increased, The ratio of pitch to 
thickness of plate does not seem to affect this matter directly, at least 
within the limits of the experiments. 

Test of Double-riveted Lap and Butt Joints. 
(Proc. Inst. M. E., October, 1888.) 


Steel plates of 25 to 26 tons per square inch T. S., steel rivets of 24.6 tons 
shearing-strength per square inch. 


Comparative 
: : Thickness of Diameter of Ratio of Pitch p 
Kind of Joint. Plate. Rivet-holes. to Diameter. eee of 
TAPS ee eeco les rs 3¢/" 0.8/7 3.62 Dee 
Butt : 38 0.7 3.93 76.5 
Tia Dea ceils ode 34 1.1 2.82 68.0 
Le see eee tore 34 1.6 3.41 73.6 
Bie eee : 34 1.1 4.00 72.4 
Slate BAe edi eis 34 1.6 8.94 46.1; 
NUALD ease cise Mee 1 1.3 2.42 63.0 
AN ets SNP BEE eae 1 1.75 8.00 70.2 
Bitte ee eae ves 1 1:3 3.92 76.1 


Some Rules which have been Proposed for the Diameter 
of the Rivet in Single Shear. (lon, June 18, 1880.) 


POW © Semeeyecienise es hiiaeusy se d = xt (with double covers 144¢) (1) 
AIPM ALEM mwars sie ee sssis sere ee = 2¢t for pilates less than 3¢ in. (2) 

REET 1 GON sg Slane i Sachets, Bose ee a & 1L4¢t for Dee greater than 3¢ in, (3) 
WGOMTAILT Ot so cisine cc molemences d= 1.5t+ 0.1 <4) 
ADUOME)s ves, dei sistyeeere ols d=11 Vt (5) 
WBOMIO fea nis cack oehis © sike ciete ss d = 2t for boiler riveting (6) 

SM Ma TS UNS Sate <a here d = 3t for extra strong riveting 1) 
Redtenbacher............-. G-— Wear borer (8) 
Unwin...... TAO Pies ett f d = 34 + 5/16 to %t+ % (9) 

SSO Suc SEITEN AIR EEie eye (10) 


The following table contains some data ot the sizes of rivets used in 
practice, and the corresponding sizes given by some of these rules. 


Diameter of Rivets for Different Thicknesses of Plates. 


Diameter of Rivets, in inches. 








Thick- 


















































5 oj = 
ness of/~ .|. 8 . |SE| au |B ae & o eS a 
plate, (93) £3 (28) 8S jo.) EX | g- | sz | te S 
Inches.|9"5| 973 |Mu) 2 ES aia ax ye a= 4 
AM) SM Ia) BS |5 le < =) e 
a aes 
S/iG) Senos Teh ey)... 56 | 56 54 56 11/16 | 5¢ 
3% 5g | 56 5g | 56 | 34] 34 23/32 | 11/16 | 34 11/16 
T/AG | 58 | 34 34 | 56 | %| 21/382} 13/16 | 34 13/16 | 34 
BF Ia OMaae yes. 4: 1 34 15/16 | 34 % 34 
9/16 | % | 13/16] %| 34 |1%| 27/8211 1B/i6 gee oe) 
5% $7) % Pt a 1144 | 15/16 | 11% % 15/16 | % 
11/16 | %\% | %\| 18/16)... | 11/32] 1°3/16 | 15/16 | 1 % 
34 % | 15/16|1 % 1 14 15/16 | 11/16 | 1 
13/16 | % |1 1° eee 1 7/82 | 13 1 1 3/32 | 1 
FA lh Stig SEV 16 ha AG BEE 1 14 1 
AG it 1 S/1C|i1g (ome ee .. tee... eee 11/16 | 13/16 | 114 
Lye Ny ig Kg Shea aa (RR 1% 14 114 


RIVETED JOINTS. 361 


Strength of Double-riveted Seams, Calculated. —W. B. 
Ruggles, Jr., in Power for June, 189, gives tables of relative strength of 
rivets and parts of sheet between rivets in double-riveted seams, compared 
with strength of shell, based on the assumption that the shearing strength 
of rivets and the tensile strength of steel are equal. The following figures 
show the sizes in his tables which show the nearest approximation to equal- 
ity of strength of rivets and parts of plates between the rivets, together 
with the percentage of each relative to the strength of the solid plate. 








A Percentage of Percentage of 
Pitch |Size of Strength of Pitch |Size of Strength of 
of Rivet- Plate. of Rivet- Plate. 


Rivets,| holes, 


Rivets,| holes, ] ] 
inches | inches. 


inches.| inches. 





Thicknesss of 
plate, inches 
Thickness of 
Plate, inches 


Rivets.| Plate. Rivets.| Plate. 





— ee | ef | | Le ee ee fe 








y%| 2 \% 739 | .765 §%/16] 234 34 734 | .728 
14 6: O/16 [7950 1 iid. A7/16l 6 Bhs. le aside | 5a i ap 
eh pk in ei 7 785 | .800 97/16} 354 U1 958 Mn eag 
354 | 11/16| .819 | .810 97716} 416 | 15/16 | 765 via 
5/16] 2 9/16 749 |- 785 —f 16| 2h 3 07 “00 
5/16] 256 | 5 FAR | 762 de | 908 1 18716: |? 721 718 
5/16| 3h 11/16 | .761 "30 f 164] 3% % 740 731 
5/16, 354 | 3% HBO 2440708. Pete. h. 85408, 10/0 (ease 750 
8 ai, | 64 vay | 792 fF ie] 4ig ’ 761 "58 
34 | 256 | 11/16] .755 | .738 99/16] 254 | 13/16] .701 690 
Bg Big ts tBZ 754 1 .760 § 9/16) | % 714 | 708 
3 354 | 13/16| .762 | .776 §9/16] 336 | 15/16] .727 | 722 
8 z 777 | .788 §9/16| 334 1 en eitens, 


Bi | 4ig 
7/16 236 11/16 714 afoul 9/16 414 1 1/16 742 .150 


H. De B. Parsons (Am. Engr. & R. R. Jour., 1893) holds that it is an error to 
assume that the shearing strength of the rivet is equal to the tensile strength. 
Also, referring to the apparent excess in strength of perforated over unper- 
forated plates, he claims that on account of the difficulty in properly match- 
ing the holes, and of the stress caused by forcing, as is too often the case 
in practice, this additional strength cannot be trusted much more than 
that of friction. 

Adopting the sizes of iron rivets as generally used in American practice 
for steel plates from 44 to 1 inch thick: the tensile strength of the plates as 
60,000 lbs.; the shearing strength of the rivets as 40,000 for single-shear and 
35,500 for double-shear, Mr. Parsons calculates the following table of 
pitches, so that the strength of the rivets against shearing will be approxi- 
mately equal to that of the plate to tear between rivet-holes. The diameter 
of the rivets has in all cases been taken at 1/16 in. larger than the nominal 
size, as the rivet is assumed to fill the hole under the power riveter. 


BRiveted Joints. 
Lap or Butt WITH SINGLE WELT—STEEL PLATES AND IRON RIVETS. 














Pitch. Efficiency: 
Thickness | Diameter 
of. of 
Plates. | Rivets. Single, Double. Single. | Double. 
in. in. in. in. 
Y, i 1 3/16 1% 55.7% "0.0% 
34 1 11/16 2°11/16 52.7 68.6 
% 1% 234 49 0 65.9 
56 % 1 11/16 27/16 43.6 60.4 
34 1 % 254 42.0 59.5 
y 1 134 27/16 38.6 55 4 
1 1/8 23/16 256 38.1 54.9 


362 RIVETED JOINTS. 


-Caleulated Efficiencies—Steel Plates and Steel Rivets.— 
The differences between the calculated efficiencies given in the two tables 
above are notable. Those given by Mr. Ruggles are probably too high, since 
he assumes the shearing strength of the rivets equal to the tensiie strength 
of the plates. Those given by Mr. Parsons are probably lower than will be 
obtained in practice, since the figure he adopts for shearing strength is 
rather low, and he makes no allowance for excess of strength of the perfo- 
rated over the unperforated plate. The following table has been calculated 
by the author on the assumptions that the excess strength of the perforated 
plate is 10%, and that the shearing strength of the rivets per square inch is 
four fifths of the tensile strength of the plate. If ¢ = thickness of’plate, 
d = diameter of rivet-hole, p = pitch, and 7 = tensile strength per square 
inch, then for single-riveted plates 


7 4 wa? 
(p -—djt X1.10T= a as x gf whence p Se +d. 
For double-riveted plates, p = 1.142 +d. 


The coefficients .571 and 1.142 agree closely with the averages of those 
given in the report of the committee of the Institution of Mechanical En- 
gineers, quoted on pages 357 and 358, ante. 























Pitch. Efficiency. Pitch. Efficiency. 
y He hee erg @imircss (i 7 Ree eg Ecotec rhe ae . ? 
o ey 9 bh wf 2 | of be bp a ry 
3 | Rivet-| 28/35) 28/229 8 | Rivet-| 25 / 2s) 25 | 25 
2 | hole zo Z 9 a3 Zo |Z | hole os Fas 26 29 
= id) md — ao) —_ Ve D a —_ iS) —_ ont 
= Pea wig Poel neal chee Dee Oe) Ae | Me | ee 
— eS ee | Fe 
Any 10 in. in. % % fin.| in. in in. % % 
3/16} 7/16 | 1.020] 1.603] 57.1 | 72.7 8 14 34 1.292] 2.085) 46.1 | 63.1 
i 1 | 1.261) 2.023) 60.5 | 75.3 f° % | 1.749 2.624] 50.0 | 66.6 
% 4% 1.071] 1.642) 53.3 | 69.6 9 ‘ 1 2.142) 3.284] 58.3 | 70.0 
+ 9/16 | 1.285} 2.008} 56.2 | 72.0 @ * 14 2.570) 4.016) 56.2") 72.0 
5/16; 9/16 | 1.137] 1.712) 50.5 | 67.1 §9/16 34 1.321} 1.892} 43.2 | 60.3 
ey 56 1.339] 2.053] 58.3 | 69.5 § ** % 1.652} 2.429) 47.0 | 64.0 
wy PV / VOR ST EOD 1 | C2 anor opavel «lvoe mh ] 2.015} 3.030) 50.4 | 67.0 
3% % 1.218) 1.810] 48.7 | 65.5 # * wy 2.410! 3.694] 53.3 ; 69.5 
ce 34 1.607) 2.463] 53.3 | 69.5 @ ‘ 14 2.836) 4.422) 55.9 | 71.5 
oe % 2.041) 3.206) 57.1 | 72.7 5% 34 1.264] 1.778! 40.7 | 57.8 
¢/16 56 12156) 15647) 545.50 55°62.0 % 1.575] 2.274] 44.4 | 61.5 
ah 34 1.484] 2.218] 49.5 | 66.2 § °° 1 1.914] 2.827) 47.7 | 64.6: 
ve % 1.869} 2.864) 53.2 | 69.4 § 1% 2.281] 3.438] 50.7 | 67.3 
a 1 2.305) 3.610} 56.6 | 72.3 & ‘S 1144 2.678} 4.105] 53.8 | 69.5 








Riveting Pressure Required for Bridge and Boiler 
Work. 


(Wilfred Lewis, Engineers’ Club of Philadelphia, Nov., 1893.) 


A number of 3-inch rivets were subjected to pressures between 10.000 and 
60,000 Ibs. At 10,000 lbs. the rivet swelled and filled the hole without forming 
a head. At 20,000 Ibs. the head was formed and the plates were slightly 
pinched. At 30.000 lbs. the rivet was well set. At 40,000 lbs. the metal in the 
plate surrounding the rivet began to stretch, and the stretching became 
more aud more apparent as the pressure was increased to 50,000 and 60,000 
lbs. From these experiments the conclusion might be drawn that the pres- 
sure required for cold riveting was about 300,000 lbs. per squareinch of rivet 
section. In hot riveting, until recently there was never any call for a pres- 
sure exceeding 60,000 lbs., but now pressures as high as 150,000 lbs. are not 
uncommon, and even 300,000 Ibs. have been contemplated as desirable. 


iSHEARING RESISTANCE OF RIVET IRON AND STEEL, 363 


Apparent Shearing Resistance of Rivet Iron and Steel. 
(Proc. Inst. M. EH., 1879, Engineering, Feb. 20, 1880.) 


The true shearing resistance of the rivets cannot be ascertained from 
experiments on riveted joints (1) because the uniform distribution of the 
load to all the rivets cannot be insured; (2) because of the friction of the 
plates, which has the effect of increasing the apparent resistance to shear- 
ing in an element uncertain in amount. Probably in the case of singles 
riveted joints the shearing resistance is not much affected by the friction, _ 


Ultimate Shearing Stress 
Tons per sq.in. Lbs. per sq. in. 
Iron, single shear (12 bars).. 24.15 54.096 {Clarke \ 


double shear (8 bars). .! 22.10 49.504 
Of WC ae ne 22.62 50.669 Barnaby. 
at - “ A 22.30 49.952 Rankine, ° 
‘°  34-in. rivets......006... 23.05 to 25.57 51.632 to 57.277 
cS SOSIN TIVES. oA veda st » 24.82 to 27.94 54.477 to 62.362 >Riley. 
‘mean value 25.0 56.000 
SOM Dein Srivietss wos Ls ee ao ; 19.01 42.582 Greig and Eyth. 
CCC UMn ee cas oe aretis uct winrels Seguate 17 to 26. 38.080 to 58.240 Parker. 


31.67 to 33.69 
30.45 to 35.7 


70.941 to 75.466 
68.208 to 80.035 > Riley. 
mean value.. 33.3 74.592 


Brownisistecls 6s ei. aeas «sense 22.18 49.683 Greig and EKyth. 


Fairbairn’s experiments show that a rivet is 614% weaker in a drilled than 
fn a punched hole. By rounding the edge of the rivet-hole the apparent 
shearing resistance is increased 12%. Mr. Maynard found the rivets 4% 
weaker in drilled holes than in punched holes. But these results were 
obtained with riveted joints, and not by direct experiments on shearing. 
There is a good deal of difficulty in determining the true diameter ofa 
punched hole, and it is doubtful whether in these experiments the diameter 
was very accurately ascertained. Messrs. Greig and Eyth’s experiments 
also indicate a greater resistance of the rivets in punched holes than in 
drilled holes. 

If, as appears above, the apparent shearing resistance is less for double 
than for single shear, it is probably due to unequal distribution of the stress 
on the two rivet sections. 

The shearing resistance of a bar, when sheared in circumstances which 
prevent friction, is usually less than the tenacity of the bar. The following 
results show the decrease : 


Landore steel, 34-in. rivets.. 
* “* %-in, rivets.. 


oe 73 





Tenacity of Shearing : 

Bar. Resistance. Ratio 
Harkort, iron..... o.. 26.4 16.5 0.62 
Lavalley ironss.e.2.<. « 25.4 20.2 0.79 
Greig and Eyth, iron... 22.2 19.0 0.85 
Hs ‘¢ steel.. 28.8 22.1 Ria 








In Wohler’s researches (in 1870) the shearing strength of iron was found 
to be four-fifths of the tenacity. Later researches of Bauschinger confirm 
this result generally, but they show that for iron the ratio of the shearing 
resistance and tenacity depends on the direction of the stress relatively to 
the direction of rolling. The above ratio is valid only if the shearis ina 
plane perpendicular to the direction of rolling, and if the tension is applied 
parallel to the direction of rolling. The shearing resistance ina plane 
parallel to the direction of rolling is different from that in a plane perpen- 
dicular to that direction, and again differs according as the plane of shear is 
perpendicular or parallel to the breadth of the bar. In the former case the 
resistance is 18 to 20% greater than in a plane perpendicular to the fibres, or 
is equal to the tenacity. In the latter caseit isonly half as great as ina 
plane perpendicular to the fibres. 


IRON AND STEEL. 


364 


IRON AND STEEL. 
CLASSIFICATION OF IRON AND STEEL, 


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CAST IRON. 365 


CAST IRON. 


Grading of Pig Iron.—Pig iron is commonly graded according to its 
fracture, the number of grades varying in different districts. In Eastern 
Pennsylvania the principal grades recognized are known as No.1 and 2 
foundry, gray forge or No. 3, mottled or No. 4,and white or No. 5. Inter- 
mediate grades are sometimes made, as No. 2 X, between No.1 and No. 2, 
and special names are given to irons more highly silicized than No. 1, as 
No. 1 X, silver-gray, and soft. Charcoal foundry pig iron is graded by num- 
bers 1 to 5, but the quality is very different from the corresponding num- 
bers in anthracite and coke pig. Southern coke pig iron is graded into ten 
or more grades. Grading by fracture is a fairly satisfactory method of 
grading irons made from uniform ore mixtures and fuel, but is unreliable as 
a means of determining quality of irons produced in different sections or 
from different ores. Grading by chemical analysis, in the latter case, is the 
only satisfactory method. The following analyses of the five standard 
grades of northern foundry and mill pig irons are given by J. M. Hartman 
(Bull. I. & S. A., Feb., 1892): 


No.1. No.2. No.3. No.4. No.4B. No.5. 


LEON ee et hints ee eae lace 92.37 92.31 -. 94.66 94.48 94.08 94.68 
Graphitic carbon.. 3.52 2.99 2.50 2.02 2.02) tata 
Combined carbon.. 13 BF Lo 1.58 1.43 3.83 
SLTCOnM ass ae taeee 2.44 2sDe 372 06 .92 41 
Phosphorus.... ... 1.25 1.08 26 .19 04 04 
SNORT Sahel see pas .02 .02 trace .08 .04 .02 
Manganese......... 28 12 34 67 2.02 .98 


CHARACTERISTICS OF THESE IRONS, 


No. 1. Gray.—A large, dark, open-grain iron, softest of all the numbers 
and used exclusively in the foundry. Tensile strength low. Elastic limit 
low. Fracturerough. Turns soft and tough, 

No. 2. Gray.—A mixed large and small dark grain, harder than No. 1 iron, 
and used exclusively in the foundry. Tensile strength and elastic limit 
higher than No. 1. Fracture less rough than No. 1. Turns harder, less 
tough, and more brittle than No. 1. 

No. 3. Gray.—Small, gray, close grain, harder than No. 2 iron, used either 
' in the rolling-millor foundry. Tensile strength and elastic limit higher than 
No. 2. Turns hard, less tough, and more brittle than No. 2, 

No. 4. Mottled.—White background, dotted closely with small black spots 
of graphitic carbon; little or no grain. Used exclusively in the rolling-mill. 
‘Tensile strength and elastic limit lower than No.3. Turns with difficulty; 
less tough and more brittle than No. 3. The manganese in the B pig iron 
replaces part of the combined carbon, making the iron harder and closing 
the grain, notwithstanding the lower combined carbon. 

No. 5. White.—Smooth, white fracture, no grain, used exclusively in the 
rolling mill. Tensile strength and elastic limit much lower than No. 4. Too 
hard to turn and more brittle than No. 4. 

Southern pig irons are graded as follows, beginning with the highest in 
silicon: Nos. 1 and 2 silvery, Nos.1 and 2 soft, all containing over 3% of 
silicon; Nos. 1, 2, and 8foundry. respectively about 2.75%, 2.5% and 2% silicon; 
No. 1 mill, or ‘‘foundry forge;’’ No. 2 mill, or gray forge; mottled; white. 

Good charcoal chilling iron for car wheels contains, as a rule, 0.56 to 0.95 
silicon, 0.08 to 0.90 manganese, 0.05 to 0.75 phosphorus. The following is an 
analysis of a remarkably strong car wheel: Si, 0.734; Mn, 0.438; P. 0.428, 
S, 0.08; Graphitic C, 3.088; Combined C, 1.247; Copper, 0.029. The chill was 
very hard—l4 in. deep at root of flange, in. deep on treacG. A. good 
ordnance iron analyzed: Si. 0.30; Graphitie C. 2.20; Combined C, 1.70; P, 
0.44; Mn, 3.55 (?), Its specific gravity was 7.22 and tenacity 31,734 lbs. 

er Sq. 11. : 
> Influence of Silicon, Phosphorus, Sulphur, and Man- 
gamese upon Cast Iron.—W. J. Keep, of Detroit, in several papers 
(Trans. A. I. M. E., 1889 to 1893), discusses the influence of various chemical 
elements on the quality of cast iron. From these the following notes have 
been condensed: 

Siticon.—Pig iron contains all the carbon that it could absorb during its 
reduction in the blast-furnace. Carbon exists in cast iron in two distinct 
forms. In chemical union, as “combined”? carbon. it cannot be discerned, 
except as it may increase the whiteness of the fracture, in so-called white 


366 TRON AND STEEL. 


iron. Carbon mechanically mixed with the iron as graphite is visible, vary- 
ing in coior from gray to black, while the fracture of the iron ranges from a 
light to a very dark gray. 

Silicon will expel carbon, if the iron, when melted, contains ail the carbon 
that it can hold and a portion of silicon be added. 

Prof. Turner concludes from his tests that the amount of silicon producing 
the maximum strength is about 1.80%. But this is only true when a white 
base is used. If an iron is used as a base which will produce a sound casting 
to begin with, each addition of silicon will decrease strength. Silicon itself 
is a weakening agent. Variations in the percentage of silicon added to a pig 
iron will not insure a given strength or physical etructure, but these results 
will depend upon the physical properties of the original iron. 

After enough silicon has been added to cause solid castings, any further 

, addition and consequent increase of graphite weakens the casting. 

» Asstrength decreases from increase of graphite and decrease of coinbined 
carbon, deflection increases ; or, in other words, bending is increased by 
graphite. When no more graphite can form and silicon still increases, de- 
flection diminishes, showing that high silicon not only weakens iron. but 
makes it stiff. This stiffness is not the same strength-stiffness which is 
caused by compact iron and combined carbon. Itis a brittle-stiffness. 

Silicon of itself, however small the quantity present, hardens cast-iron; 
but the decrease of hardness from the change of the combined carbon to 
graphite, caused by the silicon, is so much more rapid than the hardening 
produced by the increase of silicon, that the total effect is to decrease hard- 
ness, until the silicon reaches from 8 to 5%. 

As practical foundry-work does not eall for more than 38% of silicon, the 
ordinary use of silicon does reduce the hardness of castings; but this is pro- 
duced through its influence on the carbon, and not its direct influence on the 
iron. 

When the change from combined to graphite carbon has ceased to dimin- 
ish hardness, say at from 2% to 5% of silicon, the hardening by the silicon it- 
self becomes more and more apparent as the silicon increases. 

The term “chilling” irons is generally applied to such as, cooled slowly, 
would be gray, but cooled suddenly become white either to a depth suffi- 
cient for practical utilization (e.g., in car-wheels) or so far as to be detrimen- 
tal. Many irons chill more or less in contact with the cold surface of the 
mould in which they are cast, especially if they are thin. Sometimes this is 
a valuable quality, but for general foundry purposes it is desirable to have 
all parts of a casting an even gray. : 

Silicon exerts a powerful influence upon this property of irons, partially 
or entirely removing their capacity of chilling. 

When silicon is mixed with irons previously low in silicon the fluidity is 
increased. 

It is not the percentage of silicon, but the state of the carbon and the 
action of silicon through other elements, which causes the iron to be fluid. 

Silicon irons have always had the reputation of imparting fluidity to other 
irons. This comes, no doubt, from the fact that up to 3% or 4% they increase 
the quantity of graphite in the resulting casting. 

A white iron which will invariably give porous and brittle castings can be 
made solid and strong by the addition of silicon; a further addition of sili- 
con will turn the iron gray; and as the grayness increases the iron will grow 
weaker. JHixcessive silicon will again lighten the grain and cause a hard and 
brittle as well as a very weak iron. The only softening and shrinkage-les- 
sening influence of silicon is exerted during the time when graphite is being 
produced, and silicon of itself is not a softener or a lessener of shrinkage; 
but through its influence on carbon, and only during a certain stage, does it 
produce these effects. 

PHospHorus.— While phosphorus of itself, in whatever quantity present, 
weakens cast-iron, yet in quantities less than 1.5% its influence is n. t suffi- 
ciently great to overbalance other beneficial effects, which are exerted 
before the percentage reaches 1%. Probably no element of itself weakens 
cast iron as much as phosphorus, especially when present in large quantities. 

Shrinkage is decreased when phosphorus is increased. All high-phosphorus 
pig irons have low shrinkage. Phosphorus does not ordinarily harden cast 
iron, probably for the reason that it does not increase combined carbon. 

The fluidity of the metal is slightly increased by phosphorus, but not to 
apy such great extent as has been ascribed to it. 

The property of remaining long in the fluid state must not be confounded 
With fluidity, for tt is not the measure of its ability to make sharp castings, 


INFLUENCE OF SILICON, ETC., UPON CAST YRON. 36% 


or forpnd ne Are “ery eae parts 4 a mould. foals tate speaking. the state 
ment is justified that, to some extent, phosphorus prolongs the ftuidit 
the iromabHediis Alii themouldiie 104 oF Pirie oe mee 

The old Scotch irons contained about 1% of phosphorus. The foundry-irons 
which are most sought for for small and thin castings in the Eastern States 
contain, as a general thing, over 1% of phosphorus. 

Certain irons which contain from 4% to 7% silicon have been so much used 
on account of their ability to soften other irons that they have come to be 
known as “‘ softeners’ and as lesseners of shrinkage. These irons are valu- 
able as carriers of silicon; but the irons which are sold most as softeners 
and shrinkage-lesseners are those containing from 1% to 2% of phosphorus. 
We must therefore ascribe the reputation of some of them largely to the 
phosphorus and not wholly to the silicon which they contain. 

From 14% to 1% of phosphorus will do all that can be done in a beneficia) 
way, and all above that amount weakens the iron, without corresponding 
benefit. It is not necessary to search for phosphorus-irons. Most irons 
contain more than is needed, and the care should be to keep it within limits, 
_ SuLPHUR.—Only a small percentage of sulphur can be made to remain 
in carbonized iron, and it is difficult to introduce sulphur into gray cast iron 
or into any carbonized iron, although gray cast iron often takes from the 
fuel as much more sulphur as the iron originally contained. Percentages 
of sulphur that could be retained by gray cast iron cannot materially injure 
the iron except through an increase of shrinkage. The higher the carbon, 
a ae higher the silicon, the smaller will be the influence exerted by 
sulphur. 

The influence of sulphur on all cast iron is to drive out carbon and 
silicon and to increase chill, to increase shrinkage, and, asa general thing, to 
decrease strength ; but if in practice sulphur will not enter such iron, we 
shall not have any cause to fear this tendency. In every-day work, however, 
it is found at times that iron which was gray when put into the cupola comes 
out white, with increased shrinkage and chill, and often with decreased 
strength. This is caused by decreased silicon, and can be remedied by an 
increase of silicon. 

Mr. Keep’s opinion concerning the influence of sulphur, quoted above, is 
disagreed with by J. B. Nau (Iron Age, March 29, 1894). He says: 

‘Sulphur, in whatever shape it may be present, has a deleterious influence 

/ ontheiron. It has the tendency to render the iron white by the influence 
it exercises on the combination between carbon and iron. Pig iron contain- 
ing a certain percentage of it becomes porous and full of holes, and castings 
made from sulphurous iron are of inferior quality. This happens especially 
when the element is present in notable quantities. With foundry-iron con- 
taining as high as 0.1% of sulphur, castings of greater strength may be ob- 
tained than when no sulphur is present. 

That the sulphur contents of pig iron may be increased by the sulphur 
contained in the coke used, is shown by some experiments in the cupola, 
reported by Mr. Nau. Seven consecutive heats were made, 

hee sulphur content of the coke was 1%, and 11.7% of fuel was added to the 
charge. 

nhs. melting, the silicon ranged from 0.320 to 0,830 in the seven heats 3 
after inelting, it was from 0.110 to 0.534, the loss in melting being from .100 
to .3875. The sulphur before melting was from .076 to .090, and after melting 
from .132 to .174, a gain from .044 to .098. 

Fron the results the following conclusions were drawn : 

1. In all the charges, without exception, sulphur increased in the pig iron 
after its passage through the cupola. In some cases this increase more 
than doubled the original amount of sulphnr found in the pig iron. 

2. The increase of the sulphur contents in the iron follows the elimination 
of a greater amount of silicon from that same iron. A larger amount of 
limestone added to these charges would have produced a more basic cinder, 
and undoubtedly less sulphur would have been incorporated in the iron. 

3. This coke contained 1% of sulphur, and if all its sulphur had passed into 
the iron there would have been an average increase of 0.12 of sulphur for 
the seven charges, while the real increase in the pig iron amounted to only 
0.081. This shows that two thirds of the sulphur of the coke was taken up 
by the iron in its passage through the cupola. 

MANGANESE.—Manganese is a nearly white metal, having about the same 
appearance when fractured as white cast iron. As produced commercially, 
it is combined with iron, and with small percentages of silicon, phosphorus, 
and sulphur. ; 

If the manganese is under 40%, with the remainder mostly iron, and silicon 


Nt ate 


368 IRON AND STEEL. 


not over 0.50%, the alloy is called spiegeleisen, and the fracture will show flat 
reflecting surfaces, from which it takes its name. 

With manganese above 50%, the iron alloy is called ferro-manganese. 

As manganese increases beyond 50%, the mass cracks in cooling, and when 
it approaches 98% the mass crumbles or falls in small pieces. 

Manganese combines with iron in almost any proportion, but if an iron: 
containing manganeseisremelted, more or less of the manganese will escape 
by volatilization, and by oxidation with other elements present in the iron.> 
If sulphur be present, some of the manganese will be likely to unite with it 
and escape, thus reducing the amount of both elements in the casting. 

Cast iron, when free from manganese, cannot hold more than 4.50% of car- 
bon, and 3.50% isas much asis generally present; but as manganese increases, 
carbon also increases, until we often find it in spiegel as high as 5%, and in 
ferro-manganese as high as 6%. This effect on capacity to hold carbon is 
veculiar to manganese. ‘ ; 
” Manganese renders cast iron less plastic and more brittle. 

Manganese increases the shrinkage of cast iron. An increase of 1% raised 
the shrinkage 26%. Judging froin some test records, manganese does not 
influence chill at ail; but other tests show that with a given percentage of 
silicon the carbon may be a little more inclined to remain in the combined 
form, and therefore the chill may be a little deeper. Hence, to cause the 
chill to be the same, it would seem that the percentage of silicon should be 
a little higher with manganese than without it. 

An increase of 1% of manganese increased the hardness 40%. If a hard 
chillis required, manganese gives it by adding hardness to the whole casting 

J.B. Nau Uron Age, March 29, 1894), discussing the influence of manga. 
nese on cast iron, says: 

Manganese favors the combination between carbon and iron. Its influ 
ence, when present in sufficiently large quantities, is even great enough no! 
only to keep the carbon which would be naturally found in pig iron con» 
bined, but it increases the capacity of iron to retain larger amounts of car- 
bon and to retain it all in the combined state. \ 

Manganese iron is often used for foundry purposes when some chill and 
hardness of surface is required in the casting. For the rolls of steel-rail 
mills we always put into the mixture a large amount of manganiferous iron,’ 
and the rolls so obtained always presented the desired hardness of surface 
and in general a mottled structure on the outside. The inside, which al- 
ways cooled much slower, was gray iron. One of the standard mixtures that 
invariably gave good results was the following: 

50% of foundry iron with 1.3% silicon and 1.5% manganese; 
35% of foundry iron with 1% silicon and 1.5% manganese; 
15% steel (rail ends) with about 0.35% to 0.40% carbon. 

The roll resulting from this mixture contained about 1% of silicon and 1% 
of manganese. 

; einen mixture, which differed but little from the preceding, was as 
ollows: 

45% foundry iron with about 1.3% silicon and 1.5% manganese; 

30% foundry iron with about 1% silicon and 1.5% manganese; 

10% white or mottled iron with about 0.5% to 0.6% Si. and 1.2% Mn. 

15% Bessemer steel-rail ends with about 0.35% to 0.40% C. and 0.6% to 1% Mn. 

The pig iron used in the preceding mixtures contained also invariably 
from 1.5% to 1.8% of phosphorus, so that the rolls obtained therefrom carried 
about 1.3% to 1.4% of that element. The last mixture used produced rolls 
containing on the average 0.8% to 1% of silicon and 1% of manganese. When- 
ever we tried to make those rolls from a mixture containing but 0.2% to 0.3% 
manganese our rolls were invariably of inferior quality, grayer, and con- 
sequently softer. Manganese iron cannot be used indiscriminately for 
foundry purposes. When greater softness is required in the castings man- 
ganese has to be avoided, but when hardness to a certain extent has to be 
obtained manganese iron can be used with advantage. 

Manganese decreases the magnetism of the iron. This characteristic in- 
creases with the percentage of manganese that enters into the composition 
of the iron. The iron loses all its magnetism when manganese reaches 25% 
of its composition. For this reason manganese iron has to be avoided in 
castings of dynamo fields and other pieces belonging to electric machinery, 
where magnetic conductibility is one of the first considerations. 

Shrinkage of Cast Iron.—Mv. Keep gives a series of curves show- 
ing that shrinkage depends on silicon and on the cross-section of . the 
casting, decreasing as the silicon and the section increase. The following 
figures are obtained by inspection of the curves: ‘ 


TESTS OF CAST IRON. 


Size of Square Bars. | 

















369 


Size of Square Bars. 

















de es 

S30 : : c : Ce P : . 

=o intel ine p2aneaS is) Aan eOO Ne hanewet: ine 2) ims) Sim. )4in. 

as OTe ems EEE Sea 

Shrinkage, In. per Foot. Shrinkage, In. per Foot. 

HOO! et7s |) 158) e120) e124 102) 2250) S142 (et S091) 2072) 060 

1.50] .166! .145] N16] .099| .088]/ 3.00] .1380} .109] .078]| .058! .046 
.O74 |} 3.50} .118] .097] .065]| .045] .032 


2.00} .154} .133] .104]| .086 





Mr. Keep says: ‘‘ The measure of shrinkage is practically equivalent to a 


chemical analysis of silicon. 


It tells whether more or less silicon is needed 


to bring the quality of the casting to an accepted standard of excellence.’’ 
Strength in Relation to Silicon and Cross-section.— 


In castings one half-inch square in section the strength increases as silicon 
increases from 1.00 to 3.50; in castings 1 in. square in section the strength 
is practically independent of silicon, while in larger castings the strength 
decreases as silicon increases. hs 

The following table shows values taken from Mr. Keep’s curves of the 
approximate transverse strength of }-in. X 12-in. cast bars of different sizes. 
































¢ Size of Square Cast Bars. , Size of Square Cast Bars. 

ts | dg 

© | din. | 1 in.| 2 in. | 3 in. | 4 in. || SO | din. | Lin. | 2in.| 3in, | 4in. 
TA oO mh 

OG ek aan eee remem ; Oy ; Ca 
‘ Strength of a?-in. X 12-in. Strength of a }-in. X 12-in, 

Section, lbs. Section, lbs. 

1.00] 290 | 260 | 232 | 222 | 220 2.50! 392 | 278 | 212 | 190 | 184 
HHO) 9324 J 2721 e2282) 22 11208 9.004260 2760202) 180s bi 
2.00] 358 | 278 | 220 | 202 | 196 3.50] 446 | 264 | 192 | 168 | 160 


Irregular Distribution of Silicon in Pig Iron.—J. W. 
Thomas (Iron Age, Nov. 12, 1891) finds in analyzing samples taken from every 
other bed of a.cast of pig iron that the silicon varies considerably, the iron 
coming first from the furnace having pes the highest percentage, In 
one series of tests the silicon decreased from 2.040 to 1 713 from the first bed 
to the eleventh. In another case the third bed had 1.260Si.. the seventh 1.718, 
and the eleventh 1.101. He also finds that the silicon varies in each pig, be- 
ing higher at the point than at the butt. Some of his figures are: point of 
pig 2.328 Si.. butt of same 2.157; point of pig 1.834, butt of same 1.787. 

Some Tests of Cast Iron. (G. Lanza, Trans. A. S. M. E., x., 187.)~ 
The chemical analyses were as follows: 


Gun Tron, Common Iron, 

per cent. per cent. 
Total carbon dirs i044 043% See 3.51 a year 
Graphites, 207s osc svete ceteonaeeetercO M8523 
Sulphur Wee sees setasiee seeecsee mt Osis 0.173 
PhoOSpnhorush voces schists st reioca, ULM ais) 0.413 
Silicon Wye Pe Te ee 1.140 1.89 


Tensile Elastic Modulus 

Strength. Limit. ticity 
Unplaned common. 20.200 to 23.000 T. 8. Av. = 22,066 6,500 13,194,233 
Planed common.... 20,300 to 20,800 ‘* ‘ = 20,520 5,833 11.943.953 
Unplaned gun..... 27,000 to 28,075 “8  *S - ==) 28,175 11,000 16,130,800 
Planed gun......-.. 29,500 to 31,000 “© “ = 30,500 8,500 15,932,880 


370 IRON AND STEEL. 


The elastic limit is not clearly defined in cast iron, the elongations increas- 
ing faster than the increase of the loads from the beginning of the test. 
The modulus of elasticity is therefore variable, decreasing as the loads in-- 
crease. For example, see the results of test of a cast-iron bar on p. 314. 

The Strength of Cast Hron depends on many other things besides 
its chemical composition. Among them are the size and shape of the 
casting, the temperature at which the metal is poured, and the rapidity of 
cooling. Internal stresses are apt to be induced by rapid cooling, and slow 
cooling tends to cause segregation of the chemical constituents and opening 
of the grain of the metal, making it weak. The relation of these variable 
conditions to the strength of cast iron is a complex one and as yet but im- 
perfectly understood. (See ‘‘ Cast-iron Columns,”’ p. 250.) 

The author recommends that in making experiments on the strength of 
cast iron, bars of several different sizes, such as 14, 1, 114, and 2 in. square (or 
round), should be taken, and the results compared. ‘Tests of bars of one 
size only do not furnish a satisfactory criterion of the quality of the iron of 
which they are made. See Trans. A. I. M. E., xxvi., 1017. 


CHEMISTRY OF FOUNDRY IRONS. 
(C. A. Meissner, Columbia College Q’ly, 1890; Iron Age, 1890.) 


Silicon is a very important element in foundry irons. Its tendency when 
not above 214% is to cause the carbon to separate out as graphite, giving the 
casting the desired benefits of graphitic iron. Between 244% and 3142 silicon 
is best adapted for iron carrying a fair proportion of low silicon scrap and 
close iron, for ordinarily no mixture should run below 114% silicon to get 
good castings. 

From 3% to 5% silicon, as occurs in silvery iron, will carry heavy amounts 
of scrap. Castings are liable to be brittle, however, if not handled carefully 
as regards proportion of scrap used. 

From 114% to 2% silicon is best adapted for machine work ; will give strong 
clean castings if not much scrap is used with it. 

Below 1% silicon seems suited for drills and castings that have to stand 
great variations in temperature. 

Silicon has the effect of making castings fluid, strong, and open-grained ; 
also sound, by its tendency to separate the graphite from the total carbon, 
and consequent slight expansion of the iron on cooling, causing it to fill out 
thoroughly. Phosphorus, when high, has a tendency to make iron fluid,. 
retain its heat longer, thereby helping to fill out all small spaces in casting. « 
It makes iron brittle, however, when above 34% in castings. It is excellent 
when high to use in a mixture of low-phosphorus irons, up to 14% giving 
good resuits, but, as said before, the casting should be below 34%. It has a 
strong tendency when above 1% in pig to make the iron less graphitic, pre- 
venting the separation of graphite. 

Sulphur in open iron seldom bothers the founder, as itis seldom present 
to any extent. The conditions causing open iron in the furnace cause low 
sulphur. A littke manganese is an excellent antidote against sulphur in the 
furnace. Irons above 1% manganese seldom have any sulphur of any con- 
sequence. 

Graphite is the all-important factor in foundry irons ; unless thisis present 
in sufficient amount in the casting, the latter will be liable to be poor. 
Graphite causes iron to slightly expand on cooling, makes it soft, tough and 
fluid. (The statement as to expansion on cooling is denied by W. J. Keep.) 

Relation of the Appearance of Fracture to the Chemical 
Com position.—S. H. Chauvenet says when run [from the blast-fur- 
nace] the lower bed is almost always close grain, but shows practically the 
same analysis as the large grain in the rest of the cast. If the iron runs 
rapidly, the lower bed may have as large grain as any in the cast. If the 
iron runs rapidly, for, say six beds and some obstruction in the tap-hole 
causes the seventh bed to fill up slowly and sluggishly, this bed may be 
close-grain, although the eighth bed, if the obstruction is removed will be 
open-grain. Neither the graphitic carbon nor the silicon seems to have an 
influence on the fracture in these cases, since by analysis the graphite en 
silicon is the same in each. The question naturally arises whether it would 
not be better to be guided by the analysis than by the fracture. The frac- 
ture isa guide, but it is not an infallible guide. Should not the open- and 
the close-grain iron of the same cast be numbered under the same grade 
when they have the same analysis ? 

Mr, Meissner had many analyses made for the comparison of fracture 


CHEMISTRY OF FOUNDRY IRONS. — 871 


with analysis, and unless the condition of furnace, whether the iron rat 
fast or slow, and from what part of pig bed the sample is taken, are known, 
the fracture is often very misleading. Take the following analyses : 





A B (6 D. E F. 
Silicon...., .. 4.315 4.818 4.37 8.328 3.869 8.861 
SUNN eS eee 0.008 0.0u8 0.007 0.033 0.006 0.006 
Graphitie car. . 3.010 2.707 2.680 2.243 3.070 3.100 
COUT. CALDOM ee et | T.1 8. RAL antes t SEE 0.108 0.096 





A. Very close-grain iron, dark color, by fracture, gray forge. 

6. Open-grain, dark color, by fracture, No. 1. 

C. Very close-grain, by fracture, gray forge. 

D. Medium-grain, by fracture, No. 2, but much brighter and more open 
than A, C, or F. 

E. Very large, open-grain, dark color, by fracture, No. 1. 

F. Very close-grain, by fracture, gray forge. 

By comparing analyses A and B, or E and F, it appears that the close- 
grain iron is in each case the highest in graphitic carbon. Comparing A 
ath E, the graphite is about the same, but the close-grain is highest in 
silicon. 

Analyses of Foundry Iroms. (C. A. Meissner.) 
ScorcH IRons. 








Phos- |Manga-| Sul- |Graph-| Com. 


Name. Grade. /Silicon. phorus.} nese. | phur. ite. |Carbon, 











Summerlee....... 1 a (Maye | Shilstt 0.01 3.09 0.25 
Ze SCGE oe 1 2.47 0.760 2.01 0.015 
# apratte 1 3.44 1000s alee a0 0.015 
SER Succ k soe 2 Pe 0.810 | 2.90 0.02 2.00 0.80 
Welintonle asco. 1 2.15 0.618 | 2.80 0.025 | 3.76 0.21 
Coltness cet ye 1 2.59 0.840 | 1.70 0.010 | 3,75 3.7 
CANDO se covers s I 1.70 1.100 |} 1.83 0.008 | 3.50 0.40 
Glengarnock... . 1 3.03 1.200 | 2,85 
Glengarnock> said 
to carry % scrap 2 4.00 0.900 | 3.41 0.010 | 1.78 0.90 














No. “V3 Phos- No. 

Sample Silicon. phorus Manganese) Sulphur Gade 
1 6.00 0.430 8 IO Dts yy itesenctite ot See Toe sl ovate’ sensor - 
be 1.67 1.920 I, ld See ae casting. 
3 2.40 1.000 he chat ane CN ERIE 8 ate 
4 128 0.690 HRA Mle cevicss Ses esas OT | daee eee ee 
5a 3.50 0.613 ey WM | ex cretaibeeso i se okteek iakere 
5b 2.90 0.733 iL. 2W) olka eines. earner casting. 
6a 3.44 1.000 1B, CO) Uy Sh ee ee i sn 8 Ae 
6b 3.35 1.300 1.50 0.012 } pr iecarehe cotter age 
7 3.68 0.503 ote ll eee sea eee Vins He oeecenae : 





DESCRIPTION OF SAMPLES.—No. 1, Well known Ohio Scoteh iron, almost 
silvery, but carries two-thirds scrap ; made from part black-baid ore. Very 
successful brand. The high silicon gives it its scrap-carrying capacity. 

No. 2. Brier Hill Scotch castings, made at scale works ; castings demand- 
ing more fluidity than strength. 


ave TRON AND STEEL. 


No. 8. Formerly a famous Ohio Scotch brand, not now in the market 
Made mainly from black-band ore. 

No. 4. A good Ohio Scotch, very soft and fluid; made from black-band 
ore-mixture. 

Nos. 5a and 5b. Brier Hill Scotch iron and casting; made for stove pur- 
pee: 350 lbs. of iron used to 150 lbs. scrap gave very soft fluid iron; worked 
well. 

No. 6a. Shows comparison between Summerlee (Scotch) (6a) and Brier Hill 
Scotch (66). Drillings came from a Cleveland foundry, which found both 
irons closely alike in physical and working quality. i 

No. 7. One of the best southern brands, very hard to compete with, owing 
to its general qualities and great regularity of grade and general working. 


MACHINE IRONS. 


Ree Silicon. Phos- Manga: Sulphur. |Graphite. COTE De caueee 








phorus. | nese. Carbon. No. 
8 2.80 0.492 0.61 0015107) PEs ool eee 1 
9 1.30 0.262 0.70 0.080%.) 2 Re Re a Bele ieee 3 
10a 2.66 0.77 te20 0.020 2:5 age eet eee 2 
106 3.63 0.411 125 0.014 BOS") pees. 1 
il 2.10 0.415 0.60 ORO5O! Wh Paseo eslae cece 2 
12 1.37 0.294 1.51 0.080 2.31 0.78 2 
13 3.10 0.124 trace OF021 |. ee Rol eee 2 
14 2.12 0.610 OF8Oe Sls De sats Bo alr sb ais oe oe | eee 
15 1.70 0.632 TRO viel ARVO yaoree hie lets aes 4s ciclo listerstare c-tearered ee eae 
16a, 1.45 0.470 1225 O. 009 ene eee ieee es . 
16b 1.40 0.316 1.37 C2008 ese ele ee Ph ae 
17 3.26 0.426 0.25 hes 1 
18 0.80 0.164 0.90 OPOID MMe oten eel 1 





DESCRIPTION OF SAMPLES.—No. 8. A famous Southern brand noted for fine 
machine castings. 

No. 9. Also a Southern brand, a very good machine iron. 

Nos. 10a and 106. Formerly one of the best known Ohio brands. Does not 
shrink; is very fluid and strong. Foundries having used this have reported 
very favorably on it. 

No. 11. Iron from Brier Hill Co., made to imitate No. 3; was stronger 
than No. 3; did not pull castings; was fluid and soft. 

No. 12. Copy of a very strong English machine iron. 

No. 13, A Pennsylvania iron, very tough and soft. This is partially Besse- 
mer iron, which accounts for strength, while high silicon makes it soft. 

No. 14. Castings made from Brier Hill Co.’s machine brand for scale works, 
very satisfactory, strony, soft and fluid. 

No. 15. Castings made from Brier Hill Co.’s one half machine brand, one 
half Scotch brand, for scale works, castings desired to be of fair strength, 
but very fluid. and soft. 

No. 16a. Brier Hill machine brand made to compete with No. 3. 

No. 16b. Castings (clothes-hooks) from same, said to have worked badly, 
castings being white and irregular. Analysis proved that some other iron 
too high in manganese had been used, and probabiv not weii mixed. 

No. 17. A Pennsylvania iron, no shrinkage, excellent macnine iron, soft 
and strong. 


No. 18. A very good quality Northern charcoal iron. 


‘Standard Grades’? of the Brier Hill Iron and Coal 


Company, 

Brier Hill Scotch Iron.—Standard Analysis, Grade Nos. 1 and 2. 
SUCOT ite MPMI = «= o'e 0, o/0/0 sisi ats e sitenniels treks eee 2.00 to 3.00 
POS PWGLUs eet ren ssinj s,s 's;2.s se » « < ehae eiccelee iitsleeeeneee 0.50 to 0.75 
Manganese.......... Sis) esereui uri sic ove, ait sy eee eat 2.00 to 2.50 


Used successfully for scales, mowing-machines, agricultural implements, 
novelty hardware, sounding-boards, stoves, and heavy work requiring no 
special strength. 


CHEMISTRY OF FOUNDRY IRONS. 373 


Brier Hill Silvery Iron.—Standard Analysis, Grade No. 1. 


ASIN GON pases tenceetopsecetek Aa cfevoysh ace ofelngeraitse Sa Are a eis eto elo. ols 3.50 to 5.50 
IP TORII QUIS teeta cicishet feiaios Gok ane 1s 20o Sea stoieial geese Ria} 1.00 to 1.50 
INIA EER TOS Caan matty Ye sie wrasse) sielelb us cos croicbelnress Cie sehaiaeteus cies 2.00 to 2.25 


Used successfully for Rolbawenareds car-wheels, etc., stoves, bumpers, and 
similar work, with heavy amounts of scrap in all cases. Should be mainly 
used where fluidity and no great strength is required, especially for heavy 
work. When used with scrap or close pig low in phosphorus, castings of 
considerable strength and great fluidity can be made 


Fairly Heavy Machine Tron.—Standard Analysis, Grade No. 1. 


SUG OMe aust tperscapste ate siaicacios aos mie Sica tee tiara testes « 1.75 to 2.50 
PPNOSPMOLUSm eee ee rckn ec caetys | eosicie tase cusyeeiere, ceetetas 0.50 to 0.60 
WME WARE WISE). Ao Agog paeu ones one 0 dmORnonO ar SoBe a EH etAT 1.20 to 1.40 


The best iron for machinery, wagon-boxes, agricultural implements, 
pump-works, hardware specialties, lathes, stoves, etc., where no large 
amounts of scrap are to be carried, and where strength, combined with 
ea fluidity and softness, are desired. Should not have much scrap with 
it. 

Regular Machine Iron.—Standard analy 313, Grade Nos. 1 and 2. 


SILICONE 2 Myr aes ae Se ares a See VOI, CE nee Melee 1.50 to 2.00 
IPHOSPHORUS hos osc ced deiels sss Skate Mh Ss ape aah lh 0.30 to 0.50 
Manganese........ BPS hs cass Ciaks phe, oleate atet! Stas eMevayrt Las 0.80 to 1.00 


Used for hardware, lawn-mowers, mower and reaper works, oil-well 
machinery, driils, fine machinery, stoves, ete. Excellent for al} small fine 
castings requiring fair fluidity, softness, ‘and mainly strength. Cannot be 
well used alone for large castings, but gives good results on same when used 
with above-mentioned heavy machine grade; also when used with the 
Scotch in right proportion. Will carry but little scrap, and should be used 
nlone for good strong castings. 


For Axles and Materials Requiring Great Str oe tb Grade No. 2. 


BLM COMM sy tateslatersic sfile acintseriniets Ouiveles sistent e sanccits 
IPROSDHOEUS os siarstte oxstete oeslemieusie wis elt teint slaleae . 0.200 and less. 
MEAD PAT CSO yee sccctdls.< leis elon sroaisicale spat sieis are cla elais. se 0.80 


This gave excellent results. 
A good neutral iron for guns, etc., will run about as follows: 


STiCOMNe so Sep ae eee ee ETRE eee IOne Oh alee at Mattes 1.00 
IPHOSPHOLUSis incest cette case ce ete eime le cretate sreceteel-rstaret anny 0.25 
Sulphurtsr twee ae wate peelene cateceteerete eae noose «seers Rta 0.20 
MancaneS@re rs org ot hoe toes oe oe ore dee ones ence none. 


It should be open No. 1 iron. 

This gives a very tough, elastic metal. More sulphur would make tough 
but decrease elasticity. 

For fine castings demanding. elegance of design but no strength, phos- 
phorus to 3.00% is good. Can also stand 1.50% to 2.00% manganese. For work 
of a hard, abrasive character manganese can run 2.00% in casting. 


Analyses of Castings. 











oe ah Silicon. phoria Manganese) Sulphur. | Graphite. peed 
31 2.50 1.400 Be AN RE eM Mars fate hor mens. .0 s,s aie (oeteea 
32 0.85 0.351 0.92 ORO SO viral ites as:c scat S aac get 
33 1.53 0.327 1.08 0.040 3.10 0.58 
34a 1.84 0.57 ME sete seta [ dos s ace on 010: ain lalariers eet 
34D 2.20 0.742 BARI fire Xe pigcain ls 2. care. e'0 » ase ¢ fnainen Mtaaiene 
34c 2.50 1.208 ie O MMMM otto, steteranstete,9)| s.5.0; 0; <0 5.+-ail gia Rerpaieisketaies 
35a 2.80 0.418 A al ti scsmieic fe | ++. sie: 6 gs acelea sent erage 
35b 3.10 1,280 Ml CeiaRa re ccf rateataici-.=\| con o's, + os ladsieia ® [ine sae eee 
35c 3.30 0.87 CONTR isteteg toe see xe'e [ho oinie-ae chs, 6, arte | a Melega eeetets 
35d 2.88 0.408 HEN I ORRe cress aieder,«;.. |\;. «en (siere'aiecs orl ous. leee neeneee 
35e 4.50 0.660 DT hic scr Mites > «| + a 016 shoes safe gaa 
36 3.43 1.439 0.90 025: | += date aa eis oie licens eee 
10) 2.68 0.900 LaDy > lhe sa sen Babe teen el ako He nits 
37 1.90 0.980 edie ist Pcssie> > «+++ seh Gklote gee all cae ate ct 





374 IRON AND STEEL. 


No. 31. Sewing-machine casting, said to be very fluid and good casting. 
This is an odd analysis. I should say it would have been too hard and brit- 
tle, yet no complaint was made. 

No. 32. Very good machine casting, strong, soft, no shrinkage. 

No. 33. Drillings from an annealer-box that stood the heat very well. 

No. 34a. Drillings from door-hinge, very strong and soft. 

No. 34b. Drillings from clothes-hooks, tough and soft, stood severe ham- 
mering. : 

No. 34c. Drillings from window-blind hinge, broke off suddenly at light 
strain. Too high phosphorus. 

No. 35a. Casting for heavy ladle support, very strong. 

‘ Nos 355 and 35c. Broke after short usage. Phosphorus too high. Car- 
umpers. 

Noe 85d. Elbow for steam heater, very tough and strong. 

No. 36. Cog-wheels, very good, shows absolutely no shrinkage. 

No. 37. Heater top network, requiring fluidity but no strength. 

No. 37a. Gray part of above. 

No. 87b. White, honeycombed part of above. Probably bad mixing and 
got chilled suddenly. 


STRENGTH OF CAST IRON. 
Rankine gives the following figures: 


Various qualities, T. S...... 13,400 to 29,000, average 16,500 
Compressive strength...... 82,000 to 145,000, + 112,000 
Modulus of elasticity....... 14,000,000 to 22,900,000, ‘s 17,000,000 


Specific Gravity and Strength. (Major Wade, 1856.) 

A 2 eee guns: Sp. Gr. 7.087, T. S. 20,148. Another lot: least Sp. Gr. 7.168, 

. S. 22,402. 

Second-class guns: Sp. Gr. 7.154, T. S. 24,767. Another lot: mean Sp. Gr. 
7.302, TS. 27,282. 

First class guns: Sp. Gr. 7.204, T. S. 28,805. Another lo®: greatest Sp. Gr. 
7.402, T. S. 31,027. 

Strength of Charcoal Pig Iron.—Pig iron made from Salisbury 
ores, in furnaces at Wassaic and Millerton, N. Y., has shown over 40,000 Ibs: 
T. S. per square inch, one els giving 42,281 lbs. Muirkirk, Md., iron 
tested at the Washington Navy Yard showed: average for No. 2 iron, 21,601 
ae No. 8, eee lbs.; No. 4, 41,329 lbs.; average density of No. 4, 7.886 (J.C. 

. W.. v. p. 44.) 

Nos. 3 and 4 charcoal pig iron from Chapinville, Conn., showed a tensile 
strength per square inch of from 34,761 lbs. to 41,882 lbs. Charcoal pig iron 
from ;Shelby, Ala. (tests made in August, 1891), showed a strength of 
84,800 lbs. for No. 3; No. 4, 39,675 lbs.; No. 5, 46,450 Ibs.; and a mexture of 
equal parts of Nos. 2, 3, 4. and 5, 41.470 lbs. (Bull. I. & S. A.) 

Variation of Density and Tenacity of Gun-=-irons,—<An in- 
crease of density invariably follows the rapid cooling of cast iron, and asa 
general rule the tenacity is increased by the same means. The tenacity 
generaily increases quite uniformly with the density, until the latter ascends 
to some given point; after which an increased density is accompanied by a 
diminished tenacity. 

The turning-point of density at which the best qualities of gun-iron attain 
their maximum tenacity appears to be about 7.30. At this point of density, 
or near it, whether in proof-bars or gun-heads, the tenacity is greatest. 

As the density of iron is increased its liquidity when melted is diminished. 
This causes it to congeal quickly, and to form cavities in the interior of the 
casting. (Pamphlet of Builders’ Iron Foundry, 1893.) 

Specifications for Cast Iron for the World’s Fair Build- 
ings, 1892.—I*xcept where chilled iron is specified, all castings shall be 
of tough gray iron, free from injurious cold-shuts or blow-holes, true to 
pattern, and of a workmanlike finish. Sample pieces 1 in. square, cast from 
the same heat of metal i sand moulds, shall be capable of sustaining on a 
crear span of 4 feet 6 inches a central load of 500 lbs. when tested in the 
rougn bar. 

Specifications for Tests of Cast Iron in 12” B. L. Mortars, 
(Pamphlet of Builders Iron Foundry, 1893.)—Charcoal Gun Iron.—The tensile 
strength of the metal must average at each end at least 30,000 lbs, per 
square inch ; no specimen to be over 37,000lbs. per square inch; but one 
specimen from each end may be as low as 28,000 lbs. per square inch. The 


MALLEABLE CAST IRON. 375 


long extension specimens will not be considered in making up these aver- 
ages, but must show a good elongation and an ultimate strength, for each 
specimen, of not less than 24,000 lbs. The density of the metal must be such 
as to indicate that the metal has been sufficiently refined, but not carried s~a 
high as t» impair the other qualities. 

Specifications for Grading Pig Iron for Car Wheels by 
Chill Tests made at the Furnace, (Penna. R. R. Specifications, 
1s83.)—The chill cup is to be filled, even full, at about the middle of every 
cast from the furnace. The test-piece so made will be 744 inches long, 314 
inches wide, and 134 inches thick, and is to be broken across the centre when 
entirely cold. The depth of chill will be shown on the bottom of the test- 
piece, and is to be measured by the clean white portion to the point where 
gray specks begin to show in the white. The grades are to be by eighths of 
an inch, viz., 14, 14, 34, 4, 54, 34, %, etc., until the iron is mottled ; the lowest 
grade being 1g of an inch in depth of chill. The pigs of each cast are to be 
marked with the depth of chill shown by its test-piece, and each grade is to 
be kept by itself at the furnace and in forwarding. 

Mixture of Cast Iron with Steel.—Car wheels are sometimes 
made from a mixture of charcoal iron, anthracite iron, and Bessemer 
steel. The following shows the tensile strength of a number of tests of 
wh a oar the average tensile strength of the charcoal iron used being 
22,000 lbs.: 

Ibs. per sq. in. 


Charcoal irons with QUES Steel... ce Meet. <sic.areiie caine pe ole cleemccine ee 22,467 
tk ve ‘* 334% steel..... SCHEMES ots Sorpese SS MRE Las 4 26,733 
os Ms ** 614% steel and 614% anthracite............. 24,400 
ee us “ 714% steel and 714% anthracite... .... Ar eic Choly! bah) 
ce a *¢ 216% steel, 244% wro’t iron, and 614% anth... 25,550 
Se ae ‘© 5 steel, 5% wro’t iron, and 10% anth..... 26,500 


(Jour. C. I. W., iii. p. 184.) 

Cast Iron Partially Bessemerized.—Car wheels made of par- 
tially Bessemerized iron (blown in a Bessemer converter for 344 minutes), 
chilled in a chill test mould over an inch deep, just asa test of cold blast 
chareoal iron for car wheels would chill. Car wheels made of this blown 
iron have run 250,000 miles. (Jour.C. I. W., vl. p. 77.) 

Bad Cast Irom.—On October 15, 1891, the cast-iron fly-wheel of a large 
pair of Corliss engines belonging to the Amoskeag Mfg. Co., of Manchester, 
N. H., exploded from centrifugal force. The fly-wheel was 30 feet diam- 
eter and 110 inches face, with one set of 12 arms, and weighed 116,000 Ibs. 
After the accident, the rim castings, as well as the ends of the arms, were 
found to be full of flaws. caused chiefly by the drawing and shrinking of the 
metal. Specimens of the metal were tested for tensile strength, and varied 
from 15,000 lbs. per square inch in sound pieces to 1000 lbs. in spongy ones. 
None of these flaws showed on the surface, and a rigid examination of the 
parts before they were erected failed to give any cause to suspect their true 
nature. Experiments were carried on for some time after the accident in 
the Amoskeag Company’s foundry in attempting to duplicate the flaws, but 
with no success in approaching the badness of these castings, 


MALLEABLE CAST IRON, 


Malleableized cast iron, or malleable iron castings, are castings made 
of ordinary cast iron which have been subjected to a process of decarboni- 
zation, which results in the production of a crude wrought iron. Handles, 
latches, and other similar articles, cheap harness mountings, plowshares, 
iron handles for tools, wheels, and pinions, and many small parts of ma- 
chinery, are made of malleable cast iron. For such pieces charcoal cast iron 
of the best quality (or other iron of similar chemical composition), should 
be selected. Coke irons low in silicon and sulphur have been used in place 
of charcoal irons. The castings are madein the usual way, and are then 
imbedded in oxide of ircen, in the form, usually, of hematite ore, or in per- 
oxide of manganese, and exposed to a full red-heat for a sufficient length of 
time, to insure the nearly complete removal of the carbon. This decarboniza- 
tion is conducted in cast-iron boxes, in which the articles, if small, are 
packed in alternate layers with the decarbonizing material. The largest 
pieces require the longest time. The fire is quickly raised to the maximum 
temperature, but at the close of the process the furnace is cooled very 
slowly. The operation requires from three to five days with ordinary small 
castings, and may take two weeks for large pieces. 


376 IRON AND STEEL. 


Rules for Use of Malleable Castings, by Committee of Master 
Carbuilders’ Ass’n, 1890. 

1. Never run abruptly from a heavy to a light section. 

2. As the strength of malleable cast iron lies in the skin, expose as much 
surface as possible. A star-shaped section is the strongest possible from 
which a casting can be made. For brackets use a number of thin ribs instead 
of one thick one. 

3. Avoid all round sections; practice has demonstrated this to be the 
weakest form. Avoid sharp angles. 

4, Shrinkage generally in castings will be 3/16 in. per foot. 

Strength of Malleable Cast Mrom.—Experiments on the strength 
of malleable cast iron, made in 1891 by a committee of the Master Car- 
builders’ Association. The strength of this metal varies with the thickness, 
as the following results on specimens from 4 in. to 11% in. in thickness show: 


Dimensions. Tensile Strength. Elongation. Elastic Limit. 
in. in, lb, per sq. in. per cent in 4 in. lb. per sq. in. 
1.52 by .25 34,700 2 21,100 

go RNa 33,700 2 15,200 

LOB hey iro 32,800 2 17,000 

1.53 ‘*  .64 382,100 2 19,400 

Da had NT 25,100 14 15,400 

URE Pade ee] 33,600 14 19.300 

1.06 © 1.02 30,600 1 17,600 

1.28 1.3 27,400 1 

1.52 )** 154 28,200 114 


The low ductility of the metal is worthy of notice. The committee gives 
the following table of the comparative tensile resistance and ductility of 
malleable cast iron, as compared with other materials: 











. Comparative 
Ultimate ree card Elongation Ductility : 
Strength, Gast oe ;: Per Cent Malleable 
Ibspercqsint] eRe: in 4 in. Cast Iron 
Gantiron.3) 0260's 20,000 =| 1 0.35 0.17 
Malleable eastiron. 2,000 1.6 2.00 1 
Wrought iron..... 50,000 2.5 20.00 10 
Steel castings ..... 60,000 3 10.00 5 


Another series of tests, reported to the Association in 1892, gave the 
following: 














Thick- - Elastic Ultimate Elongation 
ness. Width. Area. Limit. Strength. in 8 in, 
in, in. sq in. Ib. per sq. lb. per sq. in.| percent. 
3271 2.81 7615 9.520 B62 if LES 
293 2.78 8145 22.650 28, 160 6 
.39 2.82 1.698 20,595 82,060 1.5 
41 2.79 1.144 20,220 28,850 1.0 
.529 2.76 1.46 19.520 27,875 Ta) | 
661 2.81 1.857 18.840 25,700 4 
8 2.76 2.208 18.890 25,120 1.1 
1.025 2.82 2.890 18.220 28,720 1.6 
iy ve 2.81 8.1388 17,050 25,510 1.8 
1.021 2.82 1.3 


2.879 18,410 26,950 





WROUGHT IRON, 374 


WROUGHT IRON. 


Influence of Chemical Composition on the Properties 
of Wrought Iron. (Beardslee on Wrought Iron and Chain Cables. 
Abridgement by W. Kent. Wiley & Sons, 1879.}—A series of 2000 tests of 
specimens from 14 brands of wrought iron, most of them of high repute, 
was made in 1877 by Capt. L. A. Beardslee, U.S.N., of the United States 
Testing Board. Forty-two chemical analyses were made of these irons, 
with a view to determine what influence the chemical composition had 
upon the strength, ductility, and welding power. From the report of these 
tests by A. L. Holley the following figures are taken : 


Chemical Composition. 
Average 


Brand. | Tensile 
Strength. Ss. Py Si. CG Mn. Slag. 





—_— ———_ | -———_ 





0.065 | 0.080 | 0.212} 0.005! 0.192 
L 66,598 | trace 10°0et 0.105 | 0.512} 0.029 | 0.452 


Pp 54.363 Pere 0.250 0.182 0.033 | 0.033] @.848 
’ 0.001 0.095 0.028 0.066 | 0.009 | 1.214 

B 52,64 0.008 0.231 0.156 0.015 | OL01IT4 VAT ee 
J 51. t54 Pat 0.140 0.182 0.027 | trace | 0.678 
” 0.005 0.291 0.321 0.051 | 0.053 | 1.724 

O 51.134 0.004 0.067 0.065 0.045 | 0.007} 1.168 
ABTS 0.005 0.078 0.073 0.042 | 0.005 | 0.974 

a 50,765 0.007 0.169 0.154 0.042 -|s 0,021 |. ee rome 


Where two analyses are given they are the extremes of two or more ana- 
lyses of the brand. Where one is given it is the only analysis. Brand L 
should be classed as a puddled steel. : 


ORDER OF QUALITIES GRADED FROM No. 1 To No. 19. 


Brand. erscre Hares Elongation. Welding Power. 
L 1 18 19 most imperfect. 
P 6 6 3 badly. 
B 12 16 15 best. 
J 16 19 18 rather badly. 
Oo 18 1 4 very good. 
Cc 19 12 16 —— 


The reduction of area varied from 54.2 to 25.9 per cent, and the elonga- 
tion from 29.9 to 8.3 per cent. 

Brand O, the purest iron of the series, ranked No. 18 in tensile strength, 
but was one of the most ductile; brand B, fquite impure, was below the 
average both in strength and ductility, but was the best in welding power; 
P, also quite impure, was one of the best in every respect except welding, 
while L, the highest in strength, was not the most pure, it had the least 
ductility, and its welding power was most imperfect. The evidence of the 
influence of chemical composition upon quality, therefore, is quite contra- 
dictory and confusing. The irons differing remarkably in their mechanical 
properties, it was found that a much more marked influence upon their 
qualities was caused by different treatment in rolling than by differences in 
composition. 

In regard to slag Mr. Holley says: “It appears that the smallest and 
most worked iron often has the most slag. It is hence reasonable to con: 
elude that'an iron may be dirty and yet thoroughly condensed.”* 

In his summary of ‘* What is learned from chemical analysis,’? he says: 
“So far, it may appear that little of use to the makers or users of wrought 
iron has been learned. . . . The character of steel can be surely pred- 
icated on the analyses of the materials; that of wrought iron is altered by 
subtle and unobserved causes.”’ 

Enfluence of Reduction in Rolling from Pile to Bar on 
the Strength of Wrought Iron,—tThe tensile strength of the irons 
used in Beardslee’s tests ranged from 46,000 to 62,700 lbs. per sq. in., brand 
L. which was really a steel. not being considered. Some specimens of L 
gave figures as high as 70,000 lbs. The amount of reduction of sectional 


$78. IRON AND STEEL, 


area in rolling the bars has a notable influence on the strength and elastie 
limit; the greater the reduction from pile to bar the higher the strength, 
The following are a few figures from tests of one of the brands: 


Size of bar, in, diam. 4 3 2 1 % 4 
Area of pile, sq. in.: 80 80 72 25 9 3 
Bar per cent of pile: 15.7 8.83 4.36 3.14 2.17 1.6 
Tensile strength, lb.: 46,322 47,761 48,280 51,128 52,275 59,585 
Elastic limit, Ib.: 23,480 26,400 31,892 386,467 39,126 — 


Specifications for Wrought Iron (I. H. Lewis, Engineers’ Club 
of Puiladelphia, 1891).—1. All wrought irom must be tough, ductile, fibrous, 
and of uniform quality for each class, straight, smooth, free from cinder- 
pockets, flaws, buckles, blisters, and injurious cracks along the edges, and 
must have a workmanlike finish. No specific process or provision of 
manufacture will be demanded, provided the material fulfils the require- 
ments of these specifications. 

2. The tensile strength, limit of elasticity, and ductility shall be deter- 
mined from a standard test-piece not less than 144 inch thick, cut from the 
full-sized bar, and planed or turned parallel. The area of cross-section shall 
not be less than 144 square inch. The elongation shall be measured after 
breaking on an original length of 8 inches. 

3. The tests shall show not less than the following results: 


For bar iron in tension...... T.S. = 50,000; E. L. = 26,000; E. L. in 8in., 18% 
For shape ironintension... ‘* = 48,000; ‘* = 26,000; es 15 

For plates under 36in. wide. ‘“S = 48,000; ‘“* = 26,000; ee 12% 
For plates over s6in. wide.. ‘* = 46,000; ‘“* = 25,000; oy 10% 


4. When full-sized tension members are tested to prove the strength of 
their connections, a reduction in their ultimate strength of (500 X width of 
bar) pounds per square inch will be allowed. 

5. All iron shall bend, cold, 180 degrees around a curve whose diameter 
is twice the thickness of piece for bar iron, and three times the thickness 
for plates and shapes, 

6. Iron which is to be worked hot in the manufacture must be capable 
of bending sharply to a right angle at a working heat without sigu of 
fracture. 

7, Specimens of tensile iron upon being nicked on one side and bent shall 
show a fracture nearly all fibrous. 

8. All rivet iron must be tough and soft, and be capable of bending cold 
until the sides are in close contact without sign of fracture on the convex © 
side of the curve. 

Penna. R. RR. Co.'s Specifications for Merchant-bar Iron 


(1902).—One bar will be selected for test from each 100 bars in a pile. 
All the iron of one size in the shipment will be rejected if the average ten- 
sile strength of the specimens representing it falls below 47,000 Ibs. or ex- 
erers 53,000 lbs. per sq. in., or if any single specimens show less than 45,000 

Ss. per sq. in. 

In the case of flat bars which have to be reduced in width for test an allow- 
ance of 1,000 Ibs. per sq. in. will be made, making the rejection limit 46,000 Ibs. 
per sq.in. All the iron of one size in the shipment will be rejected if the 
average elongation in 8 ins. falls below the following limits : Rounds, % in. 
and over, 20% ; less than 1g in., 16%. Flats pulled as rolled. 20%; flats reduced, 

6%. 

Nicking and Bending Tests —When necessary to make nicking and bend- 
ing tests the iron will be held firmly in a vise, nicked lightly on one side and 
then broken by a succession of light blows on the nicked side. It must 
when thus broken show a generally fibrous structure, not more than 25% 
crystalline, and must be free from admixture of steel. 

Stay-bolt Iron, (Penna. R. R. Co.’s specifications, 1900.)—Sample bars must 
show a tensile strength of not less than 48,000 lbs, per sq. in. and an elonga- 
tion of not less than 25% in 8ins. One piece from each lot will be threaded in 
dies with a sharp V thread, 12 to 1 in. and firmly screwed through two 
holders having a clear space between them of 5 ins. Ono holder will be 
rigidly secured to tre bed of a suitable machine and the other vibrated at 
right angles to the axis over a space of 14 in. or in. each side of the centre 
line, Aceeptable iron should stand 2,2U0 double vibrations before breakage. 


FORMULA FOR UNIT STRAINS FOR IRON AND STEEL, 379 


Specifications for Wrought Iron for the Worlds Fair 
Buildings. (Eng’g News, March 26, 1892.)—All iron to be used in the 
tensile members of open trusses, laterals, pins and bolts, except plate iron 
over 8 inches wide, and shaped iron, must show by the standard test-pieces 
a tensile strength in lbs. per square inch of : 

52,000 — 7,000 x area of original bar in sq. in. 


circumference of original bar in inches’ 
with an elastic limit not less than half the strength given by this formula, 
and an elongation of 20% in 8 in. 

Plate iron 24 inches wide and under, and more than 8 inches wide, must 
show by the standard test-pieces a tensile strength of 48,000 lbs. per sq. in. 
with an elastic limit not less than 26,000 lbs. per square inch, and an elon- 
gation of not less than 12%. All plates over 24 inches in width must have a 
tensile strength not less than 46,000 lbs. with an elastic limit not less than 
26,000 lbs. per square inch. Flates from 24 inches to 36 inches in width must 
have an elongation of not less than 10%; those from 36 inches to 48 inches in 
width, 8%; over 48 inches in width. 5%. 

Ail shaped iron, flanges of beams and channels, and other iron not herein- 
before specified, must show by the standard test-pieces a tensile strength in 
lbs, per square inch of : 


50,000 — 





7,000 X area of original bar 
circumference of original bar’ 


with an elastic limit of not less than half the strength given by this formula, 
and an elongation of 15% for bars 5 inch and less in thickness, and of 12% for 
bars of greater thickness. For webs of beams and channels, specifications 
for plates will apply. 

All rivet iron must be tough and soft, and pieces of the full diameter of 
the rivet must be capable of bending cold, until the sides are in close contact, 
without sign of fracture on the convex side of the curve. 

Stay-bolt Lron.—Mr. Vaucliain, of the Baldwin Locomotive Works, 
at a meeting of the American Railway Master Mechanics’ Association, in 
1892, says: Many advocate the softest iron in the market as the best for 
stay-bolts. He believed in aniron as hard as was consistent with heading 
the bolt nicely. The higher the tensile strength of the iron, the more vibra- 
tions it will stand, for it is not so easily strained beyond the yield-point. 
' The Baldwin specifications for stay-bolt iron call for a tensile strength of 
50,000 to 52,000 lbs. per square inch, the upper figure being preferred, and 
the lower being insisted upon as the minimum. 


FORMULZ FOR UNIT STRAINS FOR IRON AND 
STEEL IN STRUCTURES. 
(F, H. Lewis, Engineers’ Club of Philadelphia, 1891.) 

The following formule for unit strains per square inch of net sectional 
area shall be used in determining the allowable working stress in each mem- 
ber of the structure. (For definitions of soft and medium steel see Specifi- 
cations for Steel.) 

Tension Wiembers. 














Wrought Iron. Soft Steel. Medium Steel. 
Floor-beam hangers or 

suspenders, forged 

DANS Gets Males eee Will not be used|Will not be used 7000 
Counter-ties.......... 6000 7 s oy 7000 
Suspenders, hangers 

aud counters, riveted 

members, net sec- 

LIOR Se et. ete tthe 5000 5500 7000 
Solid rolled beams..... 8000 8000 Will not be used 
Riveted truss members 

ane pepe sh flanges 4 x ™ 

of girders, net sec- % greater than é 

tion, eds: bag 7000( 1 + Mn: ') fron 9000( 1 + ™un-) 

max. max. 
Ferged eyebars....... |} Will not be used|Will not be used 9000(1 4. ~— ) 
Lateral or cross-sec~ were eyebars 
LION TOUSHeeeee chs «else 15,000 16,000 only, 17,000 


380 IRON AND STEEL, 








Shearing. : 
Wrought Iron. Soft Steel. Medium Steel. 
On pinsand shop rivets 6000 6600 7200 
On field rivets......... 4800 5200 Will not be used 
In webs of girders..... Will not be used 5000 6000 
Bearing. 
Wrought Iron. Soft Steel. Medium Steel. 
On projected semi- 
intrados of iain-pin 
MOLES A ok oF daaianee 12,000 18,200 14,500 
On projected semi-in- 
trados of rivet-holes* 12,000 13,200 14,500 
On lateral pins.... ... 15,000 16,500 18,000 
Of bed-plates on ma- 
SOMry wees clea .|250 lbs. per sq. in. 





* Excepting that in pin-connected members taking alternate stresses, the 
bearing stress must not exceed 9000 lbs. for iron or steel. 
Bending. 
On extreme fibres of pins when centres of bearings are considered as 
points of application of strains: 
Wrought Iron, 15,000. Soft Steel, 16,000. Medium Steel, 17,000. 


Compression Members. 























Wrought Iron. Soft Steel. ee 
Chord sections : 5 1) 
> min.\ ‘,, ¢ 
Blab endely.0d7. wso.. 7000 (1 ny —~) 30 
: a min. a} 
One flat and onepin end..|7000 € + min) — 35 : 
Chords with pin ends and], as) l 
all end-posts .......... . (000 G42 = 0 F | 103 20% 
min lj, greater greater 
3 7000 (1 “fe — 35 - than than 
All trestle-posts........... max. ? Fae oan 
Intermediate posts........ 7500 — 40 r 
Lateral struts, and com- 
pression in collision 
struts. stiff suspenders 1 | 
and stiff chords.......... 10,500 — 50 - } 





In which formule J = length of compression member in inches, and r = 
least radius of gyration of member in inches. No compression member 
shall have a length exceeding 45 times its least width, and no post should be 
used in which! +r exceeds 125. 


Members Subject to Alternate Tension and Compression. 


Wrought Iron. Soft Steel. ae 








For compression only...| Use the formule above 


max. lesser 8% greater |20% greater 
For the greatest stress. .|7000( 1 — B nas eee ) (eeaairon | than iron 





Use the formula giving the greatest area of section. 
The compression flanges of beams and plate girders shall have the same 
cross-section as the tension flanges. 


FORMULZ FOR UNIT STRAINS FOR IRON AND STEEL. 381 


W. H. Burr, discussing the formule proposed by Mr. Lewis, says: ‘* Taking 
the results of experiments as a whole, I am constrained to believe that they 
indicate at least 15% increase of resistance for soft-steel columns over those 
of wrought iron, with from 20% to 25% for medium steel, rather than 10% and 
20% respectively. 

‘“*The high capacity of soft steel for enduring torture fits it eminently for 
alternate and combined stresses, and for that reason I would give it 15% 
increase over iron, with about 22% for medium steel. 

“Shearing tests on steel seem to show that 15% and 22% increases, for the 
two grades respectively, are amply justified. 

‘*T should not hesitate to assign 15% and 22% increases over values for iron 
for bearing and bending of soft and medium steel as being within the safe 
limits of experience. Provision should also be made for increasing pin- 
shearing, bending and bearing stresses for increasing ratios of fixed to mov- 
ing loads ”’ 

Maximum Permissible Stresses in Structural Materials 
used in Buildings. (Building Ordinances of the City of Chicago, 1893.) 
Cast iron, crushing stress: For plates, 15,000 lbs. per square inch; for lintels, 
brackets, or corbels, compression 13,500 lbs. per square inch, and tension 
8000 lbs. per squareinch. For girders, beams, corbels, brackets, and trusses, 
16,000 lbs. per square inch for steel and 12,000 lbs. for iron. 

For plate girders : 

maximum bending moment in ft.-lbs. 


CD, 
D = distance between centre of gravity of flanges in feet. 


73 ap 13,500 for steel. 
~ 110,000 for iron, 





Flange area = 


maximum shear { 10,000 for steel, 
Web area = —-——q =" © = }..6,000 for iron, 
For rivets in single shear per square inch of rivet area: 
Steel. Iron. 
LEShoOp-Griven ! .iweaaet Jie steer ae wales 9000 lbs. 7500 Ibs. 
Leheld:drivenye date i cin ahee wee techs o00 me 6000 * 


For timber girders: “ 
b = breadth of beam in inches. 
d= depth of beam in inches. 


cbd? l= length of beam in feet. 
S= SF Re 0 160 for long-leaf yellow pine, 
c= < 120 for oak, 
100 for white or Norway pine. 


Proportioning of Materials in the Memphis Bridge (Geo. 
S. Morison, Trans. A. S. C. H., 1893).—The entire superstructure of the Mem- 
phis bridge is of steel and it was all worked as steel, the rivet-holes being 
drilled in all principal members and punched and reamed in the lighter 
members. 

The tension members were proportioned on the basis of allowing the dead 
load to produce a strain of 20,000 lbs. per square inch, and the live load a 
strain of 10,000 lbs. per square inch. In the case of the central span, where 
the dead load was twice the live load, this corresponded to 15,000 lbs. total 
strain per square inch, this being the greatest tensile strain. 

The compression members were proportioned on a somewhat arbitrary 
basis. No distinction was made between live and dead loads. A maximum 
strain of 14,000 lbs. per square inch was allowed on the chords and other 
large compression members where the length did not exceed 16 times the 
least transverse dimension, this strain being reduced 750 lbs. for each addi: 
tional unit of length. In long compression members the maximum length 
was limited to 30 times the least transverse dimension, and the strains 
limited to 6,000 Ibs. per square inch, this amount being increased by 200 lbs. 
for each unit by which the length is decreased. 

Wherever reversals of strains occur the member was proportioned to re- 
sist the sum of compression and tension on whichever basis (tension or 
conipression) there would be the greatest strain per square inch ; and, in 
addition, the net section was proportioned to resist the maximum tension, 
and the gross section to resist the maximum compression. : 

The fioor beams and girders were calculated on the strain being limited to 
10,000 lbs. per square inch in extreme fibres. Rivet-holes in cover-plates and 
flanges were deducted. 


382 . IRON AND STEEL. 


The rivets of steel in drilled or reamed holes were proportioned on the 
basis of a bearing strain of 15,000 lbs. per square inch and a shearing strain 
of 700 lbs. per square inch, and special pains were taken to get the double 
shear in as many rivets as possible. This was the requirement for shop 
. rivets. In the case of field rivets, the number was increased One-half. 

The pins were proportioned on the basis of a bearing strain of 18,000 Ibs. 
per square inch and a bending strain of 20,000 lbs. per square inch in ex- 
treme fibre, the diameters of the pins being never made more than one inch 
less than the width of the largest eye-bar attaching to them. 

The weight on the rollers of the expansion joint on Pier II is 40,000 lbs, 
per linear foot of roller, or 3,333 lbs. per linear inch, the rollers being 15 ins. 
in diameter. 

As the seetionsof the superstructure were unusually heavy, and thestrains 
froin dead ioad greatly in excess of those from moving load, it was thought 
best to use a slightly higher steel than is now generally used for lighter 
structures, and to work this steel without punching, all holes being drilled. 
A somewhat softer steel was used in the floor-system and other lighter 

arts. 

. The principal requirements which were to be obtained as the results of 
tests on samples cut from finished material were as follows: 





Max. Min. : : 
Ultimate | Ultimate |Min. Elastic Min. per: | Min. Per- 


ass tage of |centage of 
Strength,} Strength, | Limit, lbs, Sioa : P 
lbs. per | Ibs. per | persgq. in, Elongation | Reduction 


sq. inch,| sq. inch. in 8 inches. |at Fracture 


High-grade steel.} 78,500 69,000 40,000 18 38 
Eye-bar steel....| 75,000 66,000 38,000 20 40 
Medium steel....| 72,500 64,000 37,000 99 44 
Soft steel........ 63,000 55,000 30,000 28 50 


TENACITY OF METALS AT VARIOUS 
TEMPERATURES. 


The British Admiralty made a series of experiments to ascertain what loss 
of strength and ductility takes place in gun-metal compositions when raised 
to high temperatures. It was found that all the varieties of gun-metal 
suffer a gradual but not serious loss of strength and ductility up to a certain 
temperature, at which, within a few degrees, a great change takes place, 
the strength falls to about one half the original, and the ductility is wholly 
gone. At temperatures above this point, up to 500, there is little, if any, 
further loss of strength; the temperature at which this great change and 
loss of strength takes place, although uniform in the specimens cast from 
the same pot, varies about 100° in the same composition cast at different 
temperatures, or with some varying conditions in the foundry process. 
The temperature at which the change took place in No. 1 series was ascer- 
tained to be about 370°, and in that of No. 2, at a little over 250°. Whatever 
may be the cause of this important difference in the same composition, the 
fact stated may be taken as certain. Rolled Muntz metal and copper are 
satisfactory up to 500°, and may be" used as securing-bolts with safety. 
Wrought iron, Yorkshire and remanufactured, increase in strength up to 
500°, but lose slightly in ductility up to 200°, where an increase begins and 
continues up to 500°, where it is still less than at the ordinary temperature 
of the atmosphere, The strength of Landore steel is not affected by temper- 
pture ? to 500°, but its ductility is reduced more than one half, (ron, Oct. 

AST. 

Tensile Strength of Iron and Steel at High Tempera= 
tures.—James E. Howard’s tests (Iron Age, April 10, 1890) show that the 
tensile strength of steel diminishes asthe temperature increases from 0° 
until a minimum is reached between 200° and 300° F., the total decrease 
being about 4000 lbs, per square inch in the softer steels, and from 6900 to 
8000 lbs. in steels of over 80,000 lbs. tensile strength. From this minimum point 
the strength increases up to a temperature of 400° to 650° F., the maximum 
being reached earlier in the harder steels, the increase amounting to from 
10,000 to 20,000 lbs, per square inch above the minimum strength at from 200° 


TENACITY OF METALS AT VARIOUS TEMPERATURES. 383 


to 800°. From this maximum, the strength of all the steel decreases steadily 
at arate approximating 10,000 lbs. decrease per 100° increase of tempera- 
ture. A strength of 20,000 lbs. per square inch is still shown by .10 C. steel 
at about 1000° F., and by .60 to 1.00 C. steel at about 1600° F. 

The strength of wrought iron increases with temperature from 0° up to a 
maximum at from 400 to 600° F., the increase being from 8000 to 10,000 lbs. 
per square inch, and then decreases steadily till a strength of only 6000 lbs, 
per square inch is shown at 1500° F, 

Cast iron appears to maintain its strength, with a tendency to increase, 
until 900° is reached, beyond which temperature the strength gradually 
diminishes. Under the highest temperatures, 1500° to 1600° F., numerous 
cracks on the cylindrical surface of the specimen were developed prior to 
rupture. It is remarkable that cast iron, so much inferior in strength to the 
steels at atmospheric temperature, under the highest temperatures has 
nearly the same strength the high-temper steels ther have. 

Strength of Iron and Steel Boiler-plate at High Tem- 
peratures. (Chas. Huston, Jour. F’. 1, 1877.) 


AVERAGE OF THREE TESTS OF HACH. 


Temperature F. 68° 575° 925° 
Charcoal iron plate, tensile strength, lbs....... 55,366 63,080 65,343 
a oy =. ) (CONE. (Of BreAG inate seats eis 26 23 21 
Soft open-hearth steel, tensile strength, lbs..... 54,600 66,083 64,350 
“ sf rf ONtRAGs chun} seed dase 47 38 33 
“© Crucible steel, tensile strength, lbs........ 64,000 69,266 68,600 
ap %; SUPICOMED, Gidea ooh sane wane scat le 36 30 21 


Strength of Wrought Iron and Steel at High Temper= 
atures, (Jour. F’. I, cxii., 1881, p. 241.) Kollmann’s experiments at Ober- 
hausen included tests of the tensile strength of iron and steel at tempera- 
tures ranging between 70° and 2000° F. Three kinds of metal were tested, 
viz., fibrous iron having an ultimate tensile strength of 52,464 Ibs., an elastic 
strength of 38,280 lbs., and an elongation of 17.5%; fine-grained iron having 
for the same elements values of 55,892 Ibs., 89,118 Ibs., and 20%; and Bes- 
semer steel having values of 84,826 Ibs., 55,029 lbs., and 14.5%. The mean 
ultimate tensile strength of each material expressed in per cent of that at 
ordinary atmospheric temperature is given in the following table, the fifth 
column of which exhibits, for purposes of comparison, the results of experi- 
ee carried on by a committee of the Franklin Institute in the years 
1832-36. 


Fibrous Fine-grained Bessemer Franklin 

Temperature Wrought Iron, Steel, Institute, 

Degrees F. Iron, p. ¢. per cent. per cent, per cent. 
0 100.0 100.0 100.0 96.0 
100 100.0 100.0 100.0 102.0 
200 100.0 100.0 100.0 105.0 
800 97.0 100.0 100.0 106.0 
400 95.5 100.0 100.0 106.0 
500 92.5 98.5 98.5 104.0 
600 88.5 95.5 92.0 99.5 
700 81.5 90.0 68.0 92.5 
800 67.5 iso 44.0 visye9) 
900 44.5 51.5. 36.5 53.5 
1000 26.0 36.0 31.0 36.0 
1100 20.0 30.5 26.5 ° 
1200 18.0 28.0 DAO ah)... has bitte ® 
1300 16.5 Vy. 2an0) 18.0 bine 
1400 13.5 19.0 15.0 Sidisiste 
1500 10.0 15.5 12.0 Bneee 

1600 7.0 12.5 10.0 5 
1700 5.5 10.5 8.5 er 
1800 4.5 8.5 7.5 se 

1900 8.5 7.0 Gui Vy vie tie ered 
2000 3.5 5.0 5.0 Boone! 


The Effect of Cold on the Strength of fron and Steel.— 
The following conclusions were arrived at by Mr. Styffe in 1865: 

(1) That the absolute strength of iron and steel is not diminished by 
cold, but that even at the lowest temperature which ever occurs in Sweden 
it is at least as great as at the ordinary temperature (about 60° F,), 


384 IRON AND STEEL. dis f 


(2) That neither in steel nor in iron is the extensibility less in severe coid 
than at the ordinary temperature. 

@) That the limit of elasticity in both steel and iron lies higher in severe 
cold. 

(4) That the modulus of elasticity in both steel and iron is increased on 
reduction of temperature, and diminished on elevation of temperature ; but 
that these variations never exceed 0.05 % for a change of temperature of 1.8° 
F., and therefore such variations, at least for ordinary purposes, are of no 
special importance, 

Mr. C. P. Sandberg made in 1867 a number of tests of iron rails at various 
temperatures by means of a falling weight, since he was of opinion that, 
although Mr. Styffe’s conclusions were perfectly correct as regards tensile 
strength, they might not apply to the resistance of iron to impact at low 
temperatures. Mr. Sandberg convinced himself that ‘‘ the breaking strain ”’ 
of iron, such as was usually employed for rails, * as tested by sudden blows 
or shocks, is considerably influenced by cold ; such iron exhibiting at 10° FB. 
only from one third to one fourth of the strength which it possesses at 
84° F.”? Mr. J. J. Webster (Inst. C. E., 1880) gives raasons for doubting 
the accuracy of Mr. Sandberg’s deductions, since the tests at the lower 
temperature were nearly all made with 21-ft. lengths of rail, while those at 
the higher temperatures were made with sbort lengths, the supports in 
every case being the same distance apart. 

W.H. Barlow (Proc. Inst. C. E.) made experiments on bars of wrought 
iron, cast: iron, malleable cast iron, Bessemer steel, and tool steel. The bars 
were tested with tensile and transverse strains, and also by impact; one 
half of them ata temperature of 50° F., and the other half at5° F. The 
lower temperature was obtained by placing the bars in a freezing mixture, 
care being taken to keep the bars covered with it during the whole time of 
the experiments. 

The results of the experiments were summarized as follows: 

1, When bars of wrought iron or steel were submitted to a tensile strain 
and broken, their strength was not affected by severe cold (5° F.), but their 
ductility was increased about 1% in iron and 82 in steel. 

2. When bars of cast iron were submitted to a transverse strain at a low 
temperature, their strength was diminished about 8% and their flexibility 
about 16%. 

8. When bars of wrought iron, malleable cast iron, steel, and ordinary 
east iron were subjected to impact at a temperature of 5° F., the force re- 
quired to break them, and the extent of their flexibility, were reduced as 
follows, viz.: 


Reduction of Force Reduction of Flexi- 
of Impact, per cent. bility, per cent. 
Wrought iron, about.......... ae See eta eR 18 
Steel (best cast tool), about............ 34 17 
Malleable cast iron, about............ . 44 15 
Castirom, about). 0.5... Setar ool: Gases ae 21 not taken 


The experience of railways in Russia, Canada, and other countries where 
the winter is severe is that the breakages of rails and tires are far more 
numerous in the cold weather than in the summer. On this account a 
softer elass of steel is employed in Russia for rails than is usual in more 
temperate climates. ' 

The evidence extant in relation to this matter leaves no doubt that the 
eapability of wrought iron or steel to resist impact is reduced by cold. On 
the other hand, its static strength is not impaired by low temperatures. . 

Effeet of Low Vemperatures on Streneth of Railroad 
Axles. (Thos. Andrews, Proc. Inst. C. E., 1891.)—Axles 6 ft.6 in. long 
between centres.of journals, total length 7 ft. 3144 in., diameter at middle 414 
in., at wheel-sets 514 in., Journals 334 K 7 in. were tested by impact at temper- 
atures of 0° and 100° F. Between the blows each axle was half turned over, 
and was also replaced for 15 minutes in the water-bath. 

The mean force of concussion resulting from each impact was ascertained 
as follows: 


Let h = height of free fall in feet, 2 = weight of test ball, hw = W= 
“energy,” or work in foot-tons, « = extent of deflections between bearings, 
Ww hw 


f =—_—- = —, 
then #’ (meas force) : FE 


DURABILITY OF TRON, UORROSION, ETC. 385 


The results of these experiments show that whereas at a temperature of 
0° F.a total average mean force of 179 tons was sufficient to cause the 
breaking of the axles, at a temperature of 100° F.a total average mean 
force of 428 tons was requisite to produce fracture. In other words, the re- 
sistance to concussion of the axles at a temperature of 0° F. was only about 
4% of what it was at a temperature of 100° F. 

The average total deflection ata temperature of 0° F. was 6.48 in., as 
against 15.06 in. with the axles at 100° F. under the conditions stated; this 
represents an ultimate reduction of flexibility, under the test of impact, of 
aoe 5¢% for the coid axles at 0° F., compared with the warm axles at 

o 


EXPANSION OF IRON AND STEEL BY HEAT. 


James E, Howard, engineer in charge of the U.S. testing-machine at Wa- 
tertown, Mass., gives the following results of tests made on bars 35 inches 
long (fron Age, April 10, 1890): 





Chemical composition, Coefficient of 











Expansion. 

Metal. Marks. ales Per degree 
Coe evi Sic Hite tas F. per unit 
: of length. 

WOM SE ALON ll oS ko ell sla aissdeell s dfsbela oil aishaisak pp e’aletwustole ate See. uae « OOO00G67 302 
Stéelé.i-aat BEC ae Ie la .09 SRN Para ae 99.80 -0000067561 
ReAET ROSIE Sc crete? AEN Ons te Sener efetetel ers 99.35 -0000066259 
ee a 8a 31 .Oaam aes 99.12 -0000065149 
MME Doss eel 4a: 380 OWA | Soids ee 98.93 . 0000066597 
Webitc. tard Piste SSH chars 5a ol 58 02 98.89 .0000066202 
Se are SE SEs 6a “Db, tego 07 98 .43 .0000063891 

MET Mawta Spal Sielativesave(o%s 1a Sf 58 .08 98.63 .0000064716 

A AA eee 8a 61 56 alts 98.46 -0000062167 
BUNT fos oiaiel toae te 9a 89 <DiiinaLo 98.35 .0000062335 

oe Ob ae aes gare 10a 2071, 80 28 97.95 .0000061700 
Casti(Sun) Iron ash..i\ ea yees aes Vclatatiiane Seta hSS be ocevisrers eft | OOOR0R926L 
DA Wil COPPET age «ills scicls peas shes ot SN cheetah Pate alee Mavoreuehs clash = cesta . 0000091286 





DURABILITY OF ERON, CORROSION, ETC, 


Durability of Cast Hron.—Frederick Graff,in an article on the 
Philadelphia water-supply, says that the first cast-iron pipe used there was 
laid in 1820. These pipes were made of charcoal iron, and were in constant 
use for 53 years. They were uncoated, and the inside was well filled with 
tubercles. In salt water good cast iron, even uncoated, will last for a cen- 
tury at least; but it often becomes soft enough to be cut by a knife, as is 
shown in iron cannon taken up from the bottom of harbors after long sub- 
mersion. Close-grained. hard white metal lasts the longest in sea water.— 
Engg News, April 23, 1887, and March 26.1892. 

Wests of Kron after Forty Years’? Service.—A square link 12 
inches broad, 1 inch thick and about 12 feet loug was taken from the Kieff 
bridge, then 40 years old, and tested in comparison with'a similar link which 
had been preserved in the stock-house since the bridge was built. The fol- 
Jowing is the record of a mean of four longitudinal! test-pieces, 1 x 14% x 8 
inches, taken from each link (Stahl und Hisen, 1890): 


Old Link taken New Linkfrom 
from Bridge. Store-house, 


Tensile strength per square inch, tons........ 21 .o2 PG. 
Elastic limit Me 7 ele Ra ah sili ne Peo: 
Elongation, per cent... - sess BPs vax nsi shayeie 14.05 13.42 
Contraction, (per Cen tin ctemaraa ye ism 10/2 9° 6 <1 17.35 18.75 


Durability of Irom in Bridges. (G. Lindenthal, Eng’g, May 2, 
1884, p. 139.)-—The Old Monongahela suspension bridge in Pittsburgh, built 
in 1845, was taken down in 1882. The wires of the cables were frequently 
strained to half of their ultimate strength, yet on testing them after 37 years’ 


386 IRON AND STEEL. 


use they showed a tensile strength of from 72,700 to 100,000 lbs. per square 
inch. The elastic limit was from 67,100 to 78,600 lbs. per square inch. Re- 
duction at point of fracture, 35% to 75%. Their diameter was 0.13 inch. 

A new ordinary telegraph wire of same gauge tested for comparison 
showed: T.S., of 100,000 lbs.; E. L., 81,550 Ibs.; reduction, 57%. Iron rods 
used as stays or suspenders showed: T.S., 43,770 to 49,720 lbs. per square 
nen E. L., 26,380 to 29,200. Mr. Lindenthal draws these conclusions from 

is tests: 

“The above tests indicate that iron highly strained for a long number of 
years, but still within the elastic limit, and exposed to slight vibration, will 
not deteriorate in quality. 

“That if subjected to only one kind of strain it will not change its texture, 
even if strained beyond its elastic limit, for many years. It will stretch and 
behave much as in a testing-machine during a long test. 

** That iron will change its texture only when exposed to alternate severe 
straining, as in bending in different directions. If the bending is slight but 
very rapid, as in violent vibrations, the effect is the same.”’ 

Corrosion of Iron Bolts,—On bridges over the Thames in London, 
bolts exposed to the action of the atmosphere and rain-water were eaten 
away in 25 years from a diameter of % in. to 4 in., and from % in. diameter 
to 5/16 inch. 

Wire ropes exposed to drip in colliery shafts are very liable to corrosion. 

Corrosion of Iron and Steei.—Experiments made at the Riverside 
Tron Works, Wheeling, W. Va., on the comparative liability to rust of iron 
and soft Bessemer steel: <A piece of iron plate and a similar piece of steel, 
both clean and bright, were placed in a mixture of yellowloam and sand, 
with which had been thoroughly incorporated some carbonate of soda, nitrate 
of soda, ammonium chloride, and chloride of magnesium. The earth as 
prepared was kept moist. At the end of 33 days the pieces of metal were 
taken out, cleaned, and weighed, when the iron was found to have lost 0.84% 
of its weight and the steel 0.72%. The pieces were replaced and after 28 days 
weighed again, when the iron was found to have lost 2.06% of its original 
weight and the steel 1.79%. (Hng’g, June 26, 1891.) 

Corrosive Agents in the Atmosphere.—The experiments of F. 
Crace Calvert (Chemical News, March 3, 1871) show that carbonic acid, in 
the presence of moisture, is the agent which determines the oxidation of 
iron in the atmosphere. He subjected perfectly cleaned blades of iron and 
steel to the action of different gases for a period of four months, with 
results as follows: 

Dry oxygen, dry carbonic acid, a mixture of both gases, dry and damp 
oxygen and ammonia: no oxidation. Damp oxygen: in three experiments 
one blade only was slightly oxidized. ; 

Damp earbonic acid: slight appearance of a white precipitate upon the 
iron, found to be carbonate of iron. Damp carbonic acid and oxygen: 
oxidation very rapid. Iron immersed in water containing carbonic acid 
oxidized rapidly. 

Iron immersed in distilled water deprived of its gases by boiling rusted 
the iron in spots that were found to contain impurities. 

Galvanie Action is a most active agent of corrosion. It takes place 
when two metals, one electro-negative to the other, are placed in contact 
and exposed to dampness. 

Sulphurous acid (the product of the combustion of the sulphur in coal) is 
an exceedingly active corrosive agent, especially when the exposed iron is 
coated with soot. This accounts for the rapid corrosion of iron in railway 
bridges exposed to the smoke from locomotives. (See account of experi- 
ments by the author on action of sulphurous acid in Jour Frank Inst., June, 
1875, p. 487.) An analysis of sooty iron rust from a railway bridge showed 
the presence of sulphurous, sulphuric, and carbonic acids, chlorine, and 
ammonia, Bloxam states that ammonia is formed from the nitrogen of the 
air during the proccss of rusting. 

Corrosion in Steam-boilers,—Internal corrosion may be due 
either to the use of water containing free acid, or water containing sulphate 
or chloride of magnesium, which decompose when heated, liberating the 
acid, or to water containing air or carbonic acid in solution. External 
corrosion rarely takes place when a boiler is kept hot, but when cold it is 
apt to corrode rapidly in those portions where it adjoins the brickwork or 
where it may be covered by dust or ashes, or wherever dampness may 
Oe) (See Impurities of Water, p. 551, and Incrustation and Corrosion, 
p- . 


PRESERVATIVE COATINGS. 38% 


PRESERVATIVE COATINGS, 


(The following notes have been furnished to the author by Prof, 
A. H. Sabin.) 

Cement,—Iron-work is sometimes protected by bedding in concrete, 
in which case it is first cleaned and then washed with neat cement before 
being imbedded, 

Asphaltuma.—This is applied hot either by dipping (as water-pipe) or 
by pouring it on (as bridge floors). The asphalt should be slightly elastic 
when cold, with a high melting-point, not softening much at 100° F., applied 
at 300° to 400°; surface must be dry and should be hot; coating should be of 
considerable thickness. 

Paint.—Composed of a vehicle or binder, usually linseed oii or some: 
inferior substitute, or varnish (enamel paints); and a pigment which is a/ 
more or less inert solid in the form of powder, either mixed or ground 
together. The principal pigments are white lead (carbonate) and white 
zinc (oxide), red lead (peroxide), oxides of iron, hydrated and dehydrated, 
graphite, lainp-black, chrome yellow, ultramarine and Prussian blue, and 
various tinting colors. White lead has the greatest body or opacity of white 
pigments; three coats of it equal five of white zinc; zine is more brilliant 
and permanent, but it is liable to peel, and it is customary to mix the two. 
These are the standard white paints for all uses and the basis of all light- 
colored paints. Anhydrous iron oxides are brown and purplish brown. 
hydrated iron oxides are yellowish red to reddish yellow, with more or less 
brown; most iron oxides are mixtures of both sorts. They also contain 
frequently manganese and clay. They are cheap, and are serviceable 
paints for wood, and are often used on iron, but for the latter use are 
falling into disrepute. Graphite used for painting iron contains from 10 
to 90% foreign matter, usually silicates and iron oxides. Itis very opaque, 
hence has great covering power, and may be applied in avery thin coat 
which should be avoided. It retards the drying of oil, hence the necessity 
of using dryers; these are lead and manganese compounds dissolved in oil 
and turpentine or benzine, and act as carries of oxygen; they are necessary 
in most paints, but should be used as little as possible. There are many 
grades of larnp-black; as arule the cheaper sorts contain oily matter and 
are especially hard to dry; all lamp-black is slow to dry in oil. It is the 
' principal black on wood, and is used some on iron, usually in combination 
with varnish or varnish-like compounds. It is very permanent on wood. 
A gallon of oil takes only a pound of Jamp-black to make a paint, while 
the same amount of oil requires about 40 lbs. of red lead. On this account 
red-lead paint, which weighs about 30 lbs. per gallon, is the most expensive 
of all comon paints. It does not dry slowly like other oil paints, but com- 
bines with the oil to make a sort of cement; on this account it is used on 
the joints of steam-pipes. ete. To prevent the mixture of red lead and oil 
setting into a cake, and also to cheapen it, it is often adulterated with 
whiting or sometimes with white zinc, the proportion of adulterant being 
sometimes double the lead. Red lead has long had a high reputation asa 
paint for iron and steel and is still used very extensively; but of late years 
some of the new paints and varnish-like preparations have displaced it to 
some extent even on the most important work. 

WVarnishes.—These are made by melting fossilresin, to which is then 
added from half its weight to three times its weight of refined llnseed oil, 
and the compound is thinned with turpentine; they usually contain a little 
dryer. They are chiefly used on wood, being more durable and more 
brilliant than oil, and are often used over paint to preserve it. Asphaltum 
is sometimes snbstituted in part or in whole for the fossil resin, and in this 
way are made varnishes which have been applied to ironand steel with 
good results. Asphaltum and animal and vege able tar and pitch have also 
been simply dissolved in solvents, as benzine or carbon disulphide, and used 
for the same purpose. 

All these preservative coatings are supposed to form impervious films, 
keeping out air and moisture; butin fact all are somewhat porous, On this 
account it is necessary to have a film of appreciable thickness, best formed 
by successive coats, so that the pores of one will be closed by the next. The 
pigment is used to give an agreeable color, to help fill the pores of the oil 
film, to make the paint harder so that it will resist abrasion, and to make a 
thicker film. In varnishes these results are sought to be attained by the 
resin which is dissolved in the oil, There is no sort of agreement among 


388 , IRON AND STEEL. 


practical men as to which is the best coating for any particular case; this is 
probably because so much depends on the preparation of the surface and 
the care with which the coating is applied, and also because the conditions 
of exposure vary so greatly. 

Methods of Application.—Too much care cannot be given to the 
preparation of the surface. If it is wood, it should be dry, and the surface 
of knots should be coated with some preparation which will keep the tarry 
matter in the wood from the coating. All old paint or varnish should be 
removed by burning and scraping. Metallic surfaces should be cleaned by 
wire brushes and scrapers. and if the permanence of the work is of much 
importance the scale and oxide should be completely removed by acid 
pickling or by the sand-blast or some equally efficient means. Pickling is 
usually done with a 10% solution of sulphuric acid; as the solution becomes 
exhausted it may be made more active by heating. All traces of acid must 
be removed by washing and the metal must be rapidly dried and painted 
before it becomes in the slightest degree oxidized. The sand-blast, which 
has been applied to large work recently and for many years to small work 
with good results, leaves the surface perfectly clean and dry; the paint 
must be applied immediately. Plenty of time should always be allowed, 
usually about a week, for each coat of paint to dry before the next coat is 
applied; less than two coats should never be used. Two will last three 
times as long as one coat. Benzine should not be an ingredient in coatings 
for iron-work, because its rapid evaporation lowers the temperature of the 
ron and may cause formation of dew on the surface adjacent to the pai.t 
which is immediately to be painted. 

Cast iron water-pipes are usually coated by dipping in a hot mixture of 
ecoal-tar and coal-tar pitch; riveted steel pipes by dipping in hot asphalt or 
by a japan enamel which is baked on at about 400° F. Ships’ bottoms are 
usually coated with some sort of paint to prevent rusting, over which is 
spread, hot, a poisonous, slowly soluble compound, usually a copper soap, 
to prevent adhesion of marine growths. 

Galvanizec-iron and tin surfaces should be thoroughly cleaned with 
benzine and scrubbed before painting. When new they are covered with 
grease and chemicals used in coating the plates, and these must be removed 
or the paint will be destroyed. 

Gpuantity of Paint for a Given Surface.—One gallon of paint 
will cover 250 to 350 sq. ft. as a first coat, depending on the character of the 
surface, and from 350 to 450 sq. ft. as a second coat. 


Qualities of Paints.—The Railroad and Engineering Journal, vols. 
liv and lv, 1890 and 1891, has aseries of articles on paint as applied to wooden 
structures, its chemicai nature, application, adulteration, ete., by Dr. C. B. 
Dudley, chemist, and IF’. N. Tease, assistant chemist, of the Penna. R. R. 
They give the results of a long series of experiments on paint as applied,to 
railway purposes. 

Rustless Coatings for Iron and Steel,—Tinning, enamelling, 
lacquering, galvanizing, electro-chemical painting, and other preservative 
methods are discussed in two important papers by M. P. Wood, in Trans. 
A.S. M. E.. vols. xv and xvi. 

A Miethod of Producing an Inoxidizable Surface on 
iron and steel by means of electricity has been developed by M. A. de ).eri- 
tens (Hngineering). The article to be protected is placed in a bath of ordi- 
nary or distilled water, at a temperature of from 158° to 176° F., and an 
electric current is sent through. Vhe wateris decomposed into its elements, 
oxygen and hydrogen, and the oxygen is deposited on the metal, while the 
hydrogen appears at the other pole, which may either be the tank in which 
the operation is conducted or a plate of carbon or metal. The current has 
only sufficient electromotive force to overcome the resistance of the circuit 
and to decompose the water; for if it be stronger than this. the oxygen com- 
bines with the iron to produce a pulverulent oxide, which has no adherence. 
If the conditions are as they should be, it is only a few minutes after the 
oxygen appears at the metal before the darkening of the surface shows 
that the gas has united with the iron to form the magnetic oxide Fe,Q,, 
which will resist the action of the air and protect the metai beneath it. 
After the action has continued an hour or two the coating is sufficiently 
solid to resist the serateh-brush, and it will then take a brilliant polish. 

lf a piece of thickly rusted iron be placed in the bath, its sesquioxide 
(Fe,Q3) is rapidly transformed into the magnetic oxide. This outer layer 


Se cian al 


CHEMICAL COMPOSITION AND PHYSICAL CHARACTER, 389 


has no adhesion, but beneath it there will be found a coating which is 
actually a part of the metal itself. 

In the early experiments M. de Meritens employed pieces of steel only, 
but in wrought and cast iron he was not successful, for the coating came off 
with the slightest friction. He then placed the iron at the negative pole of 
the apparatus, after it had been already applied to the positive pole. Here 
the oxide was reduced, and hydrogen was accumulated in the pores of the 
metal. The specimens were then returned to the anode, when it was found 
that the oxide appeared quite readily and was very solid. But the result 
was not quite perfect, and it was not until the bath was filled with distilled 
water, in place of that from the public supply, that a perfectly satisfactory 
result was attained. 

Manganese Plating of Iron as a Protection from Rust. 
—-Aceording to the Italian Progreso, articles of iron can be protected against 
rust by sinking them near the negative pole of an electric bath composed of 
10 litres of water, 50 grammes of chloride of manganese, and 200 grammes 
of nitrate of ammonium. Under the influence of the current the bath 
deposits on the articles a protecting film of metallic manganese. 

A Non-oxidizing Process of Anmealimg is described by H. P. 
Jones, in Mng’g News, Jan. 2, 1892. The new process uses a non-oxidizing 
gas, and is the invention of Mr, Horace K. Jones, of Hartford, Conn. Its 
principal feature consists in keeping the annealing retort in communication 
with the gas-holder or gas-main during the entire process of heating and 
cooling, the gas thus being allowed to expand back into the main, and being, 
therefore, kept at a practically constant pressure. 

The retorts are made from wrought-iron tubes. The gas is taken directly 
from the mains supplying the city with illuminating gas. If metal which 
kas been blued or slightly oxidized is subjected to the annealing process it 
comes out bright, the oxide being reduced by the action of the gas. 

Comparative tests were made of specimens of steel wire annealed in 
illuminating gas, in nitrogen, and in an open fire and cooled in ashes, and of 
specimens of the unannealed metal. The wires were .188 in. in diameter 
and were turned down to .150 in. 

The average results were as follows: 

Unannealed, two lots, 5 pieces each, tensile strength av. 97,120 and 80,790 
lbs. per sq. in., elongation 7.12% and 8.80%. Annealed in open fire, 8 tests, av. 
t. s. 63,090, el. 26.76%. Annealed in nitrogen, av. of 3 lots, 18 pieces, t. s. 
59,820, el. 29.38%. Annealed in illuminating gas, av. of 3 lots, 13 pieces, t. s. 
60,180, el. 28.29%. The elongations are referred to an original length of 
1.15 ins. 


STEEL. 


RELATION BETWREN THE CHEMICAL COMPOSI- 
TION AND PHYSICAL CHARACTER OF STEEL. 


W. R. Webster (see Trans. A. I. M. E., vols. xxi and xxii, 1893-4) gives re- 
sults of several hundred analyses and tensile tests of basic Bessemer steel 
plates, and from a study of them draws conclusions as to the relation of 
chemical composition to strength, the chief of whicb are condensed as 
follows: 

The indications are that a pure iron, without carbon, phosphorus, man- 
ganese, silicon, or sulphur, if it could be obtained, would have a tensile 
strength of 34,750 lbs. per square inch, if tested in a 3é-inch plate. With 
this as a base, a table is constructed by adding the following hardening 
effects, as shown by increase of tensile strength, for the several elements 
named. 

Carbon, a constant effect of 800 Ibs. for each 0.01%. 

Sulphur, s§ My 500 < mO Ol %. 

Phosphorus, the effect is higher in high-carbon than in low-carbon steels. 

With carbon hundreths %... ... OP OM eI) 12) 1S 14 5 aloe 

Each .01% P has an effect of Ibs. 900 1000 1100 1200 1300 1400 1500 1500 1500 

Mangauese, the effect decreases as the per cent of manganese increases. 


BOOM 1S 6.200) 25 2.30 .3506.40) 408 00 eb 
Mn being per cent...... to}. to to to to to.) tor to” to? Ho 

Bina. 20 925230 ..85 40 7645 SO oSen ana 
Str’gth increases for .01% 240 240 220 200 180 160 140 120 100 100]bs, 
Totaliner. from 0 Mn... 3600 4800 5900 6900 7800 8600 9300 9900 10,400 11,400 


890 STEEL. 


{ Lyle is so low in this steel that its hardening effect has not been con. 
sidered. 

With the above additions fer carbon and phosphorus the following table 
has been constructed (abridged from the original by Mr. Webster). To the 
figures given the additions for sulphur and manganese should be made as 
above. 


Estimated Ultimate Strengths of Basic Bessemer Steci 




















Pilates, 
For Carbon, .06 to .24; Phosphorus, .00 to .10; Manganese and Sulphur, .00 in 
all cases. 
QCarbon.-}..06.| .08.) 10) |) .12 134 1...16 | 18 S20 Pee | ae 
——— |_| —_| — |__|! |_| —_ |! 
Phos. .005 | 39,950) 41,550! 43,250] 44,950) 46,650 48,300) 49,900 51,500/53,100) 54,700 
“01 =| 40,350 41,950| 43,750 45,550] 47,350) 49,050) 50,650] 52, 250/58,850) 55,450 
se 02 141,150) 42,750) 44,750] 46,750] 48,750 50,550! 52,150 53,750|55,350! 56.950 
“6.03 | 41,950} 43,550} 45,750) 47,950] 50,150 52,050! 53,650 55,250/56,850! 58.450 
“04 142,750} 41,350) 46,750] 49, 150] 51,550| 53,550 55,150/56,750/58,350| 59,950 
“105 [43,550] 45,150] 47,750} 50,350] 52,950] 55,050 56,650/58,250/59,850| 61.450 
se 06 144,350) 45,950) 48,750) 51,550) 54,350] 56,550! 58, 150)59,750|61,3850| 62.950 
«07 =|45, 150] 46,750) 49,750 52, 750) 55,750) 58,050 59,650) 61,250)62,850| 64.450 
“6 08 | 45,950) 47,550) 50,750) 53,950] 57,150/59,550 61, 150/62, 750|64,350| 65,950 
se 09 146,750) 48,350) 51,750] 55,150] 58,550) 61,050 62,650) 64,250}65,850) 67,459 
*© 10) | 47,550) 49,150) 52,750] 56,350} 59,950] 62,550 64,150|65.750167.350) 68.950 
.001 Phos =/80 Ibs.|80 Ibs. 





100 1b1120 1b1140 1b! 150 Ib 150 1b] 150 151150 Ib] 150 Ib 


In all rolled steel the quality depends on the size of the bloom or ingot 
from which it is rolled, the work put on it, and the temperature at which it 
is finished, as well as the chemical composition. 

The above table is based on tests of plates 34 inch thick and under 70 
inches wide; for other plates Mr. Webster gives the following corrections 
for thickness and width. They are made necessary only by the effect of 
thickness and width on the finishing temperature in ordinary practice 
Steel is frequently spoiled by being finished at too high a temperature. 


Corrections for Size of Plates. 





Plates. . Up to 70 ins. wide. Over 70 ins. wide. 
Ynches thick. Lbs. bs. 

DAR ANC OVELs. ceemecciecdesics s erent — 2000 — 1000 
11/16 na ue ahicoh cmmeirccraeice caus — 1750 — 750 
5 See ean ete sernele ore Wetcleee — 1500 — 500 
9/16 5 Dale stajeineiisic aie meeiraas — 1250 — 250 
0 sis ysl oiareee sei e Shreetarets — 1000 — 0 
4/16 PAE A Wetelrarc me eetaners arta vicars — 500 + 500 
36 os ee Ae ae mela: 0 + 1000 
5/16 Seo peal alex startle alosalal ae emekeioe + 3000 + 5000 


Comparing the actual result of tests of 408 plates with the calculated 
results, Mr. Webster found the variation to range as in the table below. 


Summary of the Differences Between Calculated and 
Actual Results in 408 Tests of Plate Steel, 
In the first three columns the effects of sulphur were not considered; in 
the last three columns the effect of sulphur was estimated at 500 lbs. for 
each .01% of S. 





Rw 
= vi a . | go leis 

fas} Lie} = res} — —_ e 

a = n a [aS 0c 

sa | & | & sa.| & |e S3s 

> > Og. 

ei © FI ae o |dijsogt 

2 a 6 5 m 10° tSekor 

~Q jae) asa : 

ale pa Se IE CR PES ee nal I 
Per cent within 1000 Ibs..| 23.4 | 82.1 28.4 24.6 27.0 26.0) 28.4 
3G HEH 2000 SR penO. 9+ «| 48.9 45.6 48.5 54.9 (52.2) 55.1 
the Soh eR rs 3000 * ee. 0 71.3 67.6 67.8 | 73.0 |70.8| 74.7 
“ fe Me 4000 “*..| Sap 5 81.0 78.7 82.5 | 85.2 |84.1) 89.9 
ue y Ab 5000 SS Segoe O 91.1 90.4 93.0 | 92.8 192.9! 94.9 





—" a 


\ 
\ 


STRENGTH OF BESSEMER AND OPEN-HEARTH STEELS. 391 


The last figure in the table would indicate that if specifications were drawn 
calling for steel plates not to vary more than 5000 Ibs. T. S. from a specified 
figure (equal to a total range of 10,000 Ibs.), there would be a probability of 
the rejection of 5% of the blooms rolled, even if the whole lot was made from 
steel of identical chemical analysis. In 1000 heats only 2% of the heats failed 
to meet the requirements of the orders on which they were graded; the loss 
of plates was much less than 1%, as one plate was rolled from each heat and 
tested before rolling the remainder of the heat. 

R. A. Hadfield (Jour. Iron and Steel Inst., No.1, 1894) gives the strength of 
very pure Swedish iron, remelted and tested as cast, 20.1 tons (45,024 Ibs.) 
per sq. in.; remelted and forged, 21 tons (47,040 lbs.). The analysis of the 
cast bar was: C, 0.08; Si, 0.04; S, 0.02; P, 0.02; Mn. 0.01; Fe, 99.82. 

Effect of Oxygen upon Strength of Steel.—A. Lantz, of the 
Peine works, Germany, in a letter to Mr. Webster, says that oxygen plays’, 
an important rdle—such that, given a like content of carbon, phosphorus, 
and manganese, a blow with greater oxygen content gives a greater hard- 
ness and iess ductility than a blow with less oxygen content. The method 
used for determining oxygen is that of Prof. Ledebur, given in Stahl und 
Hisen, May, 1892, p. 193. The variation in oxygen may make a difference in 
strength of nearly 14 ton per sq. in. (Jour. Iron and Steel Inst., No. 1, 1894.) 
RANGE OF VARIATION IN STRENGTH OF BESSEMER 

AND OPEN-HEARTSH STEELS. 

The Carnegie Steel Co. in 1888 published a list of 1057 tests of Bessemer 

. and open-hearth steel, from which the following figures are selected : 


Elongation 
Elastic Limit. eirence _ per cent 
: : in 8 inches. 


Kind of Steel. 


No. of Tests. 


— | | | es E  | SO |sd -————" 


(a) Bess. structural...} 100] 46,570 } 39,230 | 71,3800 | 61,450 | 33.00 | 28.75 


(b) -.-| 170} 47,690 | 389,970 | 73,540 | 65,200 |. 80.25 | 28.15 
(c) Bess. angles...... 72) 41,890 | 32,680 | 63,450 | 56,130 |. 34.80 } 26.25 
(AOE, NTO-DOX.. cn ofa Soilacteerctoyers eeeeaerabrs 62,790 | 50,350 | 386.00 | 25.62 
(e) O. H. bridge...-... CO irehe cee sire ee tae 69,940 | 63,970 | 80.00 | 22.75 





REQUIREMENTS OF SPECIFICATIONS. 
(a) Elastic limit, 35,000; tensile strength, 62,000 to 70,000; elong. 22% in 8 in. 
(b) Elastic limit, 40,000; tensile strength, 67,000 to 75,000. 
(c) Elastie limit, 30,000; tensile strength, 56,000 to 64,000; elong. 20% in 8 in. 
(d) Tensile strength 50,000 to 62,000; elong. 26% in 4 in, 
(e) Tensile strength, 64,000 to 70,000; elong. 20% in 8 in. 

Strength of Open-hearth Structural Steel, (Pencoyd Iron 
Works.)—AS a general rule, the percentage of carbon in steel determines its 
hardness and strength. The higher the carbon the harder the steel, the 
higher the tenacity, and the lower the ductility will be. The foliowing list 
exhibits the average physical properties of good open-hearth basic steel : 


4 |oSs 5.) Ba] SP os 2 3 fe Lee| UM 
BS fae Ogle el ce bh Sad Me Rise |e he 6 | oh echoes 
o# |Sie Gea tee] 2) o8 [ska eeu | $a | 2 
BO [Snel sala| Fo | Saf 50 (Sn2LE 8H25| fo] Ba 
oO a) ~ 9) eS 4 =) a 7) aa 
08 | 54000} 32500} 32 | 60 17 | 61600 | 37000) 37 50 

09 } 54800} 33000} 31 | 58 18 | 62500 | 37500} 97 49 

10 | 55700) 33500] 31 | 57 .19 } 63300 | 38000 | 26 48 
“11 | 56500} 34000] 30 | 56 .20 | 64200{ 38500] 96 | 47 

12 | 57400} 34500] 30 | 55 21 | 65000] 39000] 25 | 46 

13 | 58200] 35000} 29 | 54 22 | 65800 | 39500 | 25 45 


35 | 60000} 36000] 28 | 52 24 7400 | 40500] 84 43 
“Phe coefficient of elasticity is practically uniform for all grades, and is 
the same as for iron, viz., 29,000,000 lbs. These figures form the average of 
a numerous series of tests from rolled bars, and can only serve as an ap. 


392 STEEL. 


proximation in single instances, when the variation from the avérage may 
be considerable. Steel below .10 carbon should be capable of doubling flat 
without fracture, after being chilled from a red heat in cold water. Steel 
of .15 carbon will occasionally submit to the same treatment, but will 
usually bend around a curve whose radius is equal to the thickuess of 
the specimen ; about 90% of specimens stand the latter bending test without 
fracture. As the steel becomes harder its ability to endure this bending 
test becomes more exceptional, and when the carbon ratio becomes .20, 
little over 25% of specimens wi'l stand the last-described bending test. Steel 
having about .40% carbon will usually harden sufficiently to cut soft iron 
and maintain an edge. 

Mehrtens gives the following tables in Stahl und Eisen (Iron Age, April 20, 
1893) showing the range of variation in strength, etc., of basic Bessemer and 
of basic open-hearth structural steel. The figures in the columns headed 
Per Cent show the per cent of the total number of charges which came 
within the range given. 


BASIC BESSEMER STEEL, 680 CHARGES. 
Elastic Limit, pe Tensile Strength, Per 


‘ 3 Elongation, Per 

Aha ie Cent. ee | Cent. per cent. Cent. 
35,500 to 38,400....... 15.0'| 55,600 to 56,900.... 18.67 | 21 to 25...2: ARO: 2.65 
38,400 to 39,800..... 81671) 56;9006°58; 2001 238 88. 67e P2510 Bee ceole stan eolee 
39,800 to 41,200..)....27.5 || 58,300 to 59,700./.. 23.53 | 27 to 29... 50.44 
41,200 to 42,700..... 16.0°| 59,700 to 61,200.:.. 15.60 | 29 to 30. fi. 2... . 14.41 
42,700 to 46,400..... 9.9 | 61,200 to 62,300.... 3.53 | 80 to 82.5......... 6.62 

BASIC OPEN-HEARTH STRUCTURAL STEEL, 489 CHARGES. 

84,400 to 37,000..,.. 12.3 | 55,800 to 56,900..... 8 On 20 tO Ross aaaieeiee WOT 
31,000: 10 89,800" 22) 3.35.9) |556,900 $059,700. 222. 5158 | 25. LO 2Ouisee sectioned oa 
39,800 to 42,700..... 30.2 | 59,700 to 61,200..... 1956) 20 tO. 28 ama eee 21,3 
42°700 to 44,100..... 11.4 | 61,200 to 62,600..... 11°%..|' 28 10: 80ness seeaei . 25.3 
44,100 to 48,400..... 8.5 | 62,600 to 65,100..... 9.4 | 30 to87.1 ......... 24.3 


Rivet steel, 19 charges, showed a total range from 51,800 to 56,900 Ibs. 
tensile strength, and 25.2 to 29.8 per cent elongation. 


In the basic Bessemer steel over 90% was below 0.08 phosphorus, and all 
were below 0.10; manganese was below 0.6 in over 90%, and below 0.9 in all, 
sulphur was below 0.05 in 84%, the maximum being 0.071; carbon was below 
0.10, and silicon below 0.01 in all. In the basic open-hearth steel phosphcrug 
was below 0.06 in 96%, the maximum being 0.08; manganese below 0.50 in 97%; 
sulphur below 0.07 in 88%, the maximum being 0.12. The carbon ranged 
from 0.09 to 0.14. 

Low Tensile Strength of Very Pure Steel.—Swedish nail-rod 
open-hearth steel, tested by the author in 1881, showed a tensile strength of 
only 42,591 lbs. per sq. in. A piece of American nail-rod steel showed 45,021 
lbs. per sq. in. Both steels contained about .10 carbon and .015 phosphorus, 
and were very low in sulphur, manganese, and silicon. The pieces tested 
were bars about 2 x 3 in. section. 

Low Strength Due to Insufficient Work. (A. E. Hunt, 
Trans. A. I. M. E., 1886.)—Soft steel ingots, made in the ordinary way for 
boiler plates, have only from 10,000 to 20,000 lbs. tensile strength per sq. in., 
an elongation of only about 10% in 8 in., and a reduction of area of less than 
20%. Such ingots, properly heated and rolled down from 10 in. to % in. 
thickness, Wai give from 55,000 to 65,000 lbs. tensile strength, an elongation 
in 8 in. of from 238% to 33%, and a reduction of area of from 55% to 70%. Any 
work stopping short of the above reduction in thickness ordinarily yields 
intermediate results in its tensile tests. 

Effect of Finishing Temperature in Rolling.—The strength 
and ductility of steel depend to a high degree upon fineness of grain, and 
this may be obtained by having the temperature of the steel rather low, say 
at a dull red heat, 1300° to 1400° F., during the finishing stage of rolling. In 
the manufacture of steel rails a great improvement in quality has beén 
obtained by finishing at alow temperature. An indication of the finishing 
temperature is the amount of shrinkage by cooling after leaving the rolls. 
The Philadelphia and Reading Railway Company’s specification for rails 
(1902) says, ‘‘ The temperature of the ingot or bloom shall be such that with 
rapid rolling and without holding before or in the finishing passes or subse- 
quently, and withoutartificial cooling after leaving the last pass, the distance 
between hot saws shall not exceed 30 ft. 6 in. for a 30-ft. rail.” 

Fining the Grain by Annealing.—Steel which is coarse-grained 


Pl 


\ 
STRENGTH OF BESSEMER AND OPEN-HEARTH STEELS. 393 


on\account of leaving the rolls at too high a temperature may be made fine- 
vrained and have its ductility greatly increased without lowering its tensile 
strength by reheating to a cherry red and cooling at once in air, (See paper 
on Steel Rails,” ly Robert Job, Trans. A. I. M. E., 1902.) ‘ 

Effect of Cold Rolling.—Cold rolling of iron and steel increases the 
elastic limit and the ultimate strength, and decreases the ductility. Major 
Waile’s experiments on bars rolled and polished cold by Lauth’s process 
showed an average increase of load required to give a slight permanent set 
as follows: Transverse, 162%; torsion, 130%; compression, 161% on short 
columns 114 in. long, and 64% on columns 8 in, long; tension, 95%. The hard- 
ness, aS measured by the weight required to produce equal indentations, 
was increased 50%; and it was found that the hardness was as great in the 
centre of the bars as elsewhere. Sir W. Fairbairn’s experiments showed an 
increase in ultimate tensile strength of 50%, and a reduction in the elongation 
in 10 in. from 2 in. or 20%, to 0.79 in. or 7.9%. 

Hardening of Soft Steel.—A. E. Hunt (Trans. A. I. M. E., 1883, vol. 
xii), says that soft steel, no matter how low in carbon, will harden to a cer- 
tain extent upon being heated red-hot and plunged into water, and that it 
hardens more when plunged into brine and less when quenched in vil. 

An illustration was a heat of open-hearth steel of 0.15% carbon and 0.29% of 
manganese, which gave the following results upon test-pieces from the same 
144 in. thick plate. 

Maximum Elongation Reduction 


Load. in 8 in. of Area. 

Ibs. persq.in. Per cent, Per cent. 
Unhardened.... ....... 55,000 Sofi 62 
Hardened in water..... 74,000 25 50 
Hardened in brine...... 84,000 22 42 
Hardened in oil......... 67,700 26 49 


While the ductility of such hardened steel does not decrease to the extent 
that the increased tenacity would indicate, and is much superior to that of 
normal steel of the high tenacity, still the greatly increased tenacity after 
hardening indicates that there must be a considerable molecular change in 
the steel thus hardened, and that if such a hardening should be created 
niet in a steel plate, there must be very dangerous internal strains caused 

hereby. 


Comparison of Tests of Full-size Eye-bars and Sample 
Test-pieces of Same Steel Used in the Memphis Bridge. 
(Geo. S. Morison, Trans. A. 8. C. E., 1893.) 


Full-Sized Eyebars, Sample Bars from Same Melts, 
Sections 10’” wide X 1 to 2 3/16” thick. about 1 in. area. 





Reduc-| Elongation. |Elastic| Max. |Reduc-]} Elon- | Elastic! Max. 
tion of Limit, | Load, | tion, |gation, | Limit, | Load, 
Area, in Sins. 

p.c. |Inches.| p.c. |lbs. per/sq. in. | p.c. p.c. |lbs. per|sq. in. 


39.6 20.2 16.8 35,100 | 67,490 47.5 27.5 41,580 73,050 
39.7 26.6 8.2 37,680 | 70,160 52.6 24.4 42,650 75,620 
44.4 36.8 11.8 39,700 | 65,500 47.9 28.8 40,280 70,280 
88.5 38.5 17.3 | 83,140 | 65,060 47.5 La) 41,580 73,050 
40.0 82.5 13.5 | 32,860 | 65,600 | 44.5 20.0 | 43,750 75,000 
39.4 36.8 15.3 31,110 | 61,060 42.7 28.8 42,210 69,730 
84.6 32.9 13.7 | 33,990 | 63,220 52.2 28.1 40,230 69,720 
32.6 13.0 13.5 29,330 | 63,100 48.3 28.8 38,090 71,300 
7.3 20.8 6.9 28,080 | 55,160 43.2 24.2 33,320 70,220 
33.1 28.9 14.1 29,670 | 62,140 59.6 26.3 40,200 71,080 
Us ee) 24.0 11.8 32,700 | 65,400 40.3 25.0 89,360 69,360 
43.6 39.4 19.3 30,500 | 58,870 40.3 25.0- | 40,910 70,360 
10.3 11.8 12.3 33,3860 | 73,550 51.5 25.5 | 40,410 69,900 
44.6 32.0 15.7 | 82,520 | 60,710 43.6 27.0 | 40,400 70,490 
46.0 35.8 14.9 28,000 | 58,720 44.4 29.5 40,000 66,800 
41.8 23.5 13.1 82,290 | 62,27 42.8 21.3 40,530 | 72,240 
41.2 47.1 15. 29.97 58.680 45.7 27.0 | 40,610 70,480 








~The average strength of the full-sized eye-bars was about 8000 lbs, per sq. 
in., or about 12%, less than that of the sample test-pieces. 





394 STEEL. . ya 


TREATMENT OF STRUCTURAL STEEL. 


(James Christie, Trans. A. 8. C, E., 1893.) 


Effect of Punching and Shearing.—There is no doubt that steel 
of higher tensile strength than is now accepted for structural purposes 
should not be punched or sheared, or that the softer material may contain 
elements prejudicial to its use however treated, but especially if punched. 
But extensive evidence is on record indicating that steel of good quality, in 
bars of moderate thickness and below or not much exceeding 80,00) Ibs. 
tensile strength, is not any more, and frequently not as much, injured as 
wrought iron by the process of punching or shearing. . 

The physical effects of punching and shearing as denoted by tensile test 
are for iron or steel: ae 

Reduction of ductility; elevation of tensile strength at elastic limit; reduc- 
tion of ultimate tensile strength. , \ } 

In very thin material the superficial disturbance described is less than in 
thick; in fact, a degree of thinness is reached where this disturbance prac- 
tically ceases. On the contrary, as thickness is increased the injury 
becomes more evident. 

The effects described do not invariably ensue; for unknown reasons there 
are sometimes marked deviations from what seems to be a general result. 

By thoroughly annealing sheared or punched steels the ductility is to a 
large extent restored and the exaggerated elastic limit reduced, the change 
being modified by the temperature of reheating and the method of cooling. 

It is probable that the best results combined with least expenditure can 
be obtained by punching all holes where vital strains are not transferred by 
the rivets; and by reaming for important joints where strains on riveted 
joints are vital, or wherever perforation may reduce sections to a minimum. 
The reaming should be sufficient to thoroughly remove the material dis- 
turbed by punching; to accomplish this it is best to enlarge punched holes 
at least 14 in. diameter with the reamer. 


Kiveting.—It is the current practice to perforate holes 1/16 in. larger 


than the rivet diameter. For work to be reamed it is also a usual require- 
ment to punch the holes from 1 to 3/16 in. less than the finished diameter, 
the holes being reamed to the proper size after the various parts are 
assembled. 

It is also excellent practice to remove the sharp corner at both ends of 
the reamed holes, so that a fillet will be formed at the junction of the bodv 
and head of the finished rivets. 

The rivets of either iron or mild steel shouid be heated toa bright red or 
yellow heat and subjected to a pressure of not less than 50 tons per square 
inch of sectional area. 

For rivets of ordinary length this pressure has been found sufficient to 
completely fill the hole. If, however, the holes and the rivets are excep- 


tionally long, a greater pressure and a slower movement of the closing tool. 


than is used for shorter rivets has been found advantageous in compelling 
the more sluggish flow of the metal throughout the longer hole. 

MOA tay o welding should be allowed on any steel that enters into 
structures, 

Upsetting.—Enlarged ends on tension bars for screw-threads, eyebars. 
etc., are formed by upsetting the material. With proper treatment and a 

_ Sufficient increment of enlarged sectional area over the body of the bar the 
result is entirely satisfactory. The upsetting process should be performed 

. that the properly heated metal is compelled to flow without folding or 
apping. 

Anneéaling.—The object of annealing structural steel is for the purpose 
of securing homogeneity of structure that is supposed to be impaired by un- 
equal heating, or by the manipulation necessarily attendant on certain pro- 
cesses. The objects to be annealed should be heated throughout to a 
uniform temperature and uniformly cooled. 

The physical effects of annealing, as indicated by tensile tests. depend on 
the grade of steel, or the amount of hardening elements assuciated with its 
also on the temperature to which the steel is raised, and the method or rate 
of cooling the heated material. 

The physical effects of annealing medium-grade steel, as indicated by ten- 
sile test, are reported very differently by different observers, some claiming 
directly opposite results from others. It is evident, when all the attendant 
conditions are considered, that the obtained results must Vary both in kind 
and degree, 


<n e 


e 


TREATMENT OF STRUCTURAL STEEL, 395 


a 

The temperatures employed will vary from 1000° to 1500° F',; possibly even 
a wider range is used. In some cases the heated steel is withdrawn at full 
temperature from the furnace and allowed to cool in the atmosphere ; in 
others the mass is removed from the furnace, but covered under a muffle, 
to lessen the free radiation; or, again, the charge is retained in the furnace, 
and the whole mass cooled with the furnace, and more slowly than by either 
of the other methods. 

The best general results from annealing will probably be obtained by in- 
troducing the material into a uniformly-heated oven in which the tempera- 
ture is not so high as to cause a possibility of cracking by sudden and 
unequal changing of temperature, then gradually raising the temperature 
of the material until it is uniformly about 1200° F., then withdrawing the 
material after the temperature is somewhat reduced and cooling under 
shelter of a muffle, sufficiently to prevent too free and unequal cooling ou 
the one hand or excessively slow cooling on the other. 

G. G. Mehrtens, Trans. A. S. C. E. 1893, says: ‘‘ Annealing is of advantage 
to all steel above 64,000 lbs. strength per square inch, but it is questionable 
whether it is necessary in softer steels. The distortions due to heating 
cause trouble in subsequent straightening, especially of thin plates. 

“In a general way all unannealed mild steel for a strength of 56,000 to 
64,000 Ibs. may be worked in the same way as wrought iron. Rough treat- 
ment or working at a blue heat must, however, be prohibited. Shearing is 
to be avoided, except to prepare rough plates, which should afterwards be 
smoothed by machine tools or files before using. Drifting is also to be 
avoided, because the edges of the holes are thereby strained beyond the 
yield point. Reaming drilled holes is not necessary, particularly when 
sharp drills are used and neat work is done. A slight countersinking of the 
edges of drilled holes is all that is necessary. Working the material while 
heated should be avoided as far as possible, and the engineer should bear 
this in mind when designing structures. Upsetting, cranking, and bending 
ought to be avoided, but when necessary the material should be annealed 
after completion. 

‘*The riveting of a mild-steel rivet should be finished as quickly as pos- 
sible, before 1t cools to the dangerous heat. For this reason machine work 
is the best. There is a special advantage in machine work from the fact 
that the pressure can be retained upon the rivet until it has cooled suffi- 
ciently to prevent elongation and the eee loosening of the rivet.” 

Punching and Drilling of Steel Plates. (Proc. Inst. M. E., 
Aug. 1887, p. 3:6.)—In Prof. Unwin’s report the results of the greater num- 
ber of the experiments made on iron and steel plates lead to the general 
conclusion that, while thin plates, even of steel, do not suffer very much 
from punching, yet in these of 44in. thickness and upwards the loss of te- 
nacity due to punching ranges from 10% to 23% in iron plates and from 11% to 
33% in the case of mild steel. Mr. Parker found the loss of tenacity in steel 
plates to be as high as fully one third of the original strength of the plate. 
In drilled plates, on the contrary, there is no appreciable loss of strength. 
It is even possible to remove the bad effects of punching by subsequent 
reaming or annealing. 

Working Steel at a Blue Heat.—Not only are wrought iron and 
steel much more brittle at a blue heat (i.e., the heat that would prc duce an 
oxide coating ranging from light straw to blue on bright steel, 430° to 600° 
F.), but while they are probably not seriously affected by simple exposure 
to blueness, even if prolonged, yet if they be worked in this range of temn- 
perature they remain extremely brittle after cooling, and may indeed be 
more brittle than when at blueness : this last point, however, is not certain. 
(Howe, ** Metallurgy of Steel,” p. 534.) 

Tests by Prof. Krohn, for the German State Railways, show that working 
at blue heat has a decided influence on all materials tested, the injury done 
being greater on wrought iron and harder steel than on the softer steel. 
The fact that wrought iron is injured by working at a blue heat was reported 
by Stromeyer. (Engineering News, Jan. 9, 1892.) 

A practice among boiler-makers for guarding against failures due to work- 
ing at a blue heat consists in the cessation of work as soon as a plate which 
had been red-hot becomes so cool that the mark produced by rubbing a 
hammer-handle or other piece of wood will not glow. A plate which is not 
hot enough to produce thls effect, yet too hot to be touched by the hand, is 
most probably blue hot, ard should under no circumstances be hammered 
or bent. (C. E. Stromeyer, Proc. Inst. C. E. 1886.) 

Welding of Steel.—-A. E. Hunt (A. I. M. E., 1892) says: I have never 
seen so-called ‘‘ welded ” ;sieces of stee] pulled apart in a testing-machine or 


396 ty Ve eas Os re, 


® 


otherwise broken at tho joint which have not shown a smooth cleavage- 
plane, as it were, such as in iron would be condemned as an imperfect 
‘weld. My experience in this matter leads me to agree with the position 
taken by Mr. William Metcalf in his paper upon Steel in the Trans. A. §. 
C. E., vol. xvi., p. 301, Mr. Metcalf says, ‘‘I do not believe steel can be 
welded.” 

Oil-tempering and Annealing of Steel Forgings.—H. Ff. J. 
Porter says (1897) thac all steet forgings above 0.1% carbon should be an- 
nealed, tc relieve them of forging and annealing strains, and that the 
process of annealing reduces the elastic limit to 47% of the ultimate strength. 
Oil-tempering should only be practised on thin sections, and large forgings 
should be hollow for the purpose. This process raises the elastic limit 
above 50% of the ultimate tensile strength, and in some alloys of steel, 
notably nickel steel, will bring it up to 60% of the ultimate. 

HMtydraulic Forging of Steel. (See pages 618 and 619.) 


INFLUENCE OF ANNEALING UPON MAGNETIO 
CAPACITY, 


Prof. D. E. Hughes (£ng’g, Feb. 8, 1881, p. 180) has invented a “* Magnetic 
Balance,” for testing the condition of iron and steel, which consists chiefly of 
a delicate magnetic needle suspended over a graduated circular index, and 
a magnet coil for magnetizing the bar to be tested. He finds that the fol- 
lowing laws hold with every variety of iron and steel : 

1, The magnetic capacity is directly proportional to the softness, or mo- 
lecular freedom. 

2. The resistance to a feeble external magnetizing force is directly as the 
hardness, or molecular rigidity. 

The magnetic balance shows that annealing not only produces softness in 
iron, and consequent molecular freedom, but it entirely frees it from all 
strains previously introduced by drawing or hammering. Thus a bar of 
iron drawn or hammered has a peculiar structure, say a fibrous one, which 

ives a greater mechanical strength in one direction than another. This 

ar, if thoroughly annealed at high temperatures, becomes homogeneous in 
all directions, and has no longer even traces of its previous strains, provided 
that there has been no actual separation into a distinct series of fibres. 


Effect of Annealing upon the Magnetic Capacity of 
Different Wires; Tests by the Magnetic Balance, 





Magnetic Capacity. 














Description. 
Bright as sent. Annealed. 
deg. on scale. deg. on scale. 
Best Swedish charcoal iron, first variety. 230 525 
ee ee 66 ee second ee 936 510 
66 66 ce 66 third 66 O75 § 503 
Swedish Siemens-Martin iron............ 165 430 
Puddled iron, best best.......... AREER 554 212 340 
Bessemer steel, SOL. i ..04 ae Vee sole ede 150 291 
“ SSMMTI ACLS 2 acc8k he Mele ae Oe 115 172 
Crucible fine cast steel.................. 50 84 
Crucible Fine Steel. "tempered. | Magnetic 
Capacity. 
Bright-yellow heat, cooled compietely in cold water......... 28 
Yellow-red heat, cooled compieteiy in coid water....:....... 32 
Bright yellow, let down in cold water to straw color......... 33 
ss i be oy Hy : DIOS oa. oan 43 
Ly cs cooled completeiv in oil .................. eye 8 51 
i. Yi let down in water to white.................... 58 
Reheat, cooled completely 1n water...............202 seeeeee 66 
ay oe ee SCROLL fe oe aioe eo. 62 cee . ace ae 72 
Annealed, ‘‘ Be ROU. yale e2 =» oh Cagle aS 84 


STANDARD SPECIFICATIONS FOR STEEL. 397 


STANDARD SPECIFICATIONS FOR STEEL. 


The following specifications are abridged from those adopted Aug. 10, 
Sade ie the American Section of the International Association for Testing 

aterials.* 

Kinds of Steel Used for Different Purposes.—O, open- 
hearth; B, Bessemer; C, crucible. 

(1) Castings, Ove GC. (2) Axles, O. (38) Forgings,O, B,C. (4) Tires, 
OF CHG) Rails, O, B. (6) Splice-bars, O. B. (7) Structural Steel for 
te O, B. (8) Structural steel for ships, O. (9) Boiler-plate and 
rivets 


CHEMICAL REQUIREMENTS FOR THE ABOVE NINE CLASSES. 
(The minus sign after the figures means ‘‘or less.’’) 
(1) ordinary, P, 0.08—; C, 0.40—; tested castings, P, 0.05—; S, 0.05—. 


(2) P, 0.06—; 8S, 0.06—. Nickel steel, Ni, 3.00 to 4.00; P, 0.04—;5S, 
0.04—. (38) soft or low carbon, P, 0.10—; S, 0.10 —; Class B (see below), 
P,0.06—; S,0.06—. Classes C and D, qin S,0.04—. (4) P, Coens 
8, 0.05 —; Mn, 0.80—; Si, 0.20+. (5) 0.10—; Si, 0.20—; C, a, 0.35 
to 0.45; b, 0.38 to 0.48; ix "0.40 to 0.50; d,0 0.43 to 0.53; e, 0.45 to 0.553 Mn, 
a, b, 0.70 to 1.00; ec, 0.75 to 1.05; d,e, 0.80 to 1.10. [a, 50 to 59+ Ibs. per 
yard; 6, 60 to 69+ Ibsisic, 70 to 79+ Ibs.; d, 80 to 89 + lbs.; e, 90 to 100 
Ibs.] (6) P,0.10—; C, 0. 1b-; ‘Mn, 0.30 to 0.60. C7) x Ba0: NOeess (8) acid, 
P, 0.08—; S. 0.06—; basic, P, 0.06—; S,0.06—. (9) a, P, 0.06—; b,c, 


0 
me O.G4 —* ‘d, Pe 0.03—; a,b,S,0.05—; Mn, 0.30 to 0.60; c, d, é, 8, 0.04—; 
Mn, 0.30 to 0.50. [a, flange or boiler steel, acid; b, do. basic; CG; fire- box, 
acid: d, do. basic; e, extra soft.] 

“Where the physical properties desired are clearly and properly specified, 
the chemistry of the steel, other than prescribing the limits of the injurious 
impurities, P and 8, may in the present state of the art of making steel be 
safely left to the manufacturer.” 


as) 


PHYSICAL REQUIREMENTS. 
(1) Castings subjected to physical tests. 


Quality. Hard. Medium. Soft. 

Tensile strength, lbs. per sq. in. .........«. 85,000 70,000 60,000 
Bexrelrd-point, Ibs. per sq. im! 5725. Hinde 38,250 31,500 27,000 
Hlongzavion, per centrin 2 inss.s). sae. 15 18 22 
Contr j.of area; per'cent.\0 30 aa, Pen, 20 25 30 


The above are the minimum requirements. Test-piece4in. diam. Bend- 
ing test: Specimen 1 X 14 ins. to bend cold around a diam. of 1 in. through 
120° for soft and 90° for medium castings. 

(2) Axles.—For car, engine-truck, and tender-truck axles no tensile 
test is required. For driving-axles, minimum requirements: T.S. 80,000; 
Y. P. 40,000 for carbon steel (a), 50,000 for nickel steel, 3 to 4 per cent 
Ni, oil-tempered or annealed (6). Elongation in 2 ins., 18 per cent fora, 25 
aus cent for 6. Contraction of area, 45 per cent for b. Test-piece 4 in. 
diam. 

Drop-test.--Not required for driving-axles. For other axles one axle 
from each melt to be tested on a standard R.R. drop-testing apparatus, with 
supports 3 ft. apart, tup 1640 lbs., anvil 17,500 lbs., supported on springs. 
The axle shall stand the number of blows named below without rupture and 
without exceeding at the first blow the deflection stated. It is to be turned 
over after the first, third, and fifth blows. 


Diam. of axle at centre,ins... 44 43 4; 4§ 42 5% 55 
5 5 5 5 5 7 


Nov ot blOWS ace cane eee 5 
Height of drop ttn scp} «sles 24 26 284 31 34 43 A438 
Deflection, ins. Sahota MLSE OS 8+ 8+ 8 8 7 54 


(3) Steel Forgings.—claesinenien: A, soft or low carbon; B, carbon 
steel, not annezled; C, do.,annealed; D, do., oil-tempered; E, nickel-steel, 
annealed: HH do., oil- tempered. Sub- classes: a, solid or- hollow forgings, 
diam. or thickness not over 10 ins. Baia solid forgings, diam. not over 20. ins., 
or thickness of section not over 15 ins. c, solid, over 20 ins. diam.; d, solid 





* The complete specifications may be found in book form in ‘‘American 
Standard Specifications for Steel,’ by Albert Ladd Colby (Chemical Pub- 
lishing Co., Easton, Pa., 1902). 


or hollow, diam. or thickness not over 3 ins.; e, do., not over 6 ins. Mini- 
mum requirements of test-piece 4 in. diameter, 2 ins. between gauge-marks; 


398 STERL, 


Ten- : El. in El. in : 
ont : Elastic 2 | Contr., Kindiot 8 eC be Contr., 


.| sile cere ins., 2 ins., 
St’gth. Limit. Por Ce: Per Ct. Per Ct Per Ct. 





Aa | 58,000/29,000 Y.P.| 28 35 Da | 80,000} 45,000} 23 40 
Ba | 75,000/37,500 Y.P.| 18 30 Ea | 80,000) 50.000) 25 45 | 











Ca | 80,000/40,000 22 35 Eb | 80,000} 45,000} 25 45 : 
Cb | 75,000/37 ,500 23 35 Ee | 80,000} 45,000} 24 40 
Ce_}70,000/35,000 24 30 Fd | 95,000} 65,000) 21 50 
Dd | 90,000/55,000 20 45 Fe | 90,000} 60,000} 22 50 
De | 85,000|50,000 22 45 Fa | 85,000} 55,000) 24 45 








The number and location of test specimens to be taken from a melt, blow, 
or forging depend upon its character and importance, and must. therefore 
be regulated by individual cases. The yiefd-point (in steels A and B) shall 
be determined by observation of the drop of the beam or halt in the gauge of 
the testing-machine. The elastic limit shall be determined by means of an 
ee and will be taken at that point where the proportionality 
changes 

Bending Test.—A specimen | X 14 ins. shall bend cold 180° without fracture 
a oat of bent portion, as follows. The test may be made by bending or 

y blows 
Around a diam. of ins...... + 14 14 1 1 4 1 
Por kind. iiick ge de. eos A B Ce Cab D E F 


(4) bh a arpsenns Nias requirements of test-piece 4 in, diam.. Tires for 
passenger engines: T.S., 100,000; El. in 2 ins., 12 percent. Tires for fr eight 
engines and car wheels: T: S., 110 000; El., 10 per cent. Tires for switching 
engines: T.8., 120,000; EL., 8 per cent. 

Drop-test, —Ifa drop-test i is called for, a selected tire shall be placed verti- 
cally under the drop on a foundation at least 10 tons in weight and subjected 
to successive blows from a tup weighing 2240 lbs. falling from increasing 
heights until the required deflection is obtained, without breaking or crack- 
ing. The minimum deflection must equal D?+(4072+2D), D being inter- 
nal diameter and T thickness of tire at centre of tread. 

(5) Bails.-—One drop-test shall be made on a piece of rail not more than 
6 ft. long, selected from every fifth blow of steel. The rail shall be placed 
head upwards on solid supports 3 ft. apart, which are part of, or firmly 
secured to, an anvil-block weighing at least 20,000 Ibs., and subjected to the 
following impact tests. 

Weight of rails, lbs. per yd.45to55 55to65 65to75 75to85 85to 10¢ 
Height of drop, ft Phan 1S 16 a7 18 19 

If any rail break when subjected to the drop-test, two additional tests 
will be made of other rails from the same blow of. steel, and if either of these 
latter tests fail, all the rails of the blow which they represent will be rejected, 
but ese tests meet the requirements, all the rails of the blow will be as- 
cepte 

(Re (6) Splice=-bars.—Tensile strength of a specimen cut from the head of 
the bar, 54,000 to 64,000 lbs.; yield-point, 32,000 lbs. Elongation in 8 ins., 
not less than 25 per cent. A. test specimen cut from the head of the bar 
shall bend 180° flat on itself without fracture on the outside of the bent 
portion. If preferred, the bending test may be made on an unpunched splice- 
bar, which shall be first flattened and then bent. One tensile test and one 
bending test to be made from each blow or melt of steel. 

(7) Structural Steel for Buildings, 








Class. Rivet-steel. . | Medium Steel. 
Tensile strength, Ibs. per sq.in.......... 50,000-60,000 | 60,000-70,000 
Yaeld-point. not: less iam nis one ests scietea.0 » T.S +T.8 


Elongation in 8 ins., not lessthan........ 26 per cent. 22 per cent. 








STANDARD SPECIFICATIONS FOR STEEL. 399 


Modifications in elongation requirements: For each increase of 4 in. in 
thickness above # in., a deduction of 1 per cent in the specified elongation. 
For each decrease of 7g in. in thickness below 7 in., a deduction of 24 per 
cent. 

For pins the required elongation shall be 5 per cent less than that speci- 
fied, as determined on a test specimen the centre of which shall be 1 in. 
from the surface. 

Bending Tests.—Rivet-steel shall bend cold 180° flat on itself, and me- 
dium steel 180° around a diameter equal to the thickness of the specimen, 
without fracture on the outside of the bent portion. 

One tensile and one bending-test specimen shall be taken from the finished 
material of each melt or blow. 


(8) Structural Material for Bridges and Ships. 





Class. Rivet-steel. Soft Steel. Medium Steel. 


Tens. str., lbs. per sq. in..| 50,000-60,000 | 52,000-62,000 | 60,000—70,000 
YP Snot less tham.. 0 2. ESS: 4+T.S. 4+T.S8. 
El. in 8 ins. not lessthan.| 26 percent. | 25 per cent. 22 per cent. 




















Modifications in elongation: Same as in structural steel for buildings. 

Eyebars.—Full-sized tests: T. 8S. not less than 55,000 lbs.; El., 124 per 
cent. in 15 ft. of the body. 

Bending Tests.—Rivet and soft steel, 180° flat on itself, and medium steel 
180° around a diameter equal to the thickness of the specimen, without 
fracture on the outside of the bent portion. 


“(9) Boiler=-plate and Rivet-steel. 

















Flange- or ae Extra-soft 
Class. Boiler-steel. | Firebox Steel. Steel. 
T.S., lbs per sq. in...... 55,000-65,000 | 52,000—62,000 | 45,000-—55,000 
,Y. P:jnot less than.,..:- 4T.58. 4+ TS. 4T.8. 
El. in 8 ins. not less than | 25 per cent. 26 per cent. 28 per cent. 


Modifications in elongation requirements for thin and thick material same 
as in structural steel for buildings. 

Bending Tests —A specimen cut from the rolled material, both before and 
after quenching, shall bend cold 180° flat on itself without fracture on the 
outside of the bent portion. For the quenched test the specimen shall be 
heated to a light cherry-red as seen in the dark and quenched in water of a 
temperature between 80° and 90° F. Number of test-pieces: One tensile, 
one cold-bending, and one quenched-bending specimen will be furnished 
from each plate as it is rolled,and two specimens for each kind of test from 
each melt of rivet-rounds. 

Homogeneity Test for Fire-box Steel—This test is made on one of the 
broken tensile-test specimens, as follows: 

A portion of the test-piece is nicked with a chisel, or grooved on a ma- 
chine, transversely about a sixteenth of an inch deep, in three places about 
2 in. apart. The first groove should be made on one side, 2 in. from the 
square end of the piece; the second, 2 in. from it on the opposite side; and 
the third, 2 in. from the last, and on the opposite side from it. The test- 
piece is then put in a vise, with the first groove about 4+ in. above the jaws, 
eare being taken to hold it firmly. The projecting end of the test-piece is 
then broken off by means of a hammer, a number of light blows being used, 
and the bending being away from the groove. ‘The piece is broken at the 
other two grooves in the same way. The object of this treatment is to open 
and render visible to the eye any seams due to failure to weld up, or to 
foreign interposed matter, or cavities due to gas bubbles in the ingot. After 
rupture, one side of each fracture is examined, a pocket lens being used if 
necessary, and the length of the seams and cavities is determined. The 
sample shall not show any single seam or cavity more than } in. long in 
either of the three fractures. 


400 "genet, 


VARIOUS SPECIFICATIONS FOR STEEL. 


Structural Steel.,—There has been achange during the ten years from 
4880 to 1890, in the opinions of engineers, as to the requirements in specifica~ 
tions for structural steel, in the direction of & preference for metal of low 
tensile strength and great ductility. The following specifications of differ- 
ent dates are given by A. E. Hunt and G. H. Clapp, Trans. A. I. M. E, 1390, 
xix, 926: 


TENSION MEMBERS. 1879. 1881. 1882. 1885. 1887. 1888. 


HUlASticuinii terse selses ce ee 50,000 40@45,000 40.000 40,000 40,000 88,000 
Tensile strength......... 80,000 70@80,000 70.000 70,000 67@75,000 63@70,000 
Elongation in 8in....... 12% 18% 18% 18% 20% 22% 
Reduction of area....... 20% 30% 45% 42% 42% 45% 


F. H. Lewis (lron Age, Nov. 3, 1892) says: Regarding steel to be used under 

the same conditions as wrought iron, that is, to be punched without ream- 
ing, there seems to be a decided opinion (and a growing one) among engi- 
neers, that itis not safe to use steel in this way, when the ultimate tensile 
strength is above 65,000 lbs. The reason for this is, not so much because 
there is any marked change in the material of this grade, but because all 
steel, especially Bessemer steel, has a tendency to segregations of carbon 
and phosphorus, producing places in the metal which are harder than they 
normally should be. As long as the percentages of carbon and phosphorus 
are kept low, the effect of these segregations is inconsiderable; but when 
these percentages are increased, the existence of these hard spots in the 
metal becomes more marked, and it is therefore less adapted to the treat- 
ment to which wrought iron is subjected. 
’ There is a wide consensus of opinion that at an ultimate of 64,000 to 65,000 
lbs. the percentages of carbon and phosphorus (which are the two harden- 
[ng elements) reach a point where the steel has a tendency to become tender, 
and to crack when subjected to rough treatment. 

A grade of steel, therefore, running in ultimate strength from 54,000 to 
62,000 lbs., or in some cases to 64,000 lbs., is now generally considered 2 
proper material for this class of work. 

A, E. Hunt, Trans. A. I. M. E. 1892, says: Why should the tests for steel 
be so much more rigid than for iron destined fov the same purpose? Some 
of the reasons are as follows: Experience shows that the acceptable quali- 
ties of one melt of steel offer no absolute guarantee that the next melt to it, 
even though made of the same stock, will be equally satisfactory. 

Again, good wrought iron, in plates and angles, has a narrow range (from. 

25,000 to 27,000 lbs.) in elastic limit per square inch, and a tensile strength of 
from 46,000 to 52,000 lbs. per square inchs; whereas for steel the range in 
elastic limit is from 27,000 to 80,000 Ibs., and in tensile strength from 48,000 te 
120,000 Ibs. per square inch, with corresponding variations in ductility. 
Moreover, steel is much more susceptible than wrougni iron to widely vary: 
ing effects of treatment, by hardening, cold rolling, or overheating. 
. Itis now almost universally recognized that soft steel, if properly made 
and of good quality, is for many purposes a safe and satisfactory substitute 
for wrought iron, being capable of standing the same shop-treatment as 
wrought iron. But the conviction is equally general, that poor steel, or an 
unsuitable grade of steel, is a very dangerous substitute for wrought iron 
even under the same unit strains. 

For this reason it is advisable to make more rigid requirements in select- 
ing material which may range between the brittleness of glass and a duc- 
tility greater than that of wrought iron, 

Boiler, Ship, and Tank Plates,—Different specifications are the 
following (1889) : 

United States Navy.—Shell: Tensile strength, 58,000 to 67,000 Ibs. per sq. 
in.; elongation, 22% in 8-in. transverse section, 25% in 8-in. longitudinalsection, 

Flange: Tensile strength, 50,000 to 58,000 lbs.; elongation. 26% in 8 inches. 

Chemical requirements: P. not over .635% ; S. not over .040%. 

Cold-bending test : Specimen to stand being bent flat on itself. 

Quenching test: Steel heated to cherry-red, plunged in water 82° F.. and 
to be bent around curve 114 times thickness of the plate. 

British Admiralty.—Tensile strength, 58,240 to 67,200 Ibs.; elongation in 
8in., 20% ; same cold-bending and quenching tests as U.S. Navy. 

American Boiler-makers’ Association.—Tensile strength, 55,000 to 65,000 
Ibs.; elongation in 8 in., 20% for plates 3¢ in. thick and under ; 22% for plates 
54 in. to 34 in. ; 20% for plates 34 in. and over. 


VARIOUS SPECIFICATIONS FOR STEEL. 401 


Cold-bending test: For plates 4 in. thick and under, specimen must bend 
back on itself without fracture; for plates over 4 in. thick, specimen must 
withstand bending 180° around a mandril 14 times the thickness of the 

late. 

4 Chemical requirements: P not over .040%; S not over .030%. 

American Shipmasters’ Association.—Tensile strength, 62,000 to 72,000 
ibs.; elongation, 16% on pieces 9 in. long, ' 

Strips cut from plates, heated to a low red and cooled in water the tem- 
perature of which is 82° F',, to undergo without crack or fracture being 
doubled over a curve the diameter of which does not exceed three times the 
thickness of the piece tested. 

Steel Plate Used in the Construction of Cars, (Penna. R. R., 
1899.*)—The material desired has the following composition: C, 0.12; Mn, 0.35; 
Si, 0.05; P, not above 0.04; S, not above 0.08. It will be rejected if P ex- 
ceeds 0,05, or if it shows a tensile strength below 52,000 or above 62,000 Ibs. 
per sq. in., or if the percentage of elongation in 8 ins. is less than the 
quotient of 1,500,000 + the tensile strength. 

Steel Billets for Wain and Parallel Rods. (Penna. R.R., 1893.) 
—One billet from each lot of 25 billets or smaller shipment of steel for main 
or parallel rods for locomotives will have a piece drawn from it under the 
hammer and a test-section will be turned down on this piece to 5 in. in 
diameter and 2 in. long. Such test-piece should show a tensile strength of 
85,000 lbs. and an elongation of 15%. 

No lot will be acceptable if the test shows less than 80,000 lbs. tensile 
streneth or 12% elongation in 2 in. 

Bar Spring Steel. (Penna. R R, 1901.)\—Bars which vary more than 
0.01 in. in thickness, or more than 0.02 in. in width, from the size ordered, or 
which break where they are not nicked, or which, when properly nicked 
and held, fail to break square across where they are nicked, will be returned. 
The metal desired has the following composition: Carbon, 1.00%; manganese, 
0.25%; phosphorus, not over 0.03%; silicon, not over 0.15%; sulphur, not over 
0.03%; copper, not over 0.03%. 

Shipments will not be accepted which show on analysis less than 0.90% or 
over 1.10% of carbon, or over 0.50% of manganese, 0.05% of phosphorus, 0.25% 
of silicon. 0.05% of sulphur, and 0.05% of copper. 

Steel for Crank=pims, (Penna. R. R., 1897.)\-—-The metal desired has 
the following composition: C, 0.45; Mn, not above 0.60; Si, not above 0.05; 
P, not above 0.03; 8S, not above 0.04. The tensile strength should be 85,000 
lbs. per sq. in., and the elongation 18% in 8in. Borings for analysis will be 
taken from one axle out of 1 lot of 51, They will be drilied parallel with the 
axis with a 5-in. drill, starting from a punch-march located on the end, 40 
per cent of the distance from the centre to the circumference. Two pieces 
from this pin will also be tested physically. The lot will be rejected if the 
P is above 0.05%, or if either test-piece shows less than 80,000 lbs. or above 
$5,000 lbs. T.S., less than 12% elongation, or if the T.S. of the two test- 
pieces differs more than 5,000 lbs. or the elongation more than 54. 

Dr. Chas. B. Dudley, chemist of the P. R.-R. (Trans. A. I. M. E. 1892), re- 
ferring to tests of crank-pins, says: In testing a recent shipment, the piece 
from one side of the pin showed 88,000 Ibs. strength and 22% elongation, and 
the piece from the opposite side showed 106,000 lbs. strength and 14% elonga- 
tion. Each piece was above the specified strength and ductility, but the 
lack of_uniformity between the two sides of the pin was so marked that it 
was finally determined not to put the lot of 50 pins in use. To guard against 
trouble of this sort in future, the specifications are to be amended to require 
that the difference in ultimate strength of the two specimens suall not be 
more than 3000 Ibs. 

Steel Bivets. (H. C. Torrance, Amer. Boiler Mfrs. Assn., 1890.)—The 
Government requirements for the rivets used in boilers of the cruisers built 
in 1890 are: For longitudinal seams, 58,000 to 67,000 Ibs. tensile strength; 
elongation, not less than 26% in 8 in., and all others a tensile strength of 
5 ‘,000 to 58,000 Ibs., with an elongation of not less than 30%. They shall be 
eapable of being flattened out cold under the hammer to a thickness of one 
half the diameter, and of being flattened out hot to a thickness of one third 





* The Penna. R. R. specifications of the several dates given are still in 
force, July, 1902. 


402 STEEL. 


the diameter without showing cracks or flaws. The steel must not contain 
more than .035 of 1% of phosphorus, nor more than .04 of 1% of sulphvr. 

A lot of 20 successive tests of rivet steel of the low tensile strength quality 
and 12 tests of the higher tensile strength gave the following results: 


Low Steel. Higher. 


Tensile strength, lbs. per sq. in... 51,230 to 54,100 59,100 to 61,850 
Elastic limit, lbs. per sq. in........ 381,050 to 33,190 82,080 to 33,070 


Elongation in 8 in., per cent....... 80.5 to 35.25 28.5 to 31,75 
Carbon; per cents o. css ids tess .11 to .14 -16 to .18 
Phosphorus 22200 Jos. foe. oldie tists .027 to .029 .08 
Sulphurwsise cic ees ece ee We aich carats oped -033 to .035 .038 to .035 


The safest steel rivets are those of the lowest tensile strength, since they 
are the least liable to become hardened and fracture by hammering, or to 
break from repeated concussive and vibratory strains to which they are 
subjected in practice. For calculations of the strength of riveted joints the 
tensile strength may be taken as the average of the figures above given, or 
52,665 lbs., and the shearing strength at 45,000 lbs. per sq. in. 


MISCELLANEOUS NOTES ON STEEL. 


May Carbon be Burned Out of Steel ?—Experiments made at 
the Laboratory of the Penna. Railroad Co. (Specifications for Springs, 1888) 
with the steel of spiral springs, show that the place from which the borings 
are taken for analysis has a very important influence on the amount of car- 
bon found. If the sample is a piece of the round bar, and the borings are 
taken from the end of this piece, the carbon is always higher than if the 
borings are taken from the side of the piece. It is common to find a differ- 
ence of 0.10% between the centre and side of the bar, and in some cases the 
Cifference is as high as 0.23%. Furthermore, experiments made with samples 
taken from the drawn out end of the bar show, usually, less carbon than 
samples taken from the round part of the bar, even though the borings may 
be taken out of the side in both cases. 

Apparently during the process of reducing the metal from the ingots to the 
round bar, with successive heatings, the carbon in the outside of the bar is 
burned out. 

6* Recalescence »? of Steel.—If we heat a bar of copper by a flame 
of constant strength, and note carefully the interval of time occupied in 
passing from each degree to the net higher degree, we find that these in- 
tervals increase regularly, ie., that the bar heats more and more slowly, as 
its temperature approaches that of the flame. If we substitute a bar of - 
steel for one of copper, we find that these intervals increase regularly up to 
a certain point, when the rise of temperature is suddenly and in most cases 
greatly retarded or even completely arrested. After this the regular rise of 
temperature is resumed, though other like retardations may recur as the 
temperature rises farther. So if we cool a bar of steel slowly the fall of 
temperature is greatly retarded when it reaches a certain point in dull red- 
ness, If the steel contains much carbon, and if certain favoring conditions 
be maintained, the temperature, after descending regularly, suddenly rises 
spontaneously very abruptly, remains stationary a while, and then rede- 
scends, This spontaneous reheating is known as ‘“‘ recalescence.”’ { 

These retardations indicate that some change which absorbs or evolves 
heat occurs within the metal. A retardation while the temperature is rising 
points to a change which absorbs heat; a retardation during cooling points 
to some change which evolves heat. (Henry M. Howe, on “* Heat Treatment 
of Steel,’ Trans. A. I. M. E., vol. xxii.) 

Effect of Nicking a Steel Bar.—The statement is sometimes made 
that, owing to the homogeneity of steel, a bar with a surface crack or nick 
in one of its edges is liable to fail by the gradual spreading of the nick, and 
thus break under a very much smaller load than a sound bar. With iron it 
is contended this does not occur, as this metal has a fibrous structure. Sir 
Benjamin Baker has, however, shown that this theory. at least so far as 
statical stress is concerned, is opposed to the facts, as he purposely made 
nicks in specimens of the mild steel used at the Forth Bridge, but found 
that the tensile strength of the whole was thus reduced by only about one 
ton per square inch of section. In an experiment by the Union Bridge Com: 
pany a full-sized steel counter-bar, with a screw-turned buckle connection, 
was tested under a heavy statical stress, and at the same time a weight 
weighing 1040 lbs. was allowed to drop on it from various heights. The bar 
was first broken by ordinary statical strain, and showed a breaking stress of 


MISCELLANEOUS NOTES ON STEEL. 403 


66,800 lbs. per square inch. The longer of the broken parts was then placed 
in the machine and put under the following loads, whilst a weight, as already 
mentioned, was dropped on it from various heights at a distance of five 
feet from the sleeve-nut of the turn-buckle, as shown below: 


Stress in pounds per sq. in...... 50,000 55,000 60,000 63,000 65,000 
ft insets.) in, ft. in, £t. in. ft. in. 
Heiehtof fallfy i iviseees acentect Aik 2 6 3 0 4 0 BU 


The weight was then shifted so as to fall directly on the sleeve-nut, and 
the test proceeded as follows: 


Stress on specimen in lbs. per square inch...... 65,350 65,350 68,800 
Heiphtrot fail. LeeG: ia. cinctve ania 2 cies ciecs esas 3 6 6 


It will be seen that under this trial the bar carried more than when origi- 
nally tested statically, showing that the nicking of the bar by screwing 
had not appreciably weakened its power of resisting shocks.—Eng’g News. 

Electric Conductivity of Stcel.—Louis Campredon reports in Le 
Genie Civil {prior to 1895] the results of experiments on the electric resist- 
ance of steel wires \of different composition, ranging from 0.09 to 0.14 C; 
0.21 to 0.54 Mn; Si, 8, and P low. The figures show that the purer and 
softer the steel the better is its electric conductivity, and, furthermore, that 
manganese is the element which most influences the conductivity. The 
results may be expressed by the formula R=5.2+6.2S+0.3; in which R= 
relative resistance, copper being taken as 1, and S=the sum of the percent- 
ages of C, P, 8, Si, and Mn. ‘The conclusions are confirmed by J. A. Capp, 
in 1903, Trans. A. I. M. E., vol. xxxiv, who made forty-five experiments on 
steel of a wide range of composition. His results may be expressed by the 
formula R=5.5+4S+1. High manganese increases the resistance at an 
increasing rate. Mr. Capp proposes the following specification for steel to 
make a satisfactory third rail, having a resistance eight times that of 
copper: C, 0.15; Mn, 0.30; P, 0.06; S, 0.06; Si, 0.05; none of these figures 
to be exceeded. ' : 

Specific Gravity of Soft Steel. (W. Kent, Trans. A.I. M. E., xiv. 
585.)—Five specimens of boiler-plate of C. 0.14, P. 0.03 gave an average sp. 
gr. of 7.932, maximum variation 0.008. The pieces were first planed to re- 
move all possible scale indentations, then filed smooth, then cleaned in 
dilute sulphuric acid, and then boiled in distilled water, to remove all traces 
of air from the surface. 

The figures of specific gravity thus obtained by careful experiment on 
bright, smooth pieces of steel are, however, too high for use in determining 
the weights of rolled plates for commercial purposes. The actual average 
thickness of these plates is always a little less than is shown by the calipers, 
on aczount of the oxide of iron on the surface, and because the surface is 
not perfectly smooth and regular. A number of experiments on commercial 
piates, and comparison of other authorities, led to the figure 7.854 as the 
average specific gravity of open-hearth boiler-plate steel. This figure is 
easily remembered as being the same figure with change of position of the 
decimal point (.7854) which expresses the relation of the area of acircle to 
that of its circumscribed square. Taking the weight of a cubic foot of water 
at 62° F. as 62.36 lbs. (average of several authorities), this figure gives 489.775. 
Ibs. as the weight of a cubic foot of steel, or the even figure, 490 lbs., may be 
taken as a convenient figure, and accurate within the limits of the error of 
observation. 

A common method of approximating the weight of iron plates is to con- 
sider them to weigh 40 lbs. per square foot one inch thick. Taking this 
weight and adding 2% gives almost exactly the weight of steel boiler-plate 
given above (40 xX 12 1.02 = 489.6 lbs. per cubic foot). 

Occasional Failures of Bessemer Steel.—G. H. Clapp and A. 
E. Hunt, in their paper on ** The Inspection of Materials of Construction in 


404 — STERL. 


the United States * (Trans. A. I. M. E., vol. xix), say: Numerous instanceg 
could be cited to show the unreliability of Bessemer steel for structural put- 
poses. One of the most marked, however, was the following: A 12-in. I-beam 
weighing 30 lbs. to the foot, 20 feet long, on being unloaded from a car 
broke in two about 6 feet from one end. 

The analyses and tensile tests made do not show any cause for the failure. 

The cold and quench bending tests of both the original 34-in. round test- 
pieces, and of pieces cut from the finished material, gave satisfactory re- 
sults; the cold-beunding tests closing down on themselves without sign of 
fracture. . 

Numerous other cases of angles and plates that were so aard in piaces as 
to break off short in punching, or, what was worse, to break the punches, 
have come under our observation, and although makers of Bessemer steel 
claim that this is just as likely to occur in open-hearth as in Bessemei steel, 
we have as yet never seen an instance of failure of this kind in open-hearth 
steel having a composition such as C 0.25%, Mn 0.70%, P 0.804. 

J. W. Wailes, in a paper read before the Chemical Section of the Eritish 
Association for the Advancement of Science, in speaking of mysterious 
failures of steel, states that investigation shows that ‘‘ these failures occur 
in steel of one class, viz., soft steel made by the Bessemer process.” 

Segregation im Steel Ingots, (A. Pourcel, Trans. A. I. M. E. 2893.7 
—H. M. Howe, in his ‘*‘ Metallurgy of Steel,” gives a résumé of observations 
with the results of numerous analyses, bearing upon the phenomena 0: seg: 
regation, 

In 18? Mr. Stubbs, of Manchester, showed the heterogeneous results of 
analyses made upon different parts of an ingot of large section. 

A test-piece taken 24 inches from the head of the ingot 7.5 feet in length 
gave by analysis very different results from those of a test-piece taken 30 
inches from the bottom. 


4 Mn. Si. Ss. Bi 
LOD ea seiiate Jeics sacs ce 0.92 0.535 0.043 0.161 0.261 
IBQULOM ele ceteris Seas Ook 0.498 0.006 0.025 0.096 


Windsor Richards says he had often observed in test-pieces taken from 
different points of one plate variations of 0.05% of carbon. Segregation is 
specially pronounced in an ingot in its central portion, and around the 
space of the piping. 

It is most observable in large ingots, but in blocks of smaller weight and 
limited dimensions, subjected to the influence of solidification as rapid as 
casting within thick walls will permit, it may still be observed distinctly, _ 
An ingot of Martin steel, weighing about 1000 lbs., and having a height of 
1.10 feet and a section of 10.24 inches square, gave the following: 

1. Upper section: C Ss. P 


JBYOy He V2) oi See a a ee bs eee 330 0.040 0.033 0.420 
entre. i es a heiea © sole Sen OSU 0.077 0.057 0.430 
2. Lower section: C. S. P. Mn. 
Border ....... bee att Shae ene L2S() 0.029 0.016 0.890 
Centre... 2 is. ihe dt ees O22 90) 0.080 0.038 0.3890 
8. Middle section: C. Ss. igh Mn. 
IBOLOER Re ihiccsices nlndee so eeeaeeO sacl 0.025 0.025 0.400 
Centres yeasts hE Ash Sere 0.320 0.048 0.048 0.4n¢ 


Segregation is less marked in ingots of extra-soft metal cast in cast-iron 
moulds of considerable thickness. It is, however, still important, and ex- 
plains the difference often shown by the results of tests on pieces taken 
from different portions of a plate. Two samples, taken from the sound part 
of a flat ingot, one on the outside and the other in the centre, 7.9inches from 
the upper edge, gave: 


C. S. P, Mn. 
Centre astmeeiierslssccieeccccss) «O14 0.058 0.072 0.576 
EEXterion./oue Metewiblese-secee-o OIL 0.036 0.027 0.610 


Manganese is the element most uniformly disseminated in hard or soft 
steel. 

Kor cannon of large calibre, if we reject, in addition to the part cast in 
sand and called the masselotte (sinking-head), one third of the upper part 
of the ingot, we can obtain a tube practically homogeneous in composition, 
because the central part is naturally removed by the boring of the tube. 
With extra-soft steels, destined for-ship- or boiler-plates, the solution for 
practically perfect homogeneity lies in the obtaining of a metal more closely 
deserving its name of axtra-soft metal, 


STEEL CASTINGS. 405 


The injurious consequences of segregation must be suppressed by reduc- 
ing. as far as possible, the elements subject to liquation. 

Earliest Uses of Steel for Structural Purposes, (G. G. 
Mehrtens, Trans. A. §. C. E. 1893).—The Pennsylvania Railroad Company 
first introduced Bessemer steel in America in locomotive boilers in the year 
1863, but the steel was too hard and brittle for such use. The first plates 
made for steel boilers had a tenacity of 85,000 to 92,000 Ibs. and an elongation 
of but 7% to 10%. The results were not favorable, and the steel works were 
soon forced to offer a material of less tenacity and more ductility. The re- 
quirements were therefore reduced to a tenacity of 78.000 lbs. or less, and 
the elongation was increased to 15% or more. The use of Bessemer steel in 
bridge-building was tried first on the Dutch State railways in 1863-64, then 
in England and Austria. The first use of cast steel for bridges was in 
America, for the St. Louis Arch Bridge and for the wire of the Hast River 
Bridge. Before 1880 the Glasgow and Plattsmouth bridges over the Missouri 
River were also built of ingot metal. Steel eyebars were applied for the first 
time in the Glasgow Bridge. Since 1880 the introduction of mild steel in 
all kinds of engineering structures has steadily increased. 

Messrs. Joseph Adamson & Co., of Hyde, England, in a letter to the author 
say: ‘*The first steel for boiler purposes was used for a locomotive firebox 
sent to Africa in 1858. The first steel steamships were built in Liverpool for 
‘blockade-running’ during the American Civil War about 1862, and at least 
5000 tons of Bessemer steel plates were rolled at Penistone by Benson, 
Adamson & Garnett for this purpose. The first Bessemer steel boilers were 
made in this neighborhood in 1858. Drilling the rivet-holes was adopted in 
1859. Some of these boilers built in 1862 worked 29 years night and day. We 
have lost trace of these boilers now, but we know that after working this 
leneth of time they were found good enough to be worth resetting and were 
set to work again foratime. Between 1870 and 1880 about 2000 steel land 
boilers were working in this country. The pressures ranged up to 150 lbs.”’ 


STEEL CASTINGS, 
{E. S. Cramp, Engineering Congress, Dept. of Marine Eng’g, Chicago, 1893.) 


In 1891 American steel-founders had successfully produced a considerable 
variety of heavy and difficult castings, of which the following are the most 
noteworthy specimens: 

Bed-plates up to 24,000 Ibs.; stern-posts up to 54,000 Ibs.; stems up to 
21,000 lbs.; hydraulic cylinders up to 11,000 lbs. ; shaft-struts up to 32,000 Ibs. ; 
hawse-pipes up to 7500 lbs.; stern-pipes up to 8000 lbs. 

The percentage of success in these classes of castings since 1890 has ranged 
from 65% in the more difficult forms to 90% in the simpler ones; the tensile 
strength has been from 62,000 to 78,000 lbs., elongation from 15% to 25%. The 
best performance recorded is that of a guide, cast in January, 1893, which 
developed 84,000 Ibs. tensile strength and 15.6% elongation. 

The first steel castings of which anything is generally known were 
crossing-frogs made for the Philadelphia & Reading R. R. in July, 1867, by 
the William Butcher Steel Works, now the Midvale Steel Co. The moulds 
were made of a mixture of ground fire-brick, black-lead crucible-pots 
ground fine, and fire-clay, and washed with a black-lead wash. The steel 
was melted in crucibles, and was about as hard as tool steel. The surface 
of these castings was very smooth, but the interior was very much honey- 
combed. This was before the days when the use of silicon was known for 
solidifying steel. The sponginess, which was almost universal, was a great 
obstacle to their general adoption. 

The next step was to leave the ground pots out of the moulding mixture 
and to wash the mould with finely ground fire-brick. This was a great im- 
provement, especially in very heavy castings; but this mixture still clung so 
strongly to the casting that only comparatively simple shapes could be made 
with certainty. A mould made of such a mixture became almost as hard as 
fire-brick, and was such an obstacle to the proper shrinkage of castings, 
that. when at all complicated in shape, they had so gréat a tendency to 
crack as to make their successful manufacture almost impossible. By this 
time the use of silicon had been discovered, and the only obstacle in the way 
of making good castings was a suitable moulding mixture. This was ulti- 
mately found in mixtures having the various kinds of silica sand-as the 
principal constituent. ; 

One of the most fertile sources of defects in castings is a bad design. 
Very intricate shapes can be cast successfully if they are so designed as to 


406 STEEL. By Me 


cool uniformly. Mr. Cramp says while he is not yet prepared to state that 
anything that can be cast successfully in iron can be cast in steel, indica- 
tions seem to point that way in all cases where it is possible to put on suit- 
able sinking-heads for feeding the casting. 

H. L. Gantt (Trans. A. S. M. E., xii. 710) says: Steel castings not only 
shrink much more than iron ones, but with less regularity. The amount of 
shrinkage varies with the composition and the heat of the metal; the hotter 
the metal the greater the shrinkage; and, as we get smoother castings from 
hot metal, it is better to make allowance for large shrinkage and pour the 
metal as hot as possible. Allow 3/16 or 14 in. per ft. in length 
for shrinkage, and 14 in. for finish on machined surfaces, except such as are 
cast ‘‘up.’? Cope surfaces which are to be machined should, in Jarge or 
hard castings, have an allowance of from % to 4 in. for finish, as a large 
mass of metal slowly rising ina mould is apt to become crusty on the sur- 
face, and such a crust is sure to be full of imperfections. On small, soft 
castings 14 in. on drag sideand 44 in. on cope side will be sufficient. No core 
should have less than 4 in. finish on a side and very large ones should have 
as much as 144in. ona side. Blow-holes can be entirely prevented in cast- 
ings by the addition of manganese and silicon in sufficient quantities; but 
both of these cause brittleness, and it is the object of the conscientious steel- 
maker to put no more manganese and silicon in his steel than is just suffi- 
cient to make it solid.“ The best results are arrived at when all portions of 
the castings are of a uniform thickness, or very nearly so. 

The following table will illustrate the effect of annealing on tensile 
strength and elongation of steel castings: 











Unannealed. Annealed. 
Carbon. 
Tensile Strength.| Elongation. |'Tensile Strength.|} Elongation. 
.23% 68,738 22.40% 67,210 81.40% 
On 85,540 8.20 82,228 21.80 
.538 90,121 2.30 106,415 9.80 





The proper annealing of large castings takes nearly a week. 

The proper steel for roll pinions, hammer dies, etc., seems to be that con- 
taining about .60% of carbon. Such castings, properly annealed, have worn. 
well and seldom broken. Miscellaneous gearing should contain carbon .40% 
to 60%, gears larger in diameter being softest. General machinery castings 
should, as a rule, contain less than .40% of carbon, those exposed to great 
shocks containing as low at .20% of carbon. Such castings will give a tensile 
strength of from 60,000 to 80,000 lbs. per sq. in. and at least 15% extension in 
a2in. long specimen. Machinery and hull castings for war-vessels for the 
United States Navy, as well as carriages for naval guns, contain from .20% to 
.30% of carbon. 

The following is a partial list of castings in which steel seems to be 
rapidly taking the place ofiron: Hydraulic cylinders, crossheads and pistons 
for large engines, roughing rolls, rolling-mill spindles, coupling-boxes, roll 
pinions, gearing, hammer-heads and dies, riveter stakes, castings for ships, 
car-couplers, etc. 

For description of methods of manufacture of steel castings by the Besse- 
mer, open-hearth, and crucible processes, see paper by P. G. Salom, Traus. 
A. I.M. E. xiv, 118. 

Specifications for steel castings issued by the U. S. Navy Department, 1889 
(abridged): Steel for castings must be made by either the open-hearth or 
the crucibie process, and must not show more than .06% of phosphorus. All 
castings must be annealed, unless otherwise directed. The tensile strength 
of steel castings shall be at least 60,000 lbs., with an elongation of at least 
15% in 8 in. for all castings for moving parts of the machinery, and at least 
10% in 8 in. for other castings. Bars 1 in. sq. shall be capable of bending 
cold, without fracture, through an angle of 90°, over a radius not greater 
than 1144 in. All castings must be sound, free from injurious roughness, 
sponginess, pitting, shrinkage, or other cracks, cavities, etc. 

Pennsylvania Railroad specifications, 1888: Steel castings should have a 
tensile strength of 70,000 Ibs. per sq. in. and an elongation of 15% in section 
originally 2 in, long, Steel castings will not be accepted if tensile strength 


MANGANESE, NICKEL, AND OTHER ‘‘ ALLOY” STEELS. 407 


falls below 60,000 Ibs., nor if the elongation is less than 122, nor if cast- 
ings have blow-holef and shrinkage cracks. Castings weighing 80 lbs. or 
more must have cast with them a strip to be used asa test-piece. The di- 
mensions of this strip must be 34 in. sq. by 12 in. long. 


MANGANESE, NICKEL, AND OTHER “ALLOY” 
STEELS, 


Manganese Steel, (H. M. Howe, Trans. A.S. M. E., vol. xii.)\—Man- 
ganese steel is an alloy of iron and manganese, incidentally, and probably 
unavoidably, containing a considerable proportion of carbon. 

The effect of small proportions of manganese on the hardness, strength, 
and ductility of iron is probably slight. The point at which manganese 
begins to have a predominant effect is not known: it may be somewhere 
about 2.5%. Asthe proportion of manganese rises above 2.5% the strength 
and ductility diminish, while the hardness increases. This effect reaches a 
maximum with somewhere about 6% of manganese. When the proportion 
of this element rises beyond 6% the strength and ductility both increase. 
while the hardness diminishes slightly, the maximum of both strength and 
ductility being reached with about 14% of manganese. With this proportion 
the metal is still so hard that it is very difficult to cut it with steel tools. As 
the proportion of manganese rises above 15% the ductility falls off abruptly, 
the strength remaining nearly constant till the manganese passes 18%, when 
it in turn diminishes suddenly. 

Steel containing from 4% to 6.5% of manganese, even if it have but 0.37% of 
carbon, is reported to be so extremely brittle that it can be powdered under 
a hand-hammer when cold ; yet it is ductile when hot. 

Manganese steel is very free from blow-holes ; it welds with great diffi- 
culty; its toughness is increased by quenching from a yellow heat ; its elec- 
tric resistance is enormous, and very constant with changing temperature ; 
itis low in thermal conductivity. Itsremarkable combination of great hard- 
mess, Which cannot be materially lessened by annealing, and great tensile 
atrength, with astonishing toughness and ductility, at once creates and 
limits its usefulness, The fact that manganese steel cannot be softened, 
{hat it ever remains so hard that it can be machined only with great diffi- 
culty, sets up a barrier to its usefulness. : 

The following comparative results of abrasion tests of manganese and 
ther steel were reported by T. T. Morrell: 


ABRASION BY PRESSURE AGAINST A REVOLVING HARDENED-STEEL SHAFT, 


Loss of weight of manganese steel........ Stiuieys ubsiieets 1.0 
a blue-tempered hard tool steel......... 0.4 
we annealed hard toolsteel. ..... ....... 7.5 
at hardened Otis boiler-plate steel...... - 7.0 
<< annealed ‘“ oa Soo ee a at 14.0 
ABRASION BY AN RMERY-WHEEL. 
Loss of weight of hard mangarese-steel wheels.......... 1.00 
OL softer s* Rename. cttea aikts 1.19 
“6 hardest carbon-steel wheels..... ..... 1.238 
+ soft ge! <P sen ks SOR 2.85 


The hardness of manganese steel seems to be of an anomalous kind. The 
alloy is hard, but under some conditions not rigid. It is very hard in its 
resistance to abrasion ; it is not always hard in its resistance to impact. 

Manganese steel forges readily at a yellow heat, though at a bright white 
heat it crumbles under the hammer. But it offers greater resistance to 
deformation, i.e., it is harder when hot, than carbon steel. 

The most important single use for manganese-steel is for the pins which 
hold the buckets of elevator dredges. Here abrasion chiefly is to be 
resisted. 

Another important use is for the links of common chain-elevators. 

As a material for stamp-shoes, for horse-shoes, for the knuckles of an 
automatic car-coupler, manganese steel has not met expectations. 

Manganese steel has been regularly adopted for the blades of the Cyclone 
pulverizer. Some manganese-steel wheels are reported to have run over 
300,000 miles each without turning, on a New England railroad. 

Nickel Steel.—The remarkable tensile strength and ductility of nickel 
steel, as shown by the test-bars and the behavior of nickel-steel armor- 
plate under shot tests, are witness of the valuable qualities conferred upon 


steel by the addition of a few per cent of nickel, j 


408 STEEL. 


The following tests were made on nickel steels by Mr. Maunsel White of 
the Bethlehem [ron Company (Hng. & M. Jour., Sept. 16, 1893.) : 


| 








és Ss Tensile | Elastic Reduc- 
Specimen S . | t_- |Str’gth,| Limit, ee tion of 
from— S$ | a |Ibs. per|lbs. per| “'0" | Area, 
A 3 Psanti(eqeint 
.625) 4 16; 800) ites Ae nO Ulead Special 
a eas e 8050) 1246 595 iu va 4.25 eof treatment. 
2 | Bs Sito SNOT ROD 13-08 19.25 | 55.0 | Annealed. 
w 564; 4 142,800 | 74,000 | 13.0 28.2 
P . i ke Cops 12.32 the 
; : 7,6 4,000 17.0 s 
= 1 aa « 1 « 1479200] 65,000 | 16.66 | 42.1 
|| pollod bart {) | ot 1) 91,6001 61,000 | 22.251 63.2 
x aun gale aise. 91,200 | 51,000 | 21.62] 53.4 


| - 
| 
« | « | g5’900| 53;000 | 21.82 | 49.5 
« | « | 36000] 48:000 | 21.25 | 47.4 
.798| 8 | 115.464 51,820 | 36.25 | 66.28 
«1 8 1442600] 60,000 | 37.87 | 62.82 
« | « | 492°010| 291180 | 41.37 | 69.59 | Annealed. 
L « | « | 402°510} 40,2001 44.00°| 68.34 «“ 
500] 2 | 114'590| 56,020 | 47.25 | 68.4 
«ol 1 475°610| 59.080 | 45.25 | 62.3 
« | « | 405/240 45:170 | 49.65 | 72.8 | Annealed. 
| « | « | 406780] 45,170 | 55.50 | 63.6 “ 


* Forged from 6-in. ingot to 5 in. diam., with conical heads for holding. 

+ Showing the effect of varying carbon. 

t+ Rolled down from 14-in. ingot to 114-in. square billet, and turned to size. 
§ Rolled down from 14-in. ingot to 1-in. round, and turned to size. 


Nickel steel has shown itself to be possessed of some exceedingly valuable 
properties; these are, resistance to cracking, high elastic limit, and homo- 
geneity. Resistance to cracking, a property to which the name of non fissi- 
bility has been given, is shown more remarkably as the percentage of nickel 
increases. Bars of 27% nickel illustrate this property. A 114-in. square bar 
was nicked 44 in. deep and bent double on itself without further fracture 
than the splintering off, as it were, of the nicked portion. Sudden failure or 
rupture of this steel would be impossible ; it seems to possess the toughness’ 
of rawhide with the strength of steel. With this percentage of nickel the 
steel is practically non-corrodible and non-magnetic. The resistance to 
eracking shown by the lower percentages of nickel is best illustrated in the 
many trials of nickel-steel armor. 

The elastic limit rises in a very marked degree with the addition of about 
3% of nickel, the other physical properties of the steel remaining unchanged 
or perhaps slightly increased. 

In such places (shafts, axles, etc.) where failure is the result of the fatigue 
of the metal this higher elastic limit of nickel steel will tend to prolong in- 
definitely the life of the piece, and at the saine time, through its superior 
toughness, offer greater resistance to the sudden strains of shock. 

Howe states that the hardness of nickel steel depends on the proportion 
of nickel and carbon jointly, nickel up toa certain percentage increasing 
the hardness, beyond this lessening it. Thus while steel with 2% of nickel 
and 0.90% of carbon cannot be machined, with less than 5% nickel it can be 
worked cold readily, providedthe proportion of carbon be low. As the 
proportion of nickel rises higher, cold-working becomes less easy. It forges 
easily whether it contain much or little nickel. 

The presence of manganese in nickel steel is most important, as it appears 
that without the aid of manganese in proper proportions, the conditions of 
treatment would not be successful. 

Tests of Nickel Steel.—Two heats of open-hearth steel were made by 
the Cleveland Rolling Mill Co., one ordinary steel made with 9000 Ibs. each 
scrap and pig, and 165 lbs. ferro-manganese, the other the same with the 
addition of 3%, or 540 lbs. of nickel. Tests of six plates rolled from each 
heat., 0.24 to 0.3 in. thick, gave results as follows : 


Ordinary steel, T. S. 52,500 to 56,500 ; E.'L. 32,800 to 37,900 ; elong. 26 to 324, 
Nickel steel, ** 63,370 to 67,100; ** 47,100 to 48,200; ‘* 2814 to 262. 


14%4-in. sq. 
bar, rolled. ¢ 


1-in, round 
bar, rolled.$ 


27% nickel steel. 
ae HA FS - 





MANGANESE, NICKEL, AND OTHER “ ALLOY” STEELS. 409 


The nickel steei averages 31% higher in elastic limit, 20% higher in ultimate 
tensile strength, with but slight reduction in ductility. (Hng. & M. Jour., 
Feb. 25, 1893.) 

Aluminum Steel.—R. A. Hadfield (Trans. A. I. M. E. 1890) says: 
Aluminum appears to be of service asan addition to baths of molten iron or 
steel unduly saturated with oxides, and this in properly regulated steel 
manufacture should not often occur. Speaking generally, its dle appears 
to be similar to that of silicon, though acting more powerfully. The state- 
ment that aluminum lowers the melting-point of iron seems to have no 
foundation in fact. If any increase of heat or fluidity takes place by the 
addition of small amounts of aluminum, it may be due to evolution of heat, 
owing to oxidation of the aluminum, as the calorific value of this metal is 
very high—in fact, higher than silicon. According to Berthollet, the con- 
version of aluminum to Al,03 equals 7900 cal.; silicon to SiOgis stated as "800. 

The action of aluminum may be classed along with that of silicon, sulphur, 
phosphorus, arsenic, and copper, as giving no increase of hardness to iron, 
in contradistinction to carbon, manganese, chromium, tungsten, and nickel. 
Therefore, whilst for some special purposes aluminum may be employed in 
the manufacture of iron, at any rate with our present knowledge of its 
properties, this use cannot be large, especially when taking into considera- 
tion the fact of its comparatively high price. Its special advantage seems to 
be that it combines in itself the advantages of both silicon and manganese ; 
but so long as alloys containing these metals are so cheap and aluminum 
dear, its extensive use seems hardly probable. 

J. E. Stead, in discussion of Mr. Hadfield’s paper, said: Every one of our 
trials has indicated that aluminum can kill the most fiery steel, providing, 
of course, that it is added in sufficient quantity to combine with all the oxy- 
gen which the steel contains. The metal will then be absolutely dead, and 
will pour like dead-melted silicon steel. Ifthe aluminum is added as metal- 
lic aluminum, and not as a compound, and if the addition is made just be- 
fore the steel is cast, 1/10% is ample to obtain perfect solidity in the steel. 

Chrome Steel. (F. L. Garrison, Jour. Ff. I., Sept. 1891.)\—Chromium 
increases the hardness of iron, perhaps also the tensile strength and elastic 
limit, but it lessens its weldibility. 

Ferro chrome, according to Berthier, is made by strongly heating the 
mixed oxides of iron and chromium in brasqued crucibles. adding powdered 
charcoal if the oxide of chromium is in excess, and fluxes to scorify the 
earthy matter and prevent oxidation. Chromium does not appear to give 
steel the power of becoming harder when quenched or chilled. Howe states 
that chrome steels forge more readily than tungsten steels, and when not 
containing over 0.5 of chromium nearly as well as ordinary carbon steels of 
like percentage of carbon. On the whole the status of chrome steel is not 
satisfactory. There are other steel alloys coming into use, which are so 
much better, that,it would seem to be only a question of time when it will 
drop entirely out of the race. Howe states that many experienced chemists 
have found no chromium, or but the merest traces, in chrome steel sold in 
the markets. 

J. W. Langley (Trans. A.S. C. E. 1892) says: Chromium, like manganese, 
is a true hardener of iron even in the absence of carbon. The addition of 1% 
or 2% of chromium to a carbon steel will make a metal which gets exces- 
sively hard. Hitherto its principal employment has been in the production 
of chilled shot and shell. Powerful molecular stresses result during cooling, 
and the shells frequently break spontaneously months after they are made. 

Tungsten Steel—Mushet Steel. (J. B. Nau, Iron Age, Feb. 11, 1892.) 
—By incorporating simultaneously carbon and tungsten in iron, it is possi- 
ble to obtain a much harder steel than with carbon alone, without danger of 
an extraordinary brittleness in the cold metal or an increased difficulty in 
the working of the heated metal. 

When a special grade of hardness is required, it is frequently the custom 
to use a high tungsten steel, known in England as special steel. A specimen 
from Sheffield, used for chisels, contained 9.8% of tungsten, 0.7% of silver, 
and 0.6% of carbon, This steel, though used with advantage in its untem- 
pered state to turn chilled rolls, was not brittle ; nevertheless it was hard 
enough to scratch glass. 

A sample of Mushet’s special steel contained 8.3% of tungsten and 1.738% of 
manganese. The hardness of tungsten steel cannot be increased by the or- 
dinary process of hardening, " ie 

The only operation that it can be submitted to when cold is grinding. It 
has to be given its final shape through hammering at a red heat, and even 


410 STEEL. 


then, when the percentage of tungsten is high, it has to be treated very 
carefully; and in order to avcid breaking it, not only is it necessary to reheat 
it several times while it is being hammered, but when the tool has acquired 
the desired shape hammering must still be continued gently and with nu- 
mer age blows until it becomes nearly cold. Then only can it be cooled en- 
tirely. 

Tungsten is not only employed to produce steel of an extraordinary hard- 
ness, but more especially to obtain a steel which, with a moderate hardness, 
allies great toughness, resistance, and ductility. Steel from Assailly, used 
for this purpose, contained carbon, 0.52%; silicon, 0.04%; tungsten, 0 32%; 
phosphorus, 0.04%; sulphur, 0.0052, 

Mechanical tests made by Styffe gave the following results : 


Breaking load per square inch of original area, pounds.. 172,424 
Reduetion,of£ ‘area; per Cent)... 2)... .csicoscnt belcs te eoeeeses 0.54 
Average elongation after fracture, per cent ............. 13 


According to analyses made by the Duc de Luynes of ten specimens of the 
celebrated Oriental damasked steel, eight contained tungsten, two of them 
in notable quantities (0.518% to 1%), while in all of the samples analyzed 
nickel was discovered ranging from traces to nearly 4%. 

Stein & Schwartz of Philadelphia, in a circular say: It is stated that 
tungsten steel is suitable for the manufacture of steel magnets, since it re- 
tains its magnetism longer than ordinary steel. Mr. Kniesche has made 
tungsten up to 98% fine a specialty. Dr. Heppe, of Leipsig, has written a 
number of articles in German publications on the subject. The following 
instructions are given concerning the use of tungsten: In order to produce 
cast iron possessing great hardness an addition of one half to one and one 
half of tungsten is all that is needed. For bar iron it must be carried up to 
1% to 2%, but should not exceed 244%. For puddled steel the range is larger, 
but an addition beyond 214% only increases the hardness, so that it is brought 
up to 114% only for special tools, coinage dies, drills, etc. For tires 214% to 5% 
have proved best, and for axles 14 to 144%. Cast steel to which tungsten has 
been added needs a higher temperature for tempering than ordinary steel, 
and should be hardened only between yellow, red, and white. Chisels made 
of tungsten steel should be drawn between cherry-red and blue, and stand 
well on iron and steel. Tempering is best done ina mixture of 5 parts of 
yellow rosin, 3 parts of tar, and 2 parts of tallow, and then the article is 
once more heated and then tempered as usual in water of about 15° C. 

Fluid-compressed [Steel by the ** Whitworth Process. 
(Proc. Inst. M. E., May, 1887, p. 107.)—In this system a gradually increasing 
pressure up to 6 or 8 tons per square inch is applied to the fluid ingot, and 
within half an hour or less after the application of the pressure the column 
of fluid steel is shortened 114 inch per foot or one-eighth of its length; the 
pressure is then kept on for several hours, the result being that the metal 
is compressed into a perfectly solid and homogeneous taterial, free frem 
blow-holes. 

In large gun-ring ingots during cooling the carbon is driven to the centre, 
the centre containing 0.8 carbon and the outer ring 0.3. The centre is bored 
out until a test shows that the inside of the ring contains the same percent- 
age of carbon as the outside. ; 

Fluid-compressed steel is made by the Bethlehem Iron Co. for gun and 
| other heavy forgings. 


CRUCIBLE STEEL. 


Selection of Grades by the Eye, and Effect of Heat Treat« 
ment, (J. W. Langley, Aner. Chemist, November, 1876.)—In 1874, Miller, 
Metcalf & Parkin, of Pittsburgh, selected eight samples of steel which were 
believed to form a set of graded specimens, the order being based on the 
quantity of carbon which they were supposed to contain. They were num- 
bered from one to eight, On analysis, the quantity of carbon was found to 
follow the order of the numbers, while the other elements present—silicon, 
phosphorus, and sulphur—did not do so. The method of selection is 
described as follows: 

The steel is melted in black-lead crucibles capable of holding about eighty 
pounds; when thoroughly fluid it is poured into cast-iron moulds. and when 
cold the top of the ingot is broken off, exposing a freshly-fractured surface. 
‘the appearance presented is that of confused groups of crystals, all appear- 
ing to have started from the outside and to have met in the centre; this 
general form is common to all ingots of whatever composition, but to the 
trained eye, and only to one long and critically exercised, a minute but in- 


CRUCIBLE STEEL. 411 


describable difference is perceived between varying samples of steel, and 
this difference is now known to be owing almost wholly to variations in the 
amount of combined carbon, as the following table willshow. Twelve sam- 
ples selected by the eye alone, and analyses of drillings taken direct from 
the ingot before it had been heated or hammered, gave results as below: 


Ingot | Iron by Diff. of 





Dian? Diff. Carbon. Garbeat Silicon. Phos. Sulph. 
1 99.614 NO eaey oD | erate cee ve 019 047 .018 
2 99.455 -490 .188 .084 -005 .016 
3 99 .363 .529 039 .043 047 .018 
4 99.270 .649 120 .039 .030 .012 
5 99.119 .801 - 152 029 .035 -016 
6 99.086 841 -040 .039 024 .010 
a 99.044 867 .026 .057 .014 .018 
8 99.040 .871 .004 .053 024 .012 
9 98.900 -955 .084 .059 .070 .016 

10 98.861 1.005 .050 .088 084 .012 
11 98.752 1.058 053 120 .064 .006 
12 98 . 834 1.079 021 .039 .044 -004 











Here the carbon is seen to increase in quantity in the order of the num- 
bers, while the other elements, with the exception of total iron, bear no rela- 
tion to the numbers on the samples. The mean difference of carbon is .071. 

In mild steels the discrimination is less perfect. 

The appearance of the fracture by which the above twelve selections 
were made can only be seen in the cold ingot before any operation, except 
the original one of casting, has been performed upon it. As soon as it is 
hammered, the structure changes in a remarkable manner, so that all trace 
of the primitive condition appears to be lost. 

Another method of rendering visible to the eye the molecular and chemi- 
cal changes which go on in steelis by the process of hardening or temper- 
ing. When the metal is heated and plunged into water it acquires an 
increase of hardness, but a loss of ductility. If the heat to which the steel 
has been raised just before plunging is too high, the metal acquires intense 
hardness, but it is so brittle as to be worthless; the fracture is of a bright, 
granular, or sandy character. In this state it is said to be burned, and it 
cannot again be restored to its former strength and ductility by annealing; 
it is ruined for all practical purposes, but in just this state it again shows 
differences of structure corresponding with its content in carbon. The 
nature of these changes can be illustrated by plunging a bar highly heated 
at one end and cold at the other into water, and then breaking it off in 
pieces of equal length, when the fractures will be found to show appear- 
ances characteristic of the temperature to which the sample was raised. 

The specific gravity of steel is influenced not only by its chemical analy- 
sis, but by the heat to which it is subjected, as is shown by the following 
table (densities referred to 60° F.): 

Specific gravities of twelve samples of steel from the ingot; also of six 
hammered bars, each bar being overheated at one end and cold at the 
other, in this state plunged into water, and then broken into pieces of 
equal length. 


1 2 3 4 5 6 (f 8 Oy eh Ol RE eal 


Ingot.......|7.855|7.836|7.841|7.829/7.83817.834/7..819|7.818|7.813|7.807|7.803)7. 805 
Bar: 














*BUFMOC be liys -ie:0|,215 10 C818] Te GOL bai gso] Ce 180) o095- (D2) ors ni Cle G4 sce tel dae) 
melliste*s) ais; Mera oft; 7.814/7.811) .. .|7.784]..... ths (D0) | ate sare 7.749)... G. #41 

Dalla cre 41) :2)¢9:0)| beg SONG OOO ue «ye ESO ere sesia| | « (OOH qissaters G08) deere 7.769 

2)" eee Cerone 7826/7 .849]...../7.808)...../7.773]...4. F.789]., om. [be (98 

Ds linia a ois fic of9 2c) € SMe BLO bevels 3° Veet} cae V. ZOO). oo) Cel glere steal (acpel 

GONE Goh s ann]. 0 oe | GoMAeMer Sah: es fl Saoln. «.. 1. 820i ave gle 7.826|...../7.825 





* Order of samples from bar. 


412 , STEED. 


Effect of Heat on the Grain of Steel. (W. Metcaif,—Jeans on 
Steel, p. 642.)—-A simple experiment will show the alteration produced in a 
high-carbon steel by different methods of hardening. Ifa bar of such steel 
be nicked at about 9 or 10 places, and about half an inch apart, a suitable 
specimen is obtained for the experiment. Place one end of the bar ina 
good fire, so that the first nicked piece is heated to whiteness, while the rest 
of the bar, being out of the fire, is heated up less and less as we approach 
the other end. As soon as the first piece is at a good white heat, which of 
course burns a high carbon steel, and the temperature of the rest of the bar 
gradually passes down to a very dull red, the metal should be taken out of 
the fire and suddenly plunged in cold water, in which it should be left till 
quite cold. It should then be taken out and carefully dried. An examina-— 
tion with a file will show that the first piece has the greatest hardness, 
while the last piece is the softest, the intermediate pieces gradually passing 
from one condition to the other. On now breaking off the pieces at each 
nick it will be seen that very considerable and characteristic changes have 
been produced in the appearance of the metal. The first burnt piece is very 
open or crystalline in fracture; the succeeding pieces become closer and 
closer in the grain until one piece is found to possess that perfectly 
even grain and velvet-like appearance which is so much prized by experi- 
enced steel users. The first pieces also, which have been too much hard- 
ened, will probably be cracked; those at the other end will not be hardened 
through. Hence if it be desired to make the steel hard and strong, the 
temperature used must be high enough to harden the metal through, but 
not sufficient to open the grain. 

Changes in Wltimate Strength and Elasticity due to 
Hammering, Annealing, and Tempering. (J. W. Langley, 
Trans. A. 8. C. KH. 1892.)—The following table gives the result of tests made 
onsome round steel bars, all from the same ingot, which were tested by 
tensile stresses, and also by bending till fracture took place: 

















3vic ;|/ #20 | go : 
Se Carbon. si 239 oe a. yh 
oF Sh) ge Nase et rikips ed aided gh 25 
: . [ssl [esl Zl see) Se) 28 | 38 
g Treatment. os] 2 | Bas e _& ay Oh 
cs S 8 S b 22 = 
5 eS) S le ss ba oe | Berl ey Sie eae 
Zi q-!1e | & A = 
1 |Cold-hammered bar} 153/1.25{ .47|.575) 92,420 | 141,500 2.00 2.42 
2 |Bar drawn black....| 75|1.25} .47!.577) 114,700 | 188,400 6.00 | 12.45 
8 |Bar annealed .......| 175|1.31] .70/}.580) 68,110} 98,410] 10.00 11.69 
4 |Bar hardened and ; 
drawn black ...... 30)1.09] .36) .578) 152,800 | 248,700 8.338 | 17.9 


The total carbon given in the table was found by the color test, which is 
affected, not only by the total carbon, but by the condition of the carbon. 
The analysis of the steel was: 


SGuiGoneerie reese cee ete es .242 Manganese. tase ees AS ee 24 
IPTOSPNOLUSHRP Rita e ss coe wn djee 02, Carbon (true total carbon, by 
SUlphutmeemeeeics. oe. se .009 COMbUStION) 294) Ss eee eae 1.31 


Heating Tool Steel. (Crescent Steel So., Pittsburg, Pa.)—There are 
three distinct stages or times of heating: First, for forging; second, for 
hardening; third, for tempering. 

The first requisite for a good heat for forging is a clean fire and plenty of 
fuel, so that jets of hot air will not strike the corners of the piece; next, the 
fire should be regular, and give a good uniform heat to the whole part to be 
forged. It should be keen enough to heat the piece as rapidly as may be, 
and allow it to be thoroughly heated through, without being so fierce as to 
overheat the corners. 

Steel should not be left in the fire any longer than is necessary to heat it 
clear through, as ‘‘ soaking ”’ in fire is very injurious; and, on the other hand, 
it is necessary that it should be hot through, to prevent surface cracks. 

By observing these precautions a piece of steel may always be heated 
safely, up to even a bright yellow heat, when there is much forging to be 
doue on it, 


——— 


CRUCIBLE STEEL. 413 


The best and most economical of welding fluxes is clean, crude borax, 
which should be first thoroughly melted and then ground to fine powder. 

After the steel is properly heated, it should be forged to shape as quickly 
as possible; and just as the red heat is leaving the parts intended for cutting 
edges, these parts should be refined by rapid, light blows, continued until 
the red disappears. 

For the second stage of heating, for hardening, great care should be used: 
first, to protect the cutting edges and working parts from heating more 
rapidly than the body of the piece; next, that the whole part to be hardened 
be heated uniformly through, without any part becoming visibly hotter 
than the other. A uniform heat, as low as will give the required hardness, 
is the best for hardening. 

For every variation of heat, which is great enough to be seen, there will 
result a variation in grain, which may be seen by breaking the piece: and. 
for every such variation in temperature, there is a very good chance for a 
crack to be seen. Many a costly toolis ruined by inattention to this point. 

The effect of too high heat is to open the grain; to make the steel coarse. 
The effect of an irregular heat is to cause irregular grain, irregular strains, 
and cracks. 

As soon as the piece is properly heated for hardening, it should be 
promptly and thoroughly quenched in plenty of the cooling medium, water, 
brine, or oil, as the case may be. 

An abundance of the cooling bath, to do the work quickly and uniformly 
all over, is very necessary to good and safe work. 

To harden a large piece safely a running stream should be used. 

Much uneven hardening is caused by the use of too small baths. 

For the third stage of heating, to temper, the first important requisite is 
again uniformity. Theenext is time; the more slowly a piece is brought 
down to its temper, the better and safer is the operation. 

When expensive tools are to be made itis a wise precaution to try small 
pieces of the steel at different temperatures, so as to find out how low a heat 
will give the necessary hardness. The lowest heat is the best for any steel. 

Heating to Forge.—tThe trouble in the forge fire is usually uneven 
heat, and not too high heat. Suppose the piece to be forged has been put 
into a very hot fire, and forced as quickly as possible to a high yellow heat, 
so that it is almost up to the scintillating point. If this be done, in a few 
minutes the outside will be quite soft and in a nice condition for forging, 
while the middle parts will not be more than red-hot. Now let the piece be 
placed under the hammer and forged, and the soft outside will yield so 
much more readily than the hard inside, that the outer particles will be torn 
asunder, while the inside will remain sound. 

Suppose the case to be reversed and the inside to be much hotter than the 
outside; that is, that the inside shall be in a state of semi-fusion, while the 
outside is hard and firm. Now let the piece be forged, and the outside will 
be all sound and the whole piece will appear perfectly good until it is 
cropped, and then it is found to be hollow inside 

In either case, if the piece had been heated soft all through, or if it had been 
only red-hot all through, it would have forged perfectly sound. 

In some cases a high heat is more desirable to save heavy labor but in 
every case where a fine steel is to be used for cutting purposes it must be 
borne in mind that very heavy forging refines the bars as they slowly cool, 
and if the smith heats such refined bars until they are soft, he raises the 
grain, makes them coarse, and he cannot get them fine again unless he has 
a very heavy steam-hammer at command and knows how to use it well. 

Annealing, (Crescent Steel Co.)\—Annealing or softening is accom- 
plished by heating steel to a red heat and then cooling it very slowly, 
to prevent it from getting hard again. 

The higher the degree of heat, the more will steel be softened, until the 
limit of softness is reached, when the steel is melted. 

It does not follow that the higher a piece of steel is heated the softer it 
will be when cooled, no matter how slowly it may be cooled; this is proved 
by the fact that an ingot is always harder than a rolled or hammered bar 
made from it. 

Therefore there is nothing gained by heating a piece of steel hotter than 
a good, bright, cherry-red; on the contrary, a higher heat has several dis- 
advantages: First. If carried too far, it may leave the steel actually harder 
than a good red heat would leave it. Second. If a scale is raised on the 
steel, this scale will be harsh, granular oxide of iron, and will spoil the tools 
used to cut it. Third. A high scaling heat continued for a little time 


414 STEEL, 


changes the structure of the steel, makes it brittle, liable to crack in hard. 
ening, and impossible to refine. 

To anneal any piece of steel, heat it red-hot ; heat it uniformly and heat it 
through, taking care not to let the ends and carners get too hot. 

As soon as it is hot, take it out of the fire, the sooner the better, and cool 
it as slowly as possible. A good rule for heating is to heat it at so low a red 
that when the piece is cold it will still show the blue gloss of the oxide that 
was put there by the hammer or the rolls. 

Steel annealed in this way will cut very soft; it will harden very hard, 
without cracking; and when tempered it will be very strong, nicely refined, 
and will hold a keen, strong edge. 

Wempering.—Tempering steel is the act of giving it, after it has been 
shaped, the hardness necessary for the work it has to do, This is done by 
first hardening the piece, generally a good deal harder than is necessary, 
and then toughening it by slow heating and gradual softening until it is just 
right for work. 

A piece of steel properly tempered should always be finer in grain than 
the bar from which it is made. If it is necessary, in order to make the piece 
as hard as is required, to heat it so hot that after being hardened the grain 
will be as coarse as or coarser than the grain in the original bar, then the 
steel itself is of too low carbon for the desired work. 

if a great degree of hardness is not desired, as in the case of taps, and 
most tools of complicated form, and it is found that at a moderate heat the 
tools are too hard and are liable to crack, the smith should first use a lower 
heat in order to save the tools already made, and then notify the steelmaker 
that his steel is too high, so as to prevent a recurrence of the trouble. 

For descriptions of various methods of tempering steel, see ‘‘ Tempering 
of Metals,’ by Joshua Rose, in App. Cyc. Mech., vol. ii. p. 8633; also, 
“Wrinkles and Recipes,” from the Scientific American. In both of these 
works Mr. Rose gives a “color scale,” lithographed in colors, by which the 
following is a list of the tools in their order on the color scale, together with 
the approximate color and the temperature at which the color appears on 
brightened steel when heated in the air : 


Scrapers for brass; very pale ‘yel- 
low, 430° F. 

Steel-engraving tools. 

Slight turning tools.g 

Hammer faces. 

Planer tools for steel. 

Ivory-cutting tools. 

Planer tools for iron. 

Paper-cutters. 

Wood-engraving tools. 

Bone cutting tools. 

Milling-cutters; straw yellow, 460° F. 

Wire-drawing dies. 

Boring-cutters. 

Leather-cutting dies, 

Screw-cutting dies. 

Inserted saw-teeth. 


Taps. 

Rock-drills. 

Chasers. 

Punches and dies. 

Penknives. 

Reamers. 

Half-round bits. 

Planing and moulding cutters. 

Stone-cutting tools; brown yellow, 
500° F. 

Gouges. 


Hand-plane irons. 

Twist-drills. 

Flat drills for brass. 

Wood-boring cutters. 

Drifts. 

Coopers’ tools. 

Edging cutters ; light purple, 530° F, 

Augers. 

Dental and surgical instruments, 

Cold chisels for steel. 

Axes ; dark purple, 550° F. 

Gimlets. 

Cold chisels for cast iron. 

Saws for bone and ivory. 

Needles. 

Firmer-chisels, 

Hack-saws. 

Framing-chisels. 

Cold chisels for wrought iron. 

pees and planing cutters to be 
ed. 


Circular saws for metal. 
Screw-drivers. 
Springs. 
Saws for wood. 
Dark blue, 370° F. 
Pale blue, 610°. 
Blue tinged with green, 630° ; 


FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 415 


MECHANICS. 


FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 


MrcuHANICS is the science that treats of the action of force upon bodies. 

A Foree is anything that tends to change the state of a body with respect 
#o rest or motion. If a body is at rest, anything that tends to put it in mo- 
tion is a force; if a body is in motion, anything that tends to change either 
its direction or its rate of motion is a force. 

A force should always mean the pull, pressure, rub, attraction (or repul- 
sion) of one body upon another, and always implies the existence of a simul- 
taneous equal and opposite force exerted by that other body on the first body, 
i.e., the reaction. In no case should we call anything a force unless we can 
conceive of it as capable of measurement by a spring-balance, and are able 
to say from what other body it comes. (I. P. Church.) 

Forces may be divided into two classes, extraneous and molecwlar: extra- 
neous forces act on bodies from without; molecular forces are exerted be- 
tween the neighboring particles of bodies. 

Extraneous forces are of two kinds, pressures and moving forees: pres- 
sures simply tend to produce motion; moving forces actually produce 
motion. Thus, if gravity act on a fixed body, it creates pressure; if ona free 
body, it produces motion. 

Molecular forces are of two kinds, attractive and repellent: attractive 
forces tend to bind the particles of a body together; repellent forces tend 
to thrust them asunder. Both kinds of molecular forces are continually 
exerted between the molecules of bodies, and on the predominance of one 
or the other depends the physical state of a body, as solid, liquid, or gaseous. 

Whe Unit of Force used in engineering, by English writers, is the 

ound avoirdupois. (For some scientific purposes, as in electro-dynamics, 

orces are sometimes expressed in *‘ absolute units.” The absolute unit of 
force is that force which acting on a unit of mass during a unit of time pro- 
duces a unit of velocity; in English measures, that force which acting on 
the mass whose weight is one pound in London will in one second produce a 
velocity of one foot per second = 1 + 82.187 of the weight of the standard 
pound avoirdupois at London, In the French C. G. S. or centimetre-gramme 
second system it is the force which acting on the mass whose weight is one 
gramme at Paris will produce in one second a velocity of one centimetre per 
second. This unit is called a ‘‘ dyne’’ = 1/981 gramme at Paris.) 

Inertia is that property of a body by virtue of which it tends to continue 
in the state of rest or motion in which it may be placed, until acted on by 
some force. 

Newton’s Laws of MWotion.—ist Law. Ifa body be at rest, it will 
remain at rest; or if in motion, it will move uniformly in a straight line till 
acted on by some force. 

2d Law. If a body be acted on by several forces, it will obey each as 
though the others did not exist, and this whether the body be at rest or in 
motion. 

3d Law. Ifa foree act to change the state of a body with respect to rest 
or motion, the body will offer a resistance equal and directly opposed to the 
force. Or, to every action there is opposed an equal and opposite reaction. 

Graphie Representation of a Force.—Forces may be repre- 
sented geometrically by straight lines, proportional to the forces. A force 
is given when we know its intensity, its point of application, and the direc- 
tion in which it acts. When a force is represented by a line, the length of the 
line represents its intensity; one extremity represents the point of applica- 
tion; and an arrow-head at the other extremity shows the direction of the 


force. : ‘<3 : 

CO Ee of Forces is the operation of finding a single force 
whose effect is the same as that of two or more given forces. The required 
force is called the resultant of the given forces. 

Resolution of Forces is the operation of finding two or more forces; 
whose combined effect is equivalent to that of a given force. The required 
forces are called components of the given force. 

The resultant of two forces applied at a point, and acting in the same di- 
rection, is equal to the sum of the forces. If two forces act in opposite 
directions, their resultant ig equal to their difference, and it acts in the 
direction of the greater, 


416 MECHANICS. 


If any number of forces be applied at a point, some in one direction and 
others in a contrary direction, their resultant is equal to the sum of those 
that act in one direction, diminished by the sum of those that act in the op- 
posite direction; or, the resultant is equal to the algebraic sum of the com- 
ponents. 

Parallelogram of Forces,—If two forces acting on a point be rep- 
resented in direction and intensity by adjacent sides of a parallelogram, 
their resultant will be represented by that diagonal of the parallelogram 

Q 5 which passes through the point. Thus OR, Fig. 
SS an Poh ag 88, is the resultant of OY and OP. 

Polygon of Forces.—lIf several forces are 
applied at a point and act in a single plane, their 
resultant is found as follows: 

Through the point draw a line representing the 
first force ; through the extremity of this draw 
o P a line representing the second force; and so on, 

Fie. 88 throughout the system; finally, draw a line from 
rar asia the starting-point to the extremity of the last line 
drawn, and this will be the resultant required. 

Suppose the body A, Fig. 89, to be urged in the directions Al, A2, 43, A4, 
and A5 by forces which are to each other as the lengths of those lines. 
Suppose these forces to act successively and the body to first move from A 
to 1: the second force A2 then acts and finding the body at 1 would take it 
to 2’; the third force would then carry it to 3’, the fourth to 4’, and the fifth 
to 5’. The line 45’ represents in magnitude and direction the resultant of 
all the forces considered. If there had 
been an additional force, Ax, in the group. 
the body would be returned by that force 
to its original position, supposing the 
forces to act successively, but if they had 
acted simultaneously the body would never 2 
have moved at all; the tendencies to mo- 
tion balancing each other. 

It follows, therefore, that if the several 
forces which tend to move a body can be 
represented in magnitude and direction 
by the sides of a closed polygon taken in 
order, the body will remain at rest; but if Fic: 89 
the forces are represented by the sides of ‘titer F GRE ee 
an open polygon, the body wil] move and the direction will be represented 
by the straight line which closes the polygon. 

Wwisted Polygon.—tThe rule of the polygon of forces holds true even 
when the forces are not in one plane. In this case the lines A1, 1-2’, 2’-3’, 
etc., form a twisted polygon, that is, one whose sides are not in one plane. 

Parallelopipedon of Forces.—If three forces acting on a point be 
represented by three edges of a parallelopipedon which meet in a common 
point, their resultant will be represented by the diagonal of the parallelo- 
pipedon that passes through their common point. : 

Thus OR, Fig. 90, is the resultant of OQ, OS, and OP. OM isthe result 
ant of OP and OQ. and OR is the resultant of OM and OS. 

Moment of a Koree.—The mo- exit 
ment of a force (sometimes called stat- - 
ical moment), with respect to a point, 
is the product of the force by the per- 
pendicular distance from the point to 
the direction of the force. The fixed 
point is called the centre of mo- 

S 











Fie. 91, 


FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 417 


ments ; the perpendicular distance is the lever-arm of the force; and the 
moment itself measures the tendency of the force to produce rotation about 


the centre of moments. 


If the force is expressed in pounds and the distance in feet, the moment 
is expressed in foot-pounds. It is necessary to observe the distinction be- 
tween foot-pounds of statical moment and foot-pounds of work or energy. 


(See Work.) 


In the bent lever, Fig. 91 (from Trautwine), if the weights » and m repre- 
sent forces, their moments about the point f are respectively n & af and 
m X fe. If instead of the weight ma pulling force to balance the weight 
n is applied in the direction bs, or by or bd, s, y, and d being the amounts of 
these forces, their respective moments are s xX ft, y x fb, d X fh. 

If the forces.acting on the lever are in equilibrium it remains at rest, and 
the moments on each side of f are equal, that is, n * af= m x fe, ors x ft, 
or y X fb, or d X hf. 

The moment of the resultant of any number of forces acting together in 
the same plane is equal to the algebraic sum of the moments of the forces 
taken separately. 

Statical Woment. Stability.—The statical moment of a body is 
the product of its weight by the distance of its line of gravity from some 
assumed line of rotation, The line of gravity is a vertical line drawn from 
its centre of gravity through the body. The stability of a body is that re- 
sistance which its weight alone enables it to oppose against forces tending 
to overturn it or to slide it along its foundation. 

To be safe against turning on an edge the moment of the forces tending to 
overturn it, taken with reference to that edge, must be less than the stati- 
cal moment. When a body rests on an inclined plane, the line of gravity 
being vertical, falls toward the lower edge of the body, and the condition of 
its not being overturned by its own weight is that the line of gravity must 
fall within this edge. In the case of an inclined tower resting on a plane 
the same condition holds—the line of gravity must fall within the base. The 
condition of stability against sliding along a horizontal plane is that the hor- 
izontal component of the force exerted tending to cause it to slide shall be 
less than the product of the weight of the body into the coefficient of fric- 
tion between the base of the body and its supporting plane. This coefficient 
of friction is the tangent of the angle of repose, or the maximum angle at 
which the supporting plane might be raised from the horizontal before the 
body would begin to slide. (See Friction.) 

The Stability of a Dama against overturning about its lower edge 
is calculated by comparing its statical moment referred to that edge with 
the resultant pressure of the water against its upper side. The horizontal 
pressure on a square foot at the bottom of the dam is equal to the weight of 
a column of water of one square foot in section, and of a height equal to the 
distance of the bottom below water-level; or, if H is the height, the pressure 
at the bottom per square foot = 62.4 x Hlbs. At the water-level the pres- 
sure is zero, and it increases uniformly to the bottom, so that the sum of the 
pressures on a vertical strip one foot in breadth may be represented by the 
area of atriangle whose base is 62.4 x H and whose altitudeis H, or 62 4H?+2. 
The centre of gravity of a triangle being 44 of its altitude, the resultant of 
all the horizontal pressures may be taken as equivalent to the sum of the 
pressures acting at 44H, and the moment of the sum of the pressures is 
therefore 62.4 x H3 + 6. 

Parallel Forces,.—lIf two forces are parallel and act in the same direc: 
tion, their resultant is parallel to both, and lies between them, and the inten- 
sity of the resultant is equal to the sum of the intensities of the two forces. 
Thus in Fig. 91 the resultant of the forces 7 and m acts vertically down- 
ward at f, and is equal ton + m. 

If two parallel forces act at the extremities of a straight line and in the 
same direction, the resultant divides the line joining the points of application 
of the components, inversely as the components. Thus in Fig. 91, m:n :: 


af : fe; and in Fig. 92, P: Q::SN: SM, N. 
The resultant of two parallel forces 7 Q 
acting in opposite directions is parallel We! 
to both, lies without both, on the side PEARANCE cit STASI eo 
and in the direction of the greater, i 
and its intensity is equal to the differ- M of La >p 
ence of the intensities of the two L 
forces. Fie. 92, 


418 MECHANICS. 


Thus the resultant of the two forces Q and P, Fig. 93, is equal to Q- Ps 
Of any two parallel forees and their 


N resultant each is proportional to the dis- 
Q eatery tance between the other two; thus in both 
es Figs. 92 and 93, P:Q@:R::SN:SM: MN, 
Ms———--> P _ Couples.—If P and Q be equal and act 
/ ' in opposite directions, R = 0; that is, they 
7 t have no resultant. Two such forces con- 
S ee t —>R stitute what is called a couple. 
Cc \ The tendency of a couple is to produce 
Fia. 93. rotation; the measure of this tendency, 


called the moment of the couple, is the 
product of one of the forces by the distance between the two. 

Since a couple has no single resultant, no single force can balance a 
couple. To prevent the rotation of a body acted on by a couple the applica- 
tion of two other forces is required, forming a second couple. Thus in Fig. 
94, Pand Q forming a couple, may be balanced 
by a second couple formed by & and S. The 
point of application of either R or S may bea 
fixed pivot or axis. 

Moment of the couple PQ = P(c+b+a)= 
moment of RS = Rb. Also, P+ R=Q4 8. 

The forces Rand S need not be parallel to P 
and Q, but if not, then their components parallel 
to PQ are to be taken instead of the forces 
themselves. 

Equilibrium of Forces.—A system of 
forces applied at points of a solid body will be 





in equilibrium when they have no tendency to — Y¥s 
produce motion, either of translation or of rota- Fig. 94, 
tion. 


The conditions of equilibrium are: 1. The algebraic sum of the compo- 
nents of the forces in the direction of any three rectangular axes must be 
separately equal to 0. 

2. The algebraic sum of the moments of the forces, with respect to any 
three rectangular axes, must be separately equal to 0. 

If the forces lie ina plane: 1. The algebraic sum of the components of the 
eye, in the direction of any two rectangular axes, must be separately 
equal to 0. 

2. The algebraic sum of the moments of the forces, with respect te any 
point in the plane, must be equal to 0. 

If a body is restrained by a fixed axis, as in case of a pulley, or wheel and 
axle, the forces will be in a equilibrium when the algebraic sum of the mo- 
ments of the forces with respect to the axis is equal to 0. 


CENTRE OF GRAVITY, 


The centre of gravity of a body, or of a system of bodies rigidly connected 
together, is that point about which, if suspended, all the parts will be in 
equilibrium, that is, there will be no tendency to rotation, It is the point 
) through which passes the resultant of the efforts of gravitation on each of 
‘the elementary particles of a body. In bodies of equal heaviness through- 
out, the centre of gravity is the centre of magnitude. 

(The centre of magnitude of a figure is a point such that if the figure be 
divided into equal parts the distanee of the centre of magnitude of the 
whole figure from any given plane is the mean of the distances of the centres 
of magnitude of the several equal parts from that plane.) 

If a body be suspended at its centre of gravity, it will be in equilibrium in 
all positions. If it be suspended at a point out of its centre of gravity, it 
will swing into a position such that its centre of gravity is vertically beneath 
its point of suspension. 

To find the centre of gravity of any plane figure mechanically, suspend 
the figure by any point near its edge, and mark on it the direction of a 
plumb-line hung from that point ; then suspend it from some other point, 
and again mark the direction of the plumb-linein like manner. Then the 
centre of gravity of the surface will be at the point of intersection of the 
two marks of the plumb-line. 

The Centre of Gravity of Regular Figures, whether plane or 
solid, is the same as their geometrical centre ; for instance, a straight line, 


MOMENT OF INERTIA. 419 


parallelogram, regular pelygon, circle, circular ring, prism, cylinder, 
sphere, spheroid, middle frustums of spheroid, ete. 

Of a triangle: On a line drawn from any angle to the middle of the op- 
posite side, at a distance of one third of the line from the side; or at the 
intersection of such lines drawn from any two angles. 

if a trapezium or trapezoid: Draw a diagonal, dividing it into two tri- 
angles. Draw a line joining their centres of gravity. Draw the other 
diagonal, making two other triangles, and a line joining their centres. The | 


_ intersection of the two lines is the centre of gravity required. 


Of a sector of a circle: On the radius which bisects the are, 2cr + 37 from 
the centre, c being the chord, 7 the radius, and / the arc. 

Of a semicircle: On the middle radius, .4244r from the centre, 

Of a quadrant: On the middle radius, .60027 from the centre, 

Of a segment of a circle ; c3 + 12a from the centre. c = chord, a= area 

Of a parabolic surface ; In the axis, 3/5 of its length from the vertex. 

Of a semi-parabola (surface) ; 3/5 length of the axis from the vertex, and 


. 36 of the semi-base from the axis. 


Of a cone or pyramid ; In the axis, 14 of its length from the base. 

Of a paraboloid ; In the axis, % of its length from the vertex. 

Of a cylinder, or regular prism ; In the middle point of the axis. 

Of a frustum of a cone or pyramid ; Let a = length of a line drawn from 
the vertex of the cone when complete to the centre of gravity of the base, and 
a’ that portion of it between the vertex and the top of the frustum; then 
distance of Oh he Neath of the frustum from centre of gravity of its 

a 


a 
pase = 4  4(a?+aa’+ ay 
For two bodies, the common centre of gravity is that point which divides 
the distance between their respective centres of gravity in the inverse ratio 
of the weights The products obtained by multiplying each weight by the 
distance of its centre of gravity from the common centre are equal. 
For more than two bodies connected in one system: Find the common 


- centre of gravity of two of them ; and find the common centre of these two 


jointly with a third body, and so on to the last body of the group. 

Another method, by the principle of moments: To find the centre of 
gravity of a system of bodies, or a body consisting of several parts, whose 
several centres are known. If the bodies are in a plane, refer their several 
centres to two rectangular co-ordinate axes. Multiply each weight by its 
distance from one of the axes, add the products, and divide the sum by the 
sum of the weights: the result is the distance of the centre of gravity from 
that axis. Do the same with regard to the other axis. If the bodies are 
not in a plane, refer them to three planes at right angles to each other, and 
determine the mean distance of the sum of the weights from each of the 


three planes. 
MOMENT OF INERTIA. 


The moment of inertia of the weight of a body with respect to an axis is 
the algebraic sum of the products obtained by multiplying the weight of 
each elementary particle by the square of its distance from the axis. If the 
moment of inertia with respect to any axis = J, the weight of any element 
of the body = w, and its distance from the axis = r, we have [= 2(wr?). 

The moment of inertia varies, in the same body, according to the position 
of the axis. Itis the least possible when the axis passes through the centre 
of gravity. To find the moment of inertia of a body, referred to a given 
axis, divide the body into small parts of regular figure. Multiply the weight 
of each part by the square of the distance of its centre of gravity from the 
axis. The sum of the products is the moment of inertia. The value of the 
moment of inertia thus obtained will be more nearly exact, the smaller and 
more numerous the parts into which the body is-divided. 

Moments or INERTIA OF REGULAR SoLIps.—Rod, or bar, of uniform thick- 
ness, with respect to an axis perpendicular to the length of the rod, 


12 
1=w(>+a?), eo. 0! # 68 CyB) (1) 
W = weight of rod, 21 = length, d = distance of centre of gravity from axis, 
Thin circular plate, axis in its v3 ; 
own plane, il pi=w(>+a"); Seen d abemeer 
7 = radius of plate. 


420 MECHANICS. 


Circular plate,axis perpendicular ; r2 
to the plate, Pa W(t Yo. 5 shel 


Circular ring, axis perpendicular | ex + 7/2 ) 
to its own plane, t I= Ww rigae o +d?), «e-e 4 


yr and7’ are the exterior and interior radii of the ring. 


Cylinder, axis perpendicular to r? 12 
the axis of the cylinder, t I= w(e ae 3 +d?), « « « « (5) 


r = radius of base, 27 = length of the cylinder. 


By making d= 0 in any of the above formule we find the momert of 
inertia for a parallel axis through the centre of gravity. 

The moment of inertia, Zwr?, numerically equals the weight of a body 
which, if concentrated at the distance unity from the axis of rotation, would 
require the same work to produce a given increase of angular velocity that the 
actual body requires. It bears the same relation to angular acceleration 
which weight does to linear acceleration (Rankine). The term moment of 
inertia is also used in regard to areas, as the cross-sections of beams under 
strain. In this case T= Sar?, in which a is any elementary area, and r its 
distance from the centre. (See under Strength of Materials, p. 247.) Some 
writers call Sr? = Swr2? + g the moment of inertia. 


CENTRE AND RADIUS OF GYRATION. 


The centre of gyration, with reference to an axis, is a point at which, if 
dhe entire weight of a body be concentrated, its moment of inertia will re- 
main unchanged; or, in a revolving body, the point in which the whole 
weight of the body may be conceived to be concentrated, as if a pound of 
platinum were substituted for a pound of revolving feathers, the angular 
velocity and the accumulated work remaining the same. The distance of 
this point from the axis is the radius of gyration. If W = the weight of a 
body, I = Swr? = its moment of inertia, and k = its radius of gyration, 


Sort 
I= Wk? = 3wr?; k= 4/ a . 


The moment of inertia = the weight x the square of the radius of gyration. 

To find the radius of gyration divide the body intoa considerable number 
of equal small parts—the more numerous the more nearly exact is the re- 
sult,—then take the mean of all the squares of the distances of the parts 
from the axis of revolution, and find the square root of the mean square. 
Or, if the moment of inertia is known, divide it by the weight and extract 
the square root. For radius of gyration of an area, as a cross-section of a 
beam, divide the moment of inertia of the area by the area and extract the 
square root. 

The radius of gyration is the least possible when the axis passes through 
the centre of gravity. This minimum radius is called the principal radius 
of gyration. If we denote it by k and any other radius of gyration by k’, 
we have for the five cases given under the head of moment of inertia above 
the following values ; ; 


(1) Rod, axis perpen.to) 7, _ re Isa 
length, ‘ele jar 4/ i; w= 4/Gr@, 


r v2 
kag Wa 4/42 





(2) Circular plate, axis 
in its plane, 


(8) Circular plate, axis 
perpen. to plane, 


perpen. to plane, 





(5) Cylinder, axis per- 


~ : : 2 74 miys 
(4) Circular ring, at bee) / ee ee (= re 
pen. to length, ; 


0 


GENTRES OF OSCILLATION AND OF PERCUSSION, 421 


Principal Radii of Gyration and Squares of Radii of 


Gyration. 


(For radii of gyration of sections of columns, see page 249.) 





Surface or Solid. 


oo 


Rad. of Gyration. 


Square of R. 


of Gyration. 





Parallelogram: } axis at its base....... TBR Yeh? 
5 peishy h ii ‘* mid-height...... o2d86h 1/12h2 

tr. alg tro . t ad 57731 12 

length J, or thin ASS ch en eroeersee de 

rectang. plate mid-length.. 28861 1/12/2 
Rectangular prism: 

axes 2a, 2b, 2c, referred to axis 2a.. BUT /b2 + c2 (b2 +c?) +3 
Par allelopiped: ‘length 1, base b, axis iD 5 Ta aa 41/2 + 62 

at one end, at mid- breadth........ 289 41? + b Daal 
Hollow square tube: 

out. side A, inn’r h’, axis mid- length.. 289 Vn? + h/2 (h2 + h/2) +12 

very thin, side = h, ait 4082 h?2 +6 
Thin rectangular tube: sides b, h, o8gh h-+- 3b hb dost 8D 

axis mid-length............ Rei as tla a ea 12 h+6 
Thincire.plate: rad.r,diam.h,ax. diam, lor Y4y2 = h2? +16 
Flat cire. ring: diams. h, h’, axis diam. Ye Vh2-h’2 


(h2 + h’2) +16 
(2 2 


Solid circular cylinder: length 7, - here 
axis diameter at mid-length..... f 289 /1? | 37? 12 a 4 
Circular plate: solid wheel of uni- 
form thickness, or cylinder of any OT1r 172 
length, cs Nabe to axis of cyl..... 

“Hollow cire. cylinder, or flat ring: ) ron, 4/2 4172 R2-+ 2) +2 
l,, length; R, 7, outer and reed Se Sata if nee lies 
radii. Axis, 1, longitudinal axis; { | 289 4/1?--3(R? + 1?) | 6: ae 
2,diam. at mid-length,:.2/... 2... J 12 pe 

Same: very thin, axis its diameter....| .289 4/12 + 6R2 at 3 
** radius r; axis, longitud’l axis.. r v2 
Cireumf. of cir cle, axis its centre..... r r2 
SS PGiaIneees:. 07Ir Llér2 
Sphere: radius 7, axis its preres SOpOL se 63257 2/572 
Spheroid: equatorial] radius r, re- RNG : 
volving polar axis a.. gree neh § -6825r 2/51? 
Paraboloid: + = rad. of base, rev. ~ : 
OMVATIS Tees 0S Es wedate on 50739 for, 2 
Ellipsoid: semi-axes a, b, c; revolv- “9 EEO OS a 
INS OMVAXISHLA Heels Lees aan A412 7b? + € 5 
Spherical shell: radii R, r, revolving ( e208 Bere 2 Ro — 75 
OUT ESE CUA TUN aie ictele scie ay se overs sivjecive) 9 tests R3 — 3 5 R38 — 73 
Same: very thin, radius'7 +s.) 3...) 4). 8165r Zr 
Solid cone: + = rad. of base, rev. on ope Bry 0.372 
axis. SP IG ae ar ee ; ; : 





CENTRES OF OSCILLATION AND OF PERCUSSION. 


Centre of Oscillation.—If a body oscillate about a fixed horizontal 
axis,not passing through its centre of gravity, there is a point in the line 
drawn from the centre of gravity perpendicular to the axis whose motion 
is the same as it would be if the whole mass were collected at that point 
and allowed to vibrate as a pendulum about the fixed axis. This point is 
called the cenrre of oscillation, 

Whe Radius of Oscillation, or distance of the centre of oscillation 
from the point of suspension = the square of the radius of gyration + dis- 
tance of the centre of gravity from the point of suspension or axis. The 
centres of oscillation and suspension are convertible. 

If a straight line, or uniform thin bar or cylinder, be suspended at one end, 
oscillating about it as an axis, the cenire of oscillation is at 6 the length of 


422 MECHANICS, 


the rod from the axis. If the point of suspension is at 4% the iength from 
the end, the centre of oscillation is also at % the length from the axis, that 
is, itis at the other end. In both cases the oscillation will be performed in 
the same time. If the point of suspension is at the centre of gravity, the 
length of the equivalent simple pendulum is infinite, and therefore the time 
of vibration is infinite. 

For a sphere suspended by a cord, r= radius, h = distance of axis of 
motion from the centre of the sphere, h’ = distance of centre of pay y 
from centre of the sphere, / = radius of oscillation = h +h’ =h + 5 > 

If the sphere vibrate about an axis tangent to its surface, h =r, andl=r 
4 2/5r. If hk = 10r,2 = 10r-+ a 


Lengths of the radius of oscillation of a few regular plane figures or thin 
plates. suspended by the vertex or uppermost point. 
rs 1st. When the vibrations are flatwise, or perpendicular to the plane of the 

gure: 

In an isosceles triangle the radius of oscillation is equal to 34 of the height 
of the triangle. 

In a circle, 5g of the diameter. 

In a parabola, 5/7 of the height. 

2d. When the vibrations are edgewise, or in the plane of the figure: 

In a circle the radius of oscillation is 34 of the diameter. 

In a rectangle suspended by one angle, % of the diagonal. 

In a parabola, suspended by the vertex, 5/7 of the height, plus 14 of the 
parameter. 

In a parabola, suspended by the middle of the base, 4/7 of the height plus 
14 the parameter. 

Centre of Percussion.—tThe centre of percussion of a body oscillat- 
ing about a fixed axis is the point at which, if a blow is struck by the body, 
the percussive action is the same as if the whole mass of the body were con- 
centrated at the point. This point is identical with the centre of oscillation. © 


THE PENDULUM. 


A body of any form suspended from a fixed axis about which it oscillates 
by the force of gravity is called a compound pendulum, The ideal body 
concentrated at the centre of oscillation, suspended from the centre of sus- 
pension by a string without weight, is called a simple pendulum. This equi- 
valent simple pendulum has the same weight as the given body, and also 
the same moment of inertia, referred to an axis passing through the point 
of suspension, and it oscillates in the same time. 

The ordinary pendulum of a given length vibrates in equal times when the 
angle of the vibrations does not exceed 4 or 5 degrees, that is, 2° or 244° each ' 
side of the vertical. This property of a pendulum is called its isochronism. 

The time of vibration of a pendulum varies directly as the square root of 
the length, and inversely as the square root of the acceleration due to grav- 
ity at the given latitude and elevation above the earth’s surface. 

If T = the time of vibration, 2 = length of the simple pendulum, g = accel- 


eration = 32.16, T= 7 (4 since z is constant, T os te At a given loca: 


g 
tion g is constant and Te Vi. If t be constant, then for any location 
2 
alee hen If T be constant, gT2 = w2l;3 Lag; g= ae From this equation 


g 
the force ot gravity at any place may be determined if the length of the 
siinple pendulum, vibrating seconds, at that place is known, At New York 
this length is 39.1017 inches = 3.2585 ft., whence g = 32.16 ft. At London the 
length is 39.1393 inches. At the equator 89.0152 or 39.0168 inches, according 
to different authorities. 

Time of vibration of a pendulum of a given length at New York 


TE: 
=e= 1 39.1017 ~ 6.253° 


t being in seconds and 2 ininches. Length of a pendulum having a given 
time of vibration, t = ¢? X 39.1017 inches, 


VELOCITY, ACCELERATION, FALLING BODIES. 423 


The time of vibration of a pendulum may be varied by the addition of a 
weight at a point above the centre of suspension, which counteracts the 
lower weight, and lengthens the period of vibration, By varying the height 
of the upper weight the time is varied. 

To find the weight of the upper bob of a compound pendulum, vibrating 
seconds, when the weight of the lower bob, and the distances of the weights 
from the point of suspension are given: 


(39.1 x D) ~ D2 
(9.1 x d) + d* 


W = the weight of the lower bob, w = the weight of the upper bob; D= 
the distance of the lower bob and d = the distanze of the upper bob from 
the point of suspension, in inches. 

Thus, by means of a second bob, short pendulums may be constructed to 
vibrate as slowly as longer pendulums. 

By increasing w ord until the lower weight is entirely counterbalanced, 
the time of vibration may be made infinite. 

Conical Pendulum.—A weight suspended by a cord and revolving 
at a uniform speed in the circumference of a circular horizontal plane 
whose radius is 7, the distance of the plane below the point of suspension be- 
ing h, is held in equilibrium by three forees—the tension in the cord, the cen- 
trifugal force, which tends to increase the radius r, and the force of gravity 
acting downward. If v= the velocity in feet per second, the centre of 
gravity of the weight, as it describes the circumference, g == 82.16, and r 
and h are taken in feet, the time in seconds of performing one revolution is 


2Qur h, La a 2 
t= U = 27 3s ~ da2 = .8146¢ e 


If — = 1 second, h = .8146 foot = 9.775 inches. : 
The principle of the conical pendulum is used in the ordinary fly-ball 
governor for steam-engines, (See Governors.) 


CENTRIFUGAL FORCE. 


A body revolving in a curved path of radius = Fin feet exerts a force, 
called centrifugal force, #, upon the arm or cord which restrains it from 
moving in a straight line, or “flying off at a tangent.” If W = weight of 
the body in pounds, NV = number of revolutions per minute, v = linear 
velocity of the centre of gravity of the body, in feet per second, g = 32.16, 
then 

Ir RN Wr? Wet  W4r9RN? WRN? _ 

Vg tS ae toes es 

If n = number of revolutions per second, F’ = 1.2276WRn?. 

(For centrifugal force in fly-wheels, see Fly-wheels.) 


VELOCITY, ACCELERATION, FALLING BODIES. 


Welocity is the rate of motion, or the distance passed over by a body in 
@ given time. ; Shine. 

If s = space in feet passed over in é seconds, and v = velocity in feet per 
second, if the velocity is uniform, 


wa=Ww 


s. —_ e akg 
Us Stes Gay. 





Ke + “2 in which 
v, is the velocity at the beginning and vg the velocity at the end of the time ¢. 


If the velocity varies uniformly, the mean velocity vg = 


pet; Ue 
es 5) ij 


ee © @ ©, eff @ Cer % - (1) 


Acceleration is the change in velocity which takes place in a unit of 
tine. Unit of acceleration =a=1 foot per second in one second. For 
uniformly varying velocity, the acceleration is a constant quantity, and 

Vg—- vV 
9 Ug=%; + at; OF ek ats t=7 o e o (2) 





Vq — Vi 
a= 
f 


424. MECHANICS. 


If the body start from rest, v, = 0; then 


a2 v 
M= 33 Vg = 2Vo$ a= 3 Uq = al; Vqg — at = 03 — 22. 
Combining (1) and (2), we have 
Vo? — V3? at? at? 


If v, = 0,s = 4. 
Retarded Motion.—Iff the body start with a velocity v, and come ta 
rest, Vg = 0; thens= ht, 


In any case, if the change in velocity is v, 
2 a 


v 
=-t: s=—:; g= —f?, 
fi ay $ 2a” : a 
For a body starting from or ending at rest, we have the equations 


at2 
2 = Qs. 


. v 
V=aAl3 8 = 585 sears } Vv 
Falling Bodies,—In the case of falling bodies the acceleration due 
to gravity is 32.16 feet per second in one second, = g. Then ifw = velocity 
acquired at the end of ¢ seconds, or final velocity, and h = height or space 
in feet passed over in the same time, 


eo 2h 
v=gt = 82.166 = V2gh= 802 Vr =F; 


t 

gt? v2 y2 vt 
= ~~ = 16.08/27 = — feof ee oss 
; 2 2g 64.32 2° 
pia el 258 8 cyt Phy AW ee oi, 
goo 82316 IG g 4.01 mn ee 


% = space fallen through in the Tth second = 9(7' — 34). 


From the avove formula for falling bodies we obtain the following: 
During the first second the body starting from a state of rest (resistane 
of the air neglected) falls g + 2 = 16.08 feet ; the acquired velocity is g = 

2 
82.16 ft. per sec.; the distance fallen in two seconds ish = mile = 16.08 Xx4= 
64.32 ft.; and the acquired velocity is v = gt = 64.32 ft. The acceleration, or 
increase of velocity in each second, is constant, and is 32.16 ft. per sec. Solv- 
ing the equations for different times, we find for 





DECOMGASE Lacie s ci c:cs-cuusere-aeeniaiens Rat a. Bids Says | 2 8 4 5 6 

Acceleration, g......... SR rcs ks Sa eG) MES 1 1 1 af 1 

Velocity acquired at ena of time, v.... 82.16 x 1 Ble Bie ay NS 6 

Height of fall im each second, w... ... as 1 Ve See ee ee 
; B 

Potaheniehtor fall, hele as ae ee We ee 


Value of g.—The value of g increases with the latitude, and decreases 
with the elevation. At the latitude of Philadelphia, 40°, its valueis 32.16. At 
the sea-level, Everett gives g = 32.178 ~ .082 cos 2 lat. —,.000003 height in 
feet. At Paris, lat. 48° 50’ N., g = 980.87 em. = 39.181 ft. 

_ Values of 2g, calculated by an equation given by ©. S. Pierce, are given 
in a table in Smith’s Hydraulics, from which we take the following : 
Latitude....... 0° 10° 20° 30° 40° 50° 60? 
Value of /2g.. 8.0112 8.0118 8.0137 8.0165 8.0199 8.0285 8.0269 

The value of 4/29 decreases about .0004 for every 1000 feet increase in ele- 
vation above the sea-level. 

Por all ordinary calculations for the United States, g is generally taken at 
82.16, and 4/2g at 8.02. In England g = 82.2, 4/29 = 8.025. Practical limite 
ing values of g for the United States, according + Pierce, are: savior © 

Latitude 49° at sea-level ............... sovcccccccesseee J = 52,186 
“ 25° 10,000 feet above the sea...........ee0ee0. G@ = 32.089 


: VELOCITY, ACCELERATION, FALLING BODIES. 425 


Fig. 95 represents graphically the velocity, space, etc., of a body falling for 
six seconds. Theverticallineattheleftis , ww ¢t 
the time in seconds, the horizontal lines 
represent the acquired velocities at the ” 
end of each second = 32.16¢. Theareaof 1 1 2 1 
the small triangle at the top represents 
the height fallen throug in the first ; 
second = 14g = 16.08 feet,andeach ofthe 4 3 4 2 
other triangles is an equa space. The 
number of triangles between each pair of 
horizontal lines represents ‘he height of 9 5 6 3” 
fall in each second, and the number of 
triangles between any horizontal line and 
the top is the total height fallen during 16 7% 8 4” 
the time. The figures under A, uw, and v 
adjoining the cut are to be multiplied by 
16.08 to obtain the actual velocities and 95 9 10 5” 
heichts for the given times. 

Angular and Linear Velocity 
of a Turning Body.—Let 7 = radius ofa 86 11 12 6” 
turning body in feet, n = number of revo- z 5 
lutions per minute, v = linear velocity of Fig, 95. 
a point on the circumference in feet per second, and 60v = velocity in feet 
per minute. 

__ 2Qarn 
me a6ht,” 

Angular velocity is a term used to denote the angle through which any 
radius of a body turns in a second, or the rate at which any point in it 
having a radius equal to unity is moving, expressed in feet per Second. The 
unit of angular velocity is the angle which at a distance = radius from the 
centre is subtended by an arc equal to the radius. This unit angle = thy 

T 

degrees = 57.3°. 2m X 57.3° = 360°, or the circumference. If 4 = angular 


Vy 2B 


velocity, v= Ar, A= TF Tee The unit angle = is called a radian. 


Height Corresponding to a Given Acquired Velocity. 





60v = 2arn. 

















# = | z 
"oo Suit feo 
© oD ® 
si > ie 
feet feet 
: feet p.sec. feet. 
47.0 97 146 
48.8 98 149 
50.5 99 BOS 
52.3 103 155 
54.1 105 171 
56. - 110 188 
57.9 115 205 
59.8 120 224 
61.7 130 263 
63.7 140 304 
65.7 150 850 
67.7 § 17 4% 
69.8 § 200 622 
71.9 300 1399 
74.0 § 400 2488 
76.2 500 3887 
78.4 600 5597 
80.6 700 7618 
82.9 § 800 9952 
85.15 1900 | 12593 
87.5 143.3 —1000 | 15547 





426 


MECHANICS. 


Falling Bodies: Velocity Acquired by a Body Falling a 
Given Height, 





EE ee ee el 


r= es 
0 5 
_ oC) 
| 
feet 
feet. p.sec. 
.005 Aay 
.010 .80 
.015 98 
20200), 11s 
0025 | 1.27 
.030 } 1.39 
.035 | 1.50 
.040 | 1.60 
.045 | 1.70 
2050 | 1.79 
-055 | 1.88 
.060 | 1.97 
065 | 2.04 
.070 | 2.12 
075 | 2.20 
.080 | 2.27 
.085 | 2.34 
.090 | 2.41 
.095 | 2.47 
.100 | 2.54 
-105 | 2.60 
-110 | 2.66 
6115 | 2.72 
.120 | 2.78 
2125 | 2.84 
.130 | 2.89 
14 | 3.00 
wld 3.11 
16 | 8.21 
ile sd | 
18 | 8.40 
19 | 8.50 
20 =} 8.59 
21 | 3.68 
622 | 3.76 
23 | 8.85 
24 =| 8.93 
25 | 4.01 
26 ; 4.09 
2 «| 4.17 
28 | 4.25 
29 | 4.32 
,80 | 4.389 
331 4.47 
32 | 4.54 
3a | 4.61 
04 | 4.68 
oo | 4.74 
.36 | 4.81 
4,88 
4.94 


(Su) 
oO 





6.06 


CH OF SD OV 09 2 Ht 


= PIR WOH HOWCMOIORMU A woot 
BeBe CRG S SR SBS CORA SDSSSMNOSNEESa 


2 00 GP 09.99 09 OH 0 OO 003 AF AVAPOD AP ABAD AVA AY DT HHH HD 


Height. 










a 

Soe 
© 
ct 


Comin to 


for] 


9.36 


- 
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e 


8 


. 


Je} 


SOMNSMS ADO 


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S ° e 
or” Dh DARW BWAnsw BDoarw 


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SB OAFSIDHD OOo 


SAIS NS EEO eee. ak aes a oe ee 8 8 as bp Oe 
> HE BD S GO OV CI F+ CO MPH AO CD. GD HE OO CO OF he A GO OD O09 09 r+ S LO LOO FAI MA ED 


oe 


OVO? OT OTE HB RB 00 09 09 09 2D WW WH RRR ODO OOOO OO OC OOOOOWO 


HB G9 09 G9 28 G8 9 G9 G9 G9 E920 29491020 10 INI rs ener ert eet ty 


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WDB Ww COVOTAwWIONM WMsaom orm 


BD Se O Ht OO Sh O94 OD OT Gd S OB ID BOO OTD 


SODAOAVIIOMHAIgE AP RW WWWWOREe 


09 G9 09 GD CS CD CD CD ON CD CD CO CHOVWWWWNWNWUENWNWNWNWNHWNWNWNWNWWNWNNWNWYN 


Ss Sd CT OF OF He He 09 0 0 COR 
Ehrre' we igh Aor Monae Ver. re ge Aer ney fern es Tee 7 
MOOROUIOMDH OH OHKOOowcosA 


G2 Co G2 
BS 
bt S309 


6.2 


Sd D2 D> BD SS SH DD & 
SIRI Ss OF GFE WB Se 


Cd et 929 FWA 


WMH HO 
e DOO 


a} a APaT ATI 


MINED DD OVO se i CO 


OD OD AF AAFP Aa Faas --9 


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WAIDWDRORWOPROUHVWOROUMA 





Parallelogram of Velocities.—The principle of the composition 
and resoiution of forees may also be applied to velocities or to distances 
moved in given ntervals of time. Referring to Fig. 88, page 416, if a body 
at O has a force applied to it which acting alone would give it a velocity 
represented by OQ per second, and at the same time it is acted on by 


VELOCITY, ACCELERATION, FALLING BODIES, 427 


another force which acting alone woz! give it a velocity OP per second, 
the result of the two forces acting together for one second will carry it to 
R, OR being the diagona: of the parallelogram of OQ and OP, and the 
resultant velocity. If the two component velocities are uniform, the result- 
ant will be uniform and the line OR will be a straight line; but if either 
velocity is a varying one, the line will be a curve. Fig. 96 shows ths 
resultant velocities, also-the path traversed 
by a body acted on by two forces, one of 
which would carry it at a uniform velocity 
over the intervais 1, 2, 3, B, and the other of 
which would carry it by an accelerated mo- 
tion over the intervals a, b, c, Din the same 
times. At the end of the respective inter- 
vals the body will be found at C,, Co, Cs, C, 
aod the mean velocity during each interval 
is represented by the distances between 
these points. Such a curved path is trav- 
ersed by a shot, the impelling force from 
the gun ziving it a uniform velocity in the 
flirection the gun is aimed, and gravity giv- 
ing it an accelerated velocity downward, Fia. 96. 
The path cf a projectile is a parabola. The 
distance it will travel is greatest when its initial direction is at an angle 45° 
above the horizontal. 

Mass—Force of Acceleration.—The mass of a body, or the quantity 
of matter it contains, is a constant quantity, while the weight varies according 
to the variation in the force of gravity at different places. If g = the acceler- 





ation due to gravity, and w = weight, then the massm = a w=mg. Weight 


here means the resultant of the force of gravity on the particles of a body, 
such as may be measured by a spring-balance, or by the extension or 
deflection of a rod of metal loaded with the given weight. 

Force has been defined as that which causes, or tends to cause, or to 
destroy, motion. It may also be defined (Kennedy’s Mechanics of Ma- 
chinery) as the cause of acceleration; and the unit of force as the force 
required to produce unit acceleration in a unit of free mass. 

Force equals the product of the mass by the acceleration, or f = ma. 

Also, if v = the velocity acquired in the time t, ft = mv; f = mv-+- 7; the 
acceleration being uniform. 

The force required to produce an acceleration of g (that is, 32.16 ft. per 


sec.) in one second is f = mg = md =w,or the weight of the body. Also, 





f=oma= m2 r ne in which vg is the velocity at the end, and v, the 
velocity at the beginning of the time ¢, and f= mg = 4 Cea 7 


ee = ft or, the force required to give any acceleration to a body is to the 


weight of the body as that acceleration is to the acceleration produced by 
gravity. (The weight w is the weight where g is measured.) 

EXxAMPLE.—Tension in a cord lifting a weight. A weight of 100 Ibs. is 
lifted vertically by a cord a distance of 80 feet in 4 seconds, the velocity 
uniformly increasing from 0 to the end of the time. What tension must be 
maintained in the cord? Mean velocity = v9 = 20 ft. per sec.; final es ipa 

pegic lig a0 We we _wva_ i) 

=Vq = 2V9= 40; accele”ation a = es 10. Force f= ma= a 32.16% 
10 = 31.1 Ibs. This is the force required to produce the acceleration only; 
to it must be added the force required to lift the weight without accelera- 
tion, or 100 lbs., making a total of 131.1 lbs. 

The Resistance to moe s the same as the force required to pro- 
Vg—V 

t Ls 


Formule for Accelerated Motion.—For cases of uniformly 
accelerated motion other than those of falling bodies, we have the formuls 


already given, f = aa = 3 = If the body starts from rest, vy = Q, Ug 


F w 
duce the acceleration = ; 


428 MECHANICS. 


= v,and f= bas gt= wv. We also haves = = Transforming and sul 
stituting for g its value 82.16, we obtain 


Je WER ONE AUD oY  eatea a wpe et _ 64.32fs , 
5 64.828 0 -<B2,16£. 0 16,0819)" Prawn tte ile, aa Rae 


_ wet 16.08/17 ot, ig og  /F8 x RO, 
5 Cay pa ot eure Bat v= a0 4/E w 





2 y,2 
For any change in velocity f = w( ee ). 
(See also Work of Acceleration, under Work.) ida 


Motion on Inclined Pianes.—The velocity acquired by a body 
descending an inclined plane by the force of gravity (friction neglected) is 
equal to that acquired by a body falling freely from the height of the plane. 

The times of descent down different inclined planes of the same height 
vary as the length of the planes. 

The rules for uniformly accelerated motion apply to inclined planes. If a 
is the angle of the plane with the horizontal, sin @ = the ratio of the height 


to the length = ia and the constant accelerating force is g sina. The final 


velocity at the end of ¢ seconds is v= gi sina. The distance passed over in 
Z seconds is? = 14 gt? sin a. The time of descent is 


Pics phy Alcs Olek Lee 
i) gsina 4.01 Vi. 


MOMENTUM, VIS-VIVA. 


Wiomentum (often erroneously defined as the quantity of motion ina 
body) is the product of the mass by the velocity at any instant = mv= ee 

Since the moving force = product of mass by acceleration, f = ma; and if 

MV 
eee jt = mv;3- that is, 
the product of a constant force into the time in which it acts equals numer 
ically the momentum. 

Since ft = mv, if t= 1 second mv = f, whence momentum might be de- 
fined as numerically equivalent to the number of pounds of force that will 
stop a moving body in 1 second, or the number of pounds of force which 
acting during 1 second will give it the given velocity. 

Vis-viva, or living force, is a term used by early writers on Mechanics 
to denote the energy stored in a moving body. Some defined it as the pro- 


the velocity acquired in ¢ seconds = v, or a = > T= 


duct of the mass into the square of the velocity, mv?, = rts others as one 


half of this quantity or }gmv?, or the same as what is now known as energy. 
The term is now practically obsolete, its place being taken by the word 
energy. 


WORK, ENERGY, POWER. 


Work is the overcoming of resistance through a certain distance. It is 
measured by the product. of the resistance into the space through which it 
is overcome. It is also measured by the product of the moving force into 
the distance through which the force acts in overcoming the resistance. 
Thus in lifting a body from the earth against the attraction of gravity, the 
resistance is the weight of the body, and the product of this weight into the 
height the body is lifted is the work done. 

The Unit of Work, in British measures, is the fcot-pound, or the 
amount of work done in Overcoming a pressure or weight equal to one 
pound through one foot of space. 


WORK, ENERGY, POWER. 425 


The work performed by a piston fn driving a fluid before ft, or by a fluid 
fn driving a piston before it, may be expressed in either of the following 
ways: 

Resistance X distance traversed 
= intensity of pressure X area X distance traversed 3 
= intensity of pressure X volume traversed. 


The work performed in lifting a body is the product of the weight of the 
body into the height through which its centre of gravity is lifted. 

it a machine lifts the centres of gravity of several bodies at once to heights 
either the same or different, the whole quantity of work performed in so 
joing is the sum oz the several products of the weights and heights ; but 
that quantity can also be computed by multiplying the sum of all the 
weights into the height through which their common certre of gravity is 
lifted. (Rankine.) 

Povwver is the rate at which work is done, and is expressed by the quo- 
tient of the work divided by the time in which it is done, or by units of work 
per second, per minute, etc., as foot-pounds per second. The most common 
unit of power is the horse-power, established by James Watt as the power of 
a strong London draught-horse to do work during a short interval, and used 
by him to measure the power of his steam-engines. This unit is 33,000 foot- 
Eeane. per minute = 550 foot-pounds per second = 1,980,000 foot-pounds per 

our. 


Expressions for Force, Work, Power, etc. 


The fundamental conceptions in Dynamics are: 

Mass, Force, Time, Space, represented by the letters M, F, T, S. 

Wiass = weight +g. If the weight of a body is determined by a spring 
balance standardized at London it will vary with the latitude, and the value 
of g to be taken in order to find the mass is that of the latitude where the 
weighing is done. If the weight is determined by a balance or by a plat- 
form seale, as is customary in engineering and in commerce, the London 
value of g. — 32.2, is to be taken. 

Welocity = space divided by time, V = S + 7, if V be uniform. 

W) ork = force multiplied by space = FS=144MV2 = FVT. (V uniform.) 

Power = rate of work = work divided by time = #S + T = P= prod- 
uct of force into velocity = FV. 

Power exerted for a certain time produces work; PT = FS = FVT. 

effort is a force which acts on a body in the direction of its motion. 

Resistance is that which is opposed to a moving force. It is eqnal and 

Op»osite to force, 
. Horse-power Hours, an expression for work measured as the 
product of a power into the time during which it acts = PT. Sometimes it 
is the summation of a variable power for a given time, or the average power 
multiplied by the time. 

Energy, or stored work, is the capacity for performing work. It is 
measured by the same unit as work, that is, in foot-pounds, It may be 
either potential, as in the case of a body cf water stored if_a reservoir, 
capable of doing work by means of ©, water-wheel, or actwal. sometimes 
called kinetic, which is the energy of a moving body. Potential energy is 
measured by the product of the weight of the stored body into the distance 
through which it is capable of acting, or by the product of the pressure it 
exerts into the distance through which that pressure is capable of acting. 
Potential energy may also exist as stored heat, or as stored chemical energy, 
as in fuel, gunpowder, etc., or as electrical energy, the measure of these 
energies being the amount of work that they are capable of performing. 
Actual energy of a moving body is tho work which it is capable of performing 
against a retarding resistance beforo being brought to rest, and is equal to 
the work which must be done upon if to brirg it from a state of rest to its 
actual velocity. 

The measure of actual energy is tho product of the weight of the body 
into the height from which it must fall to acquire its actual velocity. Ifv= 
the velocity in feet per second, according to the principle of falling bodies, 


2 
h, the height due to the velocity = om and if w = the weight, the energy = 


Yomv? = wv? + 29g = wh. Since energy is the capacity for performing 
work, the units of work and energy are equivalent, or £S = Jgmv3 = wh, 
Energy exerted = work done, 


A380 MECHANICS, 


The actual enerey of a rotating body whose angular velocity is A and 
moment of inertia Swr? = Ff is py that is, the product of the moment of 


inertia into the height due to the velocity, A, of a point whose distance from 
the axis of rotation is unity; or it is equal to sin in which wis the weight of 


the body and v is the velocity of the centre of gyration. 

Work of Acceleration. —The work done in giving acceleration to a 
body is equal to the product of the force producing the acceleration, or of 
the resistance to acceleration, into the distance moved in a giventime. This 
force, as already stated equals the product of the mass into the acceleration, 


or f= ma = - a, If the distance traversed in the time t= s, then 
‘work = fs = we Base Ny 


g t 

EXxAMpLe.—What work is required to move a body weighing 100 lbs. hori- 
zoutally a distance of 80 ft. in 4 seconds, the velocity uniformly increasing, 
friction neglected ? 

Mean velocity v9 = 20 ft. per second; final velocity = vg = 2vg = 40; initial 

: : Vg —; 40 w 

velocity v, = 0; acceleration, a = ———— = ri a 10; force = —a = 516 
40 = 81.1 lbs.3 distance 80 ft.; work = fs = 31.1 x 80 = 2488 foot-pounds. 

The energy stored inthe body moving at the final velocity of 40 ft. per 


second is ; Nite as 
w x 
Doe Sd as BU ee * 
mv? = 5 a" ede SETAC LF Ying 2488 foot-pounds, 


which equals the work of acceleration, 


If a body of the weight W falls from a height H, the work of acceleration 
is simply W4H, or the same as the work required to raise the body to the 
same height. 

Work of Accelerated Rotation.—Let 4 = angular velocity of a 
solid body rotating about an axis, that is, the velocity of a particle whose 
radius is unity. Then the velocity of a particle whose radius is risv = Ar, © 
If the angular velocity is accelerated from A, to Ag, the increase of the 
Aety, of the particle is vg — v; = 7(A, — Ag), and the work of accelerating 
it is 


9g Cay are 
in which w is the weight of the particle. 
The work of acceleration of the whole body is 


={2 Vo? — all toler aan 
9g ey Pine FRG 
The term wr? is the moment of inertia of the body. 

*¢ Force of the Blow » of a Steam Hammer or Other Fall 
ing Weight.—The question is often asked: ‘* With what force does a 
falling hammer strike ?’? The question cannot be answered directly, and 
it is based upon a misconception or ignorance of fundamental mechanical 
laws. The energy, or capacity of doing work, of a body raised to a given 
height and let fall cannot be expressed in pounds, simply, but only in foot- 
pounds, which is the product of the weight into the height through which 
it fails, or the product of its weight -- 64.32 into the square of the velocity, 
in feet per second, which it acquires after falling through the given height. 
If F = weight of the body, M its mass, g the acceleration due to gravity, 
S the height of fall, and v the velocity at the end of the fall, the energy in 
the body just before striking, is W'S = 14Mvy? = Wv? + 2g = Wv? + 64.32, 
which is the general equation of energy of a moving body. Just as the 
energy of the body is a product of a force into a distance, so the work it 
does when it strikes is not the manifestation of a force, which can be ex- 
pressed simply in pounds, but it is the overcoming of a resistance through 
a certain distance, which is expressed as the product of the average resist 


w Vy? — V,2 wr? Ao?—A,? 
_—— = ae a eas | | 


x Swr2. 


WORK, ENERGY, POWER. 431 


ance into the distance through which it is exerted. If a hammer weighing 
100 Ibs. falls 10 ft., its energy is 1000 foot-pounds, Before being brought to 
rest it must do 1000 foot-pounds of work against one or more resistances. 
These are of various kinds, such as that due to motion imparted to the body 
struck, penetration against friction, or against resistance to shearing or 
other deformation, and crushing and heating of both the falling body and the 
body struck. The distance through which these resisting forces act is gen- 
erally indeterminate, and therefore the average of the resisting forces, 
which themselves generally vary with the distance, is also indeterminate. 
Impact of Bodies.—If two inelastic bodies collide, they will move on 
together as one mass, with a common velocity. The momentum of the com- 
bined mass is equal to the sum of the momenta of the two bodies before im- 
pact. If m, and my are the masses of the two bodies and v, and vg their re- 
spective velocities before impact, and v their common velocity after impact, 
(my + Mg)V = MyVy + MQqVe, 
_ iV + MoV 
~ my +m, * 
: 0 : : 4 M,Vy—MqVq : 
If the bodies move in opposite directions v = ae sla or, the velocity 
] 2 
of two inelastic bodies after impact is equal to the algebraic sum of their 
momenta before impact, divided by the sum of their masses. 
If two inelastic bodies of equal momenta impinge directly upon one ane 
other from opposite directions they will be brought to rest. 
Impact of Inelastic Bodies Causesa oss of Energy, and 
this loss is equal to the sum of the energies due to the velocities lost and 
gained by the bodies, respectively. 


Lem 04? + Yemgt'g? — Yam, + ma)v? = 4m, (vy — Vv)? + Yemg(vg — v)?. 


In which v, — vis the velocity lost by m, and v — ve the velocity gained by mg. 
EHxample—Let m; = 10, mg = 8, vy = 12, Vy = 15. 
If the bodies collide they will come to rest, for v = ere are =e 


The energy loss is 
10 K 144-4 148 X 225 — 14418 X 0 = 141012 — 0)? + 148(15 — 0)? = 1620 ft. lbs, 

What becomes of the energy lost ? Ans. Itis used doing internal work 
on the bodies themselves, changing their shape and heating them. 

For imperfectly elastic bodies, let e = the elasticity, that is, the ratio 
which the force of restitution, or the internal force tending to restore the 
shape of a body after it has been compressed, bears to the force of compres- 
sion; and let m, and mg, be the masses, v, and v2 their velocities before im- 
pact, and v,/v,’ their velocities after impact: then 


_ MV, + MqVe = Mge(Vy — U2), 


v,’ = 
4 My, + Mg My+m, * 
1 M11 + MgVq Mm e(Uy — Ve) 
eae cp Py: eh M1 + N_ ° 
1 2 1 2 


If the bodies are perfectly elastic, their relative velocities before and after 
impact are the same. That is: v4’ — v9’ = Ve — Uy. 

In the impact of bodies, the sum of their momenta after impact is the 
same as the sum of their momenta before impact. 


MyVy" + MgVoq! = MyzVz + MgqVo. 


For demonstration of these and other laws of impact, see Smith’s Me- 
chanics; also, Weisbach’s Mechanics. 
Energy of Recoil of Guns,.—(fng’g, Jan. 25, 1884, p. 72.) 
Let W = the weight of the gun and carriage; 
V = the maximum velocity of recoil; 
w = the weight of the projectile; 
” = the muzzle velocity of the projectile. 


Then, since the momentum of the gun and carriage is equal to the momen: 
tum of the projectile, we have WV = wv, or V= wu + W. 


* The statement by Prof. We D. Marks, in Nystrom’s Mechanics, 20th edi- 
tion, p. 454, that this formula is in error is itself erroneous, 


f 





432 MECHANICS. 


Taking the case of a 10-inch gun firing a 400-lb. projectile with a muzzle 
velocity of 1400 feet per second, the weight of the gun and carriage being 22 
tons = 49,280 lbs., we find the velocity of recoil = 


1400 x 400 
aed 49,280 


Now the energy of a body in motion is WV? + 2g. 


49,280 x 112 
2 X 82.2 


400 x 14002 bs P 
“2x32 7 12,173,913 foot-pounds, 


Conservation of Emergy.—No form of energy can ever be pro. 
duced except by the expenditure of some other form, nor annihilated ex- 
cept by being reproduced in another form. Consequently the sum total of 
energy in the universe, like the sum total of matter, must always remain 
the same. (S. Newcomb.) Energy can never be destroyed or lost; it can 
be transformed, can be transferred from one body to another, but no 
matter what transformations are undergone, when the total effects of the 
exertion of a given amount of energy are summed up the result will be 
exactly equal to the amount originally expended from the source. This law 
is called the Conservation of Energy. (Cotterill and Slade.) 

A heavy body sustained at an elevated position has potential energy. 
When it falls, just before it reaches the earth’s surface it has actual or 
kinetic energy, due to its velocity. When it strikes it may penetrate the 
earth a certain distance or may be crushed. In either case friction results 
by which the energy is converted into heat, which is gradually radiated 
into the earth or into the atmosphere, or both. Mechanical energy and heat 
are mutually convertible. Electric energy is also convertible into heat or 
oe energy, and either kind of energy may be converted into the 
other. 

Sources of Energy.—tThe principal sources of energy on the earth’s 
surface are the muscular energy of men and animals, the energy of the 
wind, of flowing water, and of fuel. These sources derive their energy 
from the rays of the sun. Under the influence of the sun’s rays vegetation 
grows and wood is formed. The wood may be used as fuel under a steam 
boiler, its carbon being burned to carbonic acid. Three tenths of its heat 
energy escapes in the chimney and by radiation, and seven tenths appears 
as potential energy in the steam. In the steam-engine, of this seven tenths 
six parts are dissipated in heating the condensing water and are wasted; 
the remaining one tenth of the original heat energy of the wood is con- 
verted into mechanical work in the steam-engine, which may be used to 
drive machinery. This work is finally, by friction of various kinds, or pos- 
sibly after transformation into electric currents, transformed into heat, 
which is radiated into the atmosphere, increasing its temperature. Thus 
all the potential heat energy of the wood is, after various transformations, 
converted into heat, which, mingling with the store of heat in the atmos- 
phere, apparently is lost. But the carbonic acid generated by the combus- 
tion of the wood is, again, under the influence of the sun’s rays, absorbed 
by vegetation, and more wood may thus be formed having potential energy 
equal to the original. 

Perpetual Motiom.—The law of the conservation of energy, than 
which no law of mechanics is more firmly established, is an absolute barrier 
to all schemes for obtaining by mechanical means whatis called ‘‘ perpetual 
motion,’’ or a machine which will do an amount of work greater than the 
equivalent of the energy, whether of heat, of chemical combination, of elec- 
tricity, or mechanical energy, that is put into it. Such a result would be 
the creation of an additional store of energy in the universe, which is not 
possible by any human agency. 

he Efficiency of a Machine is a fraction expressing the ratio of 
the useful work to the whole work performed, which is equal to the energy 
expended. The limit to the efficiency of a machine is unity, denoting the 
efficiency of a perfect machine in which no work is lost. The difference 
between the energy expended and the useful work done, or the loss, is 
usually expended either in overcoming friction or in doing work on bodies 
surrounding the machine from which no useful work is received. Thus in 
an engine propelling a vessel part of the energy exerted in the cylinder 


= 11 feet per second. 


Therefore the energy of recoil = = 92,593 foot-pounds. 


The energy of the projectile is 


ANIMAL POWER. 433 


does the useful work of giving motion to the vessel, and the remainder is 
spent in overcoming the friction of the machinery and in making currents 
and eddies in the surrounding water. 


ANIMAL POWER. 
Work of a Man against Known Resistances, (Rankine.) 





7 
V, | 3600 | RV, | RVT, 
Kind of Exertion. ie ft. per |(hours| ft.-lbs. | ft.-Ibs. 
7 sec. per |per sec.} per day, 
day). 


en fe fe 





1. Raising his own weight up 

stair or ladder 2.035.004. 143 0.5 8 | %2.5 | 2,088,000 
2. Hauling up weights with rope, 

and lowering the rope un- 


IOSHOORS AT hd Jiisee ge sw dd.< 40 0.75 6 30 648,000 
8. Lifting weights by hand......] 44. 0.55 6 24.2 522,720 
4, Carrying weights up-stairs 
and returning unloaded....| 143 - | 0.13 6 18.5 399,600 
5. Shovelling up earth to a 
height of 5 ft. 3in.......... 6 1.3 10 7.8 280,800 
6. Wheeling earth in barrow up 
slope of 1 in 12, \% horiz. 
veloc. 0.9 ft. per sec. and re- 
turning unloaded....... ... 132 0.075 10 9.9 356,400 
%, Pushing or pulling horizon- 
tally (capstan or oar)....... 26.5] 2.0 8 | 53 1,526,400 
( 12.5 | 5.0 ? 62.5%]! aiuee.. gh 
8. Turning a crank or winch ...}~ 18.0] 2.5 8 45 1,296,000 
1 20:0] 14.4 |emin| 28g | 
9. Working pump.. ....... .... 13.2] 2.5 10 33 1,188,000 
AOMVAMMELIN Gees ces sieicieete sete 15 ? 8? ? 480,000 





EXPLANATION.—R, resistance; V, effective velocity = distance through 
which R is overcome ~ total time occupied, including the time of moving 
unloaded, if any; 7”’, time of working, in seconds per day; 7” -~- 3600, same 
time, in hours per day; RV, effective power, in foot-pounds per second; 
RVT, daily work. 


Performance of a Man in Transportin 
Horizontally. (Risiitine:) & mo ege 


T, 


oToka nn 
3600 | Ibs. ee 

9 * = fos 
Ibs. | ft.-sec. ( ei revert veyed 


day). | 1 foot. 1 foot. 


— | | 


Kind of Exertion. 





11. Walking untoaded,transport- 

ing his own weight........] 140 5 10 700 | 25,200,000 
12, Wheeling load Z in 2-whld. 

barrow, return unloaded..| 224 1% 10 373 | 13,428,000 
13. Ditto in 1-wh. barrow, ditto..| 182 1% 10 220 7,920,000 


14. Travelling with burden...... 90 2144 vg 225 5,670,000 
15. Carrying burden, returning 
nntoaded 2) ..ui3.3aecceeek ae 1% 6 ape 6,032,800 
: 2 0 RCE te ol) Teaches ane 
16. Carrying burden, for 30 sec- oss 
onlisonly ....1102 Jeane 1 A ei ears Wie cha rors 








ExXpPLANATION.—L, load; V, effective velocity, computed as before; 7’, 


time of working, in seconds per day; 7’ + 3600, same time in hours per day; 
LY, transport per second, in lbs. conveyed one foot; LVT, daily transport. 








434 MECHANICS. 


In the first line o..g of each of the two tables above is the weight of the 
man taken into account in computing the work done. 

Clark says that the average net daily work of an ordinary laborer at a 
pump, a winch, or a crane may be 
taken at 3300 foot-pounds per minute, 
or one-tenth of a horse-power, for 8 
hours a day; but for shorter periods 
from four to five times this rate may 
be exerted. 

Mr. Glynn says that a man may 
exert a force of 25 lbs. at the handle 
of a crane for short periods; but that 
for continuous work a force of 15 lbs. 
is all that should be assumed, moving 
through 220 feet per minute, 

WMian-w heel.—Fig. 97 isa sketch 
of a very efficient man-power hoist- 
ing-machine which the author saw in 
Berne, Switzerland, in 1889. The face 
of the wheel was wide enough for 
three men to walk abreast, so that 








¥Fia. 97. nine men could work in it at one time. 
Work ofa Horse against a Known Resistance, (Rankine.) 
| : 
: i KA. 
7 pS mee 
Kind of ee R. Ve 3600 RV. RVI, 





1. Cantering and trotting. draw- min, 22% ) 
ing a light railway carriage|< mean 3014} -1424] 4 44714) 6,444,000 
(thoroughbred)......... .. max. 50 ( 

2. Horse drawing cart or boat, 


walking (draught-horse).... 120 SOc eee 432 |12,441,600 
8. Horse drawing a gin or mill, 

Bi LT el Ae aaa has ais 100 3.0] 8 300 8,640,000 
4s Ditto, Erotting cms, she. 66 6.5 | 414 | 429 6,950,000 


EXPLANATION.—R, resistance, in Ibs.; V, velocity, in feet per second; 7” 
-+ 3600, hours work per day; RV, work per second; RVT, work per day. 

The average power of a draught-horse, as given in line 2of the above table, 
being 432 foot-pounds per second, is 432/550 = 0.785 of the conventional value 
assigned by Watt to the ordinary unit of the rate of work of prime movers. 
It is the mean of several results of experiments, and may be considered the ' 
average of ordinary performance under favorable circumstances. 


Performance of a Horse in Transporting Loads 
Horizontally. (Rankine.) 





Kind of Exertion. L. ee gu LV. LVT. 





5. Walking with cart, always 


loaded...... .| 1500 3.6 10 5400 | 194,400,600 
6. Trotting? ditto. 0)........ 450 7.2 414 | 5400 87,480,000 
%, Walking with cart, going load- 

ed, returning empty; V, 

mean velocity....... Seer 1500 2.0 10 8000 | 108,000,000 
8. Carrying burden, walking.... 270 8.6 10 972 84,992,000 
9: Ditto, trotting’..07.2ee. 32-62: 180 tae vg 1296 32,659,200 





EXpLANATION.—Z, load in lbs.; V, velocity in feet per second; T + 3600, 
working hours per day; LV, transport per second; LVT, transport per day. 

This table has reference to conveyance on common roads only, and those 
evidently in bad order as respects the resistance to traction upon them. 

HWiorse Gin.—In this machine a horse works less advantageously 
than in drawing a carriage along a straight track, In order that the best 


ELEMENTS OF MACHINES, 435 


possible results may be realized with a horse-gin, the diameter of the cir. 
suet track in which the horse walks should not be less than about forty 
eet. 

Oxen, Mules, Asses,—Authorities differ considerably as to the power 
of these animals. The following may be taken as an approximative com- 
parison between them and draught-horses (Rankine): 

Ox,—Load. the same as that of average draught-horse; best velocity and 
work, two thirds of horse. 

Mule,—Load, one half of that of average draught-horse; best velocity, 
the same with horse; work one half. 

Ass,—Load, one quarter that of average draught-horse; best velocity the 
same; work one quarter. 

Reduction of Draught of Horses by Increase of Grade 
of Roads, (nyineering Record, Prize Essays on Roads, 1892,.)—Experi- 
ments on English roads by Gayffier & Parnell: 

Cailing load that can be drawn on a level 100: 


On arise of. ......... 1 in 100. 1 in 50. 1 in 40. 1 in 30, 1 in 26. 1 in 20. 1 in 10. 
A horse can draw only 90. 81. 92, 64. 54. 40. 25. 


The Hesistance of Carriages on Roads is (according to Gen. 
Morin) given approximately by the following empirical formula; 


re 7 ta + b(u — 3.28)]. 


In this formula R = total resistance; r = radius of wheel in inches; W = 
gross load; w= velocity in feet per second; while a@ and b are constants, 
whose values are: For good broken-stone road, a = .4 to .55, b = .024 to .026; 
for paved roads, a = .27, b = .0684. 

Rankine states that on grayel the resistance is about double, and on 
sand five times, the resistance on good broken-stone roads. 


ELEMENTS OF MACHINES, 


The object of a machine is usually to transform the work or mechanical 
energy exerted at the point where the machine receives its motion into 
work at the point where the finai resistance 
is overcome. The specific end may be to A Cc B 
change the character or direction of mo- 
tion, as from circular to rectilinear, or vice 
versa, to change the velocity, or to overcome 
a@ great resistance by the application of a 
moderate force. In all cases the total energy 
exerted equals the total work done, the latter 
including the overcoming of all the frictional Fia. 98. 
resistaices of the machine as well as the use- 
ful work performed. No increase of power 
ean be obtained from any machine, since this 
is impossible according to the law of conser- 
vation of energy. In a frictionless machine the 
product of the force exerted at the driving- 
point into the velocity of the driving-point, 
or the distance it moves in a given interval 
of time, equals the product of the resistance 
into the distance through whieh the resist- 
ance is overcome in the same time. $ 

The most simple machines, or elementary 
machines, are reducible to three classes, viz., 
the Lever, the Cord, and the Inclined Plane. 

The first class includes every machine con- 
sisting of a solid body capable of revolving 
on an axis, as the Wheel and Axle. 

The second class includes every machine in 
which foree is transmitted by means of flexi- 
ble threads, ropes, etc., as the Pulley. 

The third class includes every machine in Fia. 100. 
which a hard surface inclined to the direc- nae 
tion of motion is introduced, as the Wedge and the Screw. 

A Lever is an inflexible rod capable of motion about a fixed point, 
ealled a fulcrum. The rod may be straight or bent at any angle, or curved. 

It is generally regarded, at first, as without weight, but its weight may be 








436 — MECHANICS, 


considered as another force applied in a vertical direction at its centre of 
gravity. 

The arms of a lever are the portions of it intercepted between the force, 
P, and fulcrum, C, and between the weight, W, and fulcrum. 

Levers are divided into three kinds or orders, according to the relative 
positions of the applied force, weight, and fulcrum. 

In a lever of the first order, the fulcrum lies between the points at which 
the force and weight act. (Fig. 98.) 

In a lever of the second order, the weight acts at a point between the 
fulcrum and the point of action of the force. (Fig. 99.) 

In a lever of the third order, the point of action of the force is between 
that of the weight and the fulcrum. (Fig. 100.) 

In all cases of levers the relation between the force exerted or the pull, 
P, and the weight lifted, or resistance overcome, W, is expressed by the 
equation P X AC = W X BC, in which AC is the lever-arm of P, and BC 
is the lever-arm of W, or moment of the force = the moment of the resist- 
ance. (See Moment.) 

In cases in which the direction of the force (or of the resistance) is not at 

right angles to the arm of the lever on which it acts, the ‘ lever-arm”’ is the 
length of a perpendicular from the fulcrum to the line of direction of the 
force (or of the resistance). W: P:: AC: BC, or, the ratio of theresistance to 
the applied force is the inverse ratio of their lever-arms. Also, if Vw is the 
velocity af W, and Vp is the velocity of P,W:P:: Vp : Vw,and PxXVp 
= x Vw. 
If Sp is the distance through which the applied force acts, and Sw is the 
distance the weight is lifted or through which the resistance is overcome, 
W:P:: Sp: Sw; W X Sw= PX Sp, or the weight into the distance it is lifted 
equals the force into the distance through which it is exerted. 

These equations are general for all classes of machines as well as for 
levers, it being understood that friction, which in actual machines increases 
the resistance, is not at present considered. 

Whe Bent Lever.—In the bent lever (see Fig. 91, page 416) the lever- 
arm of the weight m is cf instead of bf. The lever is in equilibrium when 
n xX af=m xX cf, but it is to be observed that the action of a bent lever may 
be very different from that of a straight lever. In the latter, so long as the 
foree and the resistance act in lines parallel to each other, the ratio of the 
lever-arms remains constant, although the lever itself changes its inclina- 
tion with the horizontal. In the bent lever, he-wever, this ratio changes: 
thus, in the cut, if the arm bf is depressed to a horizontal direction, the dis- 
tance cf lengthens while the horizontal projection of af shortens, the latter 
becoming zero when the direction of af becomes vertical. As the arm af 
approaches the vertical, the weight m which may be lifted with a given 
force s is very great, but the distance through which it may be lifted is 
very small. In all cases the ratio of the weight m to the weight 7 is the in-: 
verse ratio of the horizontal projection of their respective lever-arms. 

Whe Moving Strut (Fig. 101) is similar to the bent lever, except that 
one of the arms is missing, and that the force and the resistance to be 

overcome act at the same end of the 

single arm. The resistance in the 

PI zase shown in the cut is not the 

weight W, but its resistance to 

being moved, R, which may be sim- 

ply that due to its friction on the 

horizontal plane, or some other op- 

posing force. When the angle be- 

tween the strut and the horizontal 

plane changes, the ratio of the 

resistance to the applied force 

changes. When the angle becomes 

very small, a moderate force will 

Fia. 101. overcome a very great resistance, 

which tends to become infinite as 

the angle approaches zero. If a = the angle, P X cosa=R X sina. If 
a = 5 degrees, cos a = .99619, sin a = .08716, R = 11.44 P. 

The stone-crusher (Fig. 102) shows a practical example of the use of two 
moving struts. 

The Toggle-joint is an elbow or knee-joint consisting of two bars so 
connected that they may be brought into a straight line and made to pro- 
duce great endwise pressure when a force is applied to bring them into thiy 





ELEMENTS OF MACHINES, 437 


position. It is a case of two moving struts placed end to end, the moving 
force being applied at their point of junction, in a direction at right angles 
to the direction of the resistance, the other end of one of the struts resting 
against a fixed abutment, and that of the other against the body to be 
moved. If a = the angle each strut makes with the straight line joining the 
points about which their_outer ends rotate, the ratio of the resistance 
to the applied force is R: P::cosa:2sina; 2Rsina= Peosa. The 


to 
L( 


E> 
Th 
rp 





Fie. 102. Fie. 103. 


ratio varies when the angle varies, becoming infinite when the angle 
becomes zero. 

The toggle-joint is used where great resistances are to be overcome 
through very small distances, as in stone-crushers (Fig. 103). 

Whe Inclimed Plane, as a mechanical element, is supposed perfectly 
fiard and smooth, unless friction be considered. It assists in sustaining a 
heavy body by its reaction. This reaction, however, being normal to the 
plane, cannot entirely counteract the weight of the body, which acts verti- 
rally downward Some other force must therefore 
be made to act upon the body, in order that it may P' 
be sustained, ©) 

If the sustaining force act parallel to the plane 
(Fig. 104). the force is to the weight as the height of 
the plane is to its length, measured on the incline, 

If the force act parallel to the base of the plane, 
ae power is to the weight as the height is to the 

ase. 

If the force act at any other angle, let i = the Cc 
angle of the plane with the horizon, and e = the Fia. 104, 
angle of the direction of the applied force with the 
angle of the plane. P: W :: sini: cose; PX cose = W sin i. 

Problems of the inclined plane may be solved by the parallelogram of 
forces thus: 

Let the weight W be kept at rest on the incline by the force P, acting in 
the line bP’, parallel to the plane. Draw the vertical line ba to represent 
the weight ; also bb’ perpendicular to the plane, and complete the parallelo- 
gram b’c. Then the vertical weight ba is the resultant of bb’, the measure of 
support given by the plane to the weight, and bc, the force of gravity tend- 
ing to draw the weight down the plane. The force required to maintain 
the weight in equilikrinm is represented by this force bc. Thus the force 
and the weight are in the ratio of bc to ba. Since the triangle of forces abe 
is similar to the triangle of the incline ABC, the latter may be substituted 
for the former in determining the relative magnitude of the forces, and 


Pot Wire SsOUCRL ODE EE On. eA: 





Whe Wedge is a pair of inclined planes united by their bases. In the 
application of pressure to the head or butt end of the wedge. to cause it to 
penetrate a resisting body, the applied force is to the resistance as the 
thickness of the wedge is toits length. Let tbe the thickness, J the length, 
W the resistance, and P the applied force or pressure on the head of the 


wedge, Then, friction neglected, P: W::t:l; P= eee W= ee 


@The Serew isan inclined plane wrapped around a cylinder in such a 
way that the height of the plane is parallel to the axis of the cylinder If 
the screw is formed upon the internal surface of a hollow cylinder, it is 
usually called a nut. When force is applied to raise a weight or overcome 
a resistance by means of a screw and nut, either the screw or the nut may 


438 MECHANICS, 


be fixed, the other being movable. The force is generally applied at the end 
of a wrench or lever-arm, or at the circumference of a wheel. If 7 = radius 
of the wheel or lever-arm, and p = pitch of the screw, or distance between 
threads, that is, the height of the inclined plane 
for one revolution of the screw, P = the applied 
force, and W= the resistance overcome, then, neg- 
lecting resistance due to friction, 277 kX P= Wp; 
W = 6.283Pr+p. The ratio of Pto Wis thus 
independent of the diameter of the screw. In 
actual screws, much of the power transmitted is 
lost through friction. 


The Cam is a revolv- 

ing inclined plane. It may 

be either an inclined plane 
Tea — wrapped around a cylin- 
der in such a way that the 

height of the plane is ra- 

dial to the cylinder, such 


Fia. 105. as the ordinary lifting- Fie. 106. 
cam, used in stamp-mills 
(Fig. 105), or it may be an inclined plane curved edgew’se, ard rotating in a 
plane parallel to its base (Fig. 106). The relation of the weight to the applied 
force is calculated in the same manner as in the case of the screw. 





Di 





A.) 


Fie. 107. 


Pulleys or Blocks.—P = force applied, or pull; W = weight lifted 
or resistance. In the simple pulley A (Fig. 107) the point Pon the pulling 
rope descends the same amount that the weight is lifted, therefore P = W. 
In B and C the point P moves twice as far as the weight is lifted, there- 
fore W = 2P, In B and C there is one movable block, and two plies of the - 
rope engage with it. In Dthere are three sheaves in the movable block, 
- each with two plies engaged, or six inall. Six plies of the rope are there- 
fore shortened by the same amount that the weight is lifted, and the point 
P moves six times as far as the weight, consequently W = 6P. In general, 
the ratio of W to P is equal to the number of plies of the rope that are 
shortened, and also is equal to the number of plies that engage the lower 
block. If the lower block has 2 sheaves and the upper 8, the end of the rope 
is fastened to a hook in the top of the lower block, and then there are 5 
plies shortened instead of 6,and W=5P. If V = velocity of W. and v = 
velocity of P, then in all cases VW = vP, whatever the number of sheaves 
or their arrangement. If the hauling rope, at the pulling end, passés first 
around a sheave in the upper or stationary block, it makes no difference in 
what direction the rope is led from this block to the point at which the pull 
on the rope is applied ; but if it first passes around the movable block, it is 
necessary that the pull be exerted in a direction parallel to the line of action 
of the resistance, or a line joining the centres of the two blocks, in order to 
obtain the maximum effect. If the rope pulls on the lower block at an 
angle, the block will be pulled out of the line drawn between the weight 
and the upper block, and the effective pull will be less than the actual pull 


Fi 


ELEMENTS OF MACHINES, 439 


on the rope in the ratio of the cosine of the angle the pulling rope makes 
with the vertical, or line of action of the resistance, to unity. 

Differential Pulley. (Fig. 108.)—Two pulleys, Band C, of different 
radii, rotate as one piece about a fixed axis, A. An end- 
less chain, BDECLKH, passes over both pulleys. The 
rims of the pulleys are shaped so as to hold the chain and 
prevent it from slipping. One of the bights or loops in pg 
which the chain hangs, DH, passes under and supports the 
running block #. The other loop or bight, HKL, hangs 
freely, and is called the hauling part. It is evident that 
the velocity of the hauling part is equal to that of the 
pitch-circle of the pulley B. 

In order that the velocity-ratio may be exactly uniform, 
the radius of the sheave # should be an exact mean be- 
tween the radii of Band C. 

Consider that the point B of the cord BD moves through 
an are whose length = AB, during the same time the 
point C or the cord CE will move downward a distance = 
AC. The length of the bight or loop BDEC will be 
shortened by 4B — AC, which will cause the pulley # to 
be raised half of thisamount. If P = the pulling force on { 
the cord HK, and W the weight lifted at #, then PX \ 

' 
t 
AY 
A 





AB =W X (AB = AC). 

To calculatethe length of chain required for a differential 
pulley, take the foliowing sum: Half the circumference of 
A + half the circumference of B + half the circumference 


U 


\ ! 
of F' + twice the greatest distance of # from A + the Ya" 
least length of loop HKD. The last quantity is fixed Guat 
according to convenience, Fia. 108. 


The Differential Windlass (Fig. 109) is identical in principle 
with the differential pulley, the difference in con- 
struction being that in the differential windlass the 
running block hangs in the bight of a rope whose two 
parts are wound round, and have their ends respec- 
tively made fast to two barrels of different radii, 
which rotate as one piece about the axis A. The dif- 
ferential windlass is little used in practice, because 
of the great length of rope which it requires. 

The Differential Screw (Fig. 110) is a come 
pound screw of different pitches, in which the 
threads wind the same way. NN, and N, are the two 
nuts; S,S,, the longer-pitched thread; S,S.g, the 
shorter-pitched thread: in the figure both these 
threads are left-handed. At each turn of the screw 
the nut Ne. advances relatively to N2 through a dis- 

Fia. 109. tance equal to the difference of the pitch. The use 

of the differential screw is to combine the slowness 

of advance due to a fine pitch with the strength of thread which can be 
obtained by means of a coarse pitch only. 

A Wheel and Axle, or Windlass, resembles two pulieys on one axis, 
having different diameters. Ifa weight be lifted by means of a rope wound 
over the axle, the force being applied at the 
rim of the wheel, the action is like that of a 
Sever of which the shorter arm is equal to 
the radius of the axle plus half the thick- 
ness of the rope, and the longer arm is 
ecual to the radius of the wheel. A wheel Fic. 110 
and axle is therefore sometimes classed nat . 
as a perpetual lever. If P= the applied force, D = diameter of the wheel, 
W = the weight lifted, and d the diameter of the axle + the diameter of 
the rope, PD = Wd. 

VToothed=-wheel Gearing is a combination of two or more wheels 
and axles (Fig. 111). If aseries of wheels and pinions gear into each other, 
as in the cut, friction neglected, the weight lifted, or resistance over- 
come, is to the force applied inversely as the distances through which 
they act inagiven time. If R, R,, R, be the radii of the successive wheels, 
measured to the pitch-line of the teeth, and 7,71, 7, the radii of the cores 
responding pinions, Pthe applied force, and W the weight lifted, P x 








440 MECHANICS, 


RXR, Xk,=WxXrxX7, X re, or the applied force is to the weight 
as the product of the radii of the pinions is to the product of the radii of 
the wheels; or, as the product of the numbers expressing the teeth in 
Fate pinion is to the product of the numbers expressing the teeth in each 
wneel. 

Endless Screw, or Wormegear, (Fig. 112.)—This gear is com- 
monly used to convert motion at high speed into motion at very slow 





Fie. 111, ‘E1G. 112. 


speed. When the handle P describes a complete circumference, the -pitch- 
line of the cog-wheel moves through a distance equal to the pitch of the 
screw, and the weight W is lifted a distance equal to the pitch of the screw 
multiplied by the ratio of the diameter of the axle to the diameter of the 
pitch-circle of the wheel. The ratio of the applied force to the weight 
lifted is inversely as their velocities, friction not being considered; but the 
friction in the worm-gear is usually very great, amounting sometimes to 
three or four times the useful work done. 

If v = the distance through which the force Pacts in a given time, say 1 
second, and V = distance the weight W is lifted in the same time, r= 
radius of the crank or wheel through which P acts, t = pitchof the screw, 
and also of the teeth on the cog-wheel, d = diameter of the axle, 

9 
and D = diameter of the pitch-ime of the cog-wheel, v = ara 


XV; V=v xX td + 6.2838rd. Pv = WV + friction 


STRESSES IN FRAMED STRUCTURES. 


Framed structures in general consist of one or more triangles, for the 
reason that the triangle is the one polygonal form whose shape cannot be 
changed without distorting one of its sides. Problems in stresses of simple 
framed structures may generally be solved either by the application of the 
triangle, paralellogram, or polygon of forces, by the principle of the lever, 
or by the method of moments. We shall give a few examples, referring the 
student to the works of Burr, Dubois, Johnson, and others for more elabo- 
rate treatment of the subject. ' 

1. A Simple Crane, (Figs. 113 and 114.)—A isa fixed mast, Ba brace or 
boom, 7'a tie,and Pthe load. Required the strainsin Band T. The weight 
P, considered as acting at the end of the boom, is held in equilibrium by 
three forces: first, gravity acting downwards; second, the tension in 7; and 
third, the thrust of B. Let the length of the line p represent the magnitude 
of the downward force exerted by the load, and draw a parallelogram with 
sides bt parallel, respectively, to B and 7, such that pis the diagonal of the 
parallelogram. -'Then b and ¢ are the components drawn to the same scale 
as p, p being the resultant. Then if the length p represents the load, t is 
the tension in the tie, and b is the compression in the brace, 

Or, more simply, 7, B, and that portion of the mast included between them 
or A’ may represent a triangle of forces, and the forces are proportional to 
the length of the sides of the triangle; that is, if the height of the triangle 4’ 
= theload,.then B = the compression in the brace, and 7’= the tension in the 


tie; or if P = the load in pounds, the tension in T= PX a and the com- 


STRESSES IN FRAMED STRUCTURES. 441 


pression in B = P X s . Also, if a = the angle the inclined member makes 
with the mast, the other member being horizontal, and the triangle being 
right-angled, then the length of the inclined member = height of the tri- 
angle X secant a, and the strain in the inclined member = P secant a. Also, 
the strain in the horizontal member = P tana. 

The solution by the triangle or parallelogram of forces, and the equations 
Tension in T= P X 7/A’, and Compression in B = P X B/A’, hold true even 
if the triangle is not right-angled, as in Fig. 115; but the trigonometrical rela- 





Fia. 113, Fre. 114, Fia. 115. 


tions above given do not hold, except in the case of a right-angled triangle. 
Tt is evident that as A’ decreases, the strain in both 7’ and B increases, tend- 
ing to become infinite as 4’ approaches zero. If the tie Tis not attached to 
the mast, but is extended to the ground, as shown in the dotted line, the 
tension in it remains the same. 

2. A Guyed Crane or Derrick, (Fig. 116.)—The strain in B is, as 
before, PX B/A’, A’ being that portion of the vertical included between B and 
, 7, wherever T'may be attached to A. If, however, the tie Tis attached toB 
beneath its extremity. there may be in addition a bending strain in B due to 
a tendency to turn about the point of attachment of Tas a fulcrum. 

The strain in T may be calculated by the principle of moments. The mo- 
ment of P is Pc, that is, its weight x its perpendicular distance from the 
point of rotation of Bon the mast. The moment of the strain on Tis the 
product of the strain into the perpendicular distance from the line of its 





\N 


Le Le a 22 ee ee 






Fic. 116. 


direction to the same point of rotation of B, or Td. The strain in T there- 
fore = Pe+d. As d decreases the strain on T increases, tending to infine 
ity as d approaches zero. 

The strain on the guy-rope is also calculated by the method of moments, 
The moment of the load about the bottom of the mast O is, as before, Pc. 
If the guy is horizontal the strain in itis F and its moment is Ff, and F= 
Pe-~-f. If it is inclined, the moment is the strain G x the perpendicular 
distance of the line of its direction from O, or Gg, and G = Pe-~+g. 

The guy-rope having the least strain is the horizontal] one #, and the straiz 


443 MECHANICS. 


in G = the strain in F’ x the sé. 
cant of the angle between #' and 
G. As Gis made more nearly 
vertical g decreases, and the 
strain increases, becoming infl- 
nite when g = 0. 


3. Shear-=poles with 
Guys. (Fig. 117.)—-First assume 
that the two masts act as one 
placed at BD, and the two guys 
as one at AB. Calculate the 
strain in BD and AB as in Fig. 
115. Multiply half the strain in 
BD (or AB) by the seeant of half 

Fie. 117%. the angle the two masis (er 
guys) make with each other to find the straia in each mast (or guy). 

Two Diagonal Braces and a Tie-rod. (Fig. 118.)—Suppose the braces 
are used to sustain a single load P. Compressive stress on AD=14PX AD+ 
AB;onCA=\4PX CA+ AB. Thisis true only if CB and BDare of equcl 
length. in which case 4 of P is supported by each abutment Cand DP. If 
they are unequal in length (Fig. 119), then, 
by the principle of the lever, find the re- 
actions of theabutments R, and Ry. If P 
is the load applied at the point B on the 
lever CD, the fulcrum being D, then R, X 
CD =8 x BP and Ry xX CD =P x BC; 
Ba bX BD CDs ka= PX BC = CD. 

The strain on AC = R, X AC+ AB, and 
on AD= R, X AD+ AB. 

The strain on the tie = R, X CB+ AB Fig. 118. 


= Ra x BD a ad AB. 

When CB=BD, R,=R,. Thestrain 
on CB and BD is the same, whether 
the braces are of equal length or 
not, and is equal tol4P x 4CD=+ AB. 

If the braces support a uniform load, 
as a pair of rafters, the strains caused 
by such a load are equivalent to that 
caused by one half of the load applied 
Fre. 119. at the centre. The horizontal thrust 
t of the braces against each other at the 
apex equals the tensile strain in the tie. 

King-post Truss or Bridge. (Fig. 120.)—If the load is distributed 
over the whole length of the truss, the effect is the same as if half the load 
were placed at the centre, the other half being carried by the abutments. Let 
P= one half the load on the truss, then 
tension in the vertical tie AB = P. Com- 
pression in each of the inclined braces = 
44P X AD-=AB._ Tension in the tie CD 
= PX BD~ AB. Horizontal thrust of 
inclined brace AD at D = the tension in 
the tie. If W= the total load on onetruss 
uniformly distributed, / = its length and 
d = its depth, then the tension on the hore 
izontal tie = ald Fie. 120, 

Inverted King-post Truss, (Fig. 121.)--If P =a load applied at 
B, ov one half of a uniformly disiributed load, then compression on AB = F 

(the floor-beam CD not being considered 














B = tohave any resistance toa slight bending). 
Tension on AC or AD = 4%P X AD ~+ AB, 
Gc D Compression on CD) = 1%P X BD + AB. 


Queen-post Truss. (Fig. 122.)—If 
uniformly loaded, and the queen-posts di- 
vide the length into three equal bays, the 


A : load may be considered to be divided inte 
Fic. 121 three equal parts, two parts of which, P, 
eer and Ps, are concentrated at the panel joints 


STRESSES IN FRAMED STRUCTURES. 443 


and the remainder is equally divided between the abutments and supported 
by them directly. The two parts P, and P, only are considered to affect 
the members of the truss. Strain in 
the vertical ties BH and CF each 
equals P, or Py. Strain on AB and 
CD each = P, X CD + CF. Strain 
‘on the tie AH or EF or ED=P, X 
FD-- CF. Thrust on BC = tension 


on EHF. 

For stability to resist heavy un- 
equal loads the queen-post truss 
should have diagonal braces from 
B to Fand from Cto £. 

Inverted Queen=post 
Truss, (Fig. 123.) — Compression 
on EB and FC each=P, or Py. 
Compression on AB or BC or CD = 
P, X AB+HB. Tension on AEF or 
Fi =P, X AH+EB. Tension on 
EHF = compression on BOC, For sta- 
! bility to resist unequal loads, ties 

F should be run from C to Z and from 
Fre. 123. BtoF. 

Burr Truss of Five Panels. (Fig. 124.)—Four fifths of the load may 

oe taken as concentrated at the points H, K, L and F, the other fifth being 


B G H Cc 








Fia. 124. 


supported directly by the two abutments. For the strains in BA and CD 
the truss may be considered as a queen-post truss, with the loads P,, P, 
concentrated at H and the loads P,, P, concentrated at F, Then, compres- 
sive strainon AB=(P,+P,) X AB+BE. The strain on CDis the same if 
the loads and panel lengths are equal. The tensile strain on BE or CF = 
P,+P,. That portion of the truss between # and F’may be considered as 
a smaller queen-post truss, supporting the loads P,, P3 at K and L. The 
strain on EG or HF = P, X EG-+~-GK. The diagonals GL and KH receive no 
strain unless the truss is unequally loaded. The verticals GK and HZ each 
receive a tensile strain equal to P, or Ps. 

For the strain in the horizontal members: BG and CH receive a thrust 
equal to the horizontal component of the thrust in AB or CD, = (P,+ Pa) 
x tan angle ABE, or (P,; +P.) X AH+ BE. GH receives this thrust and 
also, in addition, a thrust equal to the horizontal component of the thrust in 
EG or HF, or, in all, (P, + P2+P3) X AH+ BE. 

The tension in AH or FD equals the thrust in BG or HO, and the tension 
in EK, KL, and LF equals the thrust in GH. 

Pratt or Whipple Truss. (Fig. 125.)—In this truss the diagonals are 
ties, and the verticals are struts or columns, 

Calculation by the method of distribution of strains; Consider first the 
load P,. The truss having six bays or panels, 5/6 of the load is transmitted 
to the abutment H, and 1/6 to the abutment O, on the principle of the lever. 
As the five sixths must be transmitted through JA and AH, write on these 
members the figure 5. The one sixth is transmitted successively through 
JC, CK, KD, DL, etc., passing alternately through a tie and a strut. Write 
on these members, up to the strut GO inclusive, the figure 1. Then consider’ 
the load P,, of which 4/6 goes to 4H and 2/6toGO. Write on KB, BJ, JA, 
and AH the figure 4, and on KD, DL, LE, etc., the figure 2, The load Pg 


444 MECHANICS. 


transmit 3/6 in each direction; write 8 on each of the members through 
which this stress passes, and so on for all the loads, when the figures on tl 4 
several members will appear as on the cut. Adding them up, we have the 
following totals: 


EN FM FO GN 
Tension on diagonals | 47 oad te sth UE i aM ce 14 (10860 is 


: O 
Compression on verticals | Sa ae ae ey ay An GS 


Each of the figures in the first line is to be multiplied by 1/6P x secant of 
angle HAJ, or 1/6P x AJ + AH, to obtain the tension, and each figure in the 
lower line is to be multiplied by 1/6P to obtain the compression. The diag- 
onals HE and FO receive no strain. 





A B Cre D E F G 
H 
P, Po P; P4 P; 
Fie. 125. 


It is common to build this truss with a diagonal strut at HB instead of the 
post HA andthe diagonal AJ; in which case 5/6 of the load Pis carried 
through JB and the strut BH, which latter then receives a strain = 15/6P X 
secant of HBJ. 

The strains in the upper and lower horizontal members or chords increase 
from the ends to the centre, as shown in the case of the Burr truss. AB 
receives a thrust equal to the horizontal component of the tension in AJ, or 
15/6PXx tan AJB. C receives the same thrust + the horizontal component 
of the tensionin BK,and so on. The tension in the lower chord of each panel 
is the same as the thrust in the upper chord of the same panel. (For calcu- 
lation of the chord strains by the method of moments, see below.) 

The maximum thrust or tension is at the centre of the chords and is equal 


to Mes in which W is the total load supported by the truss, Z is the length, 


and D the depth. This is the formula for maximum stress in the chords 
of a truss of any form whatever. 

The above calculation is based on the assumption that all the loads P,. Po, 
-ete., are equal. If they are unequal the value of each has to be taken into 
account in distributing the strains. Thus the tension in AJ, with unequal 
loads, itistead of being 15 x 1/6 P secant 6 would be sec @ X (5/6P, + 4/6 Py + 
3/6 Pz + 2/6 P, +1/6 P;.) Each panel loed, P, ete., includes its fraction of 
the weight of the truss. 

General Formula for Strains in Diacgonals and Verticals. 
—Let n= total number of panels, 2 = number of any vertical considered 
from the nearest end, counting the end as 1, r = rolling load for each panel, 
P = total load for each panel, 


[(1—~2%)+(m—a)2— (a —1)-+(ar—1)?] P 
27 q 
For a uniformly distributed load, leave out the last term, 
[r(a@ — 1) + (a — 1)2] + 2n. 

Strain on principal diagonals = strain on verticals X secant 6, that is 
secant of the angle the diagonal makes with the vertical. 

Strain on the counterbraces : The strain on the counterbrace in the first 
panel is 0, if the load is uniform. On the 2d, 3d, 4th, etc., it is P secant 6 
x 1 142 1+42+48 

Neh aes at | 


: “Beer etc., P being the total load in one panel, 


_r(a—1)+(@—1)? 
Qn : 


Strain on verticals = 





STRESSES IN FRAMED STRUCTURES. 445 


Strain in the Chords—Method of Moments.—Let the truss be 
uniformly loaded, the total load acting on it= W. Weight supported at 
each end, or reaction of the abutment= W/2. Length of the truss = ZL. 
Weight ona unit of length = W/Z. Horizontal distance from the nearest 
abutment to the point (say Min Fig. 125) in the chord where the strain is to 
be determined = x. Horizontal strain at that point (tension on the lower 
chord, compression in the upper)= H. Depth of the truss= D. By the 
method of moments we take the difference of the moments, about the point 
M, of the reaction of the abutment and of the load between M and the abut- 
ments, and equate that difference with the moment of the resistance, or of 
the strain in the horizontal chord, considered with reference to a point in 
the opposite chord, about which the truss would turn if the first chord were 
severed at M. 

The moment of the reaction of the abutment is Wx/2. The moment of 
the load from the abutment to M is W/La X the distance of its centre of 
gravity from M, which is 7/2, or moment = Wa?-2L. Moment of thestress 


P Wa Wa? Ww aw? 
in the chord = HD = amas oT, » whence H = aD aay) Ifx=0orL,; 


H=0. Ife={L2,f= ue which is the horizontal strain at the middle 
of the chords, as before given. . 

The Howe Truss, (Fig. 126.)}—In the Howe truss the diagonals are 
struts, and the verticals are ties. The caiculation of strains may be made 

















































































































Fic. 126. 


in the same method as described above fo: the Pratt truss. ; 
The Warren Girder. (Fig. 127.)—In the Warren girder, or triangular 
truss, there are no vertical struts, and the diagonals may transmit either 





Fra. 127. 


tension or compression. The strains in the diagonals may be calculated by 
the method of distribution of strains as in the case of the rectangular truss. 

On the principle of the lever, the load P, being 1/10 of the length of the 
span from the line of the nearest support a, transmits 9/10 of its weight to a@ 
and 1/10 to g. Write 9 on the right hand of the strut 1a. to represent the 
compression, and 1 on the right hand of 1b, 2c, 8d, etc., to represent com- 
pression, and on the left hand of b2, c3, etc., to represent tension. Theload Py 
transmits 7/10 of its weight to a and 3/10to g. Write 7 on each member from 
2 to a and 3 on each member from 2 to g, placing the figures representing 
compression on the right hand of the member, and those representing 
tension on the left. Proceed in the same manner with all the loads, then 


446 ; MECHANICS. 


sum up the figures on each side of each diagonal, and write the difference 
of each sum beneath, and on the side of the greater sum, to show whether 
the difference represents tension or compression. The results are as follows: 
Compression, 1a, 25; 2b, 15; 3c, 5; 3d, 5; 4e, 15; 5g, 25. Tension, 1b, 15; 2¢, 
5; 4d, 5; 5e, 15. Each of these figures is to be multiplied by 1/10 of one of 
the loads as P,, and by the secant of the angle the diagonals make with a 
vertical line. 

The strains in the horizontal chords may be determined by the method of 
moments as in the case of rectangular trusses. 

Roof-truss.—Solution by Method of Moments.—The calculation of 
strains in structures by the method of statical moments consists in taking a 
cross-section of the structure at a point where there are not more than 
three members (struts, braces, or chords). 

To find the strain in either one of these members take the moment about 
the intersection of the other two as an axis of rotation. The sum of the 
moments of these members must be 0 if the structure is in equilibrium, 
But the moments of the two members that pass throuzh the point of refer- 
ence or axis are both 0, hence one equation containing one unknown quan- 
tity can be found for each cross-section. 


@ 
/ on 3 
P GE 
She a P 
3 


in ‘ 
s 
A 
PRIN 
x 






Fia, 128. 


In the truss shown in Fig. 128 take a cross-section at ts, and determine the 
strain in the three members cut by it, viz., CH, HD, and DF. Let X = force 
exerted in direction CH, Y = force exerted in direction DE, Z = force ex- 
erted in direction FD. 
For X take its moment about the intersection of Y and Zat D= Xa. For 
Y take its moment about tiie intersection of X and Zat A = Yy. For Z take 
its moment about the intersection of X and Y at H= Zz. Letz=15,%= 
18.6, y = 38.4, AD = 50, CD = 20 ft. Let Py, Pa, Ps, Pq be equal loads, as 
‘shown, and 34 P the reaction of the abutment A. 
The sum of all the moments taken about D or A or # will be 0 when the 
structure is at rest. Then — Xx” -+3.5P X 50 — Ps X 12.5 — Py X 25 — Py X 
87.5 = 0. 
The +,signs are for moments in the direction of the hands of a watch or 
+6 elockwise ’’ and — signs for the reverse direction or anti-clockwise. Since 
P= P, = Py = Ps, —18.6X+175P—%P=0; —18.6X =—100P; X= 
100P + 18.6 = 5.876P. 

= Yy+ a + Pg X 25+ P, X 125-0; 38.4Y = 75P; Y = 75P-+ 38.4 
=f? 6 

— Zz-+- ie 87.5 — P; X 25 — Pg X 12.5-— P3 X0=0; 157 = 93.75P; Z= 
6.25P. 


In the same manner the forces exerted in the other members have been 
found as follows: HG = 6.73P; GJ = 8.07P; JA = 9.42P; JH = 1.35P; GF = 
1.59P; AH = 8.75P; HF = 7.50P. 

The Fink Roof-truss. (Fig. 129.\—An analysis by Prof. P. H. Phil- 
brick (Van N. Mag.. Aug. 1880) gives the following results: 


STRESSES IN FRAMED STRUCTURES. 447 





Fic. 129, 


W = total load on roof; 
N = No. of panels on both rafters; 
W/N = P = load at each joint 6, d, f, ete.3" 
V = reaction at A= 144W = 14NP=4P}3 
AD=S;, AC= LL; CD =D; 
t,, tg, ts = tension on De, eg, g A, respectivelys 
C1, Cg, Cg, Ce = COMPpression On Cd, bd, df, and fA. 


Strains in 

1, or De = ty = 2PS + D; %, or bC = c, =7/2 PL/D=—8 PD/Li 
> * eg st, = 3PS + D; 8, ** bc or fg= PS+L; 
, 'gA=ts = 7/2PS + D; 9, de = 2PS + L; 


/2 : 10,“ cdordg =%PS+D; 
6 fd = cg = 1/2PL/D —PD/L: 11,“ ec = PS + D; 
’ 6 db = cq =7/2PL/D—2PD/L; 12, cC = 3/2 PS + D. 


Example.—Given a Fink roof-truss of span 64 ft., depth 16 ft., with four 
panels on each side, as in the cut; total load 32 tons, or 4 tons each at the 
points f, d, b, C, etc. (and 2 tons each at A and B, which transmit no strain 
to the truss members). Here W= 82 tons, P = 4 tons, S = 32 ft., D = 16 


ft., b = VS? + D? = 2.236 X D. L+ D = 2.236, Dz- L = .4472,5 + D =2, 





S+L= .8944. Thestrains on the numbered members then are as follows: 
0 2X42 =16 tons; 7, 381.8 — 12% .447 = 25.94 tons. 
2 23K 4X2 =z 24 7 6 8, 4X .8944 = 3.58 ‘“* 
8 7/2 KIX? paiely e 9, 8x .8944= 7.16 * 
4, 7/2 X4 X 2.236 = 31.8 * 10, 2x 2 = 4 =< 
5, 31.3—4 xX .447 = 29.52 * 11, 4x 2 =8 +2 
6, 31.3-8X 447 Sires se 2, 6x 2 = 12 35 

The Economical Angle.—A structure of tri- L 


angular form, Fig. 129a, is supported at a and b. It 
sustains any load L, the elements cc being in compres- 
sion and ¢ in tension. Required the angle 6 so that 
the total weight of the structure shall be a minimum. 
F. R. Honey (Sci. Am. Supp., Jan. 17, 1895) gives a solu- 
C+T \ 
er? 
in which C and T represent the crushing and the ten- Q 
sile strength respectively of the material employed. “ 
It is applicable to any material. For C = 7. 6 = 5434°. Fia. 129a. 


For C = 0.47 (yellow pine), 6 = 49384°. For C = 0.87 (soft steel), 6 = 58142 
For C = 6T (cast iron), @ = 6914°. 









tion ef this problem, with the result tan 6 = 


448 HEAT. 


HEAT. 
THERMOMETERS, 


The Fahrenheit thermometer is generally used in English-speaking coun. 
tries, and the Centigrade, or Celsius thermometer, in countries that use the 
metric system. In many scientific treatises in English, however, the Centi- 
grade temperatures are also used, either with or without their Fahrenheit 
equivalents. ‘The Réaumur thermometer is used to some extent on the 
Continent of Europe. 

In the Fahrenheit thermometer the freezing-point of water is taken at 32°, 
and the boiling-point of water at mean atmospheric pressure at the sea- 
level, 14.7 lbs. per sq. in., is taken at 212°, the distance between these two 
points being divided into 180°. In the Centigrade and Réaumur thermometers 
the freezing-point is taken at 0°. The boiling-pointis 100° in the Centigrade 
scale, and 80° in the Réaumur. 


1 Fahrenheit degree = 5/9 deg. Centigrade = 4/9 deg. Réaumur. 
1 Centigrade degree = 9/5 deg. Fahrenheit = 4/5 deg. Réaumur. 
1 Réaumur degree = 9/4 deg. Fahrenheit = 5/4 deg. Centigrade. 


Temperature Fahrenheit = 9/5 x temp. C. + 82° = 9/4 R. + &2°, 

Temperature Centigrade = 5/9 (temp. F. — 82°) = 5/4R. 

Temperature Réaumur = 4/5 temp. C. = 4/9 (F. — 82°). 

Wereurial Thermometer. (Rankine, S. E., p. 234.)\—The rate of 
expansion of mercury with rise of temperature increases as the temperature 
becomes higher ; from which it follows, tiat if a thermometer showing the 
dilatation of mercury simply were made to agree with an air thermometer 
at 32° and 212°, the mercurial thermometer would show lower temperatures 
than the air thermometer between those standard points, and higher tem- 
peratures beyond them. 

For example, according to Regnault, when th air thermometer marked 
350° C. (=: 662° F.), the mercurial thermometer would mark 362.16° C. (= 
683.89° F’.), the error of the latter being in excess 12.16° C. (= 21.89° F.). 

Actual mercurial thermometers indicate intervals of temperature propor- | 
tional to the difference between the expansion of mercury and that of glass. 

She inequalities in the rate of expansion of the glass (which are very 
different for different kinds of glass) correct, to a greater or less extent, the 
errors arising from the inequalities in the rate of expansion of the mercury. 

For practical purposes connected with heat engines, the mercurial ther- 
mometer made of common glass may be considered as sensibly coinciding 
with the air-thermometer at all temperatures not exceeding 500° F. 


PYROMETRY. 


Principles Used in Various Pyrometers.—Contraction of clay 
by heat, as in the Wedgwood pyrometer used by potters. Not accurate, as 
the contraction varies with the quality of the clay. 

Expansion of air, as in the air-thermometers, Wiborgh’s pyrometer, Ueh- 
ling and Steinbart’s pyrometer, etc. 

Specific heat of solids, as in the copper-ball, platinum-ball, and fire-clay 
pyrometers. 

Relative expansion of two metals or other substances, as copper and iron, 
as in Brown’s and Bulkley’s pyrometers, ete. 

Melting-points of metals, or other substances, as in approximate deter: 
minations of temperature by melting pieces of zinc, lead, ete. 

Measurement of strength of a thermo-electric current produced by heat- 
ing the junction of two metals, as in Le Chatelier’s pyrometer. 

Changes in electric resistance of platinum, as in the Siemens pyrometer. 

Mixture of hot and cord air, as in Hobson’s hot-blast pyrometer, 

Time required to heat a weighed quautity of water enclosed in a vessel, 
as in the water pvrometer. 

Thermometer for Temperatures up to 950° K.—Mercury 
with compressed nitrogen in the tube above the mercury. Made by Queen 
& Co., Philadelphia, 





TEMPERATURES, CENTIGRADE AND 449 
- FAHRENHEIT. 

C. ae Cc. | F. 
—40 | —40. 950|1742 
—39 | —38.2 960|1760 
—38 | —36.4 970/177 
7 8 980|1796 
—36 | —32.8 990|1814 
ar 9) - 1000]1832 
—34 | —29.2 1010/1850 
—33 | —27.4 1020|1868, 
— 32 | —25.6 1030|1883' 
—31 | —23.8 1040/1904: 
—30 | —22. 1050|1922 
—29 | —20.2 1060] 1940 
—28 | —18.4 1070|1958 
—27 | —16.6 1080]1976 
—26 | —14.8 1090/1994 
Bee | 18: 1100|2012 
wae 211.9 1110/2030 
on i 94 1120|2048 
—22| — 7.6 1130|2066 
—21|— 5.8 1140]2084 
B90 14. 11502102 
See: 1160|2120 
Sie -= 0.8 1170|2138 
Siri ie 1180/2156 
—16| 3.2 1190|2174 
on tol pala 1200|2192 
cata 6 8 1210/2210 
B48 13.6 122012228 
-12] 10.4 1230|2246 
~11} 12.2 1240|2264 

-10| 14. 1250]2282 
9 |"" 15:8 1260]2300 
Bes (2376 1270|2318 
ey tar iG f 1280]2336 
Bye}! 21.2 1290|2354 
Eafe 1300|2372 
Bs |) 24.8 13102390 
— 3] 26.6 1320/2408 
—2| 28.4 1330/2426 
—1] 30.2 1340/2444 

0} 32. 1350/2462 
+1] 33.8 1360]2480 
2] 285.6 1370]2498 
Bi 87.4 1880}2516 
4| 39.2 1390| 2534 
5] 41. 1400|2552 
6{ 42.8 1410]2570 
71 44.6 1420|2588 
8| 46.4 1430]2606 
9] 48.2 1440] 2624 
10| 50. 1450|2642 
11| 51.8 1460|2660 
12| 53.6 1470|2678 
13| 55.4 1480|2696 
14| 57.2 1490/2714 
15| 59. 1500/2732 
16| 60.8 1510|2750 
17| 62.6 1520|2768 
18| 64.4 1530|2786 
19! 66.2 1540/2804 
20] 68. 1550/2822 
21| 69.8 1600|2912 
22] 71.6 1650/3002 
231 3.4 1700]3092 
24| 75.2 1750|3182 
25 940) 1724 











1800|3272 


450 SEMPERATURES, FAHRENHEIT AND 
CENTIGRADE. . 





























































C. 
—40 |—40. [26]— 3.3 360) 182.2 
—39 |—39.4 9 27 | — 2.8 270|187.8 
—38 |—38.9 9 28 | — 2 2 380)193.3 
—37 |—88.39 29 | — 1.7 390/198 9 
—36 |—37.84 30 | — 1.1 400|204.4 
35 |—37.24 31 | — 0.6 410|210, 
~34 |—36.7932| 0. 420|215.6 
~33 |36.19 33] + 0.6 430)221.1 
—82 |—35.6934) 1.1 440|226.7 
—31|—35. 935} 1.7 i| %5. 450/232. 2 
—30 |—34.4]36| 2.29 102] 88.99 168] 75.6 § 234 460|237.8 
—29 |—83.9437] 2.89 103 | 89.49 169] 76.1 § 235 470|243.8 
—28 | 33.3938] 3.89104] 40. $170] 76.79 236 480|248 9 
—27 |—32.8939] 3.99105] 40.6171) 77.29 237 490) 254.4 
—26 |—32.2940} 4.49108 | 41.18172| 77 89238 500260, 
—25 |—31.79 41] 6. 9107 | 41.79 173] 78.3 9 239 510|265.6 
—24|—31.19 42] 5.69108] 42.298174! 78.99 240 520(271.1 
~23|—30.6943] 6.19109 | 42.8 8175) 79.4 9241 530|276.7 
—22|—30. 944] 6.79 110| 43.39176] 80. §242 540|282,2 
—21 |—29.4945] 7.291111 | 438.99-177| 80.6 § 243 550|287.8 
—20(|—28.9946] 7.88112] 44.4178] 81.1 244 560|293.3 
—19|—98.3947} 8.39113]45. 9179] 81.7 9 245 570|298.9 
—18 |—27.89 48] 8.98114] 45.69 180] 82.29 246 580|304.4 
—17 |—27.2949} 9.49115 | 46.1 181{ 82.8 247 590|310. 
—16|—26.7950} 10. $116] 46.79 182] 83.3 | 248 600/315 6 
—15 |—26.1951] 10.68 117 | 47.29 183] 83.9 | 249 610/321.1 
—14|—25.6952] 11.19 118] 47.89 184] 84.4 250 620/326.7 
—13 |—25. 53] 11.79119] 48.3185) 85. #251 630|332.2 
—12|—24.49}54] 12.29 120 | 48.99 186] 85.6 9252 640|337.8 
—11 |—23.9955| 12.89 121 | 49.49} 187} 86.1 9253 650/343.3 
—10 |—23.3056} 13.39122/50. —/188| 86.7 §254 660|348.9 
-- 9|—22.8].57] 13.99 123 | 50.6 9189] 87.2 255 67°0/354.4 
—.8 |—22.2 : 680/360. 
— 7\—21.7 690|365.6 
— 6 |—21.1 700|371.1 
— 5 |—20.6 710|376.7 
~— 4|—20. 720|382.2 
— 3/—19.4 730|387.8 
= el—15.9 740/393.3 
—1/—18 3 750|398.9 
0 |—17.8 760|404.4 
+ 1|—17.2 770/410. 
2 |—16.7 780/415.6 
3 |—16.1 790/421.1 
4|—15.6 800|426.7 
5 \—15. 810/432.2 
6 |—14.4 820|437.8 
7113.9 830/443.3 
8 |—13.3 840|448.9 
9 |—12.8 850|454.4 
10 |—12.2 880|460. 
11142 870|465.6 
12/1191 880|471.1 
13 |—10.6 890|476.7 
14 |—10. 900|482.2 
15 |— 9.4 910|487.8 
16 |— 8.9 920|493.8 
17 |— 8.8 930|498.9 
18 |— 7.8 940|504.4 
19: |— 9.8 950/510, 
20 |— 6.7 960)515.6 
21 |— 6.1 970|521.1 
22 |~ 5.6 980|526.7 
93 |— 5. .3 | 990/532.2 
24 |— 4.4 178.9 41000|587.8 
25 |— 3.9 179.4 110101543.8 








PYROMETRY. 451 


Platinum or wopper Ball Pyrometer.—A weighed piece of 
platinum, copper, or iron is allowed to remain in the furnace or heated 
chamber till it has attained the temperature of its surroundings. It is then 
suddenly taken out and dropped into a vessel containing water of a known 
weight and temperature. The water is stirred rapidly and its maximum 
temperature taken. Let W = weight of the water, w the weight of the ball, 
t = the original and 7 the final heat of the water, and S the specific heat of 
the metal; then the temperature of fire may be found from the formula 


_ WT —t) 
- Ce + T. 


The mean specific heat of platinum between 32° and 446° F. is .03333 or 
1/30 that of water, and it increases with the temperature about .000305 for 
each 100° F. Forafuller description, by J. C. Hoadley,see Trans. A.S. M. E., 
vi. 702, Compare also Henry M. Howe, Trans. A. I. M. E., xviii. 728, 

For accuracy corrections are required for variations in the specific heat of 
the water and of the metal at different temperatures, for loss of heat by 
radiation from the metal during the transfer from the furnace to the water, 
and from thc apparatus during the heating of the water; also for the heat 
absorbing capacity of the vessel containing the water. 

Fire-clay or firo-brick may be used instead of the metal ball. 

Le Chatelier’s Thermo-electric Pyrometer.—For a very full 
description seé paper by Joseph Struthers, School of Mines Quarterly, vol. 
xii, 1891; also, paper read by Prof. Roberts-Austen before the Iron and Steel 
Institute, May 7, 1891. 

The principle upon which this pyrometer is constructed is the measure- 
ment of a current of electricity produced by heating a couple composed of 
two wires, one platinum and the other platinum with 10% rhodium—the cur- 
rent produced being measured by a galvanometer. 

The composition of the gas which surrounds the couple has no influence 
on the indications. 

When temperatures above 2500° F. are to be studied, the wires must have 
an isolating support and must be of good length, so that all parts of a fur- 
nace ean be reached. 

For a Siemens furnace, about 11144 feet is the general length. The wires 
are supported in an iron tube, 4% inch interior diameter and held in place by 
a cylinder of refractory clay having two holes bored through, in which the 
wires are placed. The shortness of time (five seconds) allows the tempera- 
ture to be taken without deteriorating the tube. 

Tests made by this pyrometer in measuring furnace temperatures under 
a great variety of conditions show that the readings of the scale uncorrected 
are always within 45° F. of the correct temperature, and in the majority of 
industrial measurements this is sufficiently accurate. Le Chatelier’s py- 
rometer Is sold by Queen & Co., of Philadelphia. 

Graduation of Le Chatelier’s Pyrometer.—wW. C. Roberts- 
Austen in his Researches on the Properties of Alloys, Proc. Inst. M. E. 1892, 
says: The electromotive force produced by heating the thermo-junction 
to any given temperature is measured by the movement of the spot of light 
on the scale graduated in millimetres. A formula for converting the divi- 
sions of the scale into thermometric degrees is given by M. Le Chatelier; but 
it is better to calibrate the scale by heating the thermo-junction to temper- 
atures which have been very carefully determined by the aid of the air- 
thermometer, and then to plot the curve from the data so obtained. Many 
fusion and boiling-points have been established by concurrent evidence of 
various kinds, and are now very generally accepted. The following table 
contains certain of these : 


Deg. F. Deg. C. Deg. F. Deg. C. 
217 100 Water boils. 1733 945 Silver melts. 
618 326 Lead melts. 1859 1015 Potassium sul- 
676 358 Mercury boils. phate melts. 
779 415 Zinc melts. 1913 1045 Gold melts. 
838 448 Sulphur boils. 1929 © 1054 Copper melts. 
1157 625 Aluminum melts, 2732 1500 Palladium melts, 
1229 665 Selenium boils. A 8227 1775 Platinum melts. 


The Temperatures Developed in Industrial Furnaces,— 
M. Le Chatelier states that by means of his pyrometer he has discovered 
that the temperatures which occur in melting steel and in other industrial 
operations have been hitherto overestimated. 


452 HEAT. 


M. Le Chatelier finds the melting heat of white cast fron 1185° (2075° F.), 
and that of gray cast iron 1220° (228° F.). Mild steel melts at 1475° (2687¢ 
F.). semi-mild at 1455° (2651° _’.), and hard steel at 1410° (2570° F.). The 
furnace for hard porcelain at the end of the baking has a heat of 1370° 
(2498° F.). The heat of a normal incandescent lamp is 1800° (3272° F.), but 
it may be pushed to beyond “.C%” (3812° F.). 

Prof. Roberts-Austen (Recent Advances in Pyrometry, Trans. A. I. M. E., 
Chicago Meeting, 193) gives an excellent description of modern forms of 
pyrometers. The following are some ©. his temperature determinations. 


GOLD-MELTING, RoyaL MINT. 
Degrees. Degrees. 
Centigrade.  Fahr, 


Temperature of standard alloy, pouring into moulds. ... 1180 2156 
Temperature of standard alloy, pouring into moulds (on 

a previous occasion, by thermo-couple)....... .....-- 1147 2097 
Annealing blanks for coinage, temperature of chamber.. 890 1634 

SILVER-MELTING, RoyvaL Mint. 
Temperature of standard alloy, pouring into mould...... 980 1796 
'TEN-TON OPEN-HEARTH FURNACE, WOOLWICH ARSENAL. 

Temperature of steel, 0.3% carbon, pouring into ladle..... 1645 2993 
Steel, 0.8% carbon, pouring into large mould.............. 1580 2876 
heheating furmace: iINeriOre wes are cis cere oties be) eles cle ares iselers 920 1706 
Cupola furnace, No. 2 cast iron, pouring into ladle....... 1600 2912 


The following determinations have been effected by M. Le Chatelier: 


BESSEMER PROCESS. 


Six-ton Converter. 
Degrees. Degrees 
Centigrade Fahr. 


Ap Bath Ol Slap. sac cs scents vere bemevite coectcas ent a tee L OCU 2876 
B. Metal in ladle,........ Sate leiticissicte aiets Se mcllajsceccs's sicciele re lOAU 2984 
C. Metal in ingot mould................ h AAR SSIES oe ii - 1580 2876 
Deine t ineheatines furnace .cr.wecss sees chistes cements 1200 2192 
Hane Ou URCeIELD Se MaMnineI. ns aemewecledecs octets ee ereien 1080 1976 


OPEN-HEARTH FURNACE (Siemens). 


Semi-Mild Steel. : 
A. Fuel gas near gas venerator..........0...- ecccecceece 720 1328 


B. Fuel gas entering into bottom of regeneratorchamber 400 752 
C. Fuel gas issuing from regenerator chamber....... ..- 1200 2192 . 
Air issuing from regenerator chamber........ deGorpndicoeon OOS; 1832 
Chimney gases. Furnace in perfect condition........... 800 590 
End of the melting of pig charge........04- Soeaetiowie ere ste 1420 2588 
Commlehon Of CONVENSION. ui acacia tele cn sails siolslelelela steele 1500 27382 
Molten steel. Inthe Mamie ee of casting.. 1580 287 
End of ecasting.. BRE Sb enh Goon COOKBEGLE Ske anctanee sae) 2714 
HMptLVGS ANOIDICLS ice ticeia ss ayeielais.« sie.c sicrere nlamiete re Cine ere ettieien ace terete 1520 2768 


For very mild (soft) steel the temperatures are higher by 50° C. 
SIEMENS CRUCIBLE oR Pot FURNACE. 
1600° C., 2912° F. 
Rotary PupDLING FURNACE. 
Perth C. Degrees F 


PUIMACE Tt eadererecmeaccs. «+ + «dee svdegvonsvesiocce resem lonsiecU mc444—0006 

Puddied ball—End of craton... Solve p cleat atachee ater 1330 2426 
BLAST-FURNACE :(G ray-Bessemer Pig). 

Opening in face of tuyere............ ......0. BG OAC ; 1930 8506 

Molten metal—Commencement of fusion.,.........ee6 1400 2552 

Hinds Or PUOLsO CAMs sels ccs s+ ocls ss’ cab tees Bs 1570 2858 


' Horrman Rep- “BRIO KILN. 
BUILDING LAMDPELALUTES.,cevcerecen-sccerecccoccgecassnce 1100 2012 


PYROMETRY. 453 


Hobson’s Hot-blast Pyrometer cunsists of a brass chamber 
having three holiow arms and a handle. ‘VYhe hot blast enters one of the 
arms and induces a current of atmospheric air to flow into the second arm. 
The two currents mix in the chamber and flow out through the third arm, 
in which the temperature of the mixture is taken by a mercury thermom- 
eter. The openings in the arms are adjusted so that the proportion of hot 
blast to the atmospheric air remains the same. 


The Wiborgh Air-pyrometer, (KE. Trotz, Trans. A.I.M.E. 
1892 )—The inventor using the expansion-coefficient of air, as determined 
by Gay-Lussac, Dulon, Rudberg, and Regnault, bases his construction on 
the following theory: If an air-volume, V, enclosed in a porcelain globe 
and counected through a capillary pipe with the outside air, be heated to 
the temperature 7’ (which is to be determined) and thereupon the connection 
be discontinued, and there be then forced into the globe containing V 
another volume of air V’ of known temperature ¢, which was previously 
under atmospheric pressure A, the additional pressure h, due to the addi- 
tion of the air-volume V’ to the air-volume V, can be measured by a ma- 
pometer. But this pressure is of course a function of the temperature T. 
Before the introduction of V’, we have the two separate air-vulumes, Y at 
the temperature 7 and V’ at the temperature f, both under the atmospheric 
pressure H. After the forcing in of V’into the globe, we have, on the 
contrary, only the volume V of the temperature 7, but under the pressure 


The Wiborgh Air-pyrometer is adapted for use at blast-furnaces, smelting- 
works, hardening and tempering furnaces, etc., where determinations of 
temperature from 0° to 2400° F.. are required. 

Seger’s Fire-clay Pyrometer, (H. M. Howe, Hng. and Mining 
Jour., June 7, 1890.)~Professor Seger uses a series of slender triangular 
fire-clay pyramids, about 3 inches high and 5g inch wide at the base, and 
each a little less fusible than the next; these he calls ‘*normal pyramids” 
(‘normal-kegel’’). When the series is placed in a furnace whose temper- 
ature is gradually raised, one after another will bend over.as its range of 
plasticity is reached ; and the temperature at which it has bent, or ‘* wept,’ 
so far that its apex touches the hearth of the furnace or other level surface 
on which it is standing, is selected as a point on Seger’s scale. These points 
may be accurately determined by some absolute method, or they may 
merely serve to give comparative results. Unfortunately, these pyramids 
afford no indications when the temperature is stationary or falling. 

Mesuré and Nouel’s Pyrometric Telescope. (lbid.)—Mesuré 
and Nouel’s pyrometric telescope gives us an immediate determination of 
the temperature of incandescent bodies, and is therefore much better 
adapted to cases where a great number of observations are to be made, and 
at short intervals, than Seger’s. Such cases arise in the careful heating of 
steel. The little telescope, carried in the pocket or hung from the neck, can 
be used by foreman or heater at any moment, 

It is based on the fact that a plate of quartz, cut at right angles to tne 
axis, rotates the plane of polarization of polarized light to a degree nearly 
inversely proportional to the square of the length of the waves; and, 
further, on the fact that while a body at dull redness merely emits red 
light, as the temperature rises, the orange, yellow, green, and blue waves 
successively appear. 

If, now, such a plate of quartz is placed between two Nicol prisms at 
right angles, ‘‘a ray of monochromatic light which passes the first, or 
polarizer, and is watched through the second, or analyzer, is not extin- 
guished as it was before interposing the quartz. Part of the light passes 
the analyzer, aud, to again extinguish it, we must turn one of the Nicolsa 
certain angle,’ depending on the length of the waves of light, and hence on 
the temperature of the incandescent object which emits this light. Hence 
the angle through which we must turn the analyzer to extinguish the light 
is a neasure of the temperature of the object observed. 

For illustrated Gescripiions of different kinds of pyrometers see circular 
issued by Queen & Co., Philadelphia. ; 

The Uehling and Steinbart Pyrometer. (For illustrated descrip- 
tion see Engineering, Aug. 24, 1894.)—The action of the pyrometer is based _ 
on a principle which involves the law of the flow of gas through minute’ 
apertures in the following manner: If aclosed tube or chamber be supplied’ 
with a minute inlet and a minute outlet aperture and air be caused by a 
constant suction to flow in through one and out through the other of these 
apertures, the tension in the chamber between the apertures will vary with 


~ 


454 & HEAT. 
the difference of temperature between the inflowing and outflowing air. If © 
the inflowing air be made to vary with the temperature to be measured, 
and the outflowing air be kept at a certain constant temperature, then the 
tension in the space or chamber between the two apertures will be an exact 
measure of the temperature of the inflowing air, and hence of the tem- 
perature to be measured. 

In operation it is necessary that the air be sucked into it through the first 
minute aperture at the temperature to be measured, through the second 
aperture at a lower but constant temperature, and that the suction be of a 
constant tension. The first aperture is therefore located in theend of a 
platinum tube in the bulb of a porcelain tube over which the hot blast 
sweeps, or inserted into the pipe or chamber containing the gas whose tem - 
perature is to be ascertained. 

The second aperture is located in a coupling, surrounded by boiling water, 
and the suction is obtained by an aspirator and regulated by a column of 
water of constant height. 

The tension in the chamber between the apertures is indicated by a 
manometer. 

Whe Air-thermometer. (Prof. R. C. Carpenter, Eng’g News, Jan. 5, 
1893.)—Air is a perfect thermometric substance, and if a given mass of air 
be considered, the product of its pressure and volume divided by its 
absolute temperature is in every case constant. If the volume of air 
remain constant, the temperature will vary with the pressure; if the 
pressure remain constant the temperature will vary with the volume. As 
the former condition is more easiy attained air-thermometers are usually 
constructed of constant volume, in which case the absolute temperature 
will vary with the pressure. 

If we denote pressure by p and p’, the corresponding absolute tempere 
atures by Zand 7’, we shuuid have 


pipsT:T! and T’ = pl 


The absolute temperature Tis to be considered in every case 460 higher 
than the thermometer-reading expressed in Fahrenheit degrees. From the 
form of the above equation, if the pressure p corresponding to a known 
absolute temperature T be known, 7’ can be found. The quotient T/pisa 
constant which may be used in all determinations with the instrument. The 
pressure on the instrument can be expressed in inches of mercury, and is 
evidently the atmospheric pressure 6 as shown by a barometer, plus or 
minus an additional amount fA shown by a manometer attached to the air 
thermometer. That is, in general, p = b + h. 

The temperature of 32° F. is fixed as the point of melting ice, in which 
case T = 460 + 32 = 492° F. This temperature can be produced by sur-' 
rounding the bulb in melting 1ce and leaving several minutes, so that the 
temperature of the confined air shall acquire that of the surrounding ice. . 
When the air is at that temperature, note the reading of the attached 
manometer A, and that of a barometer; the sum will be the value of p cor- 
responding to the absolute temperature of 492° F. The constant of the 
instrument, K = 492 + p, once obtained, can be used in all future determina- 

{ ‘ions. 


Hisch Temperatures judged by Color.—The temperature of a 
body can be approximately judged by the experienced eye unaided, and 
M. Pouillet has constructed a table, which has been generally accepted, 
giving the colors and their corresponding temperature as below: 


Deg. C. Deg. F. }- Deg. C. Deg. F. 

Incipient red heat.. 525 977 Deep orange heat... 1100 2021 
Dull red heat ...... 700 1292 Clear orange heat.. 1200 2192 
Incipient cherry-red White heat .... .... 1300 2372 

heat eet. A Se 1472 Bright white heat.. 1400 2552 
Cherry-red heat..... 900 1652 1500 2732 
Clear cherry -red - Dazzling white heat > to to 

este ce washes es - 1000 1832 1600 2912 


The results obtained, however, are unsatisfactory, as much depends on 
the susceptibility of the retina of the observer to light as well as the degree 
of illumination under which the observation is made. 


QUANTITATIVE MEASUREMENT OF HEAT. 455 


A bright bar of iron, slowly heated 1n contact with air, assumes the fol- 
lowing tints at annexed temperatures (Claudel): 


Cent. Fahr. Cent. Fahr. 
MWONOW Ab.scccnus see 225 437 Indigo at... s,s ies cere UROS 550 
Orange at........ pees 243 473 BLUIGIATe Tees cecdes ce MOD 559 
RAGA G urs «-apic dis totes . 265 509 Green at....... ddenee ORR 630 
WIOIGR AL: vast dae see 207 531 ** Oxide-gray’’....... 400 752 


BOILING POINTS AT ATMOSPHERIC PRESSURE. 
14.7 lbs. per square inch. 


Ether, sulphuric............. 100° F. Average sea-water......... 213,2° F, 
Carbon bisulphide.......... + 118 Saturated brine.......... os 226 
MIU 5.0.05 ssieaxen isc rcea. 140 Nitric. acid. St. fh. .dssc2. tse! - 248 
ChloroLorm y.... <<. SA ae 140 Oil of turpentine........ ese O15 
PUTING! iii ve exnelis does essen 140 Phosphorus: ccissesses ose 554 
WGOd SpITIb 5 e.s cerese sec isris 150 Sulphtrns wis eee tecte ces 570 
Alcohol: e.seses Hea e Pas aasls as . 173 Sulphuricsacid ficensese snes 590 
Benzine........ ecrcie ates sli Tainsé@ed toll, io) oogenesis 597 
WWADOR Att: ucsare es oles ot Sapcoo ee Mereury's.<.c0s speed oom 676 


The boiling points of liquids increase as the pressure increases. The boil- 
ing point of water at any given pressure is the same as the temperature of 
saturated steam of the same pressure. (See Steam.) 


MELTING-POINTS OF VARIOUS SUBSTANCES. 


The following figures are given by Clark (on the authority of Pouillet, 
Ciaudel, and Wilson), except those marked *, which are given by Prof. Rob- 
erts-Austen in his description of the Le Chatelier pyrometer. These latter 
are probably the most reliable figures. 


Sulphurous acid .......... — 148°F, Alloy,1tin,1lead.. 370to 466°F. 
Carbonic acid........ e-.e. — 108 ty ee rcreue ae o.-.. 442 to 446 
Mercuryiacis. ste: Bid wte elaievolale —- 39 Cadmium... AS hime ecg et ae 
Bromine Fisa cs os a a'eig'e sles weer 9.5 Bismuth............ 504 to 507 
TRUCPENtINGs 2. <.veec sss see 14 TiO insine 34 scloe eens 608 to 618* 
Hyponitric acid........... Se ete LADO AMA 6 5 pie cles e---. 680to 779% 
COM Suis c's 2a) sowt ade eareae ce aac 82 ANTIMONY 4. ee. cee 810 to 1150 
Nitro-glycerine......... Haece aD Aluminum........ a acetate ste 1157* 
WE OWisek Ses eens t ents whee ere 92 Magnesium’...c.0 08.003 csces 1200 
BHOSPNOEUS.. .../c1encctelnnemetee 112 Caleium.....7..2: Full red heat. 
Areticvecidt .0is.8) fecal. sc 113 Bronze .... . ee yr al eects 1692 
DLOALING © ces sre nels ener 109 to 120 Silvertone. ris cahde ce 1733* to 1873 
Spermaceti......... Apideogc 120 Potassium sulphate........ 1859* 
Margaric acid ........ 131 to 140 Goldie ereciiscici.« 1913* to 2282 
Potassiuwi 25 /secu Gace 136 to 144 Copper ..20. 72.0... 1929* to 1996 
DWE Scots oo ceStteeteea 142 to 154 Cast iron, white... 1922 to 2075* 
Stearic acid '\. 20ers sae 158 wy gray 2012 to 2786 2228* 
Sodium ...... Meee a 194 to 208 Steel saaactass he 3:4 2372 to 2532 
Alloy, 3lead, 2 tin, 5 bismuth 199 ** hard ..... 2570*; mild, 2687* 
LOGING {. .s accede + se) 225 Wrought iron...... 27382 to 2912 
Sulphur 2... .-csseeuseee ner se 239 alll actinic Sols ss = os cla'ee 2732* 
Alloy, 114 tin, 1 lead......... 834 PUSHIN ss uicess veep. on GORI 


For melting-point of fusible alloys, see Alloys. 

Cobalt, nickel, and manganese, fusible in highest heat of a forge. Tung- 
sten and chromium, not fusible in forge, but soften and agglomerate. Plati- 
num and iridium, fusible only before the oxyhydrogen blowpipe. 


QUANTITATIVE MEASUREMENT OF HEAT, 


Wnit of Meat,—tThe British unit of heat, or British thermal unit 
(B. T. U.), is that quantity of heat which is required to raise the temperature 
of 1 1b. of pure water 1° Fahr., at or near 39°.1 F., the temperature of maxi- 
mum density of water. 

The French thermal unit, or calorie, is that quantity of heat which is re- 
quired to raise the temperature of 1 kilogramme of pure water 1° Cent., at or 
about 4° C., which is equivalent to 39°.1 F. r 

1 French calorie = 3.968 British thermal units; 1 B. T. U. = .252 calorie. 
The ‘* pound calorie ’’ is sometimes used by English writers; it is the quan. 


456 HEAT. 


tity of heat required to raise the temperature of 1 lb. of water1°C. 1 Ib. 
calorie = 9/5 B.T.U. = 0.4536 calorie. The heat of combustion of carbon, to 
COxg, is said to be 8080 calories. This figure is used either for French calories or 
for pound calories, as it is the number of pounds of water that can be raised 
1° C. by the complete combustion of 1 lb. of carbon, or the number of 
kilogrammes of water that can be raised 1° C. by the combustion of 1 kilo. 
of carbon; assumiug in each case that all the heat generated is transferred 
to the water. 

The Mechanical Equivalent of Heat is the number of foot- 
pounds of mechanical energy equivalent td one British thermal unit, heat 
and mechanical energy being mutually convertible. Joule’s experiments, 
1843-50, gave the figure 772, which is known as Joule’s equivalent. More re- 
cent experiments by Prof. Rowland (Proc. Am. Acad. Arts and Sciences, 
1880; see also Wood’s Thermodynamics) give higher figures, and the most 
probable average is now considered to be 778. 

1 heat-unit is equivalent to 778 ft.-lbs. of energy. 1 ft. Ib. = 1/778 =.0012852 
heat-units. 1 horse-power = 33,000 ft.-lbs. per minute = 2545 heat-uuits per 
hour = 42,416 + per minute = .70694 per second. 1 1b. carbon burned to CO, 
ei Wines heat-units. 11b.C. per H.P. per hour = 2545 +-14544 = 1742 efficiency 
174986). 


Heat of Combustion of Various Substances in Oxygen. 














Heat-units. 
Authority. 
Cent. | Fahr. 
34,462} 62,032|/Favre and Silbermann. 
Hydrogen to liquid water at 0° C....|~ 33,808] 60,854) Andrews. 
84,342} 61,816/Thomsen. 
* to steam at 100° C......... 28,732| 51,717/Favre and Silbermann, 
& : 8,080} 14,544) ‘* ss 
Carbon (wood charcoal) to carbonic »’'900| 14°220| Andrews 
acid, COg; ordinary temperatures. 8°137 1 4.647 Berthelot. 
Carbon, diamond to COg............. 7,859] 14,146 he 
ce black diamond to COg. ...... 7,861) 14,150 #6 
ss graphiteto CO g =. 1-2... -.- 7,901} 14,222 ss 
Carbon to carbonic oxide, CO........ 


Carbonic oxide to COg, per unit of CO A 


CO to CO, per unit of C= 214 x 2403 


5,607 
Marsh-gas, Methane, CH, to water ae 
UTA CEG CO) ptorsielotectasel fa cists ats iets «r= 1s. oo «laf oS 


Olefiant gas, Ethylene, C,H, to vs 
WaLeTHANG COS dicceees. ovitecewcee 11.957 
10,102 

Benzole gas, CgH, to water and CO, 9915 


4,451|Favre and Silbermann. 
4,325 oe (T} 
4,376] Andrews, 
4,293|Thomsen. 
10,093)Favre and Silbermann, 
23,616|Thomsen. 
23,594] Andrews. 
23,513|/Favre and Silbermann. 
21,344, ss 
21,496) Andrews. 
21,523|Thomsen. 
18,184 . 
17,847|Favre and Silbermann, 


In burning 1 pound of hydrogen with 8 pounds of oxygen to form 9 pounds 
of water, the units of heat evolved are 62,032 (Favre and S.); but if the 
resulting product is not cooled to the initial temperature of the gases, 
part of the heat is rendered latent in the steam, The total heat of 1 lb, 
of steam at 212° F. is 1146.1 heat-units above that of water at 32°, and 
9 < 1146.1 = 10,315 heat-units, which deducted from 62,032 gives 51,717 as the 
heat evolved by the combustion of 1 lb. of hydrogen and 8 lbs. of oxyyen at 
82° F. to form steam at 212° F. 

By the decomposition of a chemical compound as much heat is absorbed 
or rendered latent as was evolved when the compound was formed. Ifilb. | 
of carbon is burned to COg, generating 14,544 B.T.U., and the CO, thus formed 
is immediately reduced to CO in the presence of glowing carbon, by the 
reaction CO, -+ C = 2CO, the result is the same asif the 2 lbs. C had been 
burned directly to 2CO, generating 2 x 4451 = 8902 heat-units; consequently 
14,544 — 8902 = 5642 heat-units have disappeared or become latent, and the 


SPECIFIC HEAT. 457 


“unburning ” of CO, to CO is thus a cooling operation. (For heats of com- 
bustion of various fuels, see Fuel.) 


SPECIFIC HEAT. 


Thermal Capacity.—The thermal capacity of a body is the quantity 
of heat required to raise its temperature one degree. The ratio of the heat 
required to raise the temperature of a certain weight of a given substance 
one degree to that required to raise the temperature of the same weight of 
water one degree from the temperature of maximum density 39.1 is com- 
monly called the specific heat of the substance. Some writers object to the 
ter.n as being an inaccurate use of the words “specific”? and ** heat.” A 
more correct name would be ‘*‘ coefficient of thermal capacity ” 

Determination of Specific Heat.—Method by Mixture.—The 
body whose specific heat is to be determined is raised to a known tempera- 
ture, and is then immersed in a mass of liquid of which the weight, specific 
heat, and temperature are known. When both the body and the liquid 
have attained the same temperature, this is carefully ascertained. 

Now the quantity of heat lost by the body is the same as the quantity of 
heat absorbed by the liquid. 

Let c, w, and t be the specific heat, weight, and temperature of the hot 
body, and c’, w’, and tv’ of the liquid. Let 7 be the temperature the mix- 
ture assumes. 

Then, by the definition of specific heat, c X w X (f — T) = heat-units lost 
by the hot body, and c’ X w’ X (T — t’) = heat-units gained by the cold 
liquid. If there is no heat lost by radiation or conduction, these must be 


equal, and 
c’w’ (T — t’) 
w(t — T) i 


Specific Heats of Various Substances. 


cw(t — T)=c'w(T—t’) or c= 


The specific heats of substances, as given by different authorities, show 
considerable lack of agreement, especially in the case of gases. 

The following tables give the mean specific heats of the substances named 
according to Regnault. (From Rontgen’s Thermodynamics, p. 134.) These 
specific heats are average values, taken at temperatures which usually come 
under observation in technical application. The actual specific heats of all 
substances, in the solid or liquid state, increase slowly as the body expands 
or as the temperature rises. It is probable that the specific heat of a body 
when liquid is greater than when solid. For many bodies this has been 
verified by experiment. 


Soups. 






Antimony........ BpROOBOS eee OFODCSE le mteela(SOLt) asi. nasicesescecctios 0.1165 
Copper....... Sntolteisiste clea cee 0.0951 | Steel (hard)........ Bale eayareie scare 01175 
Gold gos ei Pi dacendaenes contenant’ OVOS24 | ZING Waa aa taliieceses ese sone seas 0.0950 
Wroughtiron a peneesm ee ees 0.1188 | Brass........ Sees st ects ches 0.0939 
GIASS 5. vests aster eseele POM 9S Gh TCO eee atisine cise «sive eiefayoleiars 0.5040 
Cast irony... 6cccees obouTaus ee O RL ZOO ole SUL MEIetewtercteleicicls leis ce os sini cie's 0.2026 
CAS es os vis robeltoere heoaiee ee OL08T4e Ve OCharcoaltessmcrc <0: daesis oa 0.2410 
Platinum =. cst eoescismesccdes’s © 0.0324 (ATU eee ne eile: cle © PERCE 0.1970 © 
SULVOL cs cae cies cue enema 0.0570 | Phosphorus....... de oseeegecr ULuna 
Tin eOemclotitemaniesitenccs mOULU00% 
LIQUIDS. 

Water Acts cents siess Hae neice ort OOOO MTOLCIILY,c cscs cc's + 5s eden eaener U.eoe 
Lead (melted)............... . 0.0402 | Alcohol (absolute) ........... 0.7009 
Sulp hire ear cess cic ee eeecee OM SAO ME ISCLIOM i o:ceus= en's ou seversic ~2- 0.5640 
Bistnuthqegee soscecece a teatOLUGUGMIDSONZING wsics0t > sane oc cvinwioe cease ae 
Tin Eh a eee eeeeeereece 0.06387 ICDL cesses cece soca = maracas 0.5034 


Sulphuric acid......sssceeee.- 0,3350 


458 HEAT. i erie 


GASES. 
eects ppg AP Constant Volume, © 

PAID rs crctaterevslotennls cusleiaie tae slelisicinicre uianieis oVD1 0.16847 
OXY Pen ccc ccloc cote stones: sects Oat V1 9.15507 
FAV GTOS CH weeet eters <sicicranese stp acmeewiene0 G00 2.41226 
IN ELE OSEM a abate careers dicle oisisisreele WeLaee 0.24380 0.17273 
Superheated steaMm.....cceseseesese 0.4805 0.346 
CarboniGyacid ncnermiesisteatua reset cas 0.217 0.1535 
Olefiant.Gas. (CHo) i is.0:076.0:660s0% 10 s0,0/410 0.404 0.173 
Carbonic oxide........ wialetarets stecaraarseis 0.2479 0.1758 
PATITVOTIA Fore Aavals vieuald violsve nye siantcta cetsvecs 0.508 0.299 
HCN GRs ch encuci asides oe ole attns otter ieee 0.4797 0.3411 
Aleoholosaa. se. 4. afais eiateidascaysteiorors's eee 0.4584 0.8200 
FA. COLIC LAC] Wes citeeciess siearle se Race See - 0.4125 aie aiiee 
CHIOROGORNTS {i erenmicrs Sces cle oeerewie ae OVI DG cacieun ih” bial wean stsictee ete 


In addition to the above, the [following are given by other authorities. 
(Selected from various sources.) 


METALS. 
Platinum, 32° to 446° F.. 0333 Wrought i iron eae & Dulong). 

(increased .000305 for each 100° F. ) tore oe eee 
CBC II Seen Sereeee eect: 0567 oe 35° TO O02 Oe eis ai 
WraSS Wri soe cate tance vee eles waiute .0939 ss Boo LOD 12. aes 1218 
Copper, 82° to 212° F.......... . .094 ss Se- LO pUcoommamte 1255 

OVOWwO Ole Htc ccts sole cre 1013 | Wrought iron (J. C. Hoadley, 
Zine 82° to 212° F.. ene O92 A.S.M. E., vi. 718), 

St oN UOHO (Sop Lyereieis ots ale siels 1015 Wrought ir on, 32° to. 200%° 7. 5 1129 
INICKGlier niente theca ees = dee 1086 32° ton, 0082s... 1327 
Aluminum, 0° F. to melting- ~ 32° to 2000°,.... .2619 

point (A. E. Hunt).......... 0.2185 | 


OTHER SoLips. 
Brickwork and masonry, about. ctr (Oy NERA ENO eso Goobace e8) ig 


IWEATOLOs stietes cis occ oi>,.0 sseth sc c0 2 6cins WOK G é as supp vistsioc Shei seclat nceteed 

Gn ae, Feiecscs ciccie seis trae oe 318 GTaADPHIGesakies-esiee wees pinalsbeeiee 508 
CUTER ING 8 vie ses yesh eisle's/ ate (asis ss 217 | Sulphate of lime... .... 2600000 ALY 
Magnesian limestone........... ld £1 1 DLA PTLOSIO. se ae cis salen teen Bajelsiaia oor 
SHiGaP aes teas ie ste saies Sete TLGL Os SOBs. sw clepietereys prainte blots cinisnerserae nies .231 
Corundum.. Bae ofetgee feiccis esd GOL || QUALLZ Ges cure folds plete pie awraeae 188 
Stones generally.. Rolie seltese eM LOLAS | -ERLVCT SANG new cisice onelere Pico os 

Woops. 

Pine (turpentine)................ s4O7 Pil Oak tara sania colo necincacereeranrens .570 
PTT Rcte wel teivia’s welsieicre bicists Siecle see cave CUM OAT. sare ac ot SOU. See eee 500 
LIguIDs. 

Alcohol, density .793............ 6622 | Olive Oil, ...2t.2. 0. Sido iets craeveriete .310 
Sulphuric acid, density deR ieee 1380 » lt BENZING:. cers eae es oer eRe Ree ae 3893 

150) era .661 | Turpentine, density .872........ 472 
Hydrochloric acid.........-.. «+ 00>), Bromine, .) \....acccsenacaceae set daha 
GASES. 
At Constant At Constant 
Pressure. Volume. 
Suit phurOvs CM Mace: alnicls ohare cae ME oan ee eae 1553 1246 
Light carburetted hydrogen, marsh gas (CH,). .5929 -4683 
BlASUeKUIENA COLL ASCS as cic. sad:o.s.04% 2cseinpipeloe tains 2207 O80 
Specific Heat of Salt Solution, (Schuller.) 
Per cent salt in solution........ 5 10 15 20 25 
Specific heat.................... .9306 8909 .8606 .8490 8073 
Specific Heat of Air.—Regnault gives for the mean value 
Between — ae C. and POC... sek acs » oes jaielolecaisinee este Rete 0.23771 
eG 100° o ob is's ale a.6 ane abe etetene eats ste eee tmenererets 0.23741 
th ce Ofae AU Ut OEE scr ai aumico ococigd 0.23751 


Hanssen uses 0.1686 for the specific heat of air at constant volume. The 
value of this constant has never been found to any degree of accuracy by 
direct experiment. Prof. Wood gives 0.2375 ~- 1.406 = 0.1689. The ratio of 





EXPANSION BY HEAT. 459 


the specific heav of a fixed gas at constant pressure to the sp. hu. at con- 
stant volume is given as follows by different writers (Hng’g, July 12, 1889): 
Regnault, 1.3953; Molland Beck, 1.4085; Szathmari, 1.4027; J. Macfarlane 
Gray, 1.4. The first three are obtained from the velocity of sound i inair. The 
fourth is derived from theory. Prof. Wood says: The value of the ratio for 
air, as found in the days of La Place, was 1.41, and we have 0.2377 -- 1.41 
= 0.1686, the value used by Clausius, Hanssen, and many others. But this 
ratio is not definitely known, Rankine in his later writings used 1.408, and 
Tait in a recent work gives 1.404, while some experiments gives less than 
1.4 and others more than 1.41. Pr of. Wood uses 1.406. 

Specific Heat of Gases.—Experiments by Mallard and Le Chatelier 
indicate a continuous increase in the specific heat at constant volume of 
steam, COe, and even of the perfect gases, with rise of temperature. The 
variation is inappreciable at 100° C., but increases rapidly at the high tem- 
peers of the gas-engine cylinder. (Robinson’s Gas and Petroleum 

ngines 


Specific Heat and Latent Heat of Fusion of Iron and 
Steel, (H.H. Campbell, Trans. A. IL. M. E., xix. 181.) 


o 
Akerman. ‘Troilius. 


Specific heat pigiron, 0 to 1200°C............. 0.16 ars 
S i a TQ0ORE OHI SUN Se eareeeicntorae 0.21 Bisse 
ne Zs oe OOS OSI Oa emete inetrse sate ete 0.18 
a < 1G00 LO TS0U0° C. acct ese a ome a bas 0.20 


Calculating by both sets of dat. we have: 


Oo 
Akerman. Troilius. 


Heating from 0 to 1800° C., ........ 318 330 calories per kilo. 
Hence probable value is about.......... 825 calories per kilo. 
Specific heat, steel (probably high carbon).. ee eaiate 1175 
BOLO ITO. oo c bene a 8 1081 
Hence probable value solid rail steelisci2isicsesss05.06 ss 1195 
*“* melted rail steel. . See atices 1275 


° 
Akerman. Troilius. 
Latent heat of fusion, pig iron, calories per kilo.. 46 s 
ro eray pig ANE t esa od ese en Ts 33 
5 : ‘© white pig . Be 23 
From which we may assume that the truth is about : Steel, 20 ; pig iron, 30, 


EXPANSION BY HEAT. 


In the centigrade scale the coefficient of expansion of air per degree is 
0.003665 = 1/273; that is, the pressure being constant, the volume of a perfect 
gas increases 1/27 3 of its volume at 0° C. for every increase in temperature 
of J°C. In Faktrenheit units it increases 1/491.2 = .002036 of its volume at 
32° F. for every increase of 1° F. 


Expansion of Gases by Heat from 32° to 212° F. (Regnault.) 


= 





Increase in Volume, | Increase in Pressure, 











Pressure Constant. Volume Constant. 
Volume at 32° Fahr. Pressure at &2¢ 
=)),0/ 20% Fahr. = 1.0, for 
LOOKS teats 100° C. LOTR 
Hy dropen tress.) sacs ne celanten 0.3661 0.002034 0.3667 0.002037 
Atmospheric air.,.. .....-..-- 0.3670 0.002039 0.3665 0.002036 
Nitromen Grccecies ccuece tment Ofoo 10 0.002039 0.3668 0.002039 
Carbonic @eide;. jc... akan 0.3669 0.002088 0.3667 0.002037 
Carbonieiaeidy..4....2 4. cee 0.3710 0.002061 0.3688 0.002039 
Sulphurous ACIG .......02. conte, 3008 0.002168 0.3845 0.002186 








If the volume is kept constant, the pressure varies directly as the absolute 
temperature. 


460 HEAT. 


> 


Lineal Expansion of Solids at Ordinary Temperatures, 
(British Board of.Trade; from CLARK.) 























Coef- 
ficient Accord- 
of ing to 
For For Expan- On on 
1° Fahr, | 1° Cent. | sion | author. 
from iti 
39° to | ities. 
Roan 
Length =1) Length=1 
Aluminum (cast)...... NE Siena f 5.0% -00001284 | .00002221 | .002221 | ....... 
ation V (CY Sb) cs ce tats ct oese etal 00000627 | .00001129 | .001129 | .001083 
BrasS,;iCasts2.. 0... EP eia\ais averse wisisteraiee .00000957 | .00001722 | .001722 | .001868 

UIA LOe sates ac eae ree eos eet -00001052 | .00001894 | 001894 | ....... 
BSCUCK 2 cee) cree eee nien conics mekeee atne he ets or orene arcs .000003806 | .00000550 | .000550 | ....... 
Bronze (Copper, 17; Tin, 2144; Zine 1).| .00000986 | .00001774 | 001774 | ....... 
IBISTMUGH Es Se Wancse ss eters nk ce Poni -00000975 | .00001755 | .001755 | .001392 
Cement, Portland (mixed), pure . -00000594 | .00001070 | 001070 | ....... 
Concrete: cement, mortar, and pebbles -00000795 | .00001430 | .001420 | ....... 
WODPSC Gs ete Lak. «evoke asnes he eiee oom .00000887 | .00001596 | :001596 | .001718 
WO OMICO i acm a-eiee secinciarc ials asia crete eieten .00004278 | .00007700 | 007700} ......- 
Glass, Enelish flinte cr adec-sea ese esse -00000451 | .00000812 | .000812 bj 

* — thermometer........ Saaees seek 00000499 | .00000897 | .000897 | ....... 

hed 21 CENT ROR pte Meteniee eine seis s -00000397 | .00000714 | .000714 | ....... 
Granite, gray, VY jste sreizheveictetenclajoreis oe o's -00000438 | .00000789 | .000789 | ....... 

TECs, Gryicec tise radiate Cale seferests's .00000498 | .00000897 | .000897 | ....... 
COME DUT Cuek s yess ore ae secs chistes ane 00000786 | .00001415 | 001415] ....... 
Iridium, DUNG sails seetccnes ccce see setae 00000356 | .00000641 | .000641 | ....... 
Iron, wrought.. ae acccccccevesseces o».| -00000648 | .00001166 | 001166 | .001235 

Sr CAS L tata staat cts'</s's FAsey SoRAh arekele ateyens ere .00000556 | .00001001 | .001001 | .001110 
CAC oie rete stats cove chatiernc esis lcs erersieshisiele .00001571 | .00002828 | .002828|.... .. 
Magnesium........ eng le Nae A She nanea  nentneed Cane, 002694 

: : (ROMA Hats saeainlGae Oc : ; 5 bd Meee 
Marbles, various | fg07 7107 10200077 00000786 | .00001415 | .001415 | «...... 
PLOW cots selec ober -00000256 | .00000460 | .000460 | ....... 

Masonry, brick) 9) 00277202 re NAA “00000494 | '00000890 | “000890 |... .... 
Mercury (cubic expansion)............ .00009984 | .00017971 | .017971 | .018018 
INIGK CL Aeg elses c50 \ciccigpea ss ae sly ectseuaie st .00000695 | .00001251 | .001251 | .001279 
PRC WEED et hel sce s/sie se'sul oc wotenemine ,..--} -00001129 | .00002033 | .002033 | ... .... 
RIASCCI MW LEG io creas crea ate arleloteteeteiere .00000922 | .00001660 | .001660 | ....... 
Platinum Bee cet jsicieic’ «stare sien so arelateele sists .00000479 | .00000863 | .0008638 | ....... 
Saari 85 per soca emi i 00000453 | .00000815 | .000815 | .000884 
PROMO Laie stats te jescte.cie ss sce. o:s ale che sareleimnnas .00000200 | .00000360 | .000860 | ...... 5 

Quartz, parallel to major axis, ¢ 0° to 

VOTO) 65 Gk OG Re GEE ee enone .00000434 | .00000781 | .000781 | ....... 

uartz, perpendicular to major axis, 

GOS OPOSIO era p 2s 2 s,. os nies cok one .00000788 | .00001419 | .001419 | ....... 
SILVER MP ULC ett ilet\clsle << sis'e(o sis cleledersie tot .00001079 | .00001943 | .001943 | .001908 
Slate......-. Rreeatand oye NOBGQOE  evaratelele sehen .00000577 | .00001038 | 001088 | ....... 
Steels Caster sess. «ew ece ease .00000636 | .00001144 | .001144 ‘001079 

SOMO tATIEDOLGG etek bse sa 'e vise sca iets .00000689 | .00001240 | .001240| ....... 
Stone (sandstone), CUE Vistas ate a ioiaisioselen .00000652 | .000011'74 | 001174] .. .... 

Patvills’......- 06... .00000417 | .00000750 | .000750 | ....... 
Ue as eee Gn acta of ..0'204) Oe ae .00001163 | .00002094 | .002094 | .001988 
Wedgewood Ware. ccpedssse cscs ccses. cs .00000489 | .00000881 | .000881 | ....... 
IWiOOG, PINE Je occ cteieitels <0 60 0.0 5 .00000276 | .00000496 | .000496 | ....... 
Zine Sstaccisiseie 6c aeinte oot Mefeisls «ie eyetsele odd .00001407 | .00002582 | .002532 | .002942 
a i ih oslo eoes fe amamnes Bee .00001496 | .00002692 | .002692 | ....... 





Cubical expansion, or expansion of volume = linear expansion x 8, 


LATENT HEATS OF FUSION. 461 


Absoluve Temperature—Absolute Zero.—The absolute zero ofa 
gas is a theoretical consequence of the law of expansion by heat, assuming 
that it is possible to continue the cooling of a perfect gas until its volume is 
diminished to nothing. 

If the volume of a perfect gas increases 1/273 of its volume at 0° C, for 
every increase of temperature of 1° C., and decreases 1/273 of its volume for 
every decrease of temperature of 1° C., then at — 273° C. the volume of the 
imaginary gas would be reduced to nothing. This point — 273° C., or 491.2° 
F. below the melting-point of ice on the air thermometer, or 492.66° F. be- 
low on a perfect gas thermometer = — 459,2° F. (or — 460.66°), is called the 
absolute zero; and absolute temperatures are temperatures measured, on 
either the Fahrenheit or centigrade scale,:from this zero. The freezing 
point, 32° F., corresponds to 491.2° F. absolute. If po be the pressure and 
a) the volume of a gas at the temperature of 32° F. = 491.2° on the absolute 
scale = 75, and p the pressure, and v the volume of the same quantity of 
gas at any other absolute temperature 7’, then 

pv iT t+ 459.2 Pv _ Povo 
hy Ale SOT OEL cat Tenaya 

The value of poU9 = T> for air is 53.37, and pv = 58.877, calculated as fol- 
lows by Prof. Wood: 

A cubic footof dry air at 32° F. at the sea-level weighs 0.080728 lb. The 





volume of one pound is Vg = 0s = 12.387 cubic feet. The pressure per 
square foot is 2116.2 lbs. j 
Povo _ 2116.2 X 12.387 _ 26214 _ og 
Toe 491.13 py Cs CR: 


The figure 491.13 is the number of degrees that the absolute zero is below 
the melting-point of ice, by the air thermometer. On the absolute scale, 
whose divisions would be indicated by a perfect gas thermometer, the cal- 
culated value approximately is 492.66, which would make pv = 53.217’. Prof. 
Thomson considers that — 273.1° C., = — 459.4° F., is the most probable value 
of the absolute zero. See Heat in Hncy. Brit. 

Expansion of Liquids from 32° to 212° F.—Apparent ex- 
pansion in glass (Clark). Volume at 212°, volume at 82° being 1: 


IVY UN Tae ter RO opal 50/5 00 0 as. ae! slotece 1.0466 NICTIC ACI ene acetate empl 
Water saturated with salt.... 1.05 Olive and linseed oils........... 1.08 
ESP CUR Ysa eres a <isicls.ctsiaieletsin siaterctals 1.0182 Turpentine and ether.......... 1.07 
PANCOMOL gyre ee ere oz. 010 6 die este e.¢ 1 Hydrochlor. and sulphuric acids 1.06 


For water at various temperatures, see Water. 
For air at various temperatures, see Air. 


LATENT HEATS OF FUSION AND EVAPORATION. 


Latent Heat means a quantity of heat which has disappeared, having - 
been employed to produce some change other than elevation of temperature. 
LBy exactly reversing that change, the quantity of heat which has dis- 
appeared is reproduced. Maxwell defines it as the quantity of heat which 
must be communicated to a body in a given state in order to convert it into 
another state without changing its temperature. 

Latent Heat of Fusion.—When a body passes from the solid to the 
liquid state, its temperature remains stationary, or nearly stationary, at a 
certain melting point during the whole operation of melting; and in order 
to make that operation go on, a quantity of heat must be transferred to the 
substance melted, being a certain amount for each unit of weight of the 
substance. This quantity is called the latent heat of fusion. 

When a body passes from the liquid to the solid state, its temperature 
remains stationary or nearly stationary during the whole operation of freez- 
ing; a quantity of heat equal to the latent heat of fusion is produced in the 
body and rejected into the atmosphere or other surrounding bodies. 

The following are examples in British thermal units per pound, as given 
in Landolt & Boérnstein’s Physikalische-Chemische Tabellen (Berlin, 1894), 


Latent Heat Latent Heat 


Substances. Substances. 


of Fusion. of Fusion. 
PSISTAVUG EO go. cic: 22.10 SilVer.. 36 oe eee 37.93 
Gastron: gray... waegdled Beeswax ...... .- Seat Gale 
Cast Iron, white....... 59.4 Parafine eee sce 63.27 
Thea etree © +s «5.3 9.66 Spermacetiguascce rn 66.56 
(Un . Sa 0 Sa I cn 25.65 Phosphorusse.seo. ++. eG 


AVKOR I  Aane sie 'ueaaeeenens . 50.63 Sulphur 2:oeiaeses «os sloiwo 


462 HEAT. 


Pror. Wood considers 144 heat units as the most reliable value for the 
latent heat of fusion of ice. Person gives 142.65, 

Latent Mieat of Evaporation.—When a body passes from the 
solid or liquid to the gaseaus state, its temperature during the operation 
remains stationary at a certain boiling point, depending on the pressure o 
the vapor produced; and in order to make the evaporation go on, a quantity 
of heat must be transferred to the substance evaporated, whose amount for 
each unit of weight of the substance evaporated depends on the temperature. 
‘That heat does not raise the temperature of the substance, but disappears 
in causing it to assume the gaseous state, and it is called the latent heat of 
evaporation. 

When a body passes from the gaseous state to the liquid or solid state, its 
emperature remains stationary, during that operation, at the boiling-point 
20rresponding to the pressure of the vapor: a quantity of heat equal to the 
latent heat of evaporation at that temperature is produced in the body; and 
in order that the operation of condensation may go on, that heat must be 
transferred from the body condensed to some other body. 

The following are examples of the latent heat of evaporation in British 
thermal units, of one pound of certain substances, when the pressure of the 
vapor is one atmosphere of 14.7 lbs. on the square inch: 


Boiling-point under Latent Heat in 
Substance, one atm. Fahr. British units. 
Water .... .. a heieaete ate steiete octet 4 212.0 965.7 (Regnault, ) 
AICONOVM gece tactic SO GAGOO GHC 172.2 364.3 (Andrews.) 
LS ANE) Boks reir aen SIS ean ere ol che wiatete a» 95.0 162.8 Hig 
B:sulphide of carbon.........- 114.8 156.0 ss 


The latent heat of evaporation of water at a series of boiling-points ex- 
tending from a few degrees below its freezing-point up to about 375 degrees 
Fahrenheit has been determined experimentally by M. Regnault. The re- 
sults of those experiments are represented approximately by the formula. 
in British thermal units per pound, 


L nearly = 1091.7 —.0.7%(¢ — 32°) = 965.7 — 0.7(¢ — 212°). 


The Total Heat of Evaporation is the sum of the heat which 
disappears in evaporating one pound of a given substance at a given tem. 
perature (or latent heat of evaporation) and of the heat required to raise its 
temperature, before evaporation, from some fixed temperature up to the 
temperature of evaporation. The latter part of the total heat is called the 
sensible heat. 

In the case of water, the experiments of M, Regnault show that the total 
heat of steam from the temperature of melting ice increases at a uniform 
rate as the temperature of evaporation rises. The following is the formula 
in British thermal units per pound: 

h = 1091.7 +-0.305(¢ — 82°). 

Yor the total heat, latent heat, etc., of steam at different pressures, see 
table of the Properties of Saturated Steam. For tables of total heat, latent 
heat, and other properties of steams of ether, alcohol, acetone, chloroform, 
chloride of carbon, and bisulphide of carbon, see Rontgen’s Thermodynam- 
ics (Dubois’s translation.) For ammonia and sulphur dioxide, see Wood’s 
Thermodynamics; also, tables under Refrigerating Machinery, in this book. 


EVAPORATION AND DRYING. 


In evaporation, the formation of vapor takes place on the surface; in boil- 
ing, within the liquid: the former is a slow, the latter a quick, method of 
evaporation. 

If we bring an open vessel with water under the receiver of an air-pump 
and exhaust the air the water in the vessel will commence to boil, and if we 
keep up the vacuum the water will actually boil near its freezing-point. The 
formation of steam in this case is due to the heat which the water takes out 
of the surroundings. 

Steam formed under pressure has the same temperature as the liquid in 
which it was formed, provided the steam is kept under the same pressure. 

By properly cooling the rising steam from boiling water, as in the multiple- 
effect evaporating systems, we can regulate the pressure so that the water 
boils at low temperatures. 


EVAPORATION, 463 


Evaporation of Water in Reservoirs.—Experiments at the 
Mount Hope Reservoir, Rochester, N. Y., in 1891, gave the following results: 


July. Aug. Sept. Oct. 
Mean temperature of air in shade............. 70.5 70.3 68.7 53.3 


‘* water in reservoir....... 68.2 70.2 66.1 54.4 
: * humidity of air, per cent... .. Der eeee Ob. MP t4.6 VViae 94.7 
Evaporation in inches during month........... 5.59 4.98 4.05 8.23 
Rainfall in inches during month....... see tet Odd © 2:95. T.44 2.16 


Evaporation of Water from Open Channels.  (Flynn’s 
Irrigation Canals and Flow of Water.)—Experiments from 1881 to 1885 in 
Tulare County, California, showed an evaporation from a pan in the river 
equal to an average depth of one eighth of an inch per day throughout the 

ear, 

J When the pan was in the air the average evaporation was less than 3/16 
of aninch per day. The average for the month of August was 1/3 inch per 
day, and for March and April 1/12 of an inch per day. Experiments in 
Colorado show that evaporation ranges from .088 to.16 of an inch per day 
during the irrigating season. 

In Northern Italy the evaporation was from 1/12 to 1/9 inch per day, while 
in she south, under the influence of hot winds, it was from 1/6 to 1/5 irch 

er day. 

Pin the hot season in Northern India, with a decidedly hot wind blowing, 
the average evaporation was 14% inch per day. The evaporation increases 
with the temperature of the water. 

Evaporation by the Multiple System.—A multiple effect is a 
series of evaporating vessels each having a steam chamber, so connected 
that the heat of the steam or vapor produced in the first vessel heats the 
second, the vapor or steam produced in the second heats the third, and so 
on. The vapor from the last vessel is condensed in a condenser. Three 
vessels are generally used, in which case the apparatus is called a Triple 
Effect. In evaporating in a triple effect the vacuum is graduated so that the 
liquid is boiled at a constant and low temperature. 

Resistance to Boiling.—Brine. (Rankine.)—The presence in a 
liquid of a substance dissolved in it (as salt in water) resists ebullition, and 
raises the temperature at which the liquid boils, undera given pressure; but 
unless the dissolved substance enters into the composition of the vapor, the 
relation between the temperature and pressure of saturation of the vapor 
remains unchanged. A resistance to ebullition is also offered by a vessel of 
a material which attracts the liquid (as when water boils in a glass vessel). 
and the boiling take place by starts. To avoid the errors which causes of 
this kind produce in the measurement of boiling-points, it is advisable to 
place the thermometer, not in the liquid, but in the vapor, which shows the 
tiue boiling-point, freed from the disturbing effect of the attractive nature 
of the vessel. The boiling-point of saturated brine under one atmosphere 
is 226° Fahr., and that of weaker brine is higher than the boiling-point of 
pure water by 1.2° Fahr., for each 1/82 of salt that the water contains. 
Average sea-water contains 1/32; and the brine in marine boilers is not suf- 
fered to contain more than from 2/82 to 3/32. 

Methods of Evaporation Employed in the Manufacture 
of Salt. (F. E. Engelhardt, Chemist Onondaga Salt Springs; Report for 
_ 1889.)—1. Solar heat—solar evaporation. 2. Direct fire, applied to the heat- 
ing surface of the vessels containing brine—kettle and pan methods. 38. The 
steam-grainer system—steam-pans, steam-kettles, ete. 4. Use of steam and 
a reduction of the atmospheric pressure over the boiling brine—vacuum 
system. 

ae Hen a saturated salt solution boils, it is immaterial whether it is done 
under ordinary atmospheric pressure at 228° F., or under four atmospheres 
with a temperature of 320° F., or ina vacuum under 1/10 atmosphere, the 
result will always be a fine-grained salt. 

The fuel consumption is stated to be as follows: By the kettle method, 40 
to 45 bu. of salt evaporated per ton of fuel, anthracite dust burned on per- 
forated grates; evaporation, 5.53 lbs. of water per pound of coal. By the 
pan method, 70 to 75 bu. per ton of fuel. By vacuum pans, single effect, 86 
bu. per ton of anthracite dust (2000 Ibs.). With a double effect nearly 
double that amount can be produced. FS 


404 HEAT. 


Soiubility of Common Salt in Pure Water. (Andre®.) 


Temp. of brine, F........ . Seales 32 50 86 104 140) =: 176 
100 parts water dissolve parts.... 35.63 35.69 36.03 36.82 37.06 38.00 
100 parts brine contain salt...... 26.27 26.30 26.49 26.64 27.04 27.54 


According to Poggial, 100 parts of water dissolve at 229.66° F., 40.35 parts 
of salt, or in per cent of brine, 28.749. Gay Lussac found that at 229.72° F., 
100 parts of pure water would dissolve 40.388 parts of salt, in per cent of 
‘prine, 28.764 parts. : 

The solubility of salt at 229° F. is only 2.5% greater than at 32°. Hence we 
cannot, as in the case of alum, separate the salt from the water by allowing 
a saturated solution at the boiling point to cool to a lower temperature. 


Solubility of Sulphate of Lime in Pure Water. (Marignac.) 
Temperature F.. degrees. 82 64.5 89.6 100.4 105.8 127.4 186.8 212 


Parts water to dissolve > 
1 part gypsum 415 386 371 368 370 3875 417 452 


Parts water to dissolve 1 
Dann varoua Caso, 525 488 470 466 468 474 528 572 

In salt brine sulphate of lime is much more soluble than in pure water. 
In the evaporation of salt brine the accumulation of sulphate of lime tends 
to stop the operation, and it must be removed from the pans to avoid wasta 
of fuel. 

The average strength of brine in the New York salt districts in 1889 was 
69.38 degrees of the salinometer. 

Strength of Salt Brines.—tThe following table is condensed from 
one given in U. 8. Mineral Resources for 1888, on the authority of Dr. 
Englehardt. 


Relations between Salinometer Strength, Specific Gravity, 
Solid Contents, etc., of Brines of Different Strengths. 


























GH am Lo} ao Owes .| oe 
Cin. ine) o P=ie y=) ° 
i eg |8* | Ss | 52 feies| fee 
® 2s |ty | $8 |e. Ease) goa 
bo ve A : AS ao re 1 5 2 me tt sas 
3 gr] oe clare Soha bes Sei | eS Sn eee a eee 
i i > 77) Sema foo O; oO Sow Beou Ses 
8 e | £ | & [ee 223| Sa | o8s feo c8| cox 
2 Fe ee eh eo i) aes (Nae aeuct etal inca ee ae pon mem menaas 
g “ 2 SASS hen O.esl> wy nog i sore aso, 
3 & 2 | o'y |\O =| 2S | SOa5 |os,;8] O8o 
aI = o ° Oho Fes Ou ago ~O55 408 
= 3 Sofie b 2s) peob- ger (So@, Aaa ties 
D fo contac tl eine ) ow 4 ea) 
9 Uae (6 See 26] 1.002] .265) 8.347 22) 2,581 21,076 | 3,513 569 
DD ASS atin 52] 1.008 580) 8.356] 0441 1,264 10,510 | 1,752 1.141 
4 ars sistas 1,04} 1.007] 1.060] 8.389! .088| 629.7 | 5.2v7 871.2 2.295 
6 i 1.56) 1.010; 1.590] 8.414]  .133) 418.6 | 3,466 aM 3.462 
be ee aA 5 2.08! 1.014) 2.120] 8.447| .179| 312.7 } 2585 430.9 4.641 
103: Soeees 2.60) 1.017] 2650) 8.472! .2e4) 9249.4 | 2.057 842.9 5 833 
BARRE ects 3.12] 1.021) 8.180) 8.506} .270/ 207.0 | 1,705 284.2 7.088 
5 Fae 3.64] 1.025} 3.710] 8.589} .316] 176.8 1,453 242.2 8.256 
IL erre es 4.16} 1028] 4.240) 8.564] .864] 154.2 1,265 210.8 9.488 
18 Som ad ec 4.48) 1.032/ 4.770) 8.597| .410)} 136.5 | 1,118 186.3 | 10.7 
QUE cle cusse eis 5.20} 1.035} 5.300) 8.622) .457] 122.5] 1,001 176.8 | 11.99 
OU ed artete tere 7.80} 1.054) 7.950] 8.781] .698 80.21 648.4] 108.1 | 18.51 
40 cae dite 10.40} 1.073}10.600} 8.939] .947 59.09 472.3 78.71| 25.41 
DOR Nee os'ee 13.00] 1.093) 138.250] 9.105) 1.206 46.41 366.6 61.10} 32.73 
HO sis ate es 15 60} 1.114/15.900} 9.280} 1.475 37.94 296.2 49.36} 40.51 
TO waatercicels 18.20] 1.186}18.550} 9.464) 1.755 31.89 245.9 40.98] 48.80 
SO ere se gies 20.80] 1.158}21.200} 9.647} 2.045 27.38 208.1 84.69] 57.65 
OO eae Uieis 23.40] 1.182]23.850] 9 847] 2.348 23.84 178.8 29.80] 67 li 


1005.52... 26.00} 1.205] 26.500} 10.089] 2.660 21.04 155.3 25.88] 77.26 





EVAPORATION, 465 


Concentration of Sugar Solutions,* (From “ Heating and Con. 
centrating Liquids by Steam,’”’ by John G. Hudson; The Hngineer, June 18, 
1890.)—In the early stages cf the process, when the liquor is of lew density, the 
evaporative duty will be high, say two to three (British) gallons per square 
foot of heating surface with 10 lbs. steam pressure, but will gradually fall to 
an almost nominal amount as the final stage is approached. Asagenerally 
safe basis for designing, Mr. Hudson takes an evaporation of one gallon per 
hour for each square foot of gross heating surface, with steam of the pres- 
sure of about 10 lbs. 

As examples of the evaporative duty of a vacunm pan when performing 
the earlier stages of concentration, during which all the heating surface 
can be employed, he gives the following: 

Com, Vacuum Pan.—434 in. copper coils, 528 square feet of surface; 
steam in coils, 15 lbs.; temperature in pan, 141°. to 148°; density of feed, 25° 
Beaumé, and concentrated to 31° Beaumé. 

First Trial.—Evaporation at the rate of 2000 gallons per hour = 3.8 gallons 
per square foot; transmission, 376 units per degree of difference of tem- 

erature. 
2 Second Trial.—Evaporation at the rate of 1503 gallons per hour = 2.8 gal- 
lons per square foot; transmission, 265 units per degree. 

As regards the total time needed to work up a charge of massecuite from 
liquor of a given density, the following figures, obtained by plotting the 
results from a large number of pans, form a guide to practical working. 
The paus were all of the coil type, some with and some without jackets, 
the gross heating surface probably averaging, and not greatly differing 
from, .25 square foot per gallon capacity, and the steam pressure 10 lbs. per 
square inch. Both plantation and refining pans are included, making 
various grades of sugar: 

Density of Feed (degs, Beaumé). 
10° 15° 20° 0 OOS 
Evaporation required per gallon masse- 


cuite discharged....... HE ee renee 6.123 3.6 2.20 0 11.5 97 
Average working hours required per 
RARE OR ne se'clinct we Vises Degen 's sehen shes 12. 9. 614 5. 4, 


Equivalent average evaporation per hour 

per square foot of gross surface, as- 

suming .25 sq. ft. per gallon.capacity.. 2.04 1.6 1.39 1.2 .97 
Fastest working hours required per 


WIAPRO Tea res awit ce fe se setaece eae 2 - 85 5.5 3.8 2.75 2.0 
Equivalent average evaporation per 
hour per square foot......... A Se s04 ia. OGn ke, 2.88 2.18 1.9 


The quantity of heating steam needed is practically the same in vacuum 
asin open pans. The advantages proper to the vacuum system are pri- 
marily the reduced temperature of boiling, and incidentally the possibility 
of using heating steam of low pressure. 

In a solution of sugar in water, each pound of sugar adds to the volume 
of the water to the extent of .061 gallon at a low density to .0688 gallon at 
high densities. 

A Method of Evaporating by Exhaust Steam is described 
by Albert Stearus in Trans. A. S. M. E., vol. viii. A pan 17’ 6” x 11’ x 1’ 6’, 
fitted with cast-iron condensing pipes of about 250 sq. ft. of surface, evapo- 
rated 120-gallons per hour from clear water, condensing only about one half 
of the steam supplied by a plain slide-valve engine of 14’” x 32’ cylinder, 
making 65 revs. per min., cutting off about two thirds stroke, with steam at 
95 lbs. boiler pressure. 

It was found that keeping the pan-room warm and letting only sufficient 
air in to carry the vapor up out of a ventilator adds to its efficiency, as the 
averaze temperature of the water in the pan was only about 165° F, 

Experiments were made with coils of pipe in a small pan, first with no 
agitator, then with one having straight blades, and lastly with troughed 
blades; the evaporative results being about the proportions of one, two, and 
three respectively. 

In evaporating liquors whose boiling point is 220° F., or much above that 
of water, it fs found that exhaust steam can do but little more than bring 
them up to saturation strength, but on weak liquors, syrups, glues, ete., it 
should be very useful. 


For other sugar data see Ragasse as Fuel. under Fuel. 


466 HEAT. 


Drying 18 Vacuum,—An apparatus for drying grain and other sub. 
stances in vacuum is described by Mr. Emil Passburg in Proc. Inst. Mecb. 
Engrs., 1889. The three essential requirements for a successful and eco- 
nomical process of drying are: 1. Cheap evaporation of the moisture; 
2. ee eg AE: at a low temperature; 3. Large capacity of the apparatus 
employed. 

The removal of the moisture can be effected in either of two ways: either 
by slow evaporation, or by quick evaporation—that is, by boiling. 

Slow Evaporation.—The principal idea carried into practice in machines 
acting by slow evaporation is to bring the wet substance repeatedly inte 
contact with the inner surfaces of the apparatus, which are heated by 
steam, while at the same time a current of hot air is also Heitee through 
the substances for carrying off the moisture. This method requires much 
heat, because the hot-air current has to move ata considerable speed in 
order to shorten the drying process as much as possible; consequently a 
great quantity of heated air passes through and escapes unused. AS a car- 
rier of moisture hot air cannot in practice be charged beyond half its full 
saturation; and it is in fact considered a satisfactory result if even this 
proportion be attained. A great amount of heat is here produced which is 
not used; while, with scarcely half the cost for fuel, a much quicker re- 
moval of the water is obtained by heating it to the boiling point. 

Quick Evaporation by Boiling.—This does not take place until the water 
is brought up tothe boiling point and kept there, namely, 212° F., under 
atmospheric pressure. The vapor generated then escapes freely. Liquids 
are easily evaporated in this way, because by their motion consequent on 
boiling the heat is continuously conveyed from the heating surfaces through 
the liquid, but it is different with solid substances, and many more difficul- 
ties have to be overcome, vecause convection of the heat ceases entirely in 
solids. The substance remains motionless, and consequently a much 
greater quantity of heat is required than with liquids for obtaining the 
same results. 

Evaporation in Vacuum.—All the foregoing disadvantages are avoided if 
the boiling-point of water is lowered, that is, if the evaporation is carried 
out under vacuum. 

This plan has been successfully applied in Mr. Passburg’s vacuum @rying 
apparatus, which is designed to evaporate large quantities of water con- 
tained in solid substances. 

The drying apparatus consists of a top horizontal cylinder, surmounted 
by a charging vessel at one end, and a bottom horizontal cylinder with a 
discharging vessel beneath it at the same end. Both cylinders are encased 
in steam-jackets heated by exhaust steam. In the top cylinder works a re- 
volving cast-iron screw with hollow blades, which is also heated by exhaust 
steam. The bottom cylinder contains a revolving drum of tubes, consisting | 
of one large central tube surrounded by 24 smaller ones, all fixed in tube- 
plates at both ends; this drum is heated by live steam direct from the boiler. 
The substance to be dried is fed into the charging vessel through two man- 
holes, and is carried along the top cylinder by the screw creeper to the back 
end, where it drops through 4 valve into the bottom cylinder, in which it is 
lifted by blades attached to the drum and travels forwards in the reverse 
direction; from the front end of thé bottom cylinder it falls into a discharg- 
ing vessel through another valve, having by this time become dried. The 
vapor arising during the process is carried off by an air-pump, through a 
dome and air-valve on the top of the upper cylinder, and also through 
a throttle-valve on the top of the lower cylinder; both of these valves are 
supplied with strainers. 

As soon as the discharging vessel is filled with dried material the valve 
connecting it with the bottom cylinder is shut, and the dried charge taken 
out without impairing the vacuum in the apparatus. When the charging 
vessel requires replenishing, the intermediate valve between the two cylin- 
ders is shut, and the charging vessel filled with a fresh supply of wet mate- 
rial; the vacuum still remains unimpaired in the bottom cylinder, and has 
to be restored only in the top cylinder after the charging vessel has been 
closed again. 

In this vacuum the boiling-point of the water contained in the wet maie- 
rial is brought down as low as 110° F. The difference between this tempera- 
ture and that of the heating surfaces is amply sufficient for obtaining good 
results from the employment of exhaust steam for heating all the surfaces 
except the revolving drum of tubes. The water contaiped in the solid sub- 
stance to be dried-evaporates as soon as the latter is heated to about 110° F.; 


RADIATION OF HEAT. 464 


and.as long as there is any moisture to be removed the solid substance is 
not heated above this temperature. 

Wet grains from a brewery or distillery, containing from 75% to 78% of 
water, have by this drying process been converted in some localities from 
a worthless incumbrance into a valuable food-stuff. The water is removed 
by evaporation only, no previous mechanical pressing being resorted to. 

At Messrs. Guinness’s brewery in Dublin two of these machines are em- 
ployed. In each of these the top cylinder is 20’ 4” long and 2’ 8” diam., and 
the screw working insidc it makes-7 revs. per min,; the bottom cylinder ig 
19’ 2’ long and 5’ 4” diain., and the drum of the tubes inside it makes 5 revs. 
per min. The dry:ng surfaces of the two cylinders amount together toa 
total area of about 1000 sq. ft., of which about 40% is heated by exhaust steam 
direct from the boiler. There is only one air-pump, which is made large 
enough for three machines; it is horizontal, and has only one air-cylinder, 
which is double-acting, 1734 in. diam, and 1734 in. stroke; and it is driven at 
about 45 revs. per min. As the result of about eight months’ experience, the 
two machines have been drying the wet grains from about 500 cwé. of malt 
per day of 24 hours. 

Roughly speaking, 3 ewt. of malt gave 4 cwt. of wet grains, and the latter 
yield 1 ewt. of dried grains; 500 cwt. of malt will therefore yield about 670 
ewt. of wet grains, or 335 cwt. per machine. The quantity of water to be 
evaporated from the wet grains is from 75% to 78% of their total weight, or 
say about 512 cwt. altogether, being 256 cwt. per machine. 


RADIATION OF HEAT. 


Radiation of heat takes place between bodies at all distances apart, and 
follows the laws for the radiation of light. 

The heat rays proceed in straight lines, and the intensity of the rays 

radiated from any one source varies inversely as the square of their distance 
from the source. 
. This statement has heen erroneously interpreted by some writers, who 
have assumed from it that a boiler placed two feet above a fire would re- 
ceive by radiation only one fourth as much heat as if it were only one’ foot 
above. In the case of boiler furnaces the side walls reflect those rays that 
are received at an angle—following the law of opties, that the angle of inci- 
dence is equal to the angle of refiection,—with the result that the intensity 
of heat two feet above the fire is practically the same as at one foot above, 
instead of only one-fourth as much. 

The rate at which a hotter body radiates heat, and a colder body absorbs 
heat, depends upon the state of the surfaces of the bodies as well as on their 
temperatures. Tho rate of radiation and of absorption are increased by 
darkness and roughness of the surfaces of the bodies, and diminished by 
smoothness and polish. For this reason the covering of steam pipes and 
boilers should be smooth and of a light color: uncovered pipes and steam- 
cylinder covers should be polished. 

The quantity of heat radiated by a body is also a measure of its heat- 
absorbing power, under the same circumstances. When a polished body is 
struck by a ray of heat, it absorbs part of the heat and reflects the rest. 
The reflecting power of a body is therefore the complement of its absorbing 
power, which latter is the same as its radiating power. 

The relative radiating and reflecting power of different bodies has been 
determined by experiment, as shown in the table below, but as far as quan-— 
tities of heat are concerned, says Prof. Trowbridge (Johnson’s Cyclopeedia, 
art. Heat), it is doubtful whether anything further than the said relative 
determinations can, in the present state of our knowledge, be depended 
upon, the actual or absolute quantities for different temperatures being still 
uncertain. The authorities do not even agree on the relative radiating 
powers. Thus, Leslie gives for tin plate. gold, silver, and copper the figure 
12, which differs considerably from the figures in the table below, given by 
Clark, stated to be on the authority of Leslie, De La Provostaye and De- 
sains, and. Melloni. 


463 HEAT. 


Relative Radiating and Reflecting Power of Different 





Substances. 
S S tp 
a0 on ol) 
See Ash ps Roem $3 Baty 
S20 ae) cso “Oo 
SSE | SE SOEB| dF 
£38 | es 228] $2 
3 <q aa} Cee (a= 
Liceul, MCL Eerie nica Dhl Ber wl 
Lampblack .......... 100 0 Zinc,polished. ...... 19 81 
ANE RS) hats te MRA IE 100 0 Steel, polished...... 7 83 
Carbonate of lead...} 100 0 Platinum, polished.. 24 fi 
Writing-paper........| 98 2 Hy in sheet .. 17 83 
Ivory, jet, marble.../93 to 98] 7to2 § Tin... ........... .. 15 85 
Ordinary glass....... 90 10 Brass, cast, dead 
GO ra eieeratictre te nichiscele,s 85 15 polished ........... 11 89 
Gunmlacxese eee 72 2 Brass, bright pol- 
Silver-leaf on glass.. 27 % ISheEG. hace eaten vg 93 
Cast iron, bright pol- Copper, varnished .. 14 &6 
iShed vse su ere dee 25 G5 ee hammered... « 93 
Mercury, about...... 23 vue Gold, plated..... .. 5 95 
Wrought iron, pol- ** on polished 
ISHOGsas ate Bice siete 23 {Ite steel ata ee.. cn 3 97 
Silver, polished 
bright: A600 3 97 


Experiments of Dr. A. M. Mayer give the following: The relative radia- 
tions from a cube of cast iron, having faces rough, as from the foundry, 
planed, ‘* drawfiled,” and polished, and from the same surfaces oiled, are as 
below (Prof. Thurston, in Trans. A. 8. M. E., vol. xvi.): 


— 





t 
Surface. Oiled. Dry. 


Rough.. em eee 106 100 
Planed sks. 2. 7 e2 Siete cee 60 32 
Drawfiled...... each 49 20 
Polished esc ue ase Cesk ole 45 18 


It here appears that the oiling of smoothly polished castings, as of cylin- 
der-heads of steam-engines, more than doubles the loss of heat by radiation, 
while it does not seriously affect rough castings. 


CONDUCTION AND CONVECTION OF HEAT. 


Conduction is the transfer of heat between two bodies or parts of a 
body which touch each other. Internal conduction takes place betweeu the 
parts of one continuous body, and external conduction through the surface 
of contact of a pair of distinct bodies. 

The rate at which conduction, whether internal or external, goes on, 
being proportional to the area of the section or surface through which it 
takes place, may be expressed in thermal units per square foot of area pvr 
hour, 

Internal Conduction varies with the heat conductivity, which de- 
pends upon the nature of the substance, and is directly proportional to the 
difference between the temperatures of the two faces of a layer, and in- 
versely as its thickness. The reciprocal of the conductivity is called the 
internal thermal resistance of the substance. If r represents this resistance, 
ax the thickness of the layer in inches, 7” and JT the temperatures on the two 
faces, and qg the quantity in thermal units transmitted per hour per square 


hide i (Rankine.) 





foot of area, q= 


Péclet gives the following values of r: 


Gold, platinum, silverser..... 0.0016 | Lead.....cccscscoeeccssccvesss O,0000 
COPPELs tex ceacte cs ssccetieee. 20.0018], Marbles ie scesmisisincie acces 20 siete 0.0716 
TPOMG ee sisice visio «sce sie aisote Bietae «6 00043.) Brick ..sc.ces suites ssc eee, ca elouU 
FANG cee cakidas @ereeeeene eeeoe 0.0045 


CONDUCTION AND CONVECTION OF HEAT, 469 


Relative Heat-conducting Power of Metals. 
(* Calvert & Johnson ; t Weidemann & Franz.) 


Metals. *¥C. & J. tw. & F. Metals. AChR Baily 

Bilvercc. tascecess ce. 1000 1000 admin. sss ee 577 ren 

Ole cies sia see's 981 532 | Wroughtiron...... 436 119 

Gold, with 1% of silver 840 eine LUD eerste tenes wr 4a, 145 

Copper, rolled ....... 845 736 Steely se ese tea ee Oe G 116 

Coppers cast... wc. cs 811 anee PlatinumMpe see arse Oc U 84 

WCrCUT Yi. teem ee 677 Cfo SOLU Mises cts cerercice 365 ie Ae 

Mercury, with 1.25% CaStHrOneeece teeta 859 dad 
ORPUIN re cote ore 412 sieiete IGCA CL aeetectet re cite vere 287 85 

FATTIUIIINUI ete cee ents 665 ser Antimony : 

Zine : east horizontally.. 215 slerai 
cast vertically...... 62 seine east vertically.... 192 NaS 
cast horizontally... 608 Sarete BISTNUTG oe eter) eerie 61 18 
LOMCU Mae actives coca 641 ; 


ConbDUCTING POWER OF A METAL. 


Influence of carbon on iron: Cast copper 22a see ubeo mere 811 
Wrought iron..... Mioletateteleveicrerere 436 Copper with 1% of arsenic....... 57 
Steelers. e2. OO bi > ARE 397 oy with .5% of arsenic... .. 669 
CASUSILON ice ceiglae coewsiee Rivera: 859 te with .25% of arsenic..... 17 


The Rate of External Conduction through the bounding surface 
between a solid body and a fluid is approximately proportional to the 
difference of temperature, when that is small ; but when that difference is 
considerable the rate of conduction increases faster than the simple ratio of 
that difference. (Rankine.) 

If 7, as before, is the coefficient of internal thermal resistance, e and e’ the 
coefficient of external resistance of the two surfaces, x the thickness of the 
plate, and 7’ and T the temperatures of the two a in contact with the 

/ 


two surfaces, the rate of conduction is g= According to 


‘ ete+rx 
pales te tt ase: 3 

Peclet, e + e’= AN Ba — 7)’ in which the constants A and B have 
the following values: 

BB for polished metallic surfaces \.f..5sencse) = vc taecesce aeee .0028 

B for rough metallic surfaces and for non-metallic surfaces.. .0037 

‘Ai for polished metals aboutiera. + exicicets chines cts aera ee eine .90 

A for glassy and varnished surfaces............0..000 eatin whe 1.34 

A for dull metallic surfaces ........ .... Ae sictaleteisie s!tereleea eects 1.58 

PAs for lam p*blachkems oats cia edie asc ool screlal Neolarer cle sinc brs wee are ele’ ner 


When a metal plate has a liquid at each side of it, it appears from experi- 
ments by Peclet that B = .058, A = 8.8. 

The results of experiments on the evaporative power of boilers agree very 
well with the following approximate formula for the thermal resistance of 
boiler plates and tubes : 

a 


ete= W_n’ 


which gives for the rate of conduction, per square foot of surface per hour, 
CT 
oS PRET FPN We 

This formula is proposed by Rankine as a rough approximation, near 
enough to the truth for its purpose. The value of a lies between 160 and 200. 

Convection, or carrying of heat, means the transfer and diffusion of 
the heat in a fluid mass by means of the motion of the particles of that 
mass. 

The conduction, properly so called, of heat through a stagnant mass of 
ftuid is very slow in liquids, and almost, if not wholly, inappreciable in 
gases. Itis only by the continual circulation and mixture of the particles of 
the fluid that uniformity of temperature can be maintained in the fluid 
inass, or heat transferred between the fluid mass and a solid body. 

The free circulation of each of the fluids which touch the side of a solid 
plate is a necessary condition of the correctness of Rankine’s formule for 
the conduction of heat through that plate; and in these formule it is im- 


470 HEAT, 


plied that the circulation of each of the fluids by currents and eddies is 
such as to prevent any considerable difference of temperature between the 
fluid particles in contact with one side of the solid plate and those at con- 
siderable distances from it. 

When heat is to be transferred by convection from one ‘fluid to another, 
through an intervening layer of metal, the motions of the two fluid masses 
should, if possible, be in opposite directions, in order that the hottest par- 
ticles of each fluid may be in communication with the hottest particles of 
the other, and that the minimum difference of temperature between the 
adjacent particles of the two fluids may be the greatest possible. 

Thus, in the surface condensation of steam, by passing it through metal 
tubes immersed in a current of cold water or air, the cooling fluid shouid 
be made to move in the opposite direction to the condensing steam. 


Steam-pipe Coverings. 


(Experiments by Prof. Ordway, Trans. A.S.M.E., vi, 168; also Circular No. 
; 27 of Boston Mfrs. Mutual Fire Ins. Co., 1890.) 








PWater | British | acstter in [BS 

‘ heated Thermal 1sq.ft, {= = 

Substance 1 inch thick. Heat 10° F _| Units 1 q. as 

applied, 310° F. ace per sq. ft. woe on 

’ ye ’ = 

through Per partsin {4&3 

1sq. ft, | minute. 1000, |e 
1. Loose wool......... oraia gislelereirie sra/avs 8.1 1.35 
2. Live-geese feathers ..csecsse- cove 9.6 1.60 
3. Carded cotton wool...... Sara wa soe 10.4 1.73 
SH atm Felt caiwcd shi soieals Bie 4 aya bce 10.3 1.72 
Dee LOOSE LOLI OLACKaae taisiele ei-ie\c/ensi ale 9.8 1.63 
6. Compressed lampblack.....+seees 10.6 £:77 
AAOOTK CROTCOCLsenmrrareiia oe ess eles S000 11.9 1.98 
8. White-pine charcoal..... ... AG 13.9 2.32 
9. Anthracite-coal powder..... ..- 85.7 5.95 
10. Loose calcined magnesia........ 12.4 2.07 
11. Compressed calcined magnesia. . 42.6 7.10 
12. Light carbonate of magnesia.... 13.7 2.28 
13. Compressed carb. of magnesia... 15.4 2250 
14. Loose fossil-meal........ Hse 5c 14.5 2.42 
15. Crowded fossil-meal.......... mars 15.% 2.62 
16. Ground chalk (Paris white)..... 20.6 3.43 
17. Dry plaster of Paris.............. 30.9 5.15 
18. FinE ASHESTOS.....cccccccvseccvce 49.0 8.17 
POsSAIT ALONC 2. <5 Fece cna ° mslaia neces 48.0 8.00 
POR SANG sss. dees oces HBBUOENS seboness 62.1 10.35 
21. Best slag-wool............. aiefelare nis 713. Pe Hyd 
E NIGCDINC Traisthisvaceicicicie ote's)s = cy. efayeven ste oa 14. 2.33 
23. Blotting-paper wound tight..... 21. 3.50 
24, Asbestos paper wound tight..... 21.7 3.62 
25. Cork strips DOUNAd ON......eeeee 14.6 2.43 

26. Straw rope wound spirally...... 18. 3. 

OT IEOOSCINECELEILOLL] soe e100 ays «sled eoearete 18.7 3.12 
28. Paste of fossil-meal with hair.... 16.7 2.78 
29. Paste of fossil-meal with asbestos 22. 3.67 
30. Loose bituminous-coal ashes.... 21. 3.50 
831. Loose anthracite-coal ashes..... Pike 4.50 
32. Paste of clay and vegetable fibre 80.9 5.15 








It will be observed that several of the incombustible materials are nearly 
as efficient as wool, cotton, and feathers, with which they may be compared 
in the preceding table. The materials which may be considered wholly free 
from the danger of being carbonized or ignited by slow contact with pipes 
or boilers are printed in Roman type. Those which are more or less liable 
to be carbonized are printed in italics. 

The results Nos. 1 to 20 inclusive were from experiments with the 
various non-conductors each used in a mass one inch thick, placed on a flat 
surface of iron kept heated by steam to 310° F, The substances Nos. 21 to 


CONDUCTION AND CONVECTION OF HEAT, 471 


82 were tried as coverings for two-inch steam pipe; the results being re- 
duced to the same terms as the others for convenience of comparison. 

Experiments on still air gave results which differ little from those of Nos. 
8,4, and 6. The bulk of matter in the best non-conductors is relatively too 
émall to have any specific effect except to trap the air and keep it stagnant. 
These substances keep the air still by virtue of the roughness of their fibres 
or particles. The asbestos, No. 18, had smooth fibres. Asbestos with ex- 
ceedingly fine fibre made a somewhat better showing, but asbestos is really 
one of the poorest non-conductors. It may be used advantageously to hold 
together other incombustible substances, but the less of it the better. A 
‘“*magnesia’’ covering, made of carbonate of magnesia with a small per- 
centage of good asbestos fibre and containing 0.25 of solid matter, trans- 
mitted 2.5 B. T. U. per square foot per minute, and one containing 0.396 of 
solid matter transmitted 3.33 B. T. U. 

Any suitable substaace which is used to prevent the escape of steam heat 
should not be less than one inch thick. 

Any covering should be kept perfectly dry, for not only is water a good 
carrier of heat, but it has been found that still water conducts heat about 
eight times as rapidly as still air. 

Tests of Commercial Coverings were made by Mr. Geo. M. Brill 
and reported in Trans. A. 8. M. E., xvi. 827. A length of 60 feet of 8-inch 
steam-pipe was used in the tests, and the heat loss was determined by the 
condensation. The steam pressure was from 109 to 117 lbs. gauge, and the 
temperature of the air from 58° to 81°F. The difference between the tem- 
perature of steam and air ranged from 263° to 286°, averaging 272°, 

The following are the principal results : 











Sons a Soi ye 
— 77] joy fu ha o ° { 
B 188lu leete| Sh. lay | 285 
> gaia Hove 35) 2 eft 
2 We : oe Sl & gu} Qe S 
ss so /. 1eMes! oga( ee | Ls" 
Kind of Covering. 3 2 Te Or tetra ea? pee Do ll 
gs cx [Og DOD} Omy, soho Ass, 
oe é et eal | A200 See Ox. peg 
oO wn oo -* + S08 TER qe BS eS 
Gs | Re PS Ibn Ss| olen | Cog! Sua 
63 [a8 |a8 boen| E¥s | Seo [ ace 
a NPB Ol, pel pates | eet Pi CARe. bie alr oe 
Soy ee RES ee ee) 2) ae} ae 
Bare pipe...... Neosdceec | Netact (ecotouldacek|ees 400 100. 2.819 
MMASMESI an. oleate oclelos sires 1.25 | .120 1.74 384 726 14.2 .400 
LOC KEWOOl yc leveistels pe cee| oh260) 5080 1.16 256 766 9.5 267 
Mineral wool.......... 1.380 | .089 1.29 285 757 10.5 .297 
MIre-felti sides cna en 1.30 | .157 2.28 502 689 18.6 523 
Manville sectional..... ale .109 1.59 350 VEY 12.9 564 
Manv. sect. & hair-felt.| 2.40 | .066 | 0.96 212 780 Teste, 221 
Manville wool-cement.| 2.20 | .108 | 1.56) .345 738 12.7 .359 
Champion mineralwool| 1.44 | .099 | 1.44] .317 «747 rh yl 330 
Eigin-felt... Were titers 82 | .182 1.91 422 714 15.6 48 
Riley cement.......... 75 | .298 | 4.32) .953 .548 85.2 993 
Fossil-meal............ SN) Ae 3.99 879 pil 32.5 . 916 








Transmission of Heat, through Solid Plates, from 
Water to Water. (Clark, S.E.).—M. Péclet found, from experiments 
mace with plates of wrought iron, cast iron, copper, lead, zinc, and tin, 
that when the fluid in contact with the surface of the plate was not circu- 
lated by artificial means, the rate of conduction was the same for different 
metals and for plates of the same metal of different thicknesses, But 
when the water was thoroughly circulated over the surfaces, and when 
these were perfectly clean, the quantity of transmitted heat was inversely 
proportional to the thickness, and directly as the difference in temperature 
of the two faces of the plate. When the metal surface became dull, the 
rate of transmission of heat through all the metals was very nearly the 
same. ; 

It follows, says Clark, that the absorption of heat through metal plates is 
more active whilst evaporation is in progress—when the circulation of the 
water is more active—than while the water is being heated up to the boiling 
point. 


472) > HEAT. 


Transmission from Steam to Water.—M. Péclet’s principle is 
supported by the results of experiments made in 1867 by Mr. Isherwood on 
the conductivity of different metals. Cylindrical pots, 10 inches in diameter, 
2114 inches deep inside, and 1 inch, 14 inch, and 3 inch thick, turned and 
bored, were formed of pure copper, brass (60 copper and 40 zine), rolled 
wrought iron, and remelted cast iron. They were immersed in a steam 
bath, which was varied from 220° to 320° F. Water at 212° was supplied to 
the pots, which were kept filled. It was ascertained that the rate of evapora- 
tion was in the direct ratio of the difference of the temperatures inside and 
outside of the pots; that is, that the rate of evaporation per degree of 
difference of temperatures was the same for all temperatures; and that the 
rate of evaporation was exactly the same for different thicknesses of the 
metal. The respective rates of conductivity of the several metals were as 
follows, expressed in weight of water evaporated from and at 212° F. per 
square foot of the interior surface of the pots per degree of difference of 
temperature per hour, together with the equivalent quantities of heat-units: 


‘Water at 212°. Heat-units. Ratio. 


Copper wie. sce. BAe Arc Sse tm OOD ILD: 642.5 1.00 
BLASS heme mcsrrenerae ED Aieee 556.8 87 
WTOUSHtITOM scree asst oe een OC ale: 73.6 .58 
CAStHrOnitecschctrctlactae. tees ae 315.7 .49 


Whitham, ‘‘Steam Engine Design,”’ p. 283, also Trans. A.S. M. E. ix, 425, in 
using these data in deriving a formula for surface condensers calls these 
figures those of perfect conductivity, and multiplies them by a coefficient 
OC, which he takes at 0.328, to obtain the efficiency of condenser surface in 
ordinary use, i.e., coated with saline and greasy deposits. 

Transmission of Heat from Steam to Water through 
Coils of Iron Pipe.—H. G. C. Kopp and F. J. Meystre (Stevens Indi- 
cator, Jan., 1894), give an account of some experiments on transmission of 
heat through coils of pipe. They collate the results of earlier experiments 
as follows, for comparison: 





g Steam Con- Heat trans- 
3 densed per mitted per 
= Square foot per/square foot per 
a degree differ- | degree differ- 
2 ca ence of temper-|ence of temper- 
a & ature per hour.| ature per hour. Remarks. 
Z. = : - 
5 8 ae | oa | BS bx 
= 3 Sa |e s [4s fas 
rf s S35 1835, eH | sce 
& 'S) ke) PSBO o Po. 
tea ;~;>Ra&o) re | eae 
Laurens |Copper coils...| .292 .981 815 97 
ie 2 Copper coils.,; .... 1.20 ae! 1120 
Havrez..|Copper coil...| .268 1.26 280 | 1200 
Perkins. |Ivon coil...... a EA Page OnE y ts eee os 
“ ees nee ba reer armcm onc } a pressure 
Box.....|Irontube... .| .235 | ..... 980 |... ote eas 
Le etaea Ss S)-,|’, 196 aes 20 ial terete eee 
Bsc cell Pee sis: si) 00 aah PACD ively 
Havrez..|Cast-iron boil- 
33 BY See ae O77 105 82 100 


From the above it would appear that the efficiency of iron surfaces is less 
than that of copper coils, plate surfaces being far inferior. 

In all experiments made up to the present time, it appears that the tem- 
perature of the condensing water was allowed to rise, a mean between the 
initial and final temperatures being accepted as the effective temperature. 
But as water becomes warmer it circulates more rapidly, thereby causing 
the water surrounding the coil to become agitated and replaced by cooler 
water, which allows more heat to be transmitted, i re os 


CONDUCTION AND CONVECTION OF HEAT. 473 


Again, in accepting the mean temperature as that of the condensing me- 
dium, the assumption is made that the rate of condensation is in direct pro- 
portion to the temperature of the condensing water. 

In order to correct and avoid any error arising from these assumptions 
and approximations, experiments were undertaken; in which all the condi- 
tions were constant during each test. 

The pressure was maintained uniform throughout the coil, and provision 
was made for the free outflow of the condensed steam, in order to obtain 
at all times the full efficiency of the condensing surface. The condensing 
water was continually stirred to secure uniformity of temperature, which 
was regulated by means of a steam-pipe and a cold-water pipe entering the 
tank in which the coil was placed. 

The following is a condensed statement of the results 


HEAT TRANSMITTED PER SQuARE Foot or CooLine SuRFACE, PER Hour, 
PER DEGREE OF DIFFERENCE OF TEMPERATURE. (British Thermal Units.) 


; 1-in. Iron Pipe;} 134 in. Pipe; | 114 in. Pipe; | 11 in. Pipe; 
pepe Steam inside, | Steam inside, Steam outside, | Steam inside, 
ing Water, | 6°,!bs. Gauge 10 lbs, 10 lbs. 60 lbs. 





Pressure. Pressure. Pressure. Pressure. 
80 265 128 200 
100 269 130 230 239 
120 272 137 260 247 
140 277 145 267 276 
160 281 158 271 306 
180 299 174 270 349 
200 313 ron. 419 





The results indicate that the heat transmitted per degree of difference of 
temperature in general increases as the temperature of the condensing 
water is increased. 

The amount transmitted is much larger with the steam on the outside of 
the coil than with the steam inside the coil. This may be explained in part by 
the fact that the condensing water when inside the coil flows over the sur- 
face of conduction very rapidly, and is more efficient for cooling than when 
contained in a tank outside of the coil. 

This result is in accordance with that found by Mr. Thomas Craddock, 
which indicated that the rate of cooling by transmission of heat through 
metallic surfaces was almost wholly dependent on the rate of circulation of 
the cooling medium over thesurface to be cooled. 

Transmission of Heat in Condenser Tubes. (Eng’g, Dec. 
10, 1875, p. 449.).—In 1874 B. C. Nichol made experiments for determining the 
rate at which heat was transmitted through a condenser tube. The results 
went to show that the amount of heat transmitted through the walls of the 
jube per estimated degree of mean difference of temperature increased 
considerably with this difference. For example: 


Estimated mean difference of Vertical Tube. Horizontal Tube 
temperature between insideand — Ss) pats Sena 
outside of tube, degrees Fahr. . 128 151.9 152.9 111.6 146.2 150.4 

Heat-units transmitted per hour 
per square foot of surface per 
degree of mean diff. of temp.... 422 531 561 610 737 823 


These results seem to throw doubt upon Mr. Isherwood’s statement that 
the rate of evaporation per degree of difference of temperature is the same 
for all temperatures. 

Mr. Thomas Craddock found that water was enormously more efficient 
than air for the abstraction of heat through metallic surfaces in the process 
of cooling. He proved that the rate of cooling by transmission of heat 
through metallic surfaces depends upon the rate of circulation of the cool- 
ing medium over the surface to be cooled. A tube filled with hot water, 
moved by rapid rotation at the rate of 59 ft. per second, through air, lost as 
much heat in one minute as it did in still air in 12 minutes. In water, at a 
velocity of 3 ft. per second, as much heat was abstracted in half a minute as 
was abstracted in one minute when it was at rest in the water. Mr. Crad- 
dock concluded, further, that the circulation of the cooling fluid became of 








AG4 Heat. 


greater importance as the difference of temperature on the two sides of thé 
plate became less, (Clark, R. T. D., p. 461.) 

Heat Transmission through Cast-iron Plates Pickled in 
Nitric Acid.—Experiments by R. C. Carpenter (Trans. A. S. M. E., xii 
179) show a marked change in the conducting power of the plates (from 
steam to water), due to prolonged treatment with dilute nitric acid. 

The action of the nitric acid, by dissolving the free iron and not attacking 
the carbon, forms a protecting surface to the iron, which is largely com- 

‘posed of carbon. The following is a summary of results: 


roe te ae 
ermal Units ela- 
J sar ali Transmitted for| tive 
Character of Plates, each plate 8.4 in. 8.125 Ibs. of each Degree of | Trans- 
by 5.4 in., exposed surface 27 sq. ft. |" Water Difference of {mission 
Temperature per| of 


Increase in 





each 
F Square Foot per | Heat. 
Minute. Went 
Cast iron—untreated skin on, but 
clean, free from rust. ............. 13.90 113.2 100.0 
Oast iron—nitric acid, 1% sol., 9 days.. 11.5 97.7 86.3 
4 . 1% sol., 18 days. 9.7 80.08 70.7 
< “ 1% sol., 40 days. 9.6 77.8 68.7 
4 i: 5% sol., 9 days.. 9.93 87.0 76.8 
i 5% sol., 40 days. 10.6 77.4 68.5 
Plate of pine wood, same dimensions 
as the plate of cast iron........... 0.33 1.9 1.6 


The effect of covering cast-iron surfaces with varnish has been investi- 
gated by P.M. Chamberlain. He subjected the plate to the action of strong 
acid for a few hours, and then applied a non-conducting varnish. One sur: 
face only was treated. Some of his results are as follows: 


os 170. As finished—greasy. 

ne 152 Sa tiss washed with benzine and dried. 

Sg 169. Oiled with lubricating oil. 

Be ®.+| 162. After exposure to nitric acid sixteen hours, then oiled (lin- 
wo bot ; seed oil.) 
3244/1} 166 After eaLonre to hydrochloric acid twelve hours, then oiled 
asec (linseed oil.) 

Sus 113. ) After exposure to sulphuric acid 1, water 2, for 48 hours, 
so © t 117. J then oiled, varnished, and allowed to dry for 24 hours. 


Transmission of Heat through Solid Plates from Air 
or other Dry Gases to Water. (From Clark on the Steam Engine.) 
—The law of the transmission of heat from hot air or other gases to water, 
through metallic plates, has not been exactly determined by experiment. 
The general results of experiments on the evaporative action of different 
portions of the heating surface of a steam-boiler point to the general law 
that the quantity of heat transmitted per degree difference of temperature 
is practically uniform for various differences of temperature. 

The communication of heat from the gas to the plate surface is much 
er eg as. by mechanical impingement of the gaseous products upon the 
surface. 

Clark says that when the surfaces are perfectly clean, the rate of trans- 
mission of heat through plates of metal from air or gas to water is greater 
for copper, next for brass, and next for wrought iron. But when the sur- 
faces are dimmed or coated, the rate is the same for the different metals. 

With respect to the influence of the conductivity of metals and of the 
thickness of the plate on the transmission of heat from burnt gases to 
water, Mr. Napier made experiments with small boilers of iron and copper 
placed over a gas-flame. The vessels were 5 inches in diameter and 2% 
inches deep. From three vessels, one of iron, one of copper, and one of iron 
sides and copper bottom, each of them 1/30 inch in thickness, equal quanti- 
ties of water were evaporated to dryness, in the times as follows; 


CONDUCTION AND CONVECTION OF HEAT. 475. 


Tron and Copper 


Water. Tron Vessel. Copper Vessel. Uaesel. 
4 ounces 19 minutes 18.5 minutes Sete 
11 “6 33 ns 30.75 SP A aa rN a Ene! : 
Sig BO. yt 44 i ieee hdiek lig od Ue, 
4 ae OLE ct actevavate 36.83 minutes. 


Two other vessels of iron sides 1/30 inch thick, one having a 14-inch copper 
nottom and the other a 44-inch lead bottom, were tested against the iron 
and copper vessel, 1/30 inch thick. Equal quantities of water were evapo- 
rated in 54, 55, and 5314 minutes respectively. Taken generally, the results 
of these experiments show that there are practically but slight differences 
between iron, copper, and lead in evaporative activity, and that the activity 
is not affected by the thickness of the bottom. 

Mr. W. B. Johnson formed a like conclusion from the results of his obser- 
vations of two boilers of 160 horse-power each, made exactly alike, ex- 
cept that one had iron flue-tubes and the other copper flue-tubes. No dif- 
ference could be detected between the performances of these boilers. 

Divergencies between the results of different experimenters are attribut- 
able probably to the difference of conditions under which the heat was 
transmitted, as between water or steam and water, and between gaseous 
matter and water. On one point the divergence is extreme: the rate of 
transmission of heat per degree of difference of temperature. Whilst from 
400 to 600. units of heat are transmitted from water to water through iron 
plates, per degree of difference per square foot per hour, the quantity of 
heat transmitted between water and air, or other dry gas, is only about 
from 2 to 5 units, according as the surrounding air is at rest or in movement. 
In a locomotive boiler, where radiant heat was brought into play, 17 units 
of heat were transmitted through the plates of the fire-box per degree of 
difference of temperature per square foot per hour. 

Transmission of Heat through Plates and Tubes from 
Steam or Hot Water to Air.—The transfer of heat from steam or 
water through a plate or tube into the surrounding air is a complex opera- 
tion, in which the internal and external conductivity of the metal, the radi- 
ating power of the surface, and the convection of heat in the surrounding 
air are all concerned. Since the quantity of heat radiated from a surface 
varies with the condition of the surface and with the surroundings, according 
to laws not yet determined, and since the heat carried away by convection 
varies with the rate of the flow of the air over the surface, it is evident that 
no general law can be laid down for the total quantity of heat emitted. 

The following is condensed from an article on Loss of Heat from Steam- 
pipes, in The Locomotive, Sept. and Oct., 1892. 

A hot steam-pipe is radiating heat constantly off into space, but at the 
saine time it is cooling also by convection. Experimental data on which to 
base calculations of the heat radiated and otherwise lost by steam-pipes are 
neither numerous nor satisfactory. 

In Box’s Practical Treatise on Heat a number of results are given for the 
amount of heat radiated by different substances when the temperature of 
the air is 1° Fahr. lower than the temperature of the radiating body. A 
portion of this table is given below. It is said to be based on Péclet’s ex- 
periments. 


Heat Units RADIATED PER Hour, PER SQUARE Foot oF SURFACKH, FOR 
1° FAHRENHEIT EXxceEess IN TEMPERATURE. 





Copper, polished ............... .0327 | Sheet-iron, ordinary............ 5662 
Min, polished Pesgiepeycte -ecs- sexe sOSSO M Maderseee Se os ssi si cob ae Ldsse ae OLS 
Zine and brass, polished........ .0491 | Cast iron, new......... sis acai . .6480 
Tinned iron, polished..... sseeeee 20858 | Common steam-pipe, inferred... .6400 
Sheet-iron, polished........ .-.-. .0920 | Cast and sheet iron, rusted..... .6868 
Sheet lead :3....3..<. esececesese 1829 | Wood, building stone, and brick .7358 





When the temperature of the air is about 50° or 60° Fahr., and the radiat- 
ing body is not more than about 30° hotter than the air, we may ealculate 
the radiation of a given surface by assuming the amount of heat given off 
by it in a given time to be proportional to the difference in temperature be- 
tween the radiating body and the aix. This is ‘* Newton’s law of cooling.” 
But when the difference in temperature is great, Newton’s law does not hold 
good; the radiation is no longer proportional to the difference in tempera- 
ture, but must be calculated by a complex formula established experiment, 
ally by Dulong and Petit. Box has computed a table from this formula, 
which greatly facilitates its application, and which is given below : 


476 HEAT, gS 


FACTORS FOR REDUCTION TO DuLONG’s LAw OF RADIATION: 





== 


L.fferences in Tem- Temperature of the Air on the Fahrenheit Scale. 

perature between 
RadiatiigsBody™ [hte], fer pee ee ee ee ee 

and the Air. 32° | 50° | 59° | 68° | 86° |104°} 122° |140°/158°|176° |194°/212° 


























Deg. Fahr. 

18 1.00}1.07)1.12}1.16)1.25)1.36)1.47)1.58]1.70/1.85)1.99/2.15 

36 1.03)1.08)1.16}1.21)1.30/1.40)1.52]1.68)1.76)1.91'2.06/2.23 

54 1.07/1.16/1.20)1.25)1.85/1.45)1.58}1.70)1.83)1.99)2.14/2.31 

W2 1.12)1.20)1.25)1.380)1.40)1.52)1.64)/1.76}1.90/2.07/2.23/2.40 

90 1.16]1.25]1.81)1.36)1.46)1.58/1.71)1.84]1.98)2.15/2.33/2.51 
108 1.21/1.31]1.36)1.42/1.52/1.65)1.78/1.92)2.07/2.28|/2. 42/262 
126 1.26/1.86)1.42}1.48/1.50)1.72/1.86/2.00}2.16/2.34/2.52/2.72 
144 1.32/1.42/1.48)1.54/1.65/1.79)1.94}2.08)2.24/2.44/2.64/2.83 
162 1.37/1.48/1.54/1.60)1.73/1.86/2.02/2.17/2.34/2.54:2.74/2.96 
180 1.44/1.55)1.61/1.68)1.81]1.95/2.11/2.27/2.46/2.66/2.87/3.10 
198 1.50}1.62/1.69)]1.75)1.89/2.04)2.21/2.38)2.56/2.78)/3.00|3.24 
216 1.58}1.69]1.76}1.83|1.97/2.13/2.32/2.48]2.68)/2.91/3.13/3.38 
234 1.64)1.77/1.84}1 .90/2.06/2.28/2.43/2.52/2.80/8.03!3.28/3.46 
252 1.71/1.85)1.92/2.00)2.15/2.33/2.52/2.71/2.92/3.18/3.43/3.70 
270 1.79)1.93/2.01/2.09)2.22/2.44/2.64/2.84/3.06/3.32.3.58/3.87 
288 1.89/2.03/2.12)2.20/2.37/2.56/2.78/2.9913.22/3.50/3.77/4.07 
306 1.98/2.13/2.22)2.31/2.49/2.69/2.90/3.12/3.37/3.66'3.95/4.26 
324 2.07)2.23)2.33/2.42)2.62/2.81/3 .04)3. 2813 .53/3.84/4.14/4.46 
342 2.17/2.34/2.44)2.54/2.73/2.95/3.19]3.4413.70/4.02)4.34/4.68 
360 2.27/2.45)2.56/2.66/2.86/3.09)3 .385]3.60/3.88)4.22/4.55/4.91 
378 2.39/2.57/2.68/2.79/3.00/3.24/3.51/3.78/4.0814.42/4. 775.15 
396 2.50)/2.70/2.81/2.93/3.15)3.40/3.68)3.97/4.28/4.64!5.01/5.40 
414 2.63]2.84/2.95)3.07/3.31/38.51/3.87|4.12)4.48)4.87/5.26/5.67 
432 2.76/2.98 3.10 Sard oth 3.76/4.10/4.82/4.61/5.12'5.33/6.04 











The loss of heat by convection appears to be independent of the nature of 
the surface, that is, it is the same for iron, stone, wood, and other materials. 
It is different for bodies of different shape, however, and it varies with the 
position of the body. Thus a vertical steam-pipe will not lose so much heat © 
by convection as a horizontal one will; for the air heated at the lower part 
of the vertical pipe will rise along the surface of the pipe, protecting it to 
some extent from the chilling action of the surrounding cooler air. For a 
similar reason the shape of a body has an important influence on the result, 
those bodies losing most heat whose forms are such as to allow the cool air 
free access to every part of their surface. The following table from Box 
gives the number of heat units that horizontal cylinders or pipes lose by 
convection per square foot of surface per hour, for one degree difference in 
temperature between the pipe and the air. 


Heat Units Lost By CONVECTION FROM HoRIZONTAL PIPES, PER SQUARE 
Foot oF SURFACE PER Hour, FoR A TEMPERATURE 
DIFFERENCE OF 1° FAR. 














External External External 
Diameter of |Heat Units} Diameter |Heat Units} Diameter | Heat Units 

Pipe Lost. of Pipe Lost. of Pipe Lost. 

in inches. in inches. in inches. 
2 0.728 Ff 0.509 18 0.455 
3 0.626 8 0.498 24 0.447 
4 0.574 9 0.489 36 0.438 
5 0.544 10 0.482 48 0.484 
6 0.523 12 0.472 AB Pe ocd 





The loss of heat by convection is nearly proportional to the difference in 
temperature between the hot body and the air; but the experiments of 


CONDUCTION AND CONVECTION OF HEAT. 477 


Dulong and Péclet show that this is not exactly true, and we may here also 
resort to a table of factors for correcting the results obtained by simple 
proportion. 


Factors FoR REDUCTION TO DuLONG’s LAw OF CONVECTION. 





Difference Difference Difference 
in Temp. in Temp. in Temp. 
between Hot} Factor. etween Hot} Factor. between Factor. 
Body and Body and Hot Body 
Air. Air. and Air. 
18° F 0.94 180° F. 1.62 342° F 1.87 
36° 1.11 198° 1.65 360° 1.90 
54° 1.22 216° 1.68 878° 1.92 
ties 1.30 234° Tee 396° 1.94 
90° 1.37 252° 1.7 414° 1.96 
108° 1.43 270° 1.77 432° 1.98 
126° 1.49 288° 1.80 450° 2.00 
144° 1.53 806° 1.83 468° 2.02 
162° 1.58 324° 1.85 tee 


EXAMPLE IN THE USE OF THE TABLES.—Required the total loss of heat by 
both radiation and convection, per foot of length of a steam-pipe 2 11/32 
in. external diameter, steam pressure 60 lbs., temperature of the air in the 
room 68° Fahr. . 

Bee arn Corresponding to 60 lbs. equals 307°; temperature difference 
= 307 — = 239°. 

Area of one foot length of steam-pipe = 2 11/32 x 3.1416 + 12 = 0.614 sq. 
ft 


Heat pe per hour per square foot per degree of difference, from 
table, 0.64. 

Radiation loss per hour by Newton’s law = 239° x .614 ft. K .64 = 93.9 
heat units. Same reduced to conform with Dulong’s law of radiation: factor 
from table for temperature difference of 239° and temperature of air 68° = 
1.93. 93.9 x 1.93 = 181.2 heat units, total loss by radiation. 

Convection loss per square foot per hour from a 2 11/82-inch pipe: by in- 
terpolation from table, 2” = .728, 3” = .626, 2 11/32’ = .698. 

Area, .614 X .693 * 239° = 101.7 heat units. Same reduced to conform with 
Dulong’s law of convection: 101.7 x 1.73 (from table) = 175.9 heat units per 
hour. Total loss by radiation and convection = 181.2 + 175.9 = 357.1 heat 
units per hour. Loss per degree of difference of temperature per linear 
foot of pipe per hour = 357.1 + 239 = 1.494 heat units = 2.433 per sq. ft. 

It is not claimed, says The Locomotive, that the results obtained by this 
method of calculation are strictly accurate. The experimental data are not 
sufficient to allow us to compute the heat-loss from steam-pipes with any 
great degree of refinement; yet it is believed that the results obtained as 
indicated above will be sufficiently near the truth for most purposes. An 
experiment by Prof. Ordway, in a pipe 211/32 in. diam. under the above 
conditions (Trans. A. Ss. M. Ez, v. 73), Showed a condensation of steam of 181 
grammes per hour, which is equivalent to a loss of heat of 358.7 heat units 
per hour, or within half of one per cent of that given by the above calcula 

ion. 

According to different authorities, the quantity of heat given off by steam 
and hot-water radiators in ordinary practice of heating of buildings by 
direct radiation varies from 1.8 to about 3 heat units per hour per square 
foot per degree of difference of temperature. 

The lowest figure is calculated from the following statement by Robert 
Briggs in his paper on “American Practice in Warming Buildings by 
Steam ” (Proc, Inst. C. E., 1882, vol, Ixxi): ‘‘ Each 100 sq. ft. of radiating 
surface will give off 3 Fahr. heat units per minute for each degree F., of dif- 
ference in temperature between the radiating surface and the air in which 
it is exposed.”’ 

_ The figure 2 1/2 heat units is given by the Nason Manufacturing Company 
in their catalogue, and 2 to 21/4 are given by many recent writers. 

For the ordinary temperature difference in low-pressure steam-heating, 
gay 212° — 70° = 142° F., 1 lb. steam condensed from 212° to water at the 


478 HEAT. 


same temperature gives up 965.7 heat units. A loss of 2 heat units per sq. 
ft. per hour per degree of difference, under these conditions, is equivalent 
to 2 x 142-- 965 = 0.3 Ibs. of steam condensed per hour per sq. ft. of heating 
surface. (See also Heating and Ventilation.) 

Transmission of Heat through Walls, etc., of Buildings 
(Nason Manufacturing Co.) (See also Heating and Ventilation.)—Heat 
has the remarkable property of passing through moderate thicknesses of air 
and gases without appreciable loss, so that air is not warmed by radiant 
heat, but by contact with surfaces that have absorbed the radiation. 


PowERS OF DIFFERENT SUBSTANCES FOR TRANSMITTING HEAT. 


Window-glass ........... 1000 Brieks, rouch:. 2. = Tie OU LOmeo0 
Oak or walnut....... ... 66 Bricks, whitewashed.... 200 
White pines. sa-acer.. .''le 80 Granite or slate.. ....... 250 
Pitchapine tgs © ssujeatss\0ehs 100 Sheet: 1FOM.cc sc ecmeees 1030 to 1110 
Lath or plaster ........ . “sto 100 


A square foot of glass will ecol 1.279 cubie feet of air from the tempera- 
ture inside to that outside per minute, and outside wall surface is generally 
estimated at one fifth of the rate of glass in cooling effect. 

Box, in his ‘*‘ Practical Treatise on Heat,’’ gives a table of the conducting 
powers of materials prepared from the experiments of Péclet. It gives the 
quantity of heat in units transmitted per square foot per hour by a plate 1 
inch in thickness, the two surfaces differing in temperature 1 degree: 


Hine-grained gray Marlen. casiems qo-seeteja i's aye ves CO OU 
Coarse-grained white marble...........s0s-ses cect eccece 22.4 
LOMO, aCALCALCOUS,” MING via 4 Ace «ais, ce ahs dels ore ove ef aaere cleknete neta 16.7 
HLONE, CalCareOusy OLUMIATY «1. sjarsrew ci iil Morel sis susie ete etre te ete 13.68 
Balked.clay, DViGKWOr Ky sorc.<s sjspesintac sesias © coins saa clears 4.83 
Brick-GCustasilveting vcaiccs <hewes Sorce ace cdttene «come eee 1.33 


Hood, in his ‘‘ Warming and Ventilating of Buildings,” p. 249, gives the 
results of M. Depretz, which, placing the conducting power of marbleat 1.00, 
give .483 as the value for firebrick. 


THERMODYNAMECS. 


Thermodynamics, the science of heat considered as a form of 
energy, is useful in advanced studies of the theory of steam, gas, and air 
engines, refrigerating machines, compressed air, etc. The method of treat- 
ment adopted by the standard writers is severely mathematical, involving 
constant application of the calculus. The student will find the subject 
thorougly treated in the recent works by Rontgen (Dubois’s translation), 
Wood, and Peabody. 

Hirst Law of Thermodynamiics.—Heat and mechanical energy 
are mutually convertible in the ratio of about 778 foot-pounds for the British 
thermal unit. (Wood.) Heat is the living force or vis viva due to certain 
molecular motions of the molecules of bodies, and this living force may be 
stated or measured in units of heat or in foot-pounds, a unit of heat in 
British measures being equivalent to 772 [778] foot-pounds. (Trowbridge, 
Trans. A. S. M. E., vii. 727.) 

Second Law of Thermodynamics.—tThe second law has by dif- 
ferent writers been stated in a variety of ways, and apparently with ideas 
so diverse as not to cover a common principle. (Wood, Therm., p. 389.) 

It is impossible for a self-acting machine, unaided by any external agency. 
to convert heat from one body to another at a higher temperature. (Clau- 


sius.) 

If all the heat absorbed be at one temperature, and that rejected be at 
one lower temperature, then will the heat which is transmuted into work be 
to the entire heat absorbed in the same ratio as the difference between the 
absolute temperature of the source and refrigerator is to the absolute tem- 
perature of the source. In other words, the second law is an expression for 
the efficiency of the perfect elementary engine. (Wood.) 

The living force, or vis viva, of a body (called heat) is always proportional 
to the absolute temperature of the body. (Trowbridge.) 

The expression Qi = % = ge may be called the symbolical or al- 

a I 
gebraic enunciation of the second law,—the law which limits the efficiency 
of heat engines, and which does not depend on the nature of the working 
medium employed, (Trowbridge.) @Q, and 7, = quantity and absolute 


PHYSICAL PROPERTIES OF GASES. 479 


temperature of the heat received, Q, and T, = quantity and absolute tem- 
perature of the heat rejected. 

Ls 2 T, 
$iz 
which receives all its heat at the absolute temperature 7,, and rejects heat 
at the temperature 72, converting into work the difference between the 

quantity received and rejected. 

ExAaMPLE.—What is the efficiency of a perfect heat engine which receives. . 
heat at 888° F. (the temperature of steam of 200 lbs. gauge pressure) and 
rejects heat at 100° F. (temperature of a condenser, pressure 1 lb. above 
vacuum), 


The expression represents the efficiency of a perfect heat engine - 


388 -L 459.2— (100+ 459.2) 
388 + 459.2 


In the actual engine this efficiency can never be attained, for the difference 
between the quantity of heat received into the cylinder and that rejected 
into the condenser is not all converted into work, much of it being lost by 
radiation, leakage, etc. In the steam engine the phenomenon of cylinder 
condensation also tends to reduce the efficiency. 





= 34%, nearly. 


PHYSICAL PROPERTIES OF GASES. 


(Additional matter on this subject will be found under Heat, Air, Gas, and 
Steam.) 


When a mass of gas is enclosed in a vessel it. exerts a pressure against the 
walls. This pressure is uniform on every square inch of the surface of the 
vessel; also, at auy point in the fluid mass the pressure is the same in every 
direction. 

In small vessels containining gases the increase of pressure due to weight 
immay be neglected, since all gases are very light; but where liquids are con- 
cerned, the increase in pressure due to their weight must always be taken 
into account. 

Expansion of Gases, Marriotte’s Law,.—The volume of a gas 
diminishes in the same ratio as the pressure upon it is increased. : 

This law is by experiment found to be very nearly true for all gases, and 
is known as Boyle’s or Mariotte’s law. 

If p = pressure at a volume v, and p; = pressure at a volume 2, p,v; = 


v 
PU; Pi = Beet pv = a constant. 


The constant, C, varies with the temperature, everything else remaining 
the same. 

Air compressed by a pressure of seventy-five atmospheres has a volume 
about 2% less than that computed from Boyle’s law, but this is the greatest 
divergence that is found below 160 atmospheres pressure. 

Law of Charles.—The volume of a perfect gas at a constant pressure 
is proportional to its absolute temperature. If vg be the volume of a gas 
&t 32° F, and v, the volume at any other temperature, ¢,, then 


ft, + 459.2 ty — 32° 
a vol ; i + othe (14 491.2) 1 


or _-v, = [1 + 0.002086(t, — 32°)] vp. 


If the pressure also change from pp to p,, 


_ po( t+ 459.2 
ig fr ed Garr ; 


The Densities of the elementary gases are simply proportional to 
their atomic weights. The density of acompound gas, referred to hydrogen 
as 1, ie page its molecular weight ; thus the relative density of CO, is 

(12 3) = RR, 
ie ehaddno"s Law .—Equval volumes of all gases, under the same con- 
ditions of teinperature and pressure, contain the same number of molecules. 

To find the weight of a gas in pounds per cubic foot at 32° F., multiply half 
the molecular weight of the gas by .00559. Thus 1 cu. ft. marsh-gas, CHy, 


= 3612+ 4) x .00559 = .0447 Ib, 


480- PHYSICAL PROPERTIES OF GASES. 


When a certain volume of hydrogen combines with one half its volume of 
oxygen, there is produced an amount of water vapor which will occupy the 
same volume as that which was occupied by the hydrogen gas when at the 
same temperature and pressure. 

Saturation-point of Vapors.—aA vapor that is not near the satura- 
tion-point behaves like a gas under changes of temperature and pressure; 
but if it is sufficiently compressed or cooled, it reaches a point where it be- 
gins to condense: it then no longer obeys the same laws as a gas, but its 
pressure cannot be increased by diminishing the size of the vessel containing 
it, but remains constant, except when the temperature is changed. The 
only gas that can prevent a liquid evaporating seems to be its own vapor. 

Dalton’s Law of Gaseous Pressures.—Every portion of a mass 
of gas inclosed in a vessel contributes to the pressure against the sides of 
the vessel the same amount that it would have exerted by itself had no 
other gas been present. 

Mixtures of Vapors and Gases.—The pressure exerted against 
the interior of a vessel by a given quantity of a perfect gas enclosed in it 
is the sum of the pressures which any number of parts into which such quan- 
tity might be divided would exert separately, if each were enclosed in a 
vessel of the same bulk alone, at the same temperature. Although this law 
is not exactly true for any actual gas, it is very nearly true for many. Thus 
if 0.080728 lb. of air at 32° F., being enclosed in a vessel of one cubic foot 
capacity, exerts a pressure of one atmosphere or 14.7 pouuds, on each square 
inch of the interior of the vessel, then will each additional 0.080728 lb. of air 
which is enclosed, at 82°, in the same vessel, produce very nearly an addi- 
tional atmosphere of pressure. The same law is applicable to mixtures of 
gases of different kinds. For example, 0,12344 lb. of carbonic-acid gas, at 
82°, being enclosed in a vessel of one cubic foot in capacity, exerts a pressure 
of one atmosphere; consequently, if 0.080728 lb. of air and 0.12344 Ib. of 
carbonic acid, mixed, be enclosed at the temperature of 32°, in a vessel of 
one cubic foot of capacity, the mixture will exert a pressure of two atmos: 
pheres. As asecond example: Let 0.080728 lb. of air, at 212°, be enclosed in 
a vessel of one cubic foot; it will exert a pressure of 


212 + 459.2 
32+ 459.2 


Let 0.03797 Ib. of steam, at 212°, be enclosed in a vessel of onecubic foot; it 
will exert a pressure of one atmosphere. Consequently, if 0.080728 lb. of air 
and 0.03797 lb. of steam be mixed and enclosed together, at 212°, in a vessel of 
one cubic foot, the mixture will exert a pressure of 2.366 atmospheres. It is 
a common but erroneous practice, in elementary books on physics, to des 
scribe this law as constituting a difference between mixed and homogeneous 
gases; whereas it is obvious that for mixed and homogeneous gases the law 
of pressure is exactly the same, viz., that the pressure of the whole of @ 
gaseous mass is the sum of the pressures of allits parts This is one of the © 
laws of mixture of gases and vapors. 

A second law is that the presence of a foreign gaseous substance in con. 
tact with the surface of a solid or liquid does not affect the density of the 
vapor of that solid or liquid unless there is a tendency to chemical com. 
bination between the two substances. in which case the density of the 
vapor is slightly increased. (Rankine, S. E., p. 239.) 

Flow of Gases.—By the principle of the conservation of energy, it may 
be shown that the velocity with which a gas under pressure will escape into 
a vacuum is inversely proportional to the square root of its density; that is, 
oxygen, which is sixteen times as heavy as hydrogen, would, under exactly 
the same circumstances, escape through an opening only one fourth as fast 
as the latter gas. 

Absorption of Gases by Liquids.—Many gases are readily ab- 
sorbed by water. Other liquids also possess this power in a greater or less 
degree. Water will for example, absorb its own volume of carbonic-acid 
gas, 430 tinies its volume of ammonia, 2144 times its volume of chlorine, and 
only about 1/20 of its volume of oxygen. 

The weight of gas that is absorbed by a given volume of liquid is propor- 
tional to the pressure. But as the volume of a mass of gas is less as the 
pressure is greater, the volume which a given amount of liquid can absorb 
at a certain temperature will be constant, whatever the pressure. Water, 
for example, can absorb its own volume of carbonic-acid gas at atmospheric 
pressure; it will also dissolve its own volume if the pressure is twice as 
great, but in that case the gas will be twice as dense, and consequently twice 
the weight of gas is dissolved. 


= 1.366 atmospheres. 





PKESSURE OF THE ATMOSPHERE, A81 


ATR. 


Properties of Air.—Air is a mechanical mixture of the gases oxygen 
and nitrogen; 20.7 parts O and 79.3 parts N by volume, 23 parts O and 77 parts 
N by weight. ; 

The weight of pure air at 32° F, and a barometric pressure of 29.92 inches 
of mercury, or 14.6963 lbs. per sq. in., or 2116.3 lbs. per sq. ft., is .080728 lb. per 
cubic foot. Volume of 1 lb. = 12.387 cu. ft. At any other temperature and 
1.3253 x B 
‘ 459.2+ T° 
where B = height of the barometer. 7= temperature Fahr., and 1.3253 = 
weight in lbs. of 459.2 c. ft. of air at 0° F. and one inch barometric pressure. 
Air expands 1/491.2 of its volume at 32° F, for every increase of 1° F., and 
its volume varies inversely as the pressure. 


barometric pressure its weight in lbs. per cubic foot is W = 


Volume, Density, and Pressure of Air at Various 
Temperatures. (D. K. Clark.) 





Volume at Atmos. Pressure at Constant 
Pressure. Elke § lbs. Volume. 
per Cubic Foot at 
Fahr. Atmos. Pressure. 








Cubic Feet | Compara- Lbs. per | Compara- 
in 1 lb. tive Vol. Sq. In. | tive Pres. 

0 11.583 881 .086331 12.96 881 
32 12.387 943 080728 13.86 943 
40 12.586 — .958 079439 14.08 958 
50 12.840 907 077884 14.36 977 
2 13.141 1.000 -076097 14.70 1.000 
70 13.342 1.015 -074950 14.92 1.015 
80 13.593 1.034 073565 15.21 1.034 
90 13.845 1.054 -072230 15.49 1.054 
100 14.096 1.073 -070942 Dali 1.073 
110 14.344 1.092 069721 16.05 1.092 
120 14.592 1.111 -063500 16.33 De id 
130 14.846 1.130 -067361 16.61 4.130 
140 15.100 1.149 -066221 16.89 1.149 
150 15.351 1.168 -065155 17.19 1.168 
160 15.603 1.187 -064088 17.50 1.187 
170 15.854 1.206 -063089 17.76 1.206 
180 16.106 1.226 -062090 18.02 1.226 
200 16.606 1.264 -060210 18.58 1.264 
210 16.860 1.283 2059313 18.86 1.283 
212 16.910 1.287 .059135 ~ 18.92 1.287 





The Air-manometer consists of a long vertical glass tube, closed at 
the upper end, open at the lower end, containing air, provided with a scale, 
and immersed, along with a thermometer, in a transparent liquid, such as 
water or oil, contained in a strong cylinder of glass, which communicates 
with the vessel in which the pressure is to be ascertained. The scale shows 
the volume occupied by the air in the tube. 

Let vp be that volume, at the temperature of 32° Fahrenheit, and mean 
pressure of the atmosphere, pg; let v, be the volume of the air at the tem- 
perature ¢, and under the absolute pressure to be measured p; 3 then 


nt (€ + 459.2°)p ovo 
Pg rd913° 0, 1 . 
Pressure of the Atmosphere at Different Altitudes, 


At the sea-level the pressure of the air is 14.7 pounds per square inch; at 
34 of a mile above the sea-level it is 14.02 pounds; at 46 mile, 13.33; at 34 
mile, 12.66; at 1 mile, 12.02; at 114 mile, 11.42; at 14g mile, 10.88; and at $ 





482 ATR. 


miles, 9.80 pounds pet square inch. For a rough approximation we may 
assume that the pressure decreases 144 pound per square inch for every 1006 
feet of ascent. 

It is calculated that at a height of about 314 miles above the sea-level the 
weight of a cubic foot of air is only one half what it is at the surface of the 
earth, at seven miles only one fourth, at fourteen miles only one sixteenth, 
at twenty-one miles only ons sixty-fourth, and at a height of over forty- 
five miles it becomes so attenuated as to have no appreciable weight. 

The pressure of the atmosphere increases with the depth of shafts, equal 
to about one inch rise in the barometer for each 900 feet increase in depth: 
Ge ORL be taken as a rough-and-ready rule for ascertaining the depth of 
shafts. 


Pressure of the Atmosphere per Square Inch and per 
Square Foot at Various Readings of the Barometer. 


RuLe.—Barometer in inches x .4908 = pressure per square inch; pressure 
per square inch x 144 = pressure per square foot. 





Barometer, | Pressure | Pressure § parometer,| Pressure | Pressure 





per Sq. In. |} per Sq. Ft. per Sq. In.| per Sq. Ft. 

in. Ibs. lbs.* in. Ibs. Ibs.* 
28.00 13.74 197 29.75 14.60 2102 
28.25 13.86 1995 30.00 14.72 2119 
28.50 13.98 2013 30.25 14.84 2136 
28.75 14.11 2031 30.50 14.96 2154 
29.00 14.23 2049 30.75 15.09 2172 
29.25 14.35 2066 31.00 15.21 2190 
29.50 14.47 2083 








* Decimals omitted. 
For lower pressures see table of the Properties of Steam. 


Barometric Readings corresponding with Different 
Altitudes, in French and English Measures. 

















ie Beate - Reaaee | aa 
Alti- | ingo oO ti- fe) c oO 

tude. maou Altitude. Barom- tude. | Barom- Altitude. Barom- 
eter. eter. eter. eter. 

meters.| mm, feet. inches. { meters. mm. feet. inches, 
0 762 0. 30. 1147 660 3763.2 25.98 
21 760 68.9 29.92 1269 650 4163.3 25.59 
127 750 416.7 29.52 1393 640 4568.3 25.19 
234 740 767.7 29.13 1519 630 4983.1 24.80 
342 730 1122.1 28.74 1647 620 5403.2 24.41 
453 720 1486.2 28.35 SYR 610 5830.2 24.01 
564 710 1850.4 27.95 1909 600 6243. 23.62 
678 700 2224.5 Cast ye 2043 590 6702.9 23.22 
793 690 2599.7 27.16 2180 580 7152.4 22.83 
909 680 2962.1 26.77 2318 570 7605.1 22.44 
1027 670 3369.5 26.38 2460 560 S071 peaedia cee 04 








Levelling by the Barometer and by Boiling Water. 
(Trautwine.)—Mauy circumstances combine to render the results of this 
kind of levelling unreliable where great accuracy is required. It is difficult 
to read off from an aneroid (the kind of barometer usually employed for 
engineering purposes) to within from two to five or six feet, depending on 
its size. The moisture or dryness of the air affects the results; also winds, 
the vicinity of mountains, and the daily atmospheric tides, which cause 
incessant and irregular fluctuations in the barometer. A barometer hang- 
ing quietly in a room will often vary 1/4 of an inch within a few hours, cor- 
responding to a difference of elevation of nearly 100 feet. No formula can 
possibly be devised that shall embrace these sources of error, 


MOISTURE IN THE ATMOSPHERE. 483 


To Find the Difference in Altitude of Two Placés,—Take 
from the table the altitudes opposite to the two boiling temperatures, or to 
the two barometer readings. Subtract the one opposite the lower reading 
from that opposite the upper reading. The remainder will be the required 
height, as a rough approximation. To correct this, add together the two 
thermometer readings, and divide the sum by 2, for their mean. From 
table of corrections for temperature, take out the number under this mean. 
Multiply the approximate height just found by this number. 

t 70°F. pure water will boil at 1° less of temperature for an average of 
about 550 feet of elevation above sea-level, up to a height of 1/2a mile. At 
the height of 1 mile, 1° of boiling temperature will correspond to about 560 
feet of elevation. In the table the mean of the temperatures at the two 
stations is assumed to be 32°F., at which no correction for temperature is © 
necessary in using the table. : 









































ee SoD |: toe Voor T acute | Zod. 
#234 Beseleeed| 8, (BESalsess| B- |BEES 
=—S & SST oO — oO fy es fain Mie Ga) Ta fy e.5 B21 oD 
(=) =" 8h Qa @ = 3 SS oR S = g BH 
QE aos ia | me (es ia a | ee 3 
184° 15,221 | 196 | 21.71 | 8481 | 208 | 27.73 | 2,063 
185 14,649 | 197 | 22.17 | 7932 f 208.5 | 28.00 | 1,809 
186 14.075 [| 198 | 2264 | 7.381 f 209 | 28.29 | 13539 
187 | 13'498 | 199 | 23:11 | 6843 [| 209.5°/ 28.56 | 17290 
188 12934 | 200 | 2359 | 61304 J 210 | 28.85 | 1,025 
189 /12'367 f 201 | 24.08 | 5,764 f 210.5 | 29.15 | "754 
190 11,799 | 202 | 2458 | 5.295 | 211 | 2942 | 512 
191 113243 | 203 | 25.08 | gear F215 | 29.71 255 
192 10,685 | 204 | 25.59 | 4169 | 212 | 30.00 |I9.L.=0 
198 10,127 | 205 | 26.11 | 3642 | 212.5 | 30.30 | —261 
194 9579 | 206 | 26.64 | 31115 | 213 | 3059 | —514 
195 9,031 B 207 | e718 | 2,589 
CORRECTIONS FOR TEMPERATURE. 
Mean temp. F. in shade. 0} 10°| 20°) 30°) 40° | 50° | 60°) 70° j80° |90° | 100° 
Multiply by .933 |.954|.975|.996|1.016|1.036/1.058]1.079|1.100]1.121|1.142 





Moisture in the Atmosphere.—Atmospheric air always contains 
a small quantity of carbonie acid (see Ventilation, p. 528) and a varying 
quantity of aqueous vapor or moisture. The relative humidity of the air at 
any time is the percentage of moisture contained in it as compared with the 
amount it is capable of holding at the same temperature. 

The degree of saturation or relative humidity of the air is determined by 
the use of the dry and wet bulb thermometer. The degree of saturation for 
a number of different readings of the thermometer is given in the following 
table, condensed from the Hygrometric Tables of the U.S. Weather Bureau: 


RELATIVE Humipity, PER CEn'r. 













































































a Difference between the Dry and Wet Thermometers, Deg. F. 
D 2 fx, | 
a a be Lise s 4| 5) 6| 7 8 ao 11|12 | 15/16/17] 18] 19/20/21 | 22}23) 24 252330 
baa] 
A Relative Humidity, Saturation being 100. (Barometer = 20 ins.) 


32 |89|79]69]59)49]39]30]20)11| 2 

40 |92/83)]75)68).60/52) 45)37)29)23/15) 7) 0} | | 

50 |93/87|80/ 74) 67/6155) 49/43/38)32)27/21/16/ 11! 5] 0 

60' |94/89/83} 78/73) 68) 63/58)53/48)43/39]}34/30/26'21/17)138) 9) 5) 1) | 

70 |95)90}86/81|77|72| 68) 64)59)55/51/48) 44) 40/36 38 29/25 22/19/15 12) 9) 6 

80° |96)91/87|83) 79) 75) 72|68)64/61 |57/54/50/47/44 41 |38/35) 32/29/26 23/20/18) 12) 7% 

90 |96/92/S9)85|81| 78/74) 71/68/65 /61/58/55 52/49 47/44/41 39/36/84 31) 29) 26) 22) 17/13 
100 |96/93}89| 86/83/80) 77/73) 70) 68)/65/62|59/ 56/54 51/49/46 44/41/39. 37/35) 33} 28) 24) 21 
110 |97/93|90|87|84/81 | 78} 75} 73] 70 |67| 65/62/60/57 55/52/50)/48)46/44 42/40) 38} 34] 30) 26 
120 |97/94/91/88)|85| 82) 80) 77/74) 72/69) 67/65) 62/60 58/55/53'51/49/47 45) 43) 41/38) 34) 31 
140. |97|95|92|89}87|84| 82) 79/77) 7573/70/68! 66) 6462/60 5856154153 51/49) 47)44) 41/38 





























484 AIR. 


Weights of Air, Vapor of Water, and Saturated Mixtures 
of Airand Vapor at Different Temperatures, under 
the Ordinary Atmospheric Pressure of 29.921 
inches of Mercury. 








33 AS: MIxTuRES OF AIR SATURATED WITH VAPOR. 
Eo. S.. 
2e8 @ x _ | Weight of Cubic Foot of the 
ge | &8 | Elastic | Mixture of Air and Vapor. . 
5 u4 Weight 
s DA o | Force of 
Es 22 | oS |the Airin uy 
54 on) © 3 | e i, 4 Vapor 
490 was Bay Mixture : mixed 
£5 oas g&° jofAirand : Weight | Total f 
23 a n Vapor, | Weight | oe the | went of|With 1 Ib. 
ar | apa | oe DOr, | of the Sule of Air 
S3 "Ag hs Inches of ate dba Vapor, |Mixture, pounds 
OS Dau O eq |Mercury. z pounds. | pounds ; 
EAB Pom Sh 
o° 0864 044 | 29.877 .0863 .000079 .086379 .00092 
12 -0842 074 | 29.849 -0840 .000130 -084130 00155 
22 0824 118 | 29.803 .0821 - 000202 .082302 -00245 
32 -0807 181 29.740 . 0802 .000304 . 080504 .00379 
42 0791 267 | 29.654 .0784 - 000440 -078840 -00561 
52 0776 388 | 29.533 0766 .000627 077227 -00819 
62 0761 006 | 29.865 0747 .000881 .075581 .01179 
72 0747 185 | 29.136 0727 -001221 .073921 .01680 


82 0733 1.092 | 28.829 0706 .001667 | .072267 | .02861 
PAY .0720 1.501 | 28.420 .0684 -002250 | .070717 | .08289 
102 0707 2.036 | 27.885 .0659 -002997 | .068897 | .04547 
112 -0694 2.731 | 27.190 0631 .003946 | .067046 .06253 
122 0682 3.621 | 26.300 .0599 -005142 | .065042 | .08584 
132 0671 4.752 | 25.169 0564 .006639 } .063039 | .11771 
142 0660 6.165 } 23.756 0524 .008473 | .060873 | .16170 
152 .0649 7.930 | 21.991 0477 .010716 | 058416 | .22465 
162 .0638 10.099 |} 19.822 0423 -0138415 | .055715 | .31713 
172 .0628 12.758 | 17.163 .0360 .016682 } .052682 | .46338 
182 -0618 15.960 | 13.961 0288 -020536 | .049336 71800 


192 -0609 19.828 | 10.093 -0205 1025142 | 045642 | 1.22643 
202 -0600 24.450 5.471 -0109 -030545 | .041445 | 2.80230 
212 .0591 29.921 0.000 .0000  .036820 } .036820 | Infinite. 


The weight in lbs. of the vapor mixed with 100 lbs. of pure air at any 
given temperature and pressure is given by the formula 


62.3 x EB. 29.92 
20.92 — E p’ 


where E = elastic force of the vapor at the given temperature, in inches of 
mercury; p = absolute pressure in inches of mercury, = 29.92 for ordinary 
atmospheric pressure. 

Specific Heat of Air at Constant Volume and at Constant 
ressure.—Volume of 1 lb. of air at 82° F, and pressure of 14.7 lbs. per sq. 
in, = 12.387 cu.ft. = acolumn 1 sq. ft. area X 12.387 ft. high. Raising temper- 


ature 1° F. expands it —— or to 12.4122 ft. high—a rise of .02522 foot. 


Work done = 2116 lbs. per sq, ft. * .02522 = 53.87 foot-pounds, or 53.37 +778 
= .0686 heat units, 

The specific heat of air at constant pressure, according to Regnault, is 
0.2375; but this includes the work of expansion, or .0686 heat units; hence 
the specific heat at constant volume = 0.2375 — .0686 = 0.1689. 

Ratio of specific heat at constant pressure to specific heat at constant 
volume = .2375 + .1689 = 1.406. (See Specific Heat, p. 458.) 

Flow of Air through Orifices.—The theoretical velocity in feet 
per second of flow of any fluid, liquid, or gas through an orifice is v = 

W2gh = 8.02 Vh, in which h = the ‘‘ head” or height of the fluid in feet 
required to produce the pressure of the fluid at the level of the orifice. 
(For gases the formula holds good only for small differences of pressure on 
the two sides of the orifice.) The quantity of flow in cubic feet per seeond 


FLOW OF AIR IN PIPES. 485 


is equal to the product of this velocity by the area of the orifice, in square 
feet, multiplied by a ‘coefficient of flow,’’ which takes into account the 
contraction of the vein or flowing stream, the friction of the orifice, etc. 

For air flowing through an orifice or short tube, from a reservoir of the 
pressure p, into a reservoir of the pressure p,, Weisbach gives the follows 
ing values for the coefficient of flow, obtained from his experiments. 


FLow oF AIR THROUGH AN ORIFICE. 


Coefficient c in formula v = c 2gh. 
Diameter anaes of pressures ppg 1.05 1.09 1.48 1.65 1.89 2.15 


1centimetre. § Coefficient............. wee «60DDD «6«6HS9 «692 «6724 «754 «£788 
Diameter t Ratio of pressures........ DOS 09 We SOn nl Odie, Olumaeeee 
2.14 centimetres § Coefficient..............- TeeLDOO MND Om eOOsne OlOmmatoouecis 


FLow oF AIR THROUGH A SHORT TUBE. 
Diam. 1 cm., bonch of pressures p),+D)q ae P10) Thes0 Pecans 


Length 3em. § Coefficient..........c+ss06 :780.<1. 07160 S80 ud eel mee 
Diam. 1.414 cm., | Ratio of pressures........ 164159169 4 eat oste aise ctutstel ste 
Length 4.242 cm. ) Coefficient................ BOL SEM O22 wewes ats oes se6e) Saae 

Diam. 1 em. . 

’ Ratio of pressures..... wee lot  1oOn 1:09) el correla ance 
Length 1.6 cm. : 
Orifice rounded, | Coefticient......... +--+. Aon wee een kets) UO ey crak 


FLIEGNER’S EQUATION FOR FLOW oF AIR FROM A RESERVOIR THROUGH AN 
ORIFICE. (Proc. Inst. C. E., lv, 379.) 


OF se. 2 
G@ = (3465 — 10000D) F J et 


G = the flow in kilogrammes per Second ; p,po = the internal and external 
pressures in atmospheres of 10,000 kg. per sq. metre; D = diameter of the 
orifice in metres; #’ = its cross-section in sq. metres; 7'= absolute temper- 
ature, Centigrade, of the air in the reservoir. The experiments were made 
with six orifices from 3.17 to 11.86 mm. diameter, in brass plates 12mm. thick, 
drilled cylindrically for about 14g mm., and conically enlarged towards the 
outside at an angle of 45°. 

Clark (Rules, Tables, and Data, p. 891) gives, for the velocity of flow of air 
through an orifice due to small differences of pressure, 


POTS. ins ( t — 32\_. 29.92 
reo4/e x iiee2 ox bP ana Saer 


or, simplified, 


¥ = 25204/ (4+ .o0z03¢¢ — De 


in which V = velocity in feet per second; 29g = 64.4; k = height of the column 
of water in inches, measuring the difference of pressure; t = the tempera- 
ture Fahr.; and p = barometric pressure in inches of mercury. 773.2is the 
volume of air at 82° under a pressure of 29.92 inches of mercury when that of 
an equal weight of water is taken as 1. 


For 62° F., the formula becomes V = 3868C 4/2 and if p = 29.92 inchesV = 
Pp 


66.350 Vh 
The coefficient of efflux C, according to Weisbach, is: 


For conoidal mouthpiece, of form of the contracted vein, 


with pressures of from .28 to 1.1 atmospheres....... ‘staal -C= .97 to .99 
GCircularorifices in’ thin platesee sapete «ace 6. leo ds od sole costes Cis, 56:10 ee 
Short: eylindricalimouthpiecesnas ayers 2. G hse csecccs vines de dele cd C = .81 to .84 
The'same rounded atthe inner end... .52.00.000cseecceccenee = .92 to .93 
Conical converging mouthpieces 3.07.2 25h... cas. c cnc eucte gases = .90 to .99 


Flow of Air in Pipes,.—Hawksley (Proc. Inst. C. E., xxxiii, 55) 
states that his formula for flow of water in pipes v = 48 y/ a may also 
be employed for flow of air. In this case H = height in feet of a column of 
air required to produce the pressure causing the flow, or the loss of head 


486 AIR. 


for a given flow; v = velocity in feet per second, D = diameter in feee, I = 
length in feet. 

If the head is expressed in inches of water, h, the air being taken at 
62° F'., its weight per cubic foot at atmospheric pressure = .0761 lb. Then 


i = 68.32. If d = diameter in inches, D= —, and the formula 


~ 0761 x 12 2 
becomes v = 114.5 y's » in which h = inches of water column, d = diam- 


L 
EA nu In? 
Q 13110d’ ~~ 13110h* 

The quantity in cubic feet per second is 

is Gi.& hd. we OL. OL 
Q = .7854 Tad seal .6245 7 3 d= “30h? = 2006." 

The horse-power required to drive air through a pipe is the volume Q in 
cubic feet per second multiplied by the pressure in pounds per square foot 
and divided by 550. Pressure in pounds per square foot = P = inches of 
water column X 5.196, whence horse-power = 

3 
HP. = QP Qh OL 


A eo) 


eter in inches and Z = length in feet; h = 


If the head or pressure causing the flow is expressed in pounds per square 
inch = p, thenh = 27.71p, and the above formule become 


oar, / Be TIO dg tw? 





= 6 —e SS = e 
. ‘L?* P= 363,3000” 363,300p ° 
he PCRS 
Ligaerriny leaves we werate QL, 
Q = 3.2874/ “Tt P= ap gocas' = 4 10.806 
Qi4tp QL 
HP, = 550 = .2618Qp = On421-F5 


Volume of Air Transmitted in Cubic Feet per Minute in 
Pipes of Various Diameters, 


1854 
2 
144% v x 60. 





Formula Q = 





Actual Diameter of Pipe in Inches. 


Veloc’y] - 
of Flow 





| 


Pee) 
22) 2]2)8} 4181 64 84 0 12 16 | 20 | 24 
Fs, 2 Ne aes St a ee ee 
1 | .827] 1.81] 2.95] 5.24) 8.18! 11.78] 20.94] 32.73] 47.12} 83.77] 130.9] 188.5 
2 | .655| 2.62] 5.89] 10.47| 16.36] 23.56] 41.89] 65.45] 94.25] 167.5 | 261.8] 377 
3 | .982| 3.921 8.84] 15.7 | 24.5 | 35.3 | 62.8 | 98.2 | 141.4 | 251.3 | 392.7] 565.5 
4 |1.31 | 5,24(11.78| 20.9 | 82.7 | 47.1 | 88.8 |131 188 335 523 | 754 
5 1.64 | 6.54/14.7 | 26.2] 41 159 [104 163 | 285 | 419 | 654 | 942 
6 11.96 | 7.85]17.7 | 31.4 | 49.1 | 70.7 1125 «|196 =| 283 | 502 | 785 11131 
7 |2.29 | 9.16/20.6 | 86.6 | 57.2 | 82.4 |146 [229 | 330 | 586 | 916 {1319 
S [2.62 1105 |23.5 1 41.9 | 65.4] 94 [167 [262 | 877 | 670 41047 |1508 
9 12.95 111.78/265 147 | 73 (106 |188 [294 | 4294 | 754 {1178 11696 
10 |3.27 |13.1 }29.4 | 52 | 82 [118 |209 [327 | 471 | 838 {1309 |1885 





18. 5:89: 23.5 [58 94 |14% [212 137 589 848 1508 |2856 13393 
20 (6.54 (26.2 [59 |105 |164 [2385 |419 654 942 |1675 (2618 |3770 
24 17.85 [31.4 |? 125 {196 §={283 (502 {785 {11381 2010 [8141 [4524 
95 18.18 182.7 |73 1181 (204 |294 1523 (818 {1178 |2094 {8272 |4712 
28 (9.16 186.6 |82 {146 |229 |3380 |586 |916 {1319 |2346 (38665 |5278 
30 '9.8 139.3 [88 1157 [245 1353 162 982 {1414 [2513 [3927 [5655 


FLOW OF AIR IN PIPES, AS? 


In Hawksley’s formula and its derivatives the numerical coefficients are 
constant. It is scarcely possible, however, that they can be accurate except 
within a limited range of conditions. In the case of water it is found that 
the coefficient of friction, on which the loss of head depends, varies with the 
length and diameter of the pipe, and with the velocity, as well as with the 
condition of the interior surface, In the case of air and other gases we 
have, in addition, the decrease in density and consequent increase in volume 
and in velocity due to the progressive loss of head from one end of the pipe 
to the other, 

Clark states that according to the experiments of D’Aubuisson and those of 
a Sardinian commission on the resistance of air through long conduits or 
pipes, the diminution of pressure is very nearly directly as the length, and 
as the square of the velocity and inversely as the diameter. The resistance 
is not varied by the density. ; : 

If these statements are correct, then the formula h = pan andh = bie 
and their derivatives are correct in form, and they may be used when the 
numerical coefficients c and c’ are obtained by experiment. 

If we take the forms of the above formule as correct, and let C be a vari- 
able coefficient, depending upon the length, diameter, and condition of sur: 
face of the pipe, and possibly also upon the velocity, the temperature and 
the density, to be determined by future experiments, then for Ah = bead in 
inches of water, d = diameter in inches, LZ = length in feet, v = velocity in 
feet per second, and Q = quantity in cubic feet per second: 


ia _ Tat, Iw, 
par en? 7RY a 


Q = .005454C 





BAe. ee, 4 eae hh wx 28683Q2D | 
ius Ty Sc a 


C2h ~ — G2qs 


For difference or loss of pressure p in pounds per square inch, 


h = %%.71p Vii = 5.264 Vp} 
o ‘pa , be Lv? % a” Inv? fe 
v = 5.26404 / 3 a= F7iGyp P= 71rd 





5 -———- 
[pa , 1213Q2L, 1218Q°L 
Q= .02871.C - 9 ad = “Cp? 0) = “Czas ° 


(For other formule for flow of air, see Mine Ventilation.) 


Loss of Pressure in Ounces per Square Inch.—B. F. Sturte- 
vant Company uses the following formule ; 


In? , Sip f 25000d py , es Lo? ., 
Pi= s000a? ° = L ° “~~ 35000p,' 

in which p, = loss of pressure in ounces per square inch, v = velocity of air 

in feet per second, and L = length of pipe in feet. If pis taken in pounds 


per square inch, these formulee reduce to 
La? _ fdp,, 4 _. 0000025Lv? 
p= 00000257 § uv = 682.5 yt M a = ————_.. 


Dp 


Lu; 
These are deduced from the common formula (Weisbach’s), p = Sg 39° in 


which f = .0001608. : 

The following table is condensed from one given in the catalogue of B. F. 
Sturtevant Company. | : ; 

Loss of pressure in pipes 100 feet long, in ounces per square inch, For 
any other length, the loss is proportional to the length, 


488 AIR, 




















= 
a Diameter of Pipe in Inches. 
Sie Meier Gal FAD Aw ak een cs ce 
peli |e {e| a 5 | 6 v|s|o|o|u {re 
Ow Ne Ae ee et ee eee 
Sv 
e & Loss of Pressure in Ounces. 
00} .400) .200) .1383) .100) .080) .067) .057) .050} .044] .040 076! .033 


1200} 1.600} .800) .533) .400) .820) .267) .229) .200) .178] .160] .145) .133 
1800) 3.600) 1.800} 1.200} .900) .720} .600) .514| .450) .400] .360} .3827| .300 | 
2400] 6.400] 3.200) 2.133] 1.600} 1.280) 1.067) .914) .800) .711] .640] .582| .533 








3000]10. 5. 3.333] 2.5 | 2. 1.667)1.429)1.250/1.111}1.000} .909] .833 
3600}14.4 | 7.2 [4.8 (3.6 | 2.88 | 2.4 |2.057)1.8 |1.6 |1.44 |1.309|1.200 
4200 acess 9.8 } 6.553) 4.9 | 8.92 | 8.267/2.8 (2.45 |2.178)1.96 |1.782/1.633 
4800]....- 12.8 | 8.533) 6.4 | 5.12 | 4.267/8.657/8.2 |2.844/2.56 [2.3827 /2.133 
6000] .-... 20. 13.333110.0 [| 8.0 | 6.667/5.71415.0 14.444/4.0 |3 636/3.333 


Diameter of Pipe in Inches. 





| 10 | a8 | 20 | 2 24 28° 











se | a6 | a0 | a | 48 


Loss of Pressure in Ounces. 
600} .029] .026} .022} .020) .018) .017| .014] .012) .011) .010/ .009| .008 
4200] .114) .100) .089} .080) .078) .067| .057) .050} .044| .040| .036| .033 
1800] .257| .225) .200) .180) .164| .156) .129] .112} .100| .090] .082| .07 
2400! .457] .400| .856) .3820) .291) .267| .239| .200] .178| .160| .145) .133 
3600} 1.029} .900} .800) .720) .655| .600}) .514| .450) .400) .360| .3827] .300 
4200} 1.400] 1.225] 1.089} .980} .891] .817| .700} .612) .544| .490| .445] .408 
4800} 1.829] 1.600] 1.422! 1.280] 1.164) 1.067} .914] .800] .711| .640; .582) .533 
6000} 2.857} 2.500} 2.222) 2.000] 1.818) 1.667]1.429)1.250}1.111'1.000} .909| .833 


Effect of Bends in Pipes. (Norwalk Iron Works Co.) 


Radius of elbow,in diameter of pipe=5 8 2 1% 14% 1 % &% 
Equivalent lgths. of straight pipe, diams 7.85 8.24 9.03 10.36 12.72 17.51 35.09 121.2 | 


Compressed-air Transmission, (Frank Richards, Am. Mach., 
March 8, 1894 )—The volume of free air transmitted may be assumed to be 
directly as the number of atmospheres to which the air is compressed. 
Thus, if the air transmitted be at 75 pounds gauge-pressure, or six atmos- 
pheres, the volume of free air will be six times the amount given in the 
table (page 486). It is generally considered that for economical transmission 
the velocity in main pipes should not exceed 20 feet per second. In the 
smaller distributing pipes the velocity should be decidedly less than this. 

The loss of power in the transmission of compressed air in general is not 
a serious one, or at all to be coinpared with the losses of power in the opera- 
tion of compression and in the re-expansion or final application of the air. 

The formulas for loss by friction are all unsatisfactory. The statements 
of observed facts in this line are in a more or less chaotic state, and self- 
evidently unreliable. 

A statement of the friction of air flowing through a pipe involves at least 
all the following factors: Unit of time, volume of air, pressure of air, diam- 
eter of pipe, length of pipe, and the difference of pressure at the ends of 
the pipe or the head required to_maintain the flow. Neither of these factors 
can be allowed its independent and absolute value, but is subject to modifi- 
cations in deference to its associates. The flow of air being assumed to be 
uniform at the entrance to the pipe, the volume and flow are not uniform 
after that. The air is constantly losing some of its pressure and its volume 
is constantly increasing. The velocity of flow is therefore also somewhat 
accelerated continually. This also modifies the use of the length of the 
pipe asa constant factor. — : 

Then, besides the fluctuating values of these factors, there is the condition 
of the pipe itself. The actual diameter of the pipe, especially in the 
smaller sizes. is different from the nominal diameter. The pipe may be 
straight, or it may be crooked and have numerous elbows. Mr. Richards 
considers one elbow as equivalent to a length of pipe. 








FLOW OF COMPRESSED AIR IN PIPES. 489 


Formulz for Flow of Compressed Air in Pipes.—The for- 
mulee on pages 486 and 487 are for air at or near atmospheric pressure. For 
compressed air the density has to be taken into account. A common 
formula for the flow of air, gas, or steam in pipes is 





in which Q = volume in cubic feet per minute, p = difference of pressure 
in lbs. per sq. in. causing the flow, d = diameter of pipe in in., L = length 
of pipe in ft., w = density of the entering gas or steam in lbs. per cu. ft., 
and c = a coefficient found by experiment. Mr. F. A. Halsey in calculating 
a table for the Rand Drill Co.’s Catalogue takes the value of c at 58, basing 
it upon the experiments made by order of the Italian government prelim- 
inary to boring the Mt. Cenis tunnel. These experiments were made with 
pipes of 3281 feet in length and of approximately 4, 8, and 14 in. diameter. 
The volumes of compressed air passed ranged between 16.64 and 1200 cu. ft. 
per minute. The value of c is quite constant throughout the range and 
shows little disposition to change with the varying diameter of the pipe. It 
is of course probable, says Mr. Halsey, that c would be smallerif determined 
for smaller sizes of pipe, but to offset that the actual sizes of small com- 
mercial pipe are considerably larger than the nominal sizes, and as these 
calculations are commonly made for the nominal diameters it is probabie 
that in those small sizes the loss would really be less than shown by the 
table. The formula is of course strictly applicable to fluids which do not 
change their density, but within the change of density admissible in the 
transmission of air for power purposes it is probable that the errors intro- 
duced by this change are less than those due to errors of observation in the 

resent state of knowledge of the subject. Mr. Halsey’s table is condensed 

elow. 



































o Cubic feet of free air compressed to a gauge-pressure of 80 lbs. 

a and passing through the pipe each minute. ‘ 

Ay 

ree | 

= 3 50 | 100 | 200 | 400 } 800 |} 1000} 1500} 2000 2000 | 4000 | 5000 
25 | 

Ss Loss of pressure in Ibs. per square inch for each 1000 ft. 

rats of straight pipe. 

1144 | 3.61 

114 | 1.45 | 5.8 

2 0.20 | 1.05 | 4.80 

214 | 0.12 | 0.35 | 1.41 | 5.80 

Se ane nee 0.14 | 0.57 | 2.28 

BLGE| ge see «|e citaiae 0.26 | 1.05 | 4.16 | 6.4 

4 Bae oc Onl4ae OL SAN eet eal Seo tale i.O0 

Si Ae Ae eee Ge\0 0268s alesse endam| ed 5201 19).6 

Gap see ares es | eiermerel lat sce OF28 a Osi LT OOR et 5193.91 1 F210) ) 1087 
Bede [kes 25 TS aaa ea occ or 0.07 | 0:10 | 0.24 | 0.42 | 0.93 .68 | 2.59 
BO > Web cthe oi coretete wilt etermions | sicsiene alts Po Kec Ree OOS 110714 10.380 | 0555 0.84 
12 Sei acteretaline eta [actrees (MrenMeretetia stam t sists es It's 6 5s O12 02 0.34 
14 $ ois eater ioe eee! 0.10 | 0.16 








To apply the formula given above to air of different pressures it may be 
given other forms, as follows: 

Let Q = the volume in cubic feet per minute of the compressed air; Q, = 
the volume before compression, or ‘‘ free air,” both being taken at mean 
atmospheric temperature of 62° F.; w, = weight per cubic foot of Q; = 
0.0761 1b.; 7 = atmospheres, or ratio of absolute pressures, = (gauge-pres- 
sure + 14.7) + 14.7; w = weight per cu. ft. of Q; p = difference of pressure, 
in lbs. per sq. in., causing the flow; d = diam. of pipe in in.; L = length of 
pipe in ft,; c = experimental constant, Then 


490 AIR, 


5 
Qz=ec Eeng QO, = FO; writ, = .016Irs 








Ret: 6 
Q = 3.625¢ = = 5.0280 4/ e , 





Q 
{] 
Oo 
z 
= 
a 
OQ 
S 
3S 
z 
on 
w 
I] 
A] 
S 
o> 
OTN 
> 
oQ 
S 
3 
=) 
ont 
SID 
ere) 


The value of c according to the Mt. Cenis experiments is about 58 for pipes 
4, 8, and 14in. diameter, 3281 ft. long. In the St. Gothard experiments it 
ranged from 62.8 to 73.2 (see table below) for pipes 5.91 and 7.87 in. diameter, 
1713 and 15,092 ft. long. Values derived from D’Arcy’s formula for flow of 
water in pipes, ranging from 45.3 for 1 in. diameter to 63 2 for 24 in., are given 
under *“‘ Flow of Steam,” p. 671. For approximate calculations the value 60 
may be used for all pipes of 4 in, diameter and upwards. Using c = 60, the 
above formulas become 


a pdsr 
Q = 217.5 ee Gyan tite sf ows 
5 /T,OQ2y7 6 
[d= onic g/ = ossig/ Een, 
p pr 
Lot Lex? 
= 0.00002114%" = 0,00002114 222", 
p = 0.00002114—"-" = 0,00002114 43 


Loss of Pressure in Compressed Air Pipe-main, at 
St. Gothard Tunnel. 


(EK. Stockalper.) 



































isi eae res) t ' 
8 a= ® BS) bed <j | Observed Pressures. |"5 ? 
VSD SEIS alos On (fag Fiaty 
HiSn kom 1894 Ln OS io cibes ae 
2a co lek =saee Sa pS UL: 9 begs ° 3 elas 
B/G EEC SS SET EB] 32/82 aw | ae aS 
gia ope ‘o8 Sake B2n| SS <5 os of | Loss of nace Bes 
rey a CVESgS o5e Dal oa}! pa =e - gS Pressure. | 6 
2 | Eaosge BOE g8 S| Sue] qe laeel oa o il 
) i. | Buse slEusclack fa | 38 |zokl 4a Sh os 
a = ISOPGRIGOS(DOT| oH |PoR| Lo 3 
<4 |p > |= Ee |S ia i. > 
lbs. 
per 2 
No.| in. | eu.ft. jeu.ft.| den. |-lbs. | feet.| at. at. |Sq.in.| % 
7.87 33 056 | 6.534 | 00650] 2.669 | 19.32} 5.60 | 5.24 | 5.292] 6.4 YE 
i 5.91] [39-997 | + 063 | 00603] 2 669 | 37.14 | 5.24 | 5.00 | 3.5283} 4.6] 63.9 
* 8% Log 002 5.509 | .00514] 1.776 | 16.80 | 4.35 | 4.13 | 8.284 5.1 70.7 
21 |5:o1] 522: presa (2004821 1-776]... | 4.28 bias eee Tas [es 
1 |7.87] Lig g¢4 5 | 5.262 .00449| 1.483 | 15.58 | 3.84 | 8.65 | 2.793150] 67.6 
15-05) o>" +| 57580 | .00423| 11483 | 29.34 | 365 | 354 |1.617/ 3.0} 6218 








_ SO 0 EL 

The length of the pipe 7.87 in diameter was 15,092 ft., and of the smaller 
pipe 172.6 ft. The mean temperature of the air in the large pipe was 70° F. 
and in the small pipe 80° F, 


MEASUREMENT OF VELOCITY OF AIR. 491 


Equation of Pipes,.—It is frequently desired to know what number 
of pipes of a given size are equal in carrying capacity to one nipe of alarger 
size. At the same velocity of flow the volume delivered by two pipes of 
different sizes is proportional to the squares of their diameters; thus, one 
4-inch pipe wiil deliver the same volume as four 2-inch pipes. With the same 
head, however, the velocity is less in the smaller pipe, and the volume de- 


_ livered varies about as the square root of the fifth power (i.e., as the 2.5 


power). The following table has been calculated on this basis. he figures 
opposite the intersection of any two sizes is the number of the smaller-sized 
pipes required to equal one of the larger. Thus, one 4-inch pipe is equal to 
5.7 2-inch pipes. 


Saas | ere Pe te | 7 8 | 9 | 10} 12] 14 | 16 | 18 | 20 | 2¢ 
a 


a | | | | | | | | | | | ee 


























2| 5.4 1 : 

3 |15.6] 2.8] 1 

2a 32e0|0.<] 2-1) 2 

HGlOD. Qin 9.9) oO ea L 

6 |88.2)15.6) 5.7) 2.8) 1.6] 1 

7 1180 |22.9) 8.3) 4.1) 2.3) 1.5) 1 

8 |181 (382 111.7) 5.7} 8.2) 2.1| 1.4) 1 

9 |248 |43. 115.6) 7.6) 4.3) 2.8) 1.9) 1.3) 1 

10 816 |55.9)/20.3) 9.9] 5.7] 3.6) 2.4) 1.7) 1.3) 1 

11 [401 |70.9)25.7/12.5) 7.2) 4.6) 3.1) 2.2) 1.7) 1.3 

12 /499 {88.2)32 |15.6] 8.9) 5.7) 3.8} 2.8) 2.1) 1.6) 1 

13 |609 {108 {39.1/19 |10.9) 7.1) 4.7) 3.4) 2.5).1.9) 1.2 

14 |%33 |180 |47 |22.9]138.1) 8.3] 5.7) 4.1) 3.0) 2.3) 1.5) 1 

15 (871 $154 (55. 9/27.2/15.6) 9.9) 6.7) 4.8) 3.6; 2.8) 1.7) 1.2 

16 181 |65.7/382 |18.3]11.7| 7.9) 5.7) 4.2) 8.2) 2.1) 1.4) 1 

17 211 |76.4)37.2)21.3/138.5) 9.2) 6.6) 4.9) 3.8) 2.4) 1.6) 1.2 

18 243 |88.2143 [24.6/15.6/10.6] 7.4) 5.7) 4.38) 2.8) 1.9) 1.3) 1 

19 278 |101 |49.1/28.1)17.8/12.1) 8.7] 6.5) 5 | 3.2) 2.1) 1.5) 1.1 

20 316 }115 |65.9/382 |20.3/18.8) 9.9) 7.4) 5.7) 8.6) 2.4) 1.7) 1.3) 1 

22 401 }146 |70.9/40.6/25.7/17.5/12.5) 9.3) 7.2) 4.6) 3.1) 2.2) 1.7) 1.3 

24 499 |181 |88.2/50.5/32 /21.8/15.6/11.6) 8.9) 5.7) 3.8) 2.8] 2.1] 1.6) 1 
26 609 }221 [108 |61.7/389.1/26.6]19. |14.2)10.9) 7.1) 4.7) 3.4) 2.5) 1.9) 1.2 
28 733 1266 11380 |74.2/47 (82 |22.9/17.1]13.1) 8.3) 5.7) 4.1) 3 | 2.3] 1.5 
30 |....| 871 |316 |154 |88.2/55.9/388 )27.2/20.3/15.6) 9.9] 6.7) 4.8) 3.0) 2.8) 1.7 
Owais .. 499 }243 ]1380 |88.2/)60 (48 {82 |24.6/15.6)10.6) 7.6) 5.7) 4.3) 2.8 
42 | .. | ...|783 {857 |205 {180 |88.2]63.2)47 |86.2)19 |15.6)11.2) 8.3) 6.4) 4.1 
48 |... [| ...]...-]499 [286 /182 |123°)88.2)62.7/50.5/82 |21.8)15.6)11.6) 8.9) 5.7 
BSN eat peect-ail stecans 670 {383 |243 |165 1118 |88.2/67.8/43 (29.2/20.9)15.6)12 | 7.6 
GO}... - {871 |499 [316 [215 {154 [115 |88.2/55.9/88 [27.2/20.3)15.6) 9.9 


Wieasurement of the Velocity of Air in Pipes by an Ane=«= 
mometer.—Tests were made by B. Donkin, Jr. (Inst. Civil Hingis. 1892), 
to compare the velocity of air in pipes from 8 in, to 24 in. diam., as shown by 
an anemometer 234 in. diam. with the true velocity as measured by the time 
of descent of a gas-holder holding 1622 cubic feet. A table of the results 
with discussion is given in Hng’g News, Dec. 22, 1892. In pipes from 8 in. to 20 
in. diam. with air velocities of from 140 to 690 feet per minute the anemome- 
ter showed errors varying from 14.5% fast to 10% slow. With a 24-inch pipe 
and a velocity of 73 ft. per minute, the anemometer gave from 44 to 63 feet, 
or from 13.6 to 39.6% slow. The practical conclusion drawn from these ex- 
periments is that anemometers for the measurement of velocities of air in 
pipes of these diameters should be used with great caution. The percentage 
of error is not constant, and varies considerably with the diameter of the 
pipes and the speeds of air. The use of a baffle, consisting of a perforated 
plate, which tended to equalize the velocity in the centre and at the sides in 
some cases diminished the error. 


492 ATR. 


The impossibility of measuring the true quantity of air by an anemometer 
held stationary in one position is shown by the following figures, given by 
Wm. Daniel (Proce. Inst. M. E., 1875), of the velocities of air found at different 
points in the cross-sections of two different airways in a mine. 


DIFFERENCES OF ANEMOMETER READINGS IN AIRWAYS. 
§ ft. square. 5 xX 8 ft. 





1712 | 1795 | 1859 | 1329 


1170 | 1209 | 1288 














1622 | 1685 | 1782 | 1091 a | | eee 
(ik he 948 | 1104 | 1177 
1477 | 1844 | 1524 | 1049 





11 
1262 | 1356 | 1293 | 1338 34 | 1049 | 1106 





Average 1469. Average 1182. 


WIND. 
Force of the Wind.—Smeaton in 1759 published a table of the 
velocity and pressure of wind, as follows: 
VELOCITY AND FORCE OF WIND, IN POUNDS PER SQUARE INCH. 

















rs Hej Do ww % | 5 H 
Rist | o @.50!/Common Appella-fs+| © 2.55} Common Appella- 
ne BS ens tion of the nd BS 2" 8 tion of the 
== | 23 |5 98! Forceof Wind. J2m] $3 |5 78! Force of Wind. 
= fal ae Oot ce S |e? |x 
Hardly percepti-§ 18 | 26.4 | 1.55 

1 | 1.47 | 0.005 ; ble. 29.34] 1.968 t Very brisk. 

2 | 2.93! 0.020 25 | 36.67] 3.075 

3 | 43'| 0-044] ¢ Just perceptible. 35 | 4401] 4/499 Li 1 feta 

4 | 5.87} 0.079 35 | 51.34] 6.027 8 : 

5 7.33 pe Sa pleasant § 40 | 58.68 oe | 

6 | 8.8 | 0.17 wind. 45 | 66.01] 9.963 a: 

7 | 10.25] 0.241 50 | 73.35/12.30 | f Very high storm, 

8 | 11.75] 0.315!) 55 | 80.7 |14.9 | J 

9 | 13.2 | 0.400 | 60 | 88.02|17.71 

10 | 14.67] 0.492 ’ 66 | 95.4 (20.85 | © Great Storm. 
12 | 17.6 | 0.708 f aale brisk Ff 7 |102/5 [24.1 

14 | 20.5 | 0.964 . 7 1110. (27.7 

15 | 22.00] 1.107 80 |117.36|31 .49 | Hurricane. 

1600) 23-45) 15255) J 100 |146.67/49.2 tat + hurri- 

cane. 


The pressures per square foot in the above table correspond to the 
formula P = 0.005172, in which V is the velocity in miles per hour. Eng’g 
News, Feb. 9, 1898, says that the formula was never well established, and 
has floated chiefly on Smeaton’s name and for lack of a better. It was put 
forward only for surfaces for use in windmill practice. The trend of 
modern evidence is that it is approximately correct only for such surfaces, 
and that for large solid bodies it often gives greatly too large results. 
Observations by others are thus,compared with Smeaton’s formula: 


Old Snreatonmormila 2 5 02. ee BA ee ee = .005V2 
As determined by Prof. Martin..... .............00..2- i=. 004 V2 
“ © = Whipple and Dines,................P = .0029V3 


| 


WIND. 493 


At 60 miles per hour these formulas give for the pressure per square foot, 
18, 14.4 and 10.44 lbs., respectively, the pressure varving by all of them as 
the square of the velocity. Lieut. Crosby’s experiments (Eig’g, June 13, 
1890), claiming to prove that P= fV instead of P = fV?, are discredited. 

A. R. Wolff (The Windmill as a Prime Mover, p. 9) gives as the theoretical 


pressure per sq. ft. of surface, P = aQy , in‘which d = density of air in pounds 


.018743(p + FP), 
t ? 
foot at any level, and temperature of 32° F., any absolute temperature, 


Q = volume of air carried along per square foot in one second, v = velocity 


dv23 
of the wind in feet per sec., g = 32.16. Since Q = vcu. ft. per sec., P= a 


per cu. ft. = p being the barometric pressure per square 


Multiplying this by a coefficient 0.93 found by experiment, and substituting 


the above value of d, he obtains P = ABN LARS PES CD and when p 
t X 82.16 
rey ny wp 018743 
= 2116.5 lbs. per sq. ft. or average atmospheric pressure at the sea-level, 
(Beeps ERoch sia an expression in which the pressure is shown to vary 
t X 32.16 " 
RES el =3 0. 18% 43 


with the temperature; and he gives a table showing the relation between 
velocity and pressure for temperatures from 0° to 100° F., and velocities 
from 1 to 80 miles per hour. For a temperature of 45° F. the pressures agree 
with those in Smeaton’s table, for 0° F. they are about 10 per cent greater, 
and for 100° 10 per cent less. Prof. H. Allen Hazen, Hng’g News, July 5, 
1890, says that experiments with whirling arms, by exposing plates to direct 
wind, and on locomotives with velocities running up to 40 miles per hour, 
have invariably shown the resistance to vary with V2. In the formula 
P= .005SV2, in which P = pressure in pounds, S = surface in square feet, 
V = velocity in miles per hour, the doubtful question is that regarding 
the accuracy of the first two factors in the second member of this equation. 
The first factor has been variously determined from .003 to .005 [it has been 
determined as low as .0014.—Ed. Hng’g News]. 

The second factor has been found in some experiments with very short 
whirling arms and low velocities to vary with the perimeter of the plate, 
but this entirely disappears with longer arms or straight line motion, and 
the only question now to be determined is the value of the coefficient. Per- 
haps some of the best experiments for determining this value were tried in 
France in 1886 by carrying flat boards on trains. The resulting formula in 
this case was, for 44.5 miles per hour, p = .00535SV2. 

Mr. Crosby’s whirling experiments were made with an arm 5.5 ft. long. 
It is certain that most serious effects from centrifugal action would be set 
up by using such a short arm, aud nothing satisfactory can be learned with 
arms less than 20 or 30 ft. long at velocities above 5 miles per hour. 

Prof. Kernot, of Melbourne (Engineering Record, Feb. 20, 1894), states that 
experiments at the Forth Bridge showed that the average pressure on sur- 
faces as large as railway carriages, houses, or bridges never exceeded two 
thirds of that upon small surfaces of one or two square feet, such'as have 
been used at observatories, and also that an inertia effect, which is frequently 
overlooked, may cause some forms of anemometer to give false results 
enormously exceeding the correct indication. Experiments of Mr. O. T. 
Crosby showed that the pressure varied directly as the velocity, whereas all 
the early investigators, from the time of Smeaton onwards, made it vary as 
the square of the velocity. Experiments made by Prof. Kernot at speeds 
varying from 2 to 15 miles per hour agreed with the earlier authorities, and 
tended to negative Crosby’s results. The pressure upon one side ofa cube, 
or of a block proportioned like an ordinary carriage, was found to be .9 of 
that upon a thin plate of the same area. The same result was obtained for 
a square tower. <A square pyramid, whose height was three times its base, 
experienced .8 of the pressure upon a thin plate equal to one of its sides, but 
if an angle was turned to the wind the pressure was increased by fully 202. 
A bridge consisting of two plate-girders connected by a deck at the top was 
found to experience .9 of the pressure on a thin plate equal in size to one 
girder, when the distance between the girders was equal to their depth, and 
this was increased by one fifth when the distance between the girders was 


494 AiR. 


double the depth. A lattice-work in which the area of the openings was 55% 
of the whole area experienced a pressure of 80% of. that upon a plate of the 
same area. The pressure upon cylinders and cones was proved to be equal 
to half that upon the diametral planes, and that upon an octagonal prism to 
be 20% greater than upon the circumscribing cylinder. A sphere was sub- 
ject to a pressure of .36 of that upon a thin circular plate of equal diameter. 
A hemispherical cup gave the same result as the sphere; whenits concavity 
was turned to the wind the pressure was 1.15 of that on a flat plate of equal 
diameter. When a plane surface parallel to the direction of the wind was 
brought nearly into contact with a cylinder or sphere, the pressure on the 
latter bodies was augmented by about 20%, owing to the lateral escape of the 
air being checked. Thus it is possible for the security of a tower or chimney 
to be impaired by the erection of a building nearly touching it on one side. 

Pressures of Wind Registered in Storms.—Mr. Frizell has 
examined the published records of Greenwich Observatory from 1849 to 1869, 
and reports that the highest pressure of wind he finds recorded is 41 lbs. 
per sq. ft., and there are numerous instances in which it was between 30 and 
40 lbs. per sq. ft. Prof. Henry says that on Mount Washington, N. H., a ve- 
locity of 150 miles per hour has been observed, and at New York City 60 
miles an hour, and that the highest winds observed in 1870 were of 72.and 63 
miles per hour, respectively. 

Lieut. Dunwoody, U.S. A., says, in substance, that the New England coast 
is exposed to storms which produce a pressure of 50 lbs. per sq. ft. Hngi- 
neering News, Aug. 20, 1880). 


WINDMILLS. 


Power and Efficiency of Windmills.—Rankine, S. E., p. 215, 
gives the following: Let Q = volume of air which acts on the sail, or part 
of a sail, in cubic feet per second, v = velocity of the wind in feet per 
second, s = sectional area of the cylinder, or annular cylinder of wind, 
through which the sail, or part of the sail, sweeps in one revolution, c= a 
coefficient to be found by experience; then Q@ = cvs. Rankine, from experi- 
mental data given by Smeaton, and taking c to include an allowance for 
triction, gives for a wheel with four sails, proportioned in the best manner, 
c= 0.75. Let A = weather angle of the sail at any distance from the axis, 
i.e., the angle the portion of the sail considered makes with its plane of 
revolution. This angle gradually diminishes from the inner end of the sail 
to the tip; w= the velocity of the same portion of the sail, and H = the effi- | 
ciency. The efficiency isthe ratio of the useful work performed to whole 
energy of the stream of wind acting on the surface s of the wheel, which 











3 
energy is o , D being the weight of a cubic foot of air. Rankine’s formula 
for efficiency is 
bear / UW sn U2 } 
ee die sin 2A = = (1—cos2A+f)-f)¢, 
“9 


,in which c = 0.75 and f is a coefficient of friction found from Smeaton’s 
Wiata = 0.016. Rankine gives the following from Smeaton’s data: 


A = weather-angle..............+ ee RES We, 138° 19° 
V-+v=ratio of speed of greatest effi- 
ciency, for a given weather- 
angle, to that of the wind..... = 2.63 1.86 1.41 
Hy == OMICIENCY .. .,. 0.5 or-:010 010 ate eRe ee = 0.24 0.29 0.31 


Rankine gives the following as the best values for the angle of weather at 
different distances from the axis: 


Distance in sixths of totalradius... 1 2 3 4 5 6 
Weather angle...ccce-csccce0ssse ojos; Abe e AO? te LACetbely al eneo we 


But Wolff (p. 125) shows that Smeaton did not term these the best angles, 
but simply says they ‘* answer as well as any,” possibly any that were in ex- 
istence in his time. Wolff says that they ‘“‘ cannot in the nature of things 
be the most desirable angles.’?’ Mathematical considerations, he says, con- 
clusively show that the angle of impulse depends on the relative velocity of 
each point of the sail and the wind, the angle growing larger as the ratio be- 
comes greater, Smeatori’s angles do not fulfil this condition. Wolff devel- 


WINDMILLS. 495 


aps a theoretical formula for the best angle of weather, and from it 
zalculates a table for different relative vélocities of the blades (at adistance 
of one seventh of the total length from the centre of the shaft) and the wind, 
from which the following is condensed: 





Distance from the axis of the wheel in sevenths of radius. 
Ratio of the 











Speed of Blade 

at 1/7 of Radius 1 2 3 4 5 6 ie 

to Velocity of 
Wind. 

Best angles of weather. 

0.10 42° 97 1399 217 | 36°189/ | 342 ¥6” | 319 43” | 29° 31’ | 27° 30’ 
0.15 40 44 | 36 39 | 82 53 | 29 31 |26 34 |24 0 j]21 48 
0.20 439 21 184 6 |29 31 | 25 40 | 22 380 119 54 11% 46 
0.25 BY 59 136 43 | 26 34 | 22 380 119 20 | 16 51 |14 52 
0.30 36 39 | 29 31 | 24 6 119 54 116 51 [14 32112 44 
0.35 35 «21 v 30 1°21 48 | 1% 46 | 44 52 112 44 ) 11 6 
0.40 pteeGe | eo 640) 19 52 1G) OAS e i ee LO | 6 S50 
0.45 32 638 124. 0118 16 | 14 32 | 11 59 | 10 10) 8 48 
0.50 DL 4d) we 00 I10 ol Ase 17, 10 spd 9 138 7 58 





The effective power of a windmill, as Smeaton ascertained by experiment, 
varies as s, the sectional area of the acting stream of wind; that is, for:simi- 
lar wheels, as the squares of the radii. 

The value 0.75, assigned to the multiplier c in the formula Q = cvs, is 
founded on the fact, ascertained by Smeaton, that the effective power of a 
windmill with sails of the best form, and about 151% ft. radius, with a breeze 
of 13 ft. per second, is about 1 horse-power. In the computations founded 
on that fact, the mean angle of weather is made = 138°. The efficiency of 
this wheel, according to the formula and table given, is 0.29, at its best 
speed, when the tips of the sails move at a velocity of 2.6 times that of the 
wind. 

Merivale (Notes and Formule for Mining Students), using Smeaton’s co- 
efficient of efficiency, 0.29, gives the following: 


U = units of work in foot-ibs. per sec.; 

W = weight, in pounds, of the cylinder of wind passing the sails each 
second, the diameter of the cylinder being equal to the diameter 
of the sails; 

V = velocity of wind in feet per second; 
H.P. = effective korse-power; 
wv? . HP. = 0.29WV2 
oe ie f 1) 64°3C 550° 


A. R. Wolff, in an article in the American Engineer, gives the following 
{see also his treatise on Windmills): 


Let c = velocity of wind in feet per second; 
n = number of revolutions of the windmill per minute; 
by, 01, bg, bg, be the breadth of the sail or blade at distances lo, 1;, Ig, 


13, and l, respectively, from the axis of the shaft; 
ly = distance from axis of shaft to beginning of sail or blade proper; 
l = distance from axis of shaft to extremity of sail proper; 
Vo, V1, Va, Va, Uz = the velocity of the sail in feet per second at dis- 


tances lo, 11, Ig, l, respectively, from the axis of the shaft; : 
Qo, M1, Mg, Mg, Ay, = the angles ofimpulse for maximum effect at dis~ 


tances lp, 11, le, 13, l respectively from the axis of the shaft; 

a = the angle of impulse when the sails or blocks are plane surfaces, 
so that there is but one angle to be considered; 

N = number of sails or blades of windmill; 





.93. 
d = density of wind (weight of a cubic foot of air at average tempera 
ture and barometric pressure where mill is erected); 
W = weight of wind-wheel in pounds; 
f = coefficient of friction of shaft and bearings; 
D = diameter of bearing of windmill in feet. 


(Il — ly))Kc?adN 


550g 


496 AIR. 
The effective horse-power of a windmill with plane sails will equal 
. @ 
x mean of ( vo(sin a- =e COS @)bg COS @ } 
: K 


* ue SW X .05236nD 
Vy (sin a — oa COs a) by cos a) — 550 ° 
The effective horse-power of a windmill of shape of sail for maximum 
effect equals * 
Nd = 1)Kdce3 2sin? ay —1 2sin2a,—1 ; 
Sag cen Mae ee Seer sink a, C8 . 
2sin?ay —1 FW X .05236nD | 
RQ ——_—— by —, or fo eh oe le 
Sing Ay 550 q 


The mean value of quantities in brackets is to be found according to 
Simpson's rule. Dividing 1 into 7 parts, finding the angles and breadths— 
corresponding to these divisions by substituting them in quantities within 
brackets will be found satisfactory. Comparison of these formule with the 
only fairly reliable experiments in windmills (Coulomb’s) showed a close 
agreement of results. i 

Approximate formule of simpler form for windmills of present construc- 
tion can be based upon the above, substituting actual average values for a, 
c, d, and e, but since improvement in the present angles is possible, it is 
better to give the formule in their general and accurate form. 

Wolff gives the following table based on the practice of an American 
manufacturer. Since its preparation, he says, over 1500 windmills have been — 
sold on its guaranty (1885), and in all cases the results obtained did not vary 
sufficiently from those presented to cause any complaint. The actual re- 
sults obtained are in close agreement with those obtained by theoretical 
analysis of the impulse of wind upon windmill blades. 


Capacity of the Windmill. 























3 bs |E54 
sil pits a pe |eae @ 
= |e | £4 | Gallons of Water raised per Minuteto |g5 |HFo 
= |se!l us an Elevation of— BE sis @ 
a = 2 3 iS og 
° ea o¢5 = a, LE @ 
a he nS : osSH 
i) ee ag $2,:\405 
= Ope One BaS|" pe 
3 mn £0 LSoQiogd.g5) 
res = 5, Sf 2) OA OS 
w | Sa | S 25 50 75 | 100 | 150 | 200 |R_ Sif 7 a om 
Sis |S feet. | feet. | feet.) feet. | feet. | feet. |EAF|2 25's | 

~~ 

A |e os 4 <4 | 
wheel ; 
Betti 16) 170 to 75) |. 6.162 1) 8016 | eee ats nel suite) Hem eae 0.04 8 @ 
10 ** | 16 |60to65} 19.179] 9.563] 6.638) 4.750)......[ ..... 0.12 8 a 
12 “| 16 |55to60) 33.941} 17.952]11.851) 8.485) 5.680]...... 0.21 8 @ 
14 ** | 16 [50t055) 45.189} 22.569/15.304, 11.246) 7.807) 4.998) 0.28 8 @ 
16 ‘* | 16 {45050} 64 600! 31.654 ]19.542) 16.150, 9.771) 8.075) 0.41 8 @ 
18 ‘| 16 /40t045) 97.682} 52.165 |32.513] 24.421) 17.485) 12.211] 0.61 8 | 
20 * | 16 |385 to 40) 124.950 63.750 |40.800| 31.248) 19.284) 15.938) 0.7 8 
mo a 16 [30 to 35 212.281 1106.964 |71.604] 49.725! 37.349] 26.741] 1.34 S$ a 


These windmills are made in regular sizes, as high as sixty feet diameter of — 
wheel; but the experience with the larger class of mills is too limited to 
enable the presentation of precise data as to their performance. ; 

If the wind can be relied upon in exceptional localities to average a higher 
velocity for eight hours a day than that stated in the above table, the per-— 
formance or horse-power of the mill will be increased, and can be obtained — 

7 
i 


by multiplying the figures in the table by the ratio of the cube of the higher 
average velocity of wind to the cube of the velocity above recorded | 
He also gives the following table showing the economy of the windmill. — 
All the.items of expense, including both interest and repairs, are reduced to 
the hour by dividing the costs per annum by 365 X 8 = 2920; the interest, — 


WINDMILLS. 497 


ete., for the twenty-four hours being charged to the eight hours of actual 
work. By multiplying the figures in the 5t column by 584, the first cost of 
the windmill, in dollars, is obtained. 


Economy of the Windmill. 

















3 |e3) Bw Expense of Actual Useful Power | ,. 

a2) oS de eae B Developed, in cents, per hour. o 

© ih Pe |o5s as > BPR ONY OY UCP, a. 

s\l a o _C c Fe ran] wl Ow WN o- 

BO $5 Ops He ela fet oes ‘ ae 

45| 5s SOSSclzeESs es jac 3) m5 

Rasinait Slo, [SACO SCSSCE ea |eou =| S 

esignation) 25/45 |S: n4\eos5 gx lzss S 5 

of Mill, | gE ASSES oo. EY eso) 2 a 

C8] 22 lomag|SORCMEEIASZE! 8 | a 
in| Sa of eS 2 apes -Us/OHw S| 6 a ‘ ene 
Sal Fae |S Sen/F4 nas esimees id | Ola lses 
eT Se ESSE(T ES Seog fae]. | 2 | S [aoe 
3 on PIQBEBISHOOSH Ss 5AO0d 5 i) So |e SS 

és) & <q a cy a Se A a [S| 

814 ft. wheel] 370} 0.04 8 0.25 © 0.25 | 0.06} 0.04/0.60} 15.0 
a wb 1151) 0.12 8 0.30 0.30 | 0.06} 0.04/0.70) 5.8 

tose *** t 2036} 0.21 8 0.36 0.36 |0.06,0.04,0.82}] 3.9 
nas, S* ee 2708} 0.28 8 0.75 0.75 |0.06}0.07| 1.63} 5.8 
Gr eee oe 3876} 0.41 8 1.15 1.15 |0.06|0.07}2.43) 5.9 
jb Re ale 4 5861} 0.61 8 1.35 1.35 |0.06]0.07/2.83} 4.6 
a0 Fe e 7497) 0.79 8 1.70 1.70 |0.06}0.10)3.56] 4.5 
Sop S° pee liecdalMiee 8 2.05 2.05 '0.06!0.10| 4.26 3.20 


Lieut. I. N. Lewis (Eng’g Mag., Dec. 1894) gives a table of results of ex- 
periments with wooden wheels, from which the following is taken: 
eee ee eee 
Velocity of Wind, miles per hour. 














Diameter apap = < ne o> Ran? Tie eT 
of wheel, | 8 | 10 | 12 | 16 | 20 | racks an 
Feet. Se eee 
Actual Useful Horse-power developed. 
12 0 4 4 5 1 1% 2 
16 4% 38 34 1 214 314 4 
20 34 144 2 3 4 516 7 
25 114 194 3 416 6 8 10 
30 Q 3 4 51g 7 9 12 


The wheels were tested by driving a differentially wound dynamo. The 
“ useful horse-power ’? was measured by a voltmeter and ammeter, allow- 
ing 500 watts per horse-power. Details of the experiments, including the 
means used for obtaining the velocity of the wind, are not given. The re- 
sults are so far in excess of the capacity claimed by responsible manufactu- 
rers that they should not be given credence until established by further 
experiments. 

—~K recent article on windmills in the Iron Age contains the following: Ac- 
‘cording to observations of the United States Signal Service, the average 
velocity of the wind within the range of its record is 9 miles per hour for 
‘the year along the North Atlantic border and Northwestern States, 10 miles 
on the plains of the West, and 6 miles in the Gulf States. 

_ The horse-powers of windmills of the best construction are proportional 
to the squares of their diameters and inversely as their velocities; for ex- 
ample, a 10-ft. mill in a 16-mile breeze will develop 0.15 horse-power at 65 
revolutions per minute; and with the same breeze 


A 20-ft. mill, 40 revolutions, 1 horse-power. 

A 25-ft. mill, 35 revolutions, 134 horse-power. 
A 30-ft. mill, 28 revolutions, 344 horse-power. 
A 40-ft. mill, 22 revolutions, 74 horse-power. 
A 50-ft. mill, 18 revolutions, 12 horse-power. 


The increase in power from increase in velocity of the wind is equal to the. 
equare of its proportional velocity; as, for example, the 25;ff. mill rated 





498 AIR, | 7 


above for a 16-mile wind will, with a 32-mile wind, have its horsespower in — 
creased to 4 x 134 = 7 horse-power, a 40-ft. mill in a 32-mile wind will run — 
up to 80 horse-power, and a 50-ft. mill to 48 horse-power, with a small de 

duction for increased friction of air on the wheel and the machinery. | 

The modern mill of medium and large size will run and produce work ina 
4-mile breeze, becoming very efficient in an 8 to 16-mile breeze, and increase 
its power with safety to the running-gear up to a gale of 45 miles per hour. 

Prof. Thurston, in an article on modern uses of the windmill, Engineer- 
ang Magazine, Feb. 1893, says: The best mills cost from about $600 for the 
10-ft. wheel of 14 horse-power to $1200 for the 25-ft. wheel of 1144 horse-power 
or less. In the estimates a working-day of 8 hours is assumed; but the ma- 
chine, when used for pumping, its most common application, may actually 
do its work 24 hours a day for days, weeks, and even months together, — 
whenever the wind is ‘“‘stiff’? enough toturnit. It costs, for work done in 
situations in which its irregularity of action is no objection, only one half or 
one third as much as steam, hot-air, and gas engines of similar power. At 
Faversham, it is said, a 15-horse-power mill raises 2,000,000 gallons a month 
from a depth of 100 ft., saving 10 tons of coal a month, which would other- 
wise be expended in doing the work by steam. 

Electric storage and lighting from the power of a windmill has been tested 
on a large scale for several years by Charles F. Brush, at Cleveland, Ohio. 
4{n 1887 he erected on the grounds of his dwelling a windmill 56 ft. in diam- 
eter, that operates with ordinary wind a dynamo at 500 revolutions per 
yninute, with an output of 12,000 watts—16 electric horse-power—charging 
a storage system that gives a constant lighting capacity of 100 16 to 20 
candle-power lamps. The current from the dynamo is automatically regu- 
lated to commience charging at 330 revolutions and 70 volts, and eutting the: 
circuit at 75 volts. Thus, by its 24 hours’ work, the storage system of 408 
cells in 12 parallel series, each cell having a capacity of 100 ampére hours, is 
kept in constant readiness for all the requirements of the establishment, it 
‘being fitted up with 350 incandescent lamps, about 100 being in use each 
evening. The plant runs at a mere nominal expense for oil, repairs, and at: 
tention. (For a fuller description of this plant, and of a more recent one at 
Marblehead Neck, Mass., see Lieut. Lewis’s paper in Engineering Magazine, 
Dec. 1894, p. 475.) 


COMPRESSED AIR. 


Heating of Air by Compression,.—Kimball, in his treatise on Physi- 
cal Properties of Gases, says: When air is compressed, all the work which is 
done inthe compression is converted into heat, and shows itself in the rise in 
temperature of the compressed gas. In practice many devices are employed 
to carry off the heat as fast as it is developed, and keep the temperature down. 
But it is not possible in any way to totally remove this difficulty. But, itmay 
be objected, if all the work done in compression is converted into heat, and 
if this heat is got rid of as soon as possible, then the work may be virtually 
thrown away, and the compressed air can have no niore energy than it had 
before compression. It is true that the compressed gas has no more energy 
than the gas had before compression, if its temperature is no higher, but 
the advantage of the compression lies in bringing its energy into more avail- 
able form. 

The total energy of the compressed and uncompressed gas is the same at 
the same temperature, but the available energy is much greater in the former. 

When the compressed air is used in driving a rock-drill, or any other piece 
of machinery, it gives up energy equal in amount to the work it does, and 
its temperature is accordingly greatly reduced. ; 

Causes of Loss of Energy in Use of Compressed Air. 
(Zahner, on Transmission of Power by Compressed Air.)—1. The compression 
of air always develops heat, and as the compressed air always cools down to 
the temperature of the surrounding atmosphere before it is used, the me- 
chanical equivalent of this dissipated heat is work lost. 

2. The heat of compression increases the volume of the air, and hence it. 
is necessary to carry the air to a higher pressure in the compressor in order 
that we may finally have a given volume of air at a given pressure, and at 
the temperature of the surrounding atmosphere. The work spent in effect- 
ing this excess of pressure is work lost. 

3. Friction of the air in the pipes, leakage, dead spaces, the resistance of. 
fered by the valves, insufficiency of valve-area, jnferior workmanship, and 
slovenly attendance, are all more or less serious causes of loss of power. 


COMPRESSED AIR. 499 


The first cause of loss of work, namely, the heat developed by compres- 
sion, is entirely unavoidable. The whole of the mechanical energy which 
jhe compressor-piston spends upon the air is converted into heat. This heat 
s dissipated by conduction and radiation, and its mechanical equivalent is 
work lost. The compressed air, having again reached thermal equilibrium 
with the surrounding atmosphere, expands and does work in virtue of its 
ntrinsic energy. 

The intrinsic energy of a fluid is the energy which it is capable of exert. 
ng against a piston in changing from a given state as to temperature and 
volume, to a total privation of heat and indefinite expansion. 

Adiabatic and Isothermal Compression,.—Air may be com- 
pressed either adiabatically, in which all the heat resulting from com- 
pression is retained in the air compressed, or isothermailly, in which the 
heat is removed as rapidly as produced, by means of some form of refrig- 
erator. 


Volumes, Mean Pressures per Stroke, Temperatures, etc., 
in the Operation of Air-compression from 1 Atmosphere 
and 60° Fahr,. (Ff. Richards, 4m. Mach., March 30, 1898.) 









































a = Bele 5. 5. 18 
“e) <4 [ag jas | 8 : 45/4 {aq jas ja 
Ee O| agGi/cOaioe | -- Fe : 2| adl/ohalod |.- 
Sl ft) Sa Soe. sseg| Sols S (SS) SO5c S/S egies 
@) & | Fel FSieec|e<8| 2p 4| & | BS) Bsl\eae|Z=3|<5 
a) 2] oS] oc le eeleos| Sohal 3 | oe] of le eeleasiss 
“| & |] On) OLIMognA ys OF 7 a OF) Coit siaxds)~o 
€| $| £8) €elasSieeo |e 9S] S | 88) BSESSi-0 Ia 

s°| sAIS Ogos oe 5BO| sS|Seulgs 

a] Hl sols l88"|\38a 18 98) £ Soils [$8 "lga 18 
S| dal/eralr |e q Be Fo] da iePsr If = Pa 
2) 2 3 4 5 6 7 1 2 3 a 5 6 fs 
OY <1 boty al 0 0 | 60° 80| 6.442} .1552).266 | 27.38] 36.64) 432 
1/1.068] .9363) .95 “O61 oto] W 85) 6.782! .1474].2566/ 28.16) 37.94] 447 
2|1.136] .8803) .91 1.87) 1.91 | 80.49 90) 7.122).1404].248 | 28.89] 39.18] 459 

 -8/1.204].8305].876 | 2.72] 2.8 | 88.48 95) 7.462).134 |.24 | 29.57] 40.4 | 472 

— 4/1.272).7861) .84 3.53] 38.67 | 98 100} 7.802] .1281).2324} 30.21] 41.6 | 485 

| 5/1.34 |.7462).81 4.3 | 4.5 {106 105| 8.142) .1228] 2254] 80.81] 42.78] 496 
101.68 | .5952) .69 7.62) 8.27 1145 110} 8.483) .1178).2189} 31.89] 43.91} 507 
15)2.02 |.495 |.606 | 10.83)11.51 17 115} 8.823) .1133].2129) 31.98) 44.98) 518 
20)2.36 |.4237].543 | 12.62/14.4 {207 § 120) 9.163).1091].2073) 382.54] 46.04] 529 
25)2.7 |.3703}.494 | 14.59/17.01 |234 125) 9.503) .1052) .2020) 83.07] 47.06) 540 
30/3.04 |.3289].4538) 16.34]19.4 [252 § 130) 9.843).1015).1969] 33.57] 48.1 | 550 
35]3.381] .2957) .42 | 17.92/21. 281 135 '10.183) .0981| .1922) 34.05) 49.1 | 560 
40|3.721) .2687|.393 | 19.32/23.66 {302 140 10.523] .095 |.1878| 84.57] 50.02) 570 








45] 4.061) .2462).87 | 20.57/25.59 |321 145 10.864) .0921|.1887| 35.09) 51. | 580 
50/4.401).2272].35 | 21.69/27.39 |839 § 150,11.204| 0892) .1796| 35.48) 51.89] 589 
55)4.741|.2109).331 | 22.76)29.11 857 & 160 11.88 |.0841}.1722) 86.29) 53.65) 607 
60]5 .081] .1968] .3144] 23.78/380.75 j3875 § 170 12.56 |.0796).1657| 387.2 | 55.39) 62 
65/5 .422] .1844) 3801 | 24.75/382.32 [889 § 180,138.24 |.0755).1595) 37.96} 57.01) 640 
7015 .762| .1735).288 | 25.67/83.83 |405 190, 13.93 | .0718).154 | 38.68) 58.57| 657 
75/6 .102] .1639] .276 ee 420 § 200 14.61 |.0685|.149 | 39.42/ 60.14) 672 


Column 3 gives the volume of air after compression to the given pressure 
and after it is cooled to its initial temperature. After compression air loses 
its heat very rapidly, and this column may be taken to represent the volume 
of air after compression available for the purpose for which the air has 
been compressed, f 

Column 4 gives the volume of air more nearly as the compressor has to 
deal with it. In any compressor the air will lose some of its heat during 
compression. The slower the compressor runs the cooler the air and the 
smaller the volume. 

Column 5 gives the mean effective resistance to be overcome by the air- 
cylinder piston in the stroke of compression, supposing the air to remain 
constantly at its initial temperature. Of course it will not so remain, but 
this column is the ideal to be kept in view in economical air-compression. 








500 AIR. 


Column 6 gives the mean effective resistance to be overcome by the pis. 
ton, supposing that there is no cooling of the air. The actual mean effec- 
tive pressure will be somewhat less than as given in this column; but for 
computing the actual power required for operating air-compressor cylinders — 
the figures in this column may be taken and a certain percentage added— 
say 10 per cent—and the result will represent very closely the power required © 
by the compressor. j 

The mean pressures given being for compression from one atmosphere 
upward, they will not be correct for computations in compound compression 
or for any other initial pressure. 

Loss Due to Excess of Pressure caused by Heating in 
the Compression-cylinder.—If the air during compression weie 
kept at a constant temperature, the compression-curve of an indicator-dia- 
gram taken from the cylinder would be an isothermal curve, and would fol- 
low the law of Boyle and Marriotte, pv=a constant, or p,v; = pov, or 
Divs Po » Lo and vo being the pressure and volume at the beginning of — 
compression, and p,v, the pressure and volume at the end, or at any inter- 
mediate point. But as the air is heated during compression the pressure 
increases faster than the volume decreases, caus.ng the work required for 
any given pressure to be increased. If none of the heat were abstracted 
by radiation or by injection of water, the curve ore diagram would be an 
Vo . le 


adiabatic curve, with the equation p, = po\ — Cooling the air dur- 


E: 

ing compression, or compressing it in two cylinders, called compounding, 
and cooling the air asit passes from one cylinder to the other, reduces the 
exponent of this equation, and reduces the quantity of work necessary to 
effect a given compression. F. T. Gause (Am. Mach., Oct. 20, 1892), describ- 
ing the operations of the Popp air-compressors in Paris, says: The greatest 
saving realized in compressing in a single cylinder was 33 per cent of that 
theoretically possible. In cards taken from the 2000 H.P. compound com- 
pressor at Quai De La Gare, Paris, the saving realized is 85 per cent of the 
theoretical amount. Of this amount only 8 per cent is due to cooling dur- 
ing compression, so that the increase of economy in the compound com- 
pressor Is mainly due to cooling the air between the two stages of compres- 
sion, A compression-curve with exponent 1.25 is the best result that was 
obtained for compression in a single cylinder and cooling with a very fie 
spray. Thecurve with exponent 1.15 is that which must be realized ina 
single cylinder to equal the present economy of the compound compressor 
at Quai De La Gare. 


ts 


Hlorse-power 
compress and deliver one 
cubic foot of Free Air per 
inibute to a given pressure with no 
cooling of the air during the com- 
pression; also the horse-power re- 
quired, supposing the air to be main- 
tained at constant temperature 
during the compresion. 


required to|Horse-power 


required 
compress and deliver one 
cubic foot of Compressed 
Air per minute at a given pressure 
with no cooling of the air during 
the compression; also the horse- 
power required, supposing the air to 
be maintained at constant tempera- 
ture during the compression. 


Gauge- Air not Air constant | Gauge-_.- Air not Air constant 
pressure, cooled, temperature.|pressure, cooled. temperature. 
5 .0196 0188 5 0268 0251 
10 .0361 0333 10 .0606 ~ 0559 
20 0628 0551 20 1483 .1300 
30 -0846 0713 30 257 2168 
40 1032 0843 40 3842 3138 
50 1195 .0946 50 5261 4166 
60 1342 1036 60 .6818 5266 
70 1476 1120 70 .8508 6456 
80 1599 1195 80 1.0302 7700 
90 1710 1261 90 1.217 8979 
100 1815 1318 100 1.4171 1.0291 


The horse-power given above is the theoretical power, no allowance being 
made for friction of the compressor or other losses, which may amount to 


10 per cent or more. 


COMPRESSED AIR. 5OL 


Formule for Adiabatic Compression or Expansion of 
Air (or other sensibly perfect gas). 


Let air at an absolute temperature T,, absolute pressure Pp), and volume 
vp, be compressed to an absolute pressure Pp and corresponding volume vg 
and absolute temperature 74; or let compressed air of an initial pressure, 
volume, and temperature pg, Va, and Ts be expanded to pj, v,, and 1), there 
being no transmission of heat from or into the air during the operation. Then 
the following equations express the relations between pressure, volume, 
and temperature (see works on Thermodynamics): 


0-71 M,\ 1:41 . 
Su (PA et Uae Gas) al (hd ae 
a 1 Veg 9 Vy aa) ; 


Vg Pr 
; 0:41 7 T. 


The exponents are derived from the ratio cp -- cv =k of the specific heats 
of air at constant pressure and constant volume. Taking k = 1.406,1+k = 
0.711; .k—1= 0.406; 1+ (k — 1) = 2.463; k-+(k — 1) = 3.468; (hk —1)+k= 
9.289. 

Work of Adiabatic Compression of Air.—If air is com- 
pressed in a cylinder without clearance from a volume v, and pressure p, 
to a sinaller volume v, and higher pressure pg, work equal to pV, is done by 
the external air on the piston while the air is drawn into the cylinder. 
Work is then done by the piston on the air, first, in compressing it to the 
pressure p, and volume v2, and then in expelling the volume vs; from the 
cylinder against the pressure pz. If the compression is adiabatic, py" = 


DoV_" = constant. k = 1.41. 
The work of compression of 1 pound of air is 


k-1 
k—1 jie 
Pir a ie eit a ie Pan eo 
fi | ret ec pen Cayo 
0-29 
2.463p,v } (2 -1t 
PiV} bs) 


0-29 


The work of expulsion is pyv2g = PV} (22) . 
1 


or 


wo 
ri 
for) 
Co 
us} 
~ 
< 
~ 
oo 
S| 
eo ln 
NY 
o 
= 
| 
— 
Ct eal 
ll 


The total work is the sum of the work of compression and expulsion less 
the work done on the piston during admission, and it equals 


{ Fees 0-29 
Bi ee =) ‘ -| = 3.463 pits} (?2) -1f. 


The mean effective pressure during the stroke is 


—; 2 ; = 3.463 a 
2 —= = Pa =e 
Prj 1 ed 1 . Pi ) 1 . 


and pq are absolute pressures above a vacuum in atmospheres or in 
pounds per square inch or per square foot. , 
EXAMPLE.—Required the work done in compressing 1 cubic foot of air per 
second from 1 to 6 atmospheres, including the work of expulsion from the 
cylinder. 
i + p, = 6; 69°29 -- 1 = 0.€81; 3.463 x 0.681 = 2,358 atmospheres, x 14.7 = 
34.66 lbs. per sq. in. mean effective pressure, x 144 = 4991 lbs. per sq. ft., X 1 
fp. stroke = 4941 ft.-Ibs., + 550 ft.-lbs. per second = 9.08 H,P. 


501a AIR. 
If R = ratio of pressures = pg -- /;, and if v; = 1 cubic foot, the work done 
in compressing 1 cubic foot from p, to pe is in foot-pounds . 


3.463p ,(R°'29 — 1), 


p, being taken in lbs. per sq. ft. For compression at the sea-level p, may be- 
taken at 14 Ibs. per sq. in. = 2016 lbs. per sq. ft., as there is some loss of 
pressure due to friction of valves and passages. 

Indicator-cards from compressors in good condition and under working- 
speeds usually follow the adiabatic line closely. A low curve indicates 
piston leakage. Such cooling as there may be from the cylinder-jacket and 
the re-expansion of the air in clearance-spaces tends to reduce the mean 
effective pressure, while the ‘“‘camel-backs’’ in the expulsion-line, due to- 
resistance to opening of the discharge-valve, tend to increase. it. 

Work of one stroke of a compressor, with adiabatic compression, in foot- 
pounds, 


W = 3.463P, Vy(R% 29 — 1), 
in which P, = initial absolute pressure in lbs. per sq. ft. and V, = volume 
traversed by piston in eubic feet. ; 

The work done during adiabatic compression (or expansion) of 1 pound of — 
air from a volume v, and pressure p, to another volume vg and pressure pg 
is equal to the mechanical equivaient of the heating (or cooling). If ¢, isthe — 
higher and ft, the lower temperature, Fahr., the work done is c,J(t, — ty) — 
foot-pounds, ¢, being the specific heat of air at constant volume = 0.1689 ang 
J = 778, ¢,J = 131.4. 

The work during compression also equals 


Ra being the value of pv + absolute temperature for 1 pound of air = 53.3%. 
The work during expansion is 


2.468 p,v,| 1 a: oe = 2,463 pave [eye = ed 


in which p,v, are the initial and p2v2 the final pressures and volumes. 
Compressed-air Engines, Adiabatic Expansion. — Let 
the initial pressure and volume taken into the cylinder be p, lbs. per 
sq. ft. and v, cubie feet; let expansion take place to pg and vg according to 
the adiabauc law p,v,!*4! = povy! 41; then at the end of the stroke let the 
pressure drop to the back-pressure ps3, at which the air is exhausted. 
Assuming no clearance, the work done by one pound of air during ad- 
mission, measured above vacuum, is p,v,, the work during expansion is 
Ds 
2.463 pivi[ 1 — & 
Py 
i - Pe 6.29 4 : 
The total work is p,v, 4- 2.463p,v,| 1 — ei — P3V¥q, and the mean effec- 
1 


tive pressure is the total work divided by U.. 
If the air is expanded down to the back-pressure pg the total work is 


3.463p 0, ye CE eur t 
Pr 


or, in terms of the final pressure and volume, 
S405 90 4 eae ny , 
P3 
and the mean effective pressure is 


8.408» 4 Ca iam big t. 


The actual work is reduced by clearance. When this is considered, the 
product of the iuitial pressure p, by the clearance volume is to be subtracted 
from the total work calculated from the initial volume vy, including clearance, 
(See p. 744, under ‘‘ Steam-engine,”’) 


0-29 , : 
) i and the negative or back-pressure work is — p3¥. 


COMPRESSED AIR. 5016 


Mean Effective Pressures of Air Compressed A diabatically. 
(FP. A. Halsey, Am. Mach., Mar. 10, 1898.) 

















MEP from a MEP from 

Rk R029 114 Ibs. Initial. R F029 114 lbs. Initial. 
1.25 1.067 3.24 4.75 t.570 27.5 
1.50 1.125 6.04 5. 1.594 28.7 
1.75 1.176 8.51 5.25 1.617 29.8 

2. 1.223 10.8 5.5 1.639 30.8 
2.25 1.265 12. 5.75 1.660 31.8 
9.5 1.304 14.7 6. 1.681 32.8 
9.75 1.341 16.4 6.25 1.701 33.8 

3. 1.395 18.1 6.5 1.720 34.7 
3.25 1.407 19.6 6.75 1.739 35..6 
3.5 1.438 21.1 a 1.757 36.5 
3.75 1.467 92.5 25 1.77 37.4 

4. 1.495 93.9 5 1.798 38.3 
4.25 1.521 95.2 8. 1.827 39. 

4.5 1.546 26.4 








F& = final + initial absolute pressure, 

MEP = mean effective pressure, lbs. per sq. in., based on 14 Ibs. initial. 

Compound Compression, with Air Cooled between the 
Two Cylinders. (4m. Mach., March 10 and 31, 1898.)— Work in low-pres- 
sure cylinder = W,, in high-pressure cylinder Wg. Total work 

W, + We = 3.46P, V1 °29 + e297) ~ +29 — 2]. 

‘vr, =ratio of pressures in 1, p. eyl., 7, = ratio in h. p. cyl., R=7,rg. When 

TT) =7rg= VR, thesum W,+ Weisa minimum. Hence fora given total ratio 

of pressures, R, the work of compression will be least when the ratios of the 

pressures in each of the two cylinders are equal. _ 

The equation may be simplified, when +, = #/R, to the following: 

Wy + Wa = 6.92P,V,[Re-145 — 1), 

Dividing by V, gives the mean effective pressure reduced to the low-pressure 

cylinder MEP = 6.92P,[R°:145 — J], 

In the above equation the compression in each cylinder is supposed to be 
adiabatic, but the intercooler is supposed to reduce the temperature of the 
air to that at which compression began, 

Mean Effective Pressures of Air Compressed in Two 
Stages, assuming the Intercooler to Reduce the Tem- 
perature to That at which Compression Began. (F. A. 
Halsey, Am. Mach., Mar. 31, 1893.) 














| MEP | Ultimate MEp |Ultimate 

from 14 | Saving from Saving 

R [20-145 lbs. by Com- tie JR0+145 14 Ibs. | by Com- 

Initial, | pound: Initial, | Pound- 

ing, % ing, % 

5.0 1.263 25:4 TiS: 9.0 ABS ffs) 36.3 
Se 1.280 27.0 12 3 9.5 1.386 31.38 
6.0 1.296 28.6 12.8 10 1.396 88.3 
6.5 1.312 30.1 13,2 11 1.416 40.2 
7.0 1.326 vats 13.7 iP} 1.434 41.9 
sire 1.336 2.8 14.3 13 1.451 43.5 
8.0 1.352 34.0 14.8 14 1.466 45.0 
8.5 1.364 35.2 15 1.481 46.4 


Rk = final + initial absolute pressure. 

MEP= mean effective pressure lbs. per sq. in. based on 14 lbs. absolute 
initial pressure reduced to the low-pressure cylinder. 

To Find the Index of the Curve of an Air-diagram,.— 
If P,V, be pressure and volume at one point on the curve, and PV the pres. 
sure and volume at another point, then z = (— ) , in which @ is the index 

1. ‘ 
tobe found. Let P+ P, = R, and Vj+V=7; then R=71” log R=~a logy, 
whence # = log R= log 7, 


D0% ATR. 


Table for Adiabatic Compression or Expansion of Air, 
(Proc. Inst. M.E., Jan. 1881, p. 123.) 





Absolute Pressure. Absolute Temperature. Volume. 


Ratio of Ratio of Ratio of Ratio of Ratio of Ratio of 





Greater Less to Greater Less to Greater Less to 

to Less. Greater. to Less. Greater. to Less. Greater, 

{Expan- | (Compres- | (Expan- | (Compres- | (Compres- (Expan- 
sion.) sion.) sion.) sion.) sion.) sion.) 
1.2 833 1.054 948 1.138 879 
1.4 714 1.102 907 1.270 2188 
1.6 625 1.146 .873 1.396 At Gi) 
1.8 556 1.186 .843 1.518 .659 
2.0 .500 1.222 .818 1.636 611 
252 454 1.257 196 1.750 571 
2.4 417 1.289 776 1.862 Da 
2.6 385 1.319 758 1.97 507 
2.8 3857 1.348 142 2.077 .481 
3.0 333 1.375 127 2.182 -458 
aye 312 1.401 714 2,284 -438 
3.4 294. 1.426 701 2.384 .419 
3.6 278 1.450 .690 2.483 -408 
3.8 -263 1.47 .679 2.580 .3888 
4.0 250 1.495 .669 2.676 .374 
4.2 2238 1.516 .660 CATA 36k 
4.4 Past 1.537 .651 2.863 349 
4.6 217 , 1.557 642 2.955 838 
4,8 2208 1.576 -685 3.046 2828 
5.0 200 1.595 .627 3.185 319 
6.0 167 1.681 2595 3.569 .280 
7.0 143 1.758 .569 3.981 .251 
8.0 0125 1.828 547 4.37 228 
9.0 e111 1.891 .529 4.759 .210 
10.0 - 100 1.950 Po 1G 5.129 2195 


—— 


Mean Effective Pressures for the Compression Part only 
of the Stroke when compressing and delivering Air 
from one Atmosphere to given Gauge-pressure in a Sin= 
gle Cylinder. (fF. Richards, Am. Mach., Dec. 14, 1893.) 





Gauge- | Adiabatic Isothermal § Gauge- | Adiabatic Isothermal 
pressure. Compression |Compression Jpressure.|Compression.}Compression, 

















1 44 43 45 13.95 12.62 
2 96 95 50 15.05 13.48 
3 1.41 1.4 55 15.98 14.3 
4 1.86 1.84 60 16.89 15.05 
5 2.26 2.22 65 17.88 15.76 
10 4.26 4.14 70 18.74 16 43 
15 5.99 5.77 75 19.54 17.09 
20 Tig OS G2 80 20.5 Lae 
25 9.05 8.49 85 21.22 18.3 
30 10.39 9.66 90 22. 18.87 
35 11.59 10.7 95 22.7 19.4 
40 12.8 Uae 100 23.48 19,92 








The mean effective pressure for compression only is always lower than 
the mean effective pressure for the whole work. 


COMPRESSED AIR. 503 


Mean and Terminal Pressures of Compressed Air used 
Expansively for Gauge-pressures from 60 to 100 lbs. 


(Frank Richards, 4m. Mach., April 18, 1893.) 






























































Pres- 60. 70. 80. 90. 100. 
sure 
ay ¥ > l— ° . — oO Led Oo . — e . | — 
a o/s 9 o| se we} S Hla O18 O D\s3 oo 
eo [S£5\a28 |$45| 25)2e8 225/825) Ba5/a2 5/5. § 
RO Sia 6 Bie 6) SA B Sle Bl BIA & 
25 23.6 |10.65) 28.74|12.07| 83.89 13.49) 39 04,724.91) 44.19| 1.33 
30 28.9 |\13.77 | 84-10 .6 40.61} 2.44 | 46.46} 4.27 | 53.32) 6.11 
14 32.13 .96 | 38.41! 8.09 | 44.69) 5.22 | 50.98) 7.35 | 57.26] 9.48 
33 33.66} 2.33 | 40.15} 4.388 | 46.64) 6.66 | 53.13) 8.95 | 59.62) 11.23 
36 35.85| 3.85 | 42.63] 6.36 | 49.41) 7.88 | 56.2 | 11.89 ) 62.98] 13.89 
37.98) 5.64 | 44.99) 8.39 | 52.05) 11.14 | 59.11) 18.88 | 66.16) 16.64 
45 41.75) 10.71 | 49.31} 12.61 | 56.9 | 15.86 | 64 45} 19.11 | 72.02) 22.36 
50 45.14} 13.26 | 53.16] 17 61.18) 20.81 | 69.19] 24.56 | 77.21) 28.33 
60 50.75] 21.53 | 59.51] 26.4 68.28) 31.27 | 77.05} 86.14 | 85.82) 41.01 
5g 51.92} 23.69 | 60.84) 28.85 | 69.76) 34.01 | 75.69| 39.16 7.61) 44.32 
% 58.67] 27.94 | 62.83] 33.03 | 71.99) 38.68 | 81.14! 44.38 | 90.32] 49.97 
Ki 54.93] 30.39 | 64 25) 36.44 } 73.57) 42.49 | 82.9 | 48.54 | 92.22) 54.59 
75 56.52) 35.01 | 66.05) 41.68 | 75.59' 48.35 | 85.12! 55.02 | 94°66] 61.69 
80 57.79) 39.7 67.5 | 47.08 | 77.2 | 54.88 | 86.91] 61.69 | 96.61] 68.99 
% 59.15| 47.14 | 69.03) 55.43 | 78.92) 68.81 | 88.81] 72. 98.7 | 80.28 
-90 59.46! 49.65 | 69.38! 58.27 | 79.31! 66.89 | 89.24! 75.52 | 99.17! 87.82 





The pressures in the table are all gauge-pressures except those in italics, 
which are absolute pressures (above a vacuum). 
Tiountain or High-altitude Compressors. 
(Norwalk Iron Works Co.} 








: 0 At Sea- At 2000 | At 6000 | At 10,000 
& oe le nd level. feet. feet. feet. 
<q. Os On as 
S| Ss |Selsaslee |S. | gle) el|Bl el els 
oe / 33 easioss| 25 (52.5) 42 |8 |) 218 lof] S | 8 
FS | us |ASRSeSl Os |so9| 2518) 25 |e (25) 2 | Be 
25 | GH |SO0|sHo| Fa le5e| 6a)2) 5a] Sioa) & | 58, 
o H A = RG 0 ss Oo; a oO |G Oo | s 

12 il 7 10 | 190 298 35 | 280) 384 | 244) 382) 214] 30 

16 16 914} 14 150 558 70 | 524) 68 | 462} 64) 405] 6 





22 24 134% | 20 110 1160 | 145 |1090} 140 | 960) 132) 843 | 124 
26 30 | 174 | 24 90 |} 1659 | 215 |1560| 207 [1373] 195] 1200 | 184 


As the capacity decreases in a greater ratio than the power necessary to 
compress, it follows that operations at a high altitude are more expensive 
than at sea-level. At 10,000 feet this extra expense amounts to over 20 per 
cent. 


Compressors at High teenage eee (Ingersoll-Sergeant Drill Co.) 


Alt. above sea-level, ft...| 0 |1000|2000|3000| 4000/5000|600u'7000 |8000 |9000 |10000 
Barometer, in, mercury. "130. 0 289/27 .8/26.8/25. 8 24 .8/23.9/23.0/22.1/21.3) 20.5 
lbs.per sq.in.|14.7/14.2/138.7)13.2)12.7/12.2)11.7/11.3/10.9|10.5| 10.1 

Air delivered, %.......... 100} 97 | 938 | 90 | 87 |} 84 | 81 | 78 | 76] 3} 7O 
Loss of capacity, Gases MUM omen ianclOe 13 Ie16 119 | 22) | 24nd 
Decreased power re- 
Quire? pape tar <a. oie 0 }1.8/3.5|5.2) 6.9] 8.5 |10.1/11.6|138.1]14.6} 16.1 














504 ATR. 


Air-compressors. Rand Drill Co. 






































RAND-CORLISS, CLASS ‘‘ BB-3”? (COMPOUND) |CLASS “ E”’ (STRAIGHT: 
STEAM, CONDENSING; COMPOUND AIR). LINE, BELT-DRIVEN). 
FOR STEAM-PRESSURE OF 125 LBS. AND TERMINAL||FOR TERMINAL PRESSURES 

AIR-PRESSURES OF 80 AND 100 LBS. oF 80 AND 100 LBS.PER SQ IN. 

55 : & lea .|Air-Cyl-| ¢ | mai- 

o< 3 Cylinder Diameters, Ins.| = : 4 3| inder, | & | cated 
B33 BA 1) [a2 es | inces. | | H.P. 
be. 8 . “1-2 ] oP eee @ | Air- 
= ,qi| Steam, Air, St By Ne Ne ey "ate ee ‘ 
ose a : So 1/8 ak ee . | pres 
Bs 5 S15 Se lea ete eee ae 
ALR] Pa | Ra Be Ped TBs tal aR INS NP Pan ap fae 
670 | 10 18 102 | 17 | 30) 8 102 97 i 8 | 14 19140) 52 17 
1196 12 22 13 21 36 | 83 182 165 | 10 | 14 | 130} 29 
1562 14 26 15 24 36 83 238 Pol H12 | 16.) 120 45 
1650 14 26 15 24 42 75 202 392 } 14 2 | 100 69 
1920 16 30 17% | 28 36 %5 293 527 1 16 | 24) 95 94 
2242 16 30 74} 28 | 42) %5 342 633 | 173| 24] 95) 112 

2395 | 16 30 17% | 28 | 48] 70 865 


2520 | 18 34 20 32 | 386) 75 884 





In the first four sizes (Class *‘ BB-3°’) the air-cylinders have poppet inlet 
and outlet valves; in the next six the low-pressure air-cylinders have me- 
chanical inlet-valves and poppet outlet-valves; and in the last six the low- 
pressure air-cylinders have Corliss inlet-valves and poppet outlet-valves. 
All high-pressure air-cylinders have poppet inlet and outlet valves. 

* Terminal air-pressure at 89 pounds, 


CLASS “ B-2’’ (DUPLEX STEAM, NON-||CLASS “CC” (STRAIGHT-LINE, 












































CONDENSING, COMPOUND AIR). STEAM-DRIVEN). 
FOR STEAM- AND TERMINAL AIR-PRESSURES|| FOR STEAM- AND TERMINAL AIR- 
oF 80 AND 100 LBs. PRESSURES OF 100 LBS. PER Sq. IN. 
2 5 oes Laer eee a 
ate Cylinder Diam- a tO) | Sem Cyl. S is 
26 o| eters, Inches. y |e | kis Ot g| Diam.,| . | & 
De (Em |).4 Os ns 4 Eto 
peal. | Aireyls. |= | & luGel/REE S| 5 | ge 
mele = frp eee eal lee cruel eg s a | eo 
ORE G o 2 Et S4//Odael 2 i SA 
SO, lace a Di wll go As n Ou 
aso/S8eih.p.|l.p.| 2] & jos Sl/oss]/ FS) en lf) & | se 
B fy OB 5 o 2 | 8 |Ss82F, | 8h 0) 2 la |e) 2 | sh 
Oo = Ww fave} Bem | /O MN _ M fea} ei 
220 8 7% } 22 7:12 1 140 35 97 | 8 | 8 | 12) 140 20 
300 9 14 12 | 140 47 165 | 10 | 10 | 14; 130 35 
393 10 93 15 16 | 120 62 251, 4-12 4.12 | 16.) 120 52 
565 12 11 18 16 | 120 89 3892 | 14 | 14 | 22} 100 82 
770 | 14 13 21 16 | 120 4} 121 527 | 16) 162d 95. || 110 
882 | 14 13 21 22 | 100 | 139 671 | 18} 18.| 241.95 | 140 
1152 16 15 24 22 | 100 182 950 | 20 | 20 | 30 87 200 


2085 | 2 19 : Sel EEN CE Ry 
= x All air-cylinders have poppet 

2356 | 20 19 30 | 48 | 60 | 370 F 

9848 | 22 at 33 | 48 | 60 | 446 inlet and outlet valves. 

The first six sizes (Class **‘ B-2”’) have both air-cylinders fitted with poppet- 
valves (inlet and discharge). The last four have low-pressure air-cylinders 
fitted with mechanical inlet-valve; high-pressure air-cylinders fitted with 
poppet inlet and discharge valves. 


1812; 18 | 28 | 380] 85 | 285 1335 | 24 | 24 1 80! 85 | 280 





STANDARD AIR COMPRESSORS, 505 
(The Ingersoll-Sergeant Drill Co., New York City.) 





























Diam. of Cyl. gs fad) ,2 : 
sat ni MD Se Aas of 3 <48/ £5 Space oS 
Steam.| Air. ou| Ga Occupied. E 
Class 5 |e Sl a2 ° 
ann aid gs ate S64, Bs 
ype q : ail] a [Pal # n 
Bp PB evra be || pl lee : is 
=~|!a!loln!lfio 4 ia Length.| Width. o * 
Hlalaglila]e idol ge S jan) 
10°} 053. )1004) 2. | 12) 160) 177) 50-100" |,107 (2/4 |) 87 0” 25-385 
A* 12 }....{1244)....] 14 | 155) 285) 50-100 | 12 3.9 40-56 
Serai ree 14 ]....|1414]....| 18 | 120) 382) 50-100 | 15 4 3 50-76 
he 16 |..../1614]....} 18 | 120) 498) 50-100 | 15 4 3 66-100 
Bisamec Ibe Fal heicicical pete tea 2! 94} 657) 50-100 | 19 Deo 86-131 
Briven 20) |22. 12054). 5. 24 94} 809) 50-100 | 19 Dao 113-160 
" 22 |reeeleee4g|....| 24 94) 960) 50-100 | 19 Das 126-192 
24 |....|2444]. 30 80}1225} 50-100 | 22 0 oe) 160-245 
B. Straight-line, iaimacitan Same as A in sizes up to 16 x 1614 x 18 ins. 
C.t all price bleaile «toupee 90| 576 100 817m 0!" |) 10% 677 115 
Du les 16 .--|1614)....) 386 | 82/1346} 100 36. 6 12 6 274 
Corliss 20 |....|2084)....)| 42 | 75/2239). 100 | 41. 0 13 6 454 
ateam 24 ..|2414|....1 42 | 75/8208) 100 | 48 0 14 6 646 
Duplex a 30 |..../3014|....} 48 65/4932} 100 | 41 O 16 6 1011 
P “182 |..../38244|....] 60 | 62/6717 100 | 60 0 196 1375 











Cy. 1014} 18 |1614|1014| 380 | 90) 615; 100 | 39 6 0 

Compound |14 | 26 |2214|1314] 36 | 85/1306} 100 | 43 0 6 
Corliss |16 | 30 |2414/1514) 42) 78)1668) 100 | 49 6 | 15 6 284 

6 6 

6 6 

0 6 





steam, {18 34 9814 1714|.48 | '75)2187 100 | 55 
Compound |22 | 40 [8414/2014] 48 | 72/3515) 100 | 56 











air.t  |24 | 44 |3614/2214| 48 | 70/3850] 100 | 58 19 664 
6 |....{6 |....] 6 | 150] 28] 50-80] 5 8 22 | 454 
gma {8 |--:-|.8 |---| 8 | 150} 69} 50-80} 6 8 25 | 934-13 
straicht- [10 |----[10 |....] 10 | 150] 134} 50-80 | 7 10 30 | 1834-25 
433 12 |..../12 |....| 12] 150} 287) 50-80| 8 6 30 | 3314-44 
> 12 |....]1614]....! 12 | 150] 415] 15-40 | 10 10 35 | 2434-50 
E. Belt-driven. Same as F'in sizes up to 144% diam. by 10 ins. stroke. 
G. vee{10 |....|1084] 12 | 160; 354; 100 | 14’ 6” | 7% 0” 75 
Steam- |....|12 | ...|12!4| 14 | 155] 570) 100 |16 6 | 9 0 121 
actuated, |....|14 |..../1414| 18 | 120] 764 100 | 20 0 | 10 0 163 
duplex |....|16 |....|1614] 18 | 120] 996) 100 | 20 0 | 10 0 212 
orhalf |... |18 |....{1814| 24 | 94/1314] 100 | 23 6 | 11 6 280 
duplex. |... |20 |....|2014| 24 | 94/1618) 100 | 25 6 | 12 0 344 








a en ee ee eee ee ey ee ee ees ee ey 


G. 10 |1614]....}1014] 12 | 160! 446) 80-100 | 16 3 (8) 71-80 
Duplex st.,|16 (2414|....|1544) 18 | 120/1130] 80-100 | 23 0 | 10 0 180-203 
comp. air. |20 |3014|....|1814] 24 | 100/1963) 100 | 30 Q 12 0 

G. 10 {17 |1444| 914] 12 | 160] 344] 80-100 | 16 3 7 6 55-62 
Comp. st., |16 {26 |2214/141%4| 18 | 120| 950) 80-100 | 23 0 | 10 0 152-171 
comp. air. |20 |32 |2814/1714| 24 | 100/1710) 80-100 | 30 0 | 12 0 274-308 





























ish Peeicd jar oth bal ee laze: 8 | 150} 138] 60-100 | 8 6 4 6 20-28 
Duplex st.,|....]10 |....110° | 10 | 150) 268) 70-100 | 10 0 4 9 43-54 
duplex air.|....{12 |....]12 | 12 | 150] 474) 80-100 | 11 8 5 10 83-95 

ole eben) Oy) (dk yD 8 | 150) 210} 80-100 | 8 6 5 3 82-36 
Duplex st.,}..../10 {16 |10 | 10 | 150) 342} 80-100 | 10 2 5 9 52-58 
comp. air. !....112 |18 |12 | 12 } 150! 519} 80-100 | 11 10 6:9 78-88 


J. Belted duplex or compound. 8 to 98 H.P.; 56 to 1059 cu. ft. per m. 


* Classes A, OC, G, and H are also built in intermediate sizes for lower 

ressures. t Furnished either duplex or half duplex. + Most economical 

orm of compressor. Compound air-cylinders are two-stage. § Self-con- 
tained steam-compressor, 





505a 4 AIR. pe 
e 
Cubic Feet of Free Air Required to Bun from One to 
Forty irs with 60 Ibs. Pressure. (Ingersoll-Sergeant 
Drill Co. 


For 75 lbs. Pressure add 1/5. For 90 lbs. add 2/5. 





CoAL- 
. ROcK-DRILLS. CUTTERS. 





oon AG aR ti unl ue ace eas etl. Gaal ice 
Machines} 2 in. |2%in.|234in.| 3 in. |844in./344in.j444in.| 5in. | 8lgin.| 4in. 


10 400 ; 450] 650] %50) 800 { 900 | 1000 | 1150 700 930 
12 480 | 540] 780] 900} 960 | 1080 | 1200 | 1380 840 | 1116 
HGR) WbABS as 675 | 975 | 1125 | 1200 | 1350 | 1500 | 1725 ; 1050 | 13895 
CUE tO ASSbg \sencbe 1300 | 1500 | 1600 } 1800 | 2000 | 2300 | 1400 | 1860 
ROME ereisteral|{ers eteters 1625 | 1875 | 2000 | 2250 | 2500 | 2775 | 1750 | 2325 
So = iprios se .-.-.]| 1950 | 2250 | 2400 | 2700 | 3000 | 3450 | 2100 | 2790 
AOE Ba ate 6 diste'| le steets 2600 | 8000 | 3200 | 3600 | 4000 | 4600 | 2800} 38720 





Compressed-air Table for Pumping Plants. 
(Ingersoll-Sergeant Drill Co.) 

For the convenience of engineers and others figuring on pumping plants 
to be operated by compressed air, we subjoin a table by which the pressure 
and volume of air required for any size pump can be readily ascertained. 
Reasonable allowances have been made for loss due to clearances in pump 
and friction in pipe. 


Perpendicular Height, in Feet, to which the Water is to be 








Ratio of 
Diam- Pumped. 
eae he: 25 | 50] 75 | 100/| 7125 | 150| 175] 200 | 250] 300] 400 
1 to14| A |13-75/27.5 |41.25/55.0 |68.25 |82.5 | 96.25)110.0 
Y B | 0.21] 0.45] 0.60] 0.75} 0.89 | 1.04] 1.20] 1.34 
5 to1} ING a a 12.22]18.33/24.44/30.83 | 36.66] 42.76] 48.88] 61.11173.32197.66 
1% B| ....| 0.65] 0.80] 0.95) 1.09 | 1.24] 1.39] 1.53} 1.83] 2.12] 2.70 
1% tois| Alec 13.75/19.8 |22.8 127.5 |82.1 | 36.66] 45.83/55.0 |78.33 
34 Te A 0.94] 1.14] 1.24 | 1.30] 1.54] 1.69] 1.99] 2.39] 2.88 
5 tot} US 13.75|17.19 | 20.63] 24.06] 27.5 |34.38141.25/55.0 
Be laws lo cece| 1. 2Bb 2.8% 1 1,52]; 1.66) 51181), 211i) 2401 2e88 
214 to} Ngee we castle a 13.75 116.5 | 19.25] 22.0 [27.5 |83.0 144.0 
oe TESS] jap Gla | ESE eral amen 1.533] 1.68] 1.83) 1.97] 2.26] 2.56] 3.15 
214 to14 veh, AE 8 AG or Be i 13.2 115.4 | 17.6 |22.0 |26.4 135.2 
2 ee eae 1.79} 1.98] 2.06] 2.34] 2.62] 3.18 





A = air-pressure tt pump. B = cubic feet of free air per gallon of water. 


To find the amount of air and pressure required to pump a given quantity 
of water a given height, find the ratio of diameters between water and air 
cylinders, and multiply the number of gallons of water by the figure found 
in the column for the require« lift. The result is the number of cubic feet 
of free air. The pressure required on the pump will be found directly above 
in the same column. For example. The ratio between cylinders being 2 to 
1, required to pump 100 gallons, height of lift 250 feet. We find under 250 
feet at ratio 2 to 1 the figures 2.11; 2.1. ¥ 100 = 211 cubic feet of free air. 
The pressure required is 34,38 pounds, 


COMPRESSED AIR. 5050 


Compressed-air Table for Hoisting-engines,. 
(Ingersoll-Sergeant Drill Co.) 


The following table gives an approximate idea of the volume of free air 
required for operating hoisting-engines, the air being delivered at 60 lbs. 
gauge-pressure. There are so many variable conditions to the operation of 
hoisting-engines in common use that accurate computations can only be 
offered when fixed data are given. In the table the engine is assumed to 
actually run but one-half of the time for hoisting, while the compressor, of 
course, runs continuously. If the engine runs less than one-half the time, 
as it usually does, the volume of air required will be proportionately less, 
and vice versa. The table is computed for maximum loads, which also in 
practice may vary widely. From the intermittent character of the work of 
a hoisting-engine the parts are able to resume their normal temperature 
between the hoists, and there is little probability of the annoyance of freez- 
ing up the exhaust-passages. 


VOLUME OF FREE AIR REQUIRED FOR OPERATING HOISTING- 
ENGINES, THE AIR COMPRESSED TO 60 POUNDS GAUGE. 
PRESSURE. 

SINGLE-CYLINDER HOISTING-ENGINE. 


Diam. of} giroke. | Revolu- | Normal | Actual oe Cubic Ft. 
Cylinder,| Tiches’ | tions per} Horse- | Horse- Single’ of Free Air 
Inches. * | Minute. | power. | power. Rope. Required. 
5 6 200 3 5.9 600 7% 

5 8 160 4 6.3 1,000 80 
614 8 160 6 9.9 1,500 125 

10 125 10 12.1 2,000 151 

814 10 125 15 16.8 3,000 170 
816 12 110 20 18.9 5,000 238 
10 12 110 25 26.2 6,090 330 

DOUBLE-CYLINDER HOISTING;ENGINE. 

5 6 200 6 11.8 1,000 150 
5 - 8 160 8 12.6 1,650 160 
614 8 160 12 19.8 2,500 250 
7 10 125 20 24.2 3,500 302 
814 yp 10 125 30 33.6 6,000 340 
8 12 110 40 37.8 8,000 476 
10 12 110 50 52.4 10,000 660. 
1214 15 100 75 GOL 2 i cpetee Weve! ealaield’s 1,125 
14 18 90 100 125 Gy yell die asses stce's 1,587 


Practical Results with Compressed Air.—Compressed-air 
System at the Chapin, Mines, Iron Mountain, Mich.—These mines are three 
miles from the falls which supply the power. There are four turbines at the 
falls, one of 1000 horse-power and three of 900 horse-power each. The press- 
ure is 60 pounds at 60° Fahr. Each turbine runs a pair of compressors. 
The pipe to the mines is 24 ins. diameter. The power is applied at the mines 
to Corliss engines, running pumps, hoists, etc., and direct to rock-drills. 

A test made in 1888 gave 1430.27 H.P. at the compressors, and 390.17 H.P. 
as the sum of the horse-power of the engines at the mines. Therefore, only 
27% of the power generated was recovered at the mines. This includes the 
loss due to leakage and the loss of energy in heat, but not the friction in the 
engines or compressors. (F. A. Pocock, Trans. A. I. M. E., 1890.) 

W. L. Saunders (Jour. F’. I. 1892) says: ‘‘There is not a properly designed 
compressed-air installation in operation to-day that loses over 5% by trans- 
mission alone. The question is altogether one of the size of pipe; and if the 
pipe is large enough, the friction loss is a small item. 

‘«The loss of power in common practice, where compressed air is used to 
drive machinery in mines and tunnels, is about 70%, In the best practice, 
with the best air-compressors, and without reheating, the loss is about 602%. 
These losses may be reduced to 4 point as low as 20% by combining the best 
systems of reheating with the best air-compressors,” 


506 AIR. 


Gain due to Reheating.—Prof. Kennedy says compressed-air 
transmission system is now being carried on, on a large commercial scale, 
in such a fashion that a small motor four miles away from the central sta- 
tion can indicate in round numbers 10 horse-power, for 20 horse-power at 
the station itself, allowing for the value of the coke used in heating the air. 

The limit to successful reheating lies in the fact that air-engines canacsS 
work to advantage at temperatures over 350°, 

The efficiency of the common system of reheating is shown by the re- 
sults obtained with the Popp system in Paris. Air is admitted to the re- 
heater at about 83°, and passes to the engine at about 315°, thus being in- 
ereased in volume about 42%. The air used in Paris is about 11 cubic feet of 
free air per minute per horse-power. The ordinary practice in America 
with cold air is from 15 to 25 cubic feet per minute per horse-power. When 
the Paris engines were worked without reheating the air consumption was 
increased to about 15 cubic feet per horse-power per minute. The amount 
of fuel consumed during reheating is trifling. 


Efficiency of Compressed-air Engines.—tThe efficiency of an 
air-engine, that is, the percentage which the power given out by the air-en- 
gine bears to that required to compress the air in the compressor, depends 
on the loss by friction in the pipes, valves, etc., as well as in the engine itself. 
This question is treated at length in the catalogue of the Norwalk Iron Works 
Co., from which the following is condensed. As the friction increases the 
most economical pressure increases. In fact, for any given friction in a 
pipe, the pressure at the compressor must not be carried below a certain 
limit. The following table gives the lowest pressures which should be used 
at the compressor with varying amounts of friction in the pipe: 


Friction, lbs. ..2.):..... 2.9 45.8 8.8 911.7 14.7%,.17.6' (2015 4 23.5 126.4 529.4 
Lbs. at Compressor... 20.5 29.4 88.2 47. 52.8 61.7 70.5 76.4 82.3 88.2 
Efficiency %........... 70.9 64.5 60.6 57.9 55.7 54.0 52.5 51.38 50.2 49.2 


An increase of pressure will decrease the bulk of air passing the pipe and 
its velocity. This will decrease the loss by friction, but we subject ourselves 
to a new loss, z.e. the diminishing efficiencies of increasing pressures. Yet as 
each cubic foot of air is at a higher pressure and therefore carries more 
power, we will not need as many cubic feet as before, for the same work. 
With so many sources of gain or Joss, the question of selecting the proper 
pressure is not to be decided hastily. 

The losses are, first, friction of the compressor. This will amount ordinarily 
to 15 or 20 per cent, and cannot probably be reduced below 10 per cent. 
Second, the loss occasioned by pumping the air of the engine-room, rather 
than the air drawn from acooler place. This loss varies with the season and. 
amounts from 3 to 10 per cent. This can all be saved. The third loss, or series 
of losses, arises in the compressing cylinder, viz., insufficient supply, difficult 
discharge, defective cooling arrangements, poor lubrication, etc. The fourth 
loss is found in the pipe. This loss varies with the situation, and is subject 
to somewhat complex influences. The fifth loss is chargeable to fall of 
temperature in the cylinder of the air-engine. Losses arising from leaks 
are often serious. 

Effect of Temperature of Intake upon the Discharge ofa 
Compressor.—aAir should be drawn from outside the engine-room, and 
from as coo] a place as possible. The gain amounts to one per cent for every 
five degrees that the air is taken in lower than the temperature of the engine- 
room. The inlet conduit should have an area at least 50% of the area of the 
air piston and should be made of wood, brick, or other non-conductor of 

eat. 

Discharge of a compressor having an intake capacity of 1000 cubic feet 
per minute, and volumes of the discharge reduced to cubic feet at atmos- 
pheric pressure and at temperature of 62 degrees Fahrenheit: 


Temperature of Intake, F............... 0° 32° 62° 75° 80° 90° 100° 110° 
Relative volume discharged, cubic ft... 1135 1060 1000 975 966 949 932 916 


Requirements of Rock-drills Driven by Compressed 
Air. (Norwalk Iron Works Co.)—The speed of the drill, the pressure of 
air, and the nature of the rock affect the consumption of power of drills. 

A three-inch drill using air at 30 lbs. pressure made 300 blows per minute 
and consumed the equivalent of 64 cubic feet of free air per minute. The 
same drill, with air of 58 lbs. pressure, made 450 blows per minute and 
consumed 160 cubic feet of free air per minute, At Hell Gate different 





COMPRESSED AIR, 507 


\ 


machines doing the same work used from 80 to 150 cubic feet free air per 
minute. 

An average consumption may be taken generally from 80 to 100 cubic feet 
per minute, according to the nature of the work. 

The Popp Compressed-air System in Paris.—A most exten- 
sive system of distribution of power by means of compressed air is that of 
M. Popp, in Paris. One of the central stations is laid out for 24,000 horse- 
power. Fora very complete description of the system, see Engineering, 
Feb, 15, June 7, 21, and 28, 1889, and March 13 and 29, April 10, and May 1, 
1891. Also Proc. Inst. M. E., July, 1889. A condensed description will be 
found in Modern Mechanism, p. 12. 

Utilization of Compressed Air im Small Motors,—In the 
earliest stages of the Popp system in Paris it was recognized that no good 
results could be obtained if the air were allowed to expand direct into the 
motor; not only did the formation of ice due to the expansion of the air 
rapidly accumulate and choke the exhaust, but the percentage of useful 
work obtained, compared with that put into the air at the central station, 
was so small as to render commercial results hopeless. 

After a number of experiments M. Popp adopted a simple form of cast- 
iron stove lined with fire-clay, heated either by a gas jet or by a small coke 
fire. This apparatus answered the desired purpose until some better ar- 
rapgement was perfected, and the type was accordingly adopted through- 
out the whole system, The economy resulting from the use of an improved 
form was very marked, as will be seen from the following table. 


EFFICIENCY OF AIR-HEATING STOVES. 


4 








Cast-iron Box pia sey 5 

Stoves. Tubes. 
Heating Surrace, Sutbescsic..s cece sees asec cles 14 14 46.3 
Aur heated per hour, Cus ites esse ete eke meen 20,342 | 11,054 88,428 
Temp. of air admitted to oven, deg. F....... bias 45 45 41 

rh dg SS" BE OXI1D, CES e Era tincs th hh ateenne sets 215 864 847 

Total heat absorbed per hour, calories...... ... 17,900 | 17,200 39,200 
Do. per sq. ft. of heating surface per hour, ecals.| 1,278 1,228 830 
Do. per ld. OF COG ies wees cee e cat ee eel ots 2,032 2,058 2,545 


The results given in this table were obtained from a large number of 
trials. From these trials it was found that more than 70%-of the total num- 
ber of calories in the fuel employed was absorbed by the air and trans- 
formed into useful work, Whether gas or coal be employed as the fuel, the 
amount required is so small as to be scarcely worth consideration; accord- 
ing to the experiments carried out it does not exceed 0.2 lb. per 
horse-power per hour, but it is searcely to be expected that in regular prae- 
tice this quantity is not largely exceeded. The efficiency of fuel consumed 
in this way is at least six times greater than when utilized in a boiler and 
steam-engine. 

According to Prof. Riedler, from 15% to 20% above the power at the central 
station can be obtained by means at the disposal of the power users, and it 
has been shown by experiment that by heating the air to 480° F. an in- 
creased efficiency of 30% can be obtained. 

A large number of motors in use among thesubscribers to the Compressed 
Air Company of Paris are rotary engines developing 1 horse-power and 
less, and these in the early times of the industry were very extravagant in 
their consumption. Small rotary engines, working cold air without expan- 
sion, used as high as 2330 cu. ft. of air per brake horse-power per 
hour, and with heated air 1624 cu. ft. Working expansively, a 1 horse- 
power rotary engine used 1469 cu. ft. of cold air, or 960 cu. ft. of heated air, 
and a 2-horse-power rotary engine 1059 cu. ft. of cold air, or 847 cu. ft. of air, 
heated to about 50° C, 

The efficiency of this type of rotary motors, with air heated to 50° C., may 
now be assumed at 43%. With such an efficiency the use of small motors in 
many industries becomes possible, while in cases where it is necessary to 
have a constant supply of cold air economy ceases to be a matter of the first 
importance. on . 

Tests of a small Riedinger rotary engine, used for driving sewing-machines 
and indicating about 0,1 H,P, showed an air-consumption of 1377 cu, ft. per 


508 ATR. 


H P. per hour when the initial pressure of the air was 86 lbs, per sq. in. and 
its temperature 54° F., and 988 cu. ft. when the air was heated to 338° F., its 
pressure being 72° lbs. With a one-half horse-power variable-expansiom 
rotary engine the air-consumption was from 800 to 900 cu. ft. per H.P. pet 
hour for initial pressures of 54 to & lbs. per sq. in. with the air heated from 
336° to 388° F., and 1148 cu. ft. with cold air, 46° F., and an initial pressure 
of 72 lbs. The volumes of air were all taken at atmospheric pressure. 

Trials made with an old single-cylinder 80-horse-power Farcot steam-en. 
gine, indicating 72 horse-power, gave a consumption of air per brake horse- 
power as low as 465 cu. ft. per hour. The temperature of admission was 
820° F., and of exhaust 95° F. 

Prof. Elliott gives the following as typical results of efficiency for various 
systems of compressors and air-motors: 


Simple compressor and simple motor, efficiency .............- 39.1% 

Compound compressorand simple motor, “S — ..........eece0 44.9 
os Se ‘* compound motor, efficiency....... 50.7 

Triple compressor and triple motor, saa pul sto ey aT 55.3 


The efficiency is the ratio of the indicated horse-power in the motor cylin. 
ders to the indicated horse-power in the steam-cylinders of the compressor. 
The pressure assumed is 6 atmospheres absolute, and the losses are equal 
to those found in Paris over a distance of 4 miles. 


Summary of Efficiencies of Compressed-air Transmission 
at Paris, between the Central Station at St, Fargeau and 
a 10-horse-power Motor Working with Pressure Re- 
duced to 444 Atmospheres. y 


(The figures below correspond co mean results of two experiments cold and 
two heated.) 


1 indicated horse-power at central station gives 0.845 indicated horse-power 
in compressors, and corresponds to the compression of 348 cubic feet of air 
per hour from atmospheric pressure to 6 atmospheres absolute. (The weight 
of this air is about 25 pounds.) 

0.845 indicated horse-power in compressors delivers as much air as will do 
0.52 indicated horse-power in adiabatic expansion after it has fallenin tem-— 
perature to the normal temperature of the mains. 

The fall of pressure in mains between central station and Paris (say 5 kilo- 
metres) reduces the. possibility of work from 0.52 to 0.51 indicated horse- — 


ower. 

The further fall of pressure through the reducing valve to 4144 atmospheres 
(absolute) reduces the possibility of work from 0.51 to 0.50. 

Incomplete expansion, wire-drawing, and other such causes reduce the 
actual indicated horse-power of the motor from 0.50 to 0.39. 

By heating the air before it enters the motor to about 320° F., the actual 
indicated horse-power at the motor is, however, increased to 0.54. The ratio 
of gain by heating the air is, therefore, 0.54 + 0.39 = 1.88. 

In this process additional heat is supplied by the combustion of about 0.39 
pounds of coke per indicated horse-power per hour, and if this be taken into 
account, the real indicated efficiency of the whole process becomes 0.47 
instead of 0.54. 

Working with cold air the work spent in driving the motor itself reduces 
the available horse-power from 0.39 to 0.26. 

Working with heated air the work spent in driving the motoritself reduces 
the available horse-power from 0.54 to 0.44. 

A summary of the efficiencies is as follows: 

Efficiency of main engines 0.845. 

Efficiency of compressors 0.52 + 0.845 = 0.61. 

Efficiency of transmission through mains 0.51 -+ 0.52 = 0.98, 

Efficiency of reducing valve 0.50 0.51 = 0.98. 

The combined efficiency of the mains and reducing valve between 5 and 
4464 atmospheres is thus 0.98 « 0.98 = 0.96. If the reduction had been to 4, 

, or 3 atmospheres, the corresponding efficiencies would have been 0.93, 
0.89, and 0.85 respectively. 

Indicated efficiency of motor 0.39 + 0.50 = 0.78. 

Indicated efficiency of whole process with cold air 0.89. Apparent indi: 
cated efficiency of whole process with heated air 0.54. 

Real indicated efficiency of whole process with heated air 0,47, 

Mechanical efficiency of motor, cold, 0.67, 

Mechanical efficiency of motor, hot, 0.81, 


COMPRESSED AIR. 509 


Most of the compressed air in Paris is used for driving motors, but the 
work done by these is of the most varied kind. A list of motors driven from 
St. Fargeau station shows 225 installations, nearly all motors working at 
from 4g horse-power to 50 horse-power, and the great majority of them more 
than two miles away from the station. The new station at Quai de la Gare 
is much larger than the one at St. Fargeau. Experiments on the Riedler 
air-compressors at Paris, made in December, 1891, to determine the ratio 
between the indicated work done by the air-pistons and the indicated work 
in the steam-cylinders, showed a ratio of 0.8997. 'Thecompressors are driven 
by four triple-expansion Corliss engines of 2000 horse-power each. 

Shops Operated by Compressed Air.—The Iron Age, March 2, 
1893, describes the shops of the Wuerpei Switch and Signal Co., East St. Louis, 
the machine tools of which are operated by compressed air, each of the 
larger tools having its own air engine, and the smaller tools being belted 
from shafting driven by an air engine. Power is supplied by a compound 
compressor rated at 55 horse-power. The air engines are of the Kriebel 
make, rated from 2 to 8 horse-power. 

Pneumatic Postal Transmission.—A paper by A. Falkenau, 
Eng'rs Club of Philadelphia, April 1894, entitled the ‘‘ First United States 
Pneumatic Postal System,” gives a description of the system used in London 
and Paris, and that recently introduced in Philadelphia between the main 
post-office and a substation. In London the tubes are 214 and 3 inch lead 
pipes laid in cast-iron pipes for protection. The carriers used in 214-inch 
tubes are but 114 inches diameter, the remaining space being taken up by 

acking. Carriers are despatched singly. First, vacuum alone was used}; 
ater, vacuum and compressed air. The tubes used in the Continental cities 
in Europe are wrought iron, the Paris tubes being 244 inches diameter. 
There the carriers are despatched in trains of six to ten, propelled by a 
piston. In Philadelphia the size of tube adopted is 64% inches, the tubes 
being of cast iron bored to size. The lengths of the outgoing and return 
tubes are 2928 feet each. The pressure at the main station is 7 lbs., at the 
substation 4 lbs., and at the end of the return pipe atmospheric pressure. 
The compressor has two air-cylinders 18 X 24 in. Each carrier holds about 
200 letters, but 100 to 150 are taken as an average. Hight carriers may be 
despatched in a minute, giving a delivery of 48,000 to 72,000 letters per hour, 
The time required in transmission is about 57 seconds. 

Pneumatic postal transmission tubes were laid in 1898 by the Batcheller 
Pneumatic Tube Co. between the general post-offices in New York and 
Brooklyn, crossing the East River on the bridge. The tubes are cast iron, 
12-ft. lengths, bored to 84% in. diameter. The joints are bells, calked with 
lead and yarn. There are two tubes, one operating in each direction. Both 
lines are operated by air-pressure above the atmospheric pressure. One 
tube is operated by an air-compressor in the New York office and the other 
by one located in the Brooklyn office. 

The carriers are 24 in. long, in the form of a cylinder 7 in. in diameter, 
and are made of steel, with fibrous bearing-rings which fit the tube. Each 
carrier will contain about 600 ordinary letters, and they are despatched at 
intervals of 10 seconds in each direction, the time of transit between the two 
offices being 344 minutes, the carriers travelling at a speed of from 30 to 35 
miles per hour. 

The air-compressors were built by the Rand Drill Co. and the Ingersoll- 
Sergeant Drill Co. The Rand Drill Co. compressor is of the duplex type 
and has two steam-cylinders 10 X 20 in. and two air-cylinders 24 < 20in., 
delivering 1570 cu. ft. of free air per minute, at 75 revclutions, the power 
being about 50 H.P. Corliss valve-gear is on the steam-cylinders and the 
Rand mechanical valve-gear on the air-cylinders. 

The Ingersoll-Sergeant Drill Co. furnished two duplex Corliss air-com- 
pressors, with mechanically moved valves on air-cylinders. The steam- 
cylinders are 14 X 18 in. and the air-cylinders 26144 « 18in. They are de- 
signed for 80 to 90 revs. per min. and to compress to 20 lbs. per sq. in. 

Another double line of pneumatic tubes has been laid between the main 
office and Postal Station H, Lexington Ave. and 44th St., in New York City. 
This line is about 344 miles inlength. There are three intermediate stations: 
Third Ave. and 8th St., Madison Square, and Third Ave. and 28th St. The 
carriers can be so adjusted when they are put into the tube that they will 
traverse the line and be discharged automatically from the tube at the sta- 
tion for which they are intended. The tubes are of the same size as those 
of the Brooklyn line and are operated in a similar manner, The initial air- 
compression is about 12 to 15lbs. On the Brooklyn line it is about 7 lbs. 


510 ATR. 


There is alsoa tube system between the New York Post-office and the 
Produce Exchange. For avery complete description of the system and its 
machinery see ‘‘The Pneumatic Despatch Tube System,”’ by B. C. Batchel- 
ler. J. B. Lippincott Co., Philadelphia, 1897, 

The Mekarski Compressed-air Tramway at Berne, 
Switzerland. (Engg News, April 20, 1898.)\—The Mekarski system has 
been introduced in Berne, Switzerland, on a line about two miles long, with 
grades of 0.25% to 3.7% and 5.2%. The air is heated by passing it through 
superheated water at 330° F. It thus becomes saturated with steam, which 
subsequently partly condenses, its latent heat being absorbed by the exe 
panding air. The pressure iu the car reservoirs is 440 lbs. per sq. in. 

The engine is constructed like an ordinary steam tramway locomotive, 
and drives two coupled axles, the wheel-base being 5.2 ft. It has a pair of 
outside horizontal cylinders, 5.1 x 8.6 in.; four coupled wheels, 27.5 in. 
diameter. The total weight of the car including compressed air is 7.25 tons, 
and with 30 passengers, including the driver and conductor, about 9.5 tong, 

The authorized speed is about 7 miles per hour. Taking the resistance 
due to the grooved rails and to curves under unfavorable conditions at 30 
lbs. per ton of car weight, the engine has to overcome on the steepest grade, 
5%, a total resistance of about 0.63 ton, and has to develop 25 H.P. At the 
maximum authorized working pressure in cylinders of 176 lbs. per sq. in. the 
motors can develop a tractive force of 0.64 ton. This maximum is, there- 
fore, just sufficient to take the car up the 5.2% grade, while on the flatter 
sections of the line the working pressure does not exceed 73 to 147 Ibs. per 
od. ai Sand has to be frequently used to increase the adhesion on the 2% to 

% grades. . 

Between the two car frames are suspended ten horizontal compressed-air 
storage-cylinders, varying in length according to the available space, but of 
uniform inside diameter of 17.7 in., composed of riveted 0.27-in. sheet iron, 
and tested up to 588 lbs. per sq. in. These cylinders have a collective 
capacity of 64.25 cu. {t., which, according to Mr. Mekarski’s estimate, 
should have been sufficient for a double trip, 434 miles. The trial trips, 
however, showed this estimate to be inadequate, and two further small 
storage-cylinders had therefore to be added of 5.3 cu. ft. capacity each, 
bringing the total cubic contents of the 12 storage-cylinders per car up to 
75 cu. ft., divided into two groups, the working and the reserve battery, the 
former of 49 cu. ft. the latter of 26 cu. ft. capacity. 

' From the results of six official trips, the pressure and the mean consump- 
tion of air during a double journey per motor car are as follows: 

Pressure of air in storage-cylinders at starting 440 lbs. per sq. in.; at end © 
of up-journey 176 lbs., reserve 260 lbs.; at end of down-journey 103 lbs., 
reserve 176 lbs. Consumption of air during up-journey 92 1bs., during down- 
journey 31 lbs. 

The working experience of 1891 showed that the air consumption per 
motor car for a double journey was from 103 to 154 lbs., mean 123 lbs., and 
per car mile from 28 to 42 15s., mean 35 lbs. 

The principal advantages of the compressed-air system for urban and 
suburban tramway traffic as worked at Berne consist in the smooth 
and noiseless motion; in the absence of smoke, steam, or heat, of overhead 
or anderground conductors, of the more or less grinding motion of most 
electric cars, and of the jerky motion to which underground cable traction 
Is subject. On all these grounds the system has vindicated its claims as 
being preferable to any other so far known system of mechanical traction 
for street tramways. Its disadvantages, on the other hand, consist in the 
extremely delicate adjustment of the different parts of the system, in the 
comparatively small supply of air carried by one motor car, which necessi- 
tates the car returning to the depot for refilling after a run of only four 
miles or 40 minutes, although on the Nogent and Paris lines the cars, 
which are, moreover, larger, and carry outside passengers on the top, 
run seven miles, and the loading pressure is 547 Ibs. per sq. in. as against 
only 440 lbs. at Berne. } 

Longer distances in the same direction would involve either more power- 
ful motors, a larger number of storage-cylinders, and consequently heavier 
cars, or loading suations every four or seven miles; and in this respect the 
system is manifestly inferior to electric traction, which easily admits of @ 
line of 10 to 15 miles in length being continuously fed from one central 
station without the loss of time and expense caused by reloading. 

The cost of working the Berne line is compared in the annexed table 


FANS AND BLOWERS, 511] 


with some other tramways worked under similar conditions by horse and 
mechanical traction for the year 1891. 

For description of the Mekarski system as used at Nantes, France, see 
paper by Prof. D. S. Jacobus, Trans. A. I. M. E., xix. 553. G 

American Experiments on Compressed Air for Street 
Railways.—Experiments have been made recently in Washington, D.C., 
and in New York City on the use of compressed air for street-railway trac- 
tion. The air was compressed to 2000 lbs. per sq. in. and passed through a 
reducing-valve and a heater before being admitted to the engine. For an 
extended discussion of the relative merits of compressed air and electric 
traction, with an account of a test of a four-stage compressor giving a 
pressure of 2500 lbs. per sq. in., see Hng’g News, Oct. ? and Nov. 4, 1897. A 
summarized statement of the probable efficiency of compressed-air traction 
is given as follows: Efficiency of compression to 2000 Ibs. per sq. in. 65%. 
By wire-drawing to 100 lbs. 57.5% of the available energy of the air will be 
lost, leaving 65 X .425 = 27.625% as the net efficiency of the air. This may 
be doubled by heating, making 55.25%, and if the motor has an efficiency of 
80% the net efficiency of traction by compressed air will be 55.25 x .80 = 44.22. 
For a description of the Hardie compressed-air locomotive, designed for 
street-railway work, see Hng’g News, June 24, 1897. For use of compressed 
air in mine haulage, see Hng’g News, Feb. 10, 1898. 

Compressed Air for Working Underground Pumps in 
Wiimes.—Hng’g Record, May 19, 1894, describes an installation of com- 
pressors for working a number of pumps in the Nottingham No. 15 Mine, 
Plymouth, Pa., which is claimed to be the largest in America. The com- 
pressors develop above 2300 H.P., and the piping, horizontal and vertical, is 
§000 feet in length. About 25,000 gallons of water per hour are raised. 


FANS AND BLOWERS. 


Centrifugal Fans.—tTheo ordinary centrifugal fan consists of a num- 
ber of blades fixed to arms, revolving on a shaft at high speed. The width 
of the blade is parallel to the axis of the shaft. Most engineers’ reference 
books quote the experiments of W. Buckle, Proc. Inst. M.E., 1847, as still 
standard. Mr. Buckle’s conclusions are given below, together with data of 
more recent experiments. 

Experiments were made as to the proper size of the inlet openings and on 
the proper proportions to be given to the vane, The inlet openings in the 
sides of the fan-chest were contracted from 1714 in., the original diameter, 
to 12 and 6 in. diam., when the following results were obtained: 

First, that the power expended with the opening contracted to 12in. diam. 
was as 214 to 1 compared with the opening of 1714 in. diam.; the velocity of 
the fan being nearly the same, as also the quantity and density of air 
delivered. 

Second, that the power expended with the opening contracted to 6 in. 
diam. was as 24% to 1 compared with the opening of 1714 in. diam.; the 
velocity of the fan being nearly the same, and also the area of the efflux 
pipe, but the density of the air decreased one fourth. 

These experiments show that the inlet openings must be made of sufficient 
size, that the air may have a free and uninterrupted action in its passage to 
the blades of the fan; for if we impede this action we do so at the expense 
of power. 

With a vane 14 in. long, the tips of which revolve at the rate of 236.8 ft. 
per second, air is condensed to 9.4 ounces per square inch above the pres- 
sure of the atmosphere, with a power of 9.6 H. P.; but a vane 8 inches long, 
the diameter at the tips being the same, and having, therefore, the same 
velocity, condenses air to 6 ounces per square inch only, and takes 12 H. P. 

Thus the density of the latter is ttle better than six tenths of the former, 
while the power absorbed is nearly 1.25 to 1. Although the velocity of the 
tips of the vanes is the same in each case, the velocities of the heels of the 
respective blades are very different, for, while the tips of the blades in each 
case move at the same rate, the velocity of the heel of the 14-inchis in the 
ratio of 1 to 1.67 to the velocity of the heel of the 8-inch blade. The 
longer blades approaching nearer the centre, strikes the air with less velo- 
city, and allows it to enter on the blade with greater freedom, and with 
considerably iess force than the shorter one. The inference is, that the 
short blade must take more power at the same time that it accumulates a 
less quantity of air. These experiments lead to the conclusion that the 
feneth of the vane demands as great a consideration as the proper 
diameter of the inlet opening. If there were no other object in view, it 


51% ATR. 


would be useless to make the vanes of the fan of a greater width than the 
inlet opening can freely supply. On the proportion of the length and width 
of the vane and the diameter of the inlet opening rest the three most im- 
portant points, viz., quantity and density of air, and expenditure of power. 

In the 14-inch blade the tip has a velocity 2.6 times greater than the 
heel; and, by the laws of centrifugal force, the air will have a density 2.6 
times greater at the tip of the blade than that at the heel. The air cannot 
enter on the heel with a density higher than that of the atmosphere; but in 
its passage along the vane it becomes compressed in proportion to its 
centrifugal force. The greater the length of the vane, the greater will be 
the difference of the centrifugal force between the heel and the tip of the 
blade; consequently the greater the density of the air. 

Reasoning from these experiments, Mr. Buckle recommends for easy ref- 
erence the following proportions for the construction of the fan: 

1. Let the width of the vanes be one fourth of the diameter; 2. Let the 
diameter of the inlet openings in the sides of the fan-chest be one half the 
diameter of the fan; 3. Let the length of the vanes be one fourth of the 
diameter of the fan. 

In adopting this mode of construction, the area of the inlet openings in 
the sides of the fan-chest will be the same as the circumference of the heel 
of the blade, multiplied by its width; or the same area as the space 
described by the heel of the blade. 


Best Proportions of Fans. (Buckle.) 


PRESSURE FROM 3 OUNCES TO 6 OUNCES PER SQUARE INCH} OR 5.2 INCHES 
To 10.4 INCHES OF WATER. 














Diameter Diameter 

Diameter Vanes. of Inlet | Diameter Vanes. of Inlet 
of Fan, |_—___-______|_ Open- of Fan. |__________| Open- 
Width. |Length,| ings. Width. |Length.| 1ngs. 

ft. ins. |ft. ins.|ft. ins.| ft. ins. ft. ins. | ft. ins. | ft. ins.| ft. ins, 
Bk Om ale Ora Oe, (i OA le ORO 4,6. .4], Linedebod atte e ae 
3 66 0 10%) 0 10%) 1 9 5 0 1 3 dtd 2 6 
4 0 1 0]1 0 Biv O 6 0 Laiteteas 38 0 


PRESSURE FROM 6 OUNCES TO 9 OUNCES PER SQUARE INCH, AND UPWARDS, 
oR 10.4 INCHES TO 15.6 INCHES OF WATER. 


San, £10. 7 WelaeOud 100 4,.6., (0.101414 9 agi oe 
Sere rt QO. Siar aerial) fens Be Ori Ou | ae 6 eee 
4 0 {0 9441 1 3i4l 1 6 eel ined be Boye Gah ges CP a3 


The dimensions of the above tables are not laid down as prescribed limits, 
but as approximations obtained from the best results in practice. 

Experiments were also made with reference to the admission of air into 
the transit or outlet pipe. By a slide the width of the opening into this pipe 
was varied from 12 to 4 inches. The object of this was to proportion the 
opening to the quantity of air required, and thereby to lessen the power 
necessary to drive the fan. It was found that the less this opening is made, 
provided we produce sufficient blast, the less noise will proceed from the 
fan; and by making the tops of this opening level with the tips of the vane, 
the column of air has little or no reaction on the vanes. 

The number of blades may be 4 or6. The case is made of the form of 
an arithmetical spiral, widening the space between the case and the revolv- 
ing blades, circumferentially, from the origin to the opening for discharge. 

The following rules deduced from experiments are given in Spretson’s 
treatise on Casting and Founding: 

The fan-case should be an arithmetical spiral to the extent of the depth 
of the blade at least. 

The diameter of the tips of the blades should be about double the diameter 
of the hole in the centre; the width to be about two thirds of the radius of 
the tips of the blades. The velocity of the tips of the blades should be rather 


FANS AND BLOWERS. 513 


moré than the velocity due to the air at the pressure required, say one 
eighth more velocity. 

In some cases, two fans mounted on one shaft would be more useful than 
one wide one, as in such an arrangement twice the area of inlet opening is 
obtained as compared with a single wide fan. Such an arrangement may 
be adopted where occasionally half the full quantity of air is required, as 
one of them may be put out of gear, thus saving power. 

Pressure due to Velocity of the Fan-blades.—‘By increas- 
ing the number of revolutions of the fan the head or pressure is increased, 
the law being that the total head produced is equal (in centrifugal fans) to 
twice the height due to the velocity of the extremities of the blades, or 

2 


H=— approximatelyin practice’? (W. P. Trowbridge, Trans. A. S. M. E., 


vii. 536.) This law is analogous to that of the pressure of a jet striking a 
plane surface. T. Hawksley, Proc. Inst. M. E., 1882, vol. Ixix.. says: ‘‘ The 
pressure of a fluid striking a plane surface perpendicularly and then escap- 
ing at right angles to its original path is that due to twice the height h due 
the velocity.”’ 

(For discussicn of this question, showing thatit is an error to take the 
pressure as equal to a column of air of the height h = v2 + 29, see Wolff on 
Windmills, p. 17.) ‘ 

Buckle says: ‘* From the experiments it further appears that the velocity 
of the tips of the fan is equal to nine tenths of the velocity a body wovld 
acquire in falling the height of a homogeneous column of air equivalent to 
the density.’’ D. K. Clark (R. T. & D., p. 924), paraphrasing Buckle, appar- 
ently, says: ‘‘It further appears that the pressure generated at the circum: 
ference is one ninth greater than that which is due to the actual circumfer- 
ential velocity of the fan.’”?> The two statements, however, are not in 


q2 uy v2 
: v2 - a 6 CaS nen 
harmony, for ifv = 0.9 /2gH, H= O81 x 2g 1 234 5 and not 13 sa 


g 
If we take the pressure as that equal to a head or column of air of twice 
the height due the velocity, as is correctly stated. by Trowbridge, the para- 
doxical statements of Buckle and Clark—which would indicate that the 
actual pressure is greater than the theoretical—are explained, and the 


2 eas 
formula becomes H = .617 ks and v = 1.273 /gH = 0.9 29H, in which H 


is the head of a column producing the pressure, which is equal to twice the 
theoretical head due the velocity of a falling body (or f= a)" multiplied 


by the coefficient .617. The difference between 1 and this coefficient ex- 
presses the loss of pressure due to friction, to the fact that the inner por- 
tions of the blade have a smaller velocity than the outer edge, and probably 
to other causes. The coefficient 1.273 means that the tip of the blade must 
be given a velocity 1.273 times that theoretically required to produce the 
head H. 

To convert the head H expressed in feet to pressure in lbs. per sq. in. 
multiply it by the weight of a cubic foot of air at the pressure and tempera- 
ture of the air expelled from the fan (about .08 lb. usually) and divide by 
144. Multiply this by 16 to obtain pressure in ounces per sq. in. or by 2.035 
to obtain inches of mercury, or by 27.71 to obtain pressure in inches of 
water column. Taking .08 as the weight of a cubic foot of air, 


p Ibs. per sq. in. = ,00001066v2; v = 810 /p nearly; 
p1 ounces per sq. in. = .0001706u23 v= 80Vp, “ 
Pq inches of mercury = .00002169v?; v= 2201p, “ 
p3 inches of water = .0002954v2; v= 60Vp, “ 


jin which v = velocity of tips of blades in feet per second. 

Testing the above formula by the experiment of Buckle with the vane 
24 inches long, quoted above, we have p = .00001066v2 = 9.56 oz. The ex- 
periment gave 9.4 oz. 

Testing it by the experiment of H. I. Snell, given below. in which the 
circumferential speed was about 150 ft. per second, we obtain 3.85 ounces, 
while the experiment gave from 2.38 to 3.50 ounces. according to the amount 
of opening for discharge. The numerical coefficients of the above formulsa 
are all based on Buckle’s statement that the velocity of the tips of the fan 
is equal to nine tenths of the velocity a body would acquire in falling the 


514 “ATR. ba 


height of a homogeneous column of air equivalent to the pressure. Should 
other experiments show a different law, the coefficients can be corrected 
accordingly. It is probable that they will vary to some extent with differ- 


ent proportions of fans and different speeds. 

Taking the formula v = 80 //p,, we have for different pressures in ounces 
per square inch the following velocities of the tips of the blades in feet per 
second: 

go, = ounces persquareinch.... 2 3 4 5 6 % 8 10 12 14 

@ i= LeeU Per SCCONG. vec .e ss on 113 189 160 179°196 212 226 253% 277 299 


Arule in App. Cyc. Mech, article ‘‘ Blowers,”’ gives the following velocities 
of circumference for different densities of blast in ounces: 3, 170; 4, 180; 5, 
195; 6, 205; 7%, 215. 

The same article gives the following tables, the first of which shows that 
the density of blast is not constant for a given velocity, but depends on the 
ratio of area of nozzle to area of blades: 


Velocity of circumference, feet per second. 150 150 150 170 200 200 220 
Area of nozzle + area of blades............ 21%4%%16% 
Density of blast, oz. per squareinch........ 1 2 8 4 4 6 6 
QUANTITY OF AIR OF A GIVEN DENSITY DELIVERED BY A FAN. 
Total area of nozzles in square feet * velocity in feet per minute corre: 
sponding to density (see table) = air delivered in cubic feet per minute. 


Density, Velocity, feet Density, Velocity, feet Density, velocity, feet 


n ¥ , 4 
5 . nigee per minute. | |, PRs per min. par Bath. per minute. 
1 5000 5 11,000 9 15,000 
2 7000 6 12,250 10 15,800 
3 8600 7 13/200 i1 $6,500 
4 10,000 8 14150 | 12 17°300 


Experiments with Blowers. (Henry I. Snell, Trans. A. §. M. E. 
ix. 51.)—The following tables give velocities of air discharging through an 
aperture of any size under the given pressures into the atmosphere. The 
volume discharged can be obtained by multiplying the area of discharge 
opening by the velocity, and this product by the coefficient of contraction: 
.65 for a thin plate and .93 when the orifice is a conical tube with a conver- 
gence of about 3.5 degrees, as determined by the experiments of Weisbach. 

The tables are calculated for a barometrical pressure of 14.69 Ibs. (= . 


235 oz.), and for a temperature of 50° Fahr., from the formula V= 4/2gh. 
Allowances have been made for the effect of the compression of the air, 
but none for the heating effect due to the compression. 
At atemperature of 50 degrees, a cubic foot of air weighs .078 Ibs., and 
calling g = 32.1602, the above formula may be reduced to 


V, = 60 31.5812 X (285 + P) x P, 


where V; = velocity in feet per minute. 
P = pressure above atmosphere, or the pressure shown by gauge, in oz. 
per square inch. 





Corre- Velocity 3 Corre- 

Neri te sponding incite ete sponding Nec due 
.per Sq. in. /Pressure in|Pressure in § .P€T S4- 'D. |prescure in| “We ¢ ressure 
in inches of oz. per sq feet per in inches of Oe He's in feet per 

water. ‘inch. | minute. Baer teem: 1) minute. 
1/32 .01817 696.7 56 36340 8118.38 
1/16 .03634 987 .66 34 -43608 8416.64 
1% 07268 1393.75 % 5087 3690.62 
3/16 . 10902 1707.00 1 .58140 8946.17 
14 - 14536 1971.80 114 1267 4362.62 
5/16 .18170 2204.16 1% 8721 4836.06 
21804 2414.70 134 1.0174 5224.98 


29072 2788.74 2 1.1628 5587.58 





FANS AND BLOWERS. 





o15 





Press- | Velocity | Press- | Velocity | Press- | Velocity Velocity 
ure due the ure ; due the ure | due the § Pressure} due the 
in 0Z Pressuref in oz. | Pressuref in oz. | Pressuref inoz. | Pressure 
per s in ft. perg per sq.| in ft. perf per sq.|in ft. perfper sq. in.| in ft. per 
inch minute. § inch. | minute. @ inch. | minute. minute. 
e20 2,582 Pls "787 5.50 12,259 11.00 17,534 
-50 3,658 2.50 8,213 6.00 12,817 12.00 18,350 
£05 4,482 QEUD 8,618 6.50 13,354 13.00 19,188 
1.00 5,178 3.00 9,006 7.00 13,8738 14.00 19,901 
1.25 5,792 3.50 9,739 7.50 14,374 15.00 20,641 
1.50 6,349 4.00 10,421 8.00 14,861 16.00 21,360 
1.75 6,861 4.50 11,065 9.00 15,795 
2.00 7,838 5.00 11,676 § 10.00 16,684 








Pressure in ounces| Velocity in feet | Pressure in ounces|Velocity in feet per 
per square inch. 


per minute. 


per square inch. 


minute. 


01 516.90 06 1266.24 
02 722.64 07 1367.76 
08 895 .26 08 1462.20 
04 1033.86 09 1550.70 
05 1155.90 10 1635.00 


Experiments on a Fan with Varying Discharge-opening. 
Revolutions nearly constant, 











Ay | 

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goon BS 3p BO apes Som |aree | 33 
a a 3) PA ha ® uty ere rea my 
my oe 29 46 H Sa. [s8as 4] 
ne Z ae Qs - o Pans bod. re) 
ao face = wv E 52m we ow © 5 
os | 35 ote ° er) 885) BS 
28 te DO os 3, sia] ess eas be BE 
24 1.0 |b bal B83 $ gu5 | 228%2) Sag 
iS 3 a = 2 5.3 C3 Ot ‘Ono 
5 eS gioh Oe S35 6 855 Segue mod 
ms < ° > oa <j H a 
1519 0 3.50 0 .80 Ss 1048 pals 
147 6 3.50 406 1.15 353 1048 337 
1480 10 8.50 676 1.30 520 1048 496 
1471 20 8.50 1353 1.95 694 1048 .66 
1485 28 3.50 1894 2.55 742 1048 . 709 
1485 36 3.40 “2400 3.10 774 1078 .718 
1465 40 3.25 2605 3.30 790 1126 70 
1468 44 3.00 2752 3.55 115 1222 .635 
1590 48 3.00 8002 3.80 790 1222 .646 
1426 89.5 | 2.38 3972 4.80 827 1544 536 





The fan wheel was 23 inches in diameter, 65 inches wide at its periphery, 

and had an inlet of 124% inches in diameter on either side, which was 
artially obstructed by the pulleys, which were 5 9/16 inches in diameter. It 

hal eight blades, each of an area of 45.49 square inches, 

The discharge of air was through a conical tin tube with sides tapered at 
an angle of 344 degrees. The actual area of opening was 7% greater than 
given in the tables, to compensate for the vena contracta, 

Tn the last experiment, 89.5 sq. in. represents the actual area of the mouth 
of the blower less a deduction for a narrow strip of wood placed across it for 
the purpose of holding the pressure-gauge. In calculating the volume of air 
discharged in the last experiment the value of vena contracta is taken at .80, 


516 ATR. 


Experiments were undertaken for the purpose of showing the results ob- 
tained oy running the same fan at different speeds with the discharge-open- 
ing the same throughout the series. 

The discharge-pipe was a conical tube 81% inches inside diameter at the 
end, having an area of 56.74, which is 7% larger than 53 sq. inches ; therefore 
58 square inches, equal to .868 square feet. is called the area of discharge, as 
that is the practical area by which the volume of air is computed. 

Experiments on a Fan with Constant Discharge-open= 
ing and Varying Speed.—tThe first four columns are given by Mr. 
Snell, the others are calculated by the author. 


Lal 5 U ’ o 3 o 2: 
ie Leer: S38 |e |sleg|/ seb. | g |e 
° si ge 1 S80 |e Re ee) 5 ie 
shh S ae . | 22 |asldla 86) S82] o, | 
— to) ao te BH Bs o&~>I10o o <q a o o 
5 a ae) 2 Be Fao]fs | a8 t Ge a 
uo ek a9 5 oe Tog qo. a ° od Sie) =a) 
© 9 <{:4 & be | bo o Alps ef =H gm 
a = wf e £0 168 Il-fes-e g|2Sg © a 
; z op ® oS So d|es O-a8. ps a 
mM M mM Olea fs) =e) (Silo ° (3) 
> o a a 2 aS SiS Eh|/ag 0) 
o pan om ° oA oo = s) ba) © AY Ro] & 
es os > Sy > > e) > = i 
600 50 1336 25 60.2 56.6 | 85.1 3,630 .182 | 73 
800 88 1787 70 80.3 75.0 | 85.6 4,856 -429 | 61 
1000 | 1.38 2245 1.35 100.4 94, 85.4 6,100 .845 | 63 
1200 |} 2.00 2712 2.20 120.4) 113, 85.1 7,370 1.479 | 67 
1400 | 2.7% 3177 3.45 140.5 | 133. 84.8 8,633 2.283 | 66 
1600 } 3.80 367 5.10 160.6 ; 156. 82.4 9,973 8.803 | 74 
1800 | 4.80 4172 8.00 180.6 | 175. 82.4 | 11,3887 | 5.462 | 68 
2000 ' 5.95 4674 ' 11.40 200.7 / 195. 85.6 J 12,701 7.586 ' 67 


Mr. Snell has not found any practical difference between the efficiencies 
of blowers with curved blades and those with straight radial ones. 

From these experiments. says Mr. Snell, it appears that we may expect to 
receive back 65% to 75% of the power expended, and no more. 

The great amount of power often used to run a fan is not due to the fan 
itself, but to the method of selecting, erecting, and piping it. 

(For opinions on the relative merits of fans and positive rotary blowers, 
see discussion of Mr. Snell’s paper, Trans. A. S. M. E., ix, 66, etc.) 

Comparative Efficiency of Fans and Positive Blowers.—- 
(H. M. Howe, Trans. A. I. M. E., x. 482.)—Experiments with fans and positive 
(Baker) blowers working at moderately low pressures, under 20 ounces, show 


that they work more efficiently at a given pressure when delivering large. 


volumes (7.e., when working nearly up to their maximum capacity) than 
when delivering comparatively small volumes. Therefore, when great vari- 
ations in the quantity and pressure of blast required are liable to arise, the 
highest efficiency would be obtained by having a number of blowers, always 

- driving them up to their full capacity, and regulating the amount of blast 
by altering the number of blowers at work, instead of having one or two 
very large blowers and regulating the amount of blast by the speed of the 
blowers. 

There appears to be little difference between the efficiency of fans and of 
Baker blowers when each works under favorable conditions as regards 
quantity of work, and when each is in good order. 

For a given speed of fan, any diminution in the size of the blast-orifice de- 
creases the consumption of power and at the same time raises the pressure 
of the blast ; but it increases the consumption of power per unit of orifice 
for a given pressure of blast. When the orifice has been reduced to the 
normal size for any given fan, further diminishing it causes but 
slight elevation of the blast pressure; and, when the orifice becomes com. 
paratively small, further diminishing it causes no sensible elevation of the 
blast pressure, which remains practically constant, even when the orifice is 
entirely closed. 

Many of the failures of fans have been due to too low speed, to too small 
pulleys, to improper fastening of belts, or to the belts being too nearly ver- 
tical; in brief, to bad mechanical arrangement, rather than to inherent de- 
fects in the principles of the machine, * 


FANS AND BLOWERS. ~ 517 


If several fans are used, it is probably essential to high efficiency to pro- 
vide a separate blast pipe for each (at least if the fans are of different size 
or speed), while any number of positive blowers may deliver into the same 
pipe without lowering their efficiency. 


Capacity of Fans and Blowers. 


The following tables show the guaranteed air-supply and air-removal of 
leading forms of blowers and exhaust fans. The figures given are often 
exceeded in practice, especially when the blowers and fans are driven at 
higher speeds than stated. The ratings, particularly of the blowers, are 
below those generally given in catalogues, but it was the desire to present 
only conservative and assured practice. (A. R. Wolff on Ventilation.) 


QUANTITY OF AIR SUPPLIED TO BUILDINGS BY BLOWERS OF VARIOUS SIZEs. 























papacity pee 

Diam- |Ordinary | Horse- ou.t Diam- | Ordinary| Horse- BIE So 
eter of | Number | power ties ao eter of | Number | power Pet a 
Wheel | of Revs. |to Drive Proakiine ‘Wheel | of Revs. |to Drive ete 
in feet.| per min. | Blower. ‘of Louncel = feet.| per min. | Blower. | 5-4 ounbe 
per sq. in. per sq. in. 

4 350 6. 10,635 9 175 29 56,800 

5 325 9.4 17,000 10 160 35.5 70,340 

6 275 13.5 29,618 12 130 49.5 102,000 

7 _ 230 18.4 42,700 14 110 66 139,000 

8 200 24 46,000 15 100 v7 160,000 





If the resistance exceeds the pressure of one ounce per square inch, of 
above table, the capacity of the blower will be correspondingly decreased, 
or power increased, and allowance for this must be made when the distrib- 
uting ae are small, of excessive length, and contain many contractions 
and bends. 


QUANTITY OF AIR MOVED BY AN APPROVED ForM oF EXHAUST FAN, THE 
FAN DISCHARGING DIRECTLY FROM ROOM INTC THE ATMOSPHERE, 












Diam- | Ordinary| Horse- 
eter of | Number | power |. 
Wheel | of Revs. |to Drive| 12 cu. ft. 
in feet.| permin.| fan. : 


Diam- | Ordinary} Horse- 4 

eter of | Number | power epeatpes 
Wheel | of Revs. |to Drive| 1 Cu. ft. 
in feet.| per min.| Fan, | P&F mn. 





2.0 600 0.50 475 3.50 28,000 
2.5 550 0.75 350 4.50 35,000 
3.0 500 1.00 3800 7.00 50,000 
3.5 500 2.50 250 9.00 80,000 





The capacity of exhaust fans here stated, and the horse-power to drive 
them, are for free exhaust from room into atmosphere. The capacity de- 
creases and the horse-power increases materially as the resistance, resulting 
from lengths, smallness and bends of ducts, enters as a factor. The differ- 
ence in pressures in the two tables is the main cause of variation in the re- 
spective records. The fan referred to in the second table could not be used 
with as high a resistance as one ounce per square inch, the rated resistance 
of the blowers. 


Caution in Regard to Use of Fan and Blower Tables.— 
Many engineers report that manufacturers’ tables overrate the capacity of 
their fans and underestimate the horse-power required to drive them. In 
some cases the complaints may be due to restricted air outlets, long and 
crooked pipes, slipping of belts, too small engines, etc, 


518 “ AIR. 


CENTRIFUGAL FANS. 
Flow of Air through an Orifice. 


VELOCITY, VOLUME, AND HP. REQUIRED WHEN AIR UNDER GIVEN PRESSURE 
IN OUNCES PER 8Q. IN. IS ALLOWED TO ESCAPE INTO THE ATMOSPHERE. 


(B. F. Sturtevant Co.) 


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Didi moet Slkel uA eg o | * |§8 din SB lag 

Aa 43 LE aa|LOS RRS) ER 4 cA aeal|o os 0 
4 |S G88lssp ) Fos “ |S efkiESe | Bog 
8a) 8 jotdy|Soge| BSE 2835/5 lotts|aocu| ase 
aan Sa | abot Seed OF, aa | Oe Ast po Ad OG! Oo, 
Qa Oa | E2p | hlna| Pod Fas g os (S25 s/ZOR | 258 
COG| BSA |SHBHIORD SO] San FloR| ch |Susdissds| Sana 
4 > > am 8) A > le a8) as 











SY ee | ee eee 


1% 11,828] 12.69 | 00043} .0340 f 2 | 7,284] 50.59 | .02759 | .5454 
i, |2,585| 17.95 | .00122 | .0680 | 214] 7,507|/ 52.13 | .08021 | .5795 
$4 13,165| 21.98 | .00225 | 11022 § 214 | 7,722| 53.68 | .03291 | 6136 
44 |3,654| 25.37 | .00346 | 11363 § 236 | 7,982] 55.08 | .08568 | .647 
54 |4,084| 28.36 | .00483 | .1703 24 | 81136] 56.50 | .03852 | 6818 
84 143473] 31.06 | .00635 | 12044 f 256 | 8.384] 57.88 | .04144 | 7160 
% | 4,880] 33.54 | .00800 | .2385 | 234 | 8.528] 59.22 | .04442 | 7500 

1 5,162 | 35.85 | .00978 | .2728 | 27% | 8,718] 60.54 | 04747 | 17841 

114 |5,473| 38.01 | .01166 | .3068 f 3 | 8,903] 61.83 | .05058 | .8180 

1144 |5,768| 40.06 | .01366 | .3410 | 314 | 9,084] 63.08 | .05376 | 8522 

13g | 6,048] 42.00 | .01575 | .3750 f 314 | 9,262/ 64.32 | .05701 | .8863 

144 |6,315| 43.86 | .01794| .4090 | 334 | 9,435) 65.52 | .06031 | .9205 

154 |6571| 45.63 | .02022 | .4431 | 314} 9,606] 66.71 | .06R68 | .9546 

134 | 6,818] 47.34 | .02260 | .477 354 | 9,773] 67.87 | .06710 | .9887 

12% | 7,055] 49.00 | .02505 | .5112 | 334 | 9,938] 69.01 | .07058 | 1.0227 

3% |10,100| 70.14 | .07412 | 1.0567 


The headings of the 2d and 3d columns in the above table have been 
abridged from the original, which read as follows: Velocity of dry air, 50° 
F., escaping into the atmosphere through any shaped orifice in any pipe or 
reservoir in which the given pressure is maintained. . Volume of air in cubic 
feet which may be discharged in one minute through an orifice having an 
effective area of discharge of one square inch. The 5th column, not in the 
original, has been calculated by the author. The figures represent the 
horse-power theoretically required to move 1000 cu. ft. of air of the given 
pressures through an orifice, without allowance for the work of compression 
or for.friction or other losses of the fan. These losses may amount to from 
60% to 100% of the given horse-power. ' 

The change in density which results from a change in pressure has been 
taken into account in the calculations of the table. The volume of air at a 
given velocity discharged through an orifice depends upon its shape, and is 
always less than that measured by its full area. “For a given effective area 
the volume is proportional to the velocity. The power required to move air 
through an orifice is measured by the product of the velocity and the total 
resisting pressure. This power for a given orifice varies as the cube of the 
velocity. For a given volume it varies as the square of the velocity. In the 
movement of air by means of a fan there are unavoidable resistances 
which, in proportion to their amount, increase the actual power consider- 
ably above the amount here given. 

For any size of centrifugal fan there exists a certain maximum area over 
which a given pressure may be maintained, dependent upon and propor: 
tional to the speed at which it is operated. If this area, known asits 
‘‘capacity area,” or square inches of blast, be increased, the pressure is 
lowered (the volume being increased), but if decreased the pressure remains 
constant. The revolutions of a given fan necessary to maintain a given 
pressure under these conditions are given in the table on p. 519, which is 
based upon the abve table. The pressure produced by a given fan and its 
effective capacity area being known, its nominal capacity and the horse- 
power required, without allowance for frictional losses, may be determined 
from the table above. 

In practice the outlet of a fan greatly exceeds the capacity area; hence 
the volume moved and the horse-power required are in excess of the 
amounts determined as above. 








CENTRIFUGAL FANS. 519 


Steei-plate Full Heusing Fans. (Buffalo Forge Co.) 
Capacities in cubic feet of air per minute. (See also table on p. 525.) - 





Revolutions per Minute. 
Size, 
™- | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 | 550 | 600 











50 1650) 2475] 33800} 4125) 4950) 5775) 6600, 7425) 8250) 9075) 9900 
60 2480) 8720) 4960) 6200} 7440; 8680) 9920) 11160) 12400] 13640) 14880 
70 4500) 6750) 9000} 11250} 138500} 15750) 18000) 20250} 22500 

80 7070) 10605) 14140) 17675} 21210) 24745] 28280) 31815 

90 | 10400) 15600} 20800} 26000} 31200] 36400) 41600 

100 | 14280) 21420) 28560) 35700) 42840] 49980} 57120 

110 | 18960} 28440) 87920} 47400] 56880} 66360 

120 | 24800} 37200} 49600) 62000} 74400 

180 | 31200) 46800) 62400} 78000)109200 | | 











140 | 38354) 57531} 76708) 95885 
150 | 49260) 73890} 98520)123150 





The Sturtevant Steel Pressure-blower Applied to Cupola 
Furnaces and Forges. 





























Cupola Furnaces. Forges. 
; Blast- Rev. per Rev. per 
Number eee Melting | pressure] min. of Number /|min. Blower 
of Cupola Capacity | required |Blower nec-| of Forges! necessary 
Blower. | inside of |Of Cupola| in Wind-| essary to | supplied | to produce 
Lining, | Per hour; box in produce by pressure 
in, | inlbs. | ounces | required | Blower. for 
per sq.in.| pressure. forge fire. 
4/0 1 5,548 
2/0 2 4,294 
0 3 3,645 
1 22 1,200 5 3,569 4 8,199 
2 26 1,900 6 3,282 6 2,691 
3 30 2,900 ¢ 3,030 8 2,305 
4 385 4,200 8 2,818 10 2,009 
5 40 6,200 10 2,690 14 1,722 
6 46 8,900 12 2,670 19 1,567 
7 53 2,500 14 2,316 25 1,264 
8 60 16,500 14 2,023 35 1,104 
9 Ke 24,000 16 1,854 45 950 
10 84 34,000 16 1,627 60 834 





The above table relates to common cupolas under ordinary conditions and | 
to forges of medium size. The diameter of cupola given opposite each size 
blower is the greatest which is recommended; in cases where there is a sur- 
plus of power one size larger blower may be used to advantage. ‘The melt- 
ing capacity per hour is based upon an average of tests on some of the best ° 
cupolas found, and is reliable in cases where the cupola is well constructed 
and carefully operated. The blast-pressure required in wind-box is the 
maximum under ordinary conditions when coal is used as fuel. When coke 
is employed the pressure may be lower. 

The cupola pressures given are those in the wind-box, while the basis 
pressure for forges is 4 ounces in the tuyere pipe. The corresponding rev- 
olutions of fan given are in each case sufficient to maintain these pressures 
at the fan outlet when the temperature is 50°. The actual speed must be 
higher than this by an amount proportional to the resistance of pipes and 
the increase of temperature, and can only be determined by a knowledge of 
the existing conditions. 

(For other data concerning Cupolas see Foundry Practice.) 


— 


520 AIR. 


Diameters of Blast-pipes Required for Steel Pressure=- 
blowers, (B. I. Sturtevant Co.) 


Based on the loss of pressure resulting from transmission being limited to 
one-half ounce per square inch. 


























Pres- | Length Number of Blower. 
sure per| of Pipe 
Bq tae) Patt) 1/4701 2/01. 0 1 dal 2a, 8 cd | bath Olga Shanon AAO 
100 | 434] 584] 614| 654] 746] 814] 836) 914|1014]1214]1434|1544| 2014 
s 200 | 5841 644] 44| 7541 Stel 914] 95/1014] 1154) 1444] 1614|1714|2314 
pid 300 | 596 4g] 734] 814] 824{1044] 1034/1144 |1254|1544)1774|19 — | 2544 
400 | 644] 744| 814| 884 93¢|1034|11° [12° |1344|1614|19 |201¢|2684 
: 100 | 53g| er! rg] 714] 8141 914] 916]/1036]1134|1414|163¢]1714|2814 
S 200 | 6t4l The| 814] 8341 95¢|1054|11° [12 |13%4|1644| 1874120 [2614 
= 300 | 6561 Shel 826 93410. |1114|1174)13 |144¢|1714] 2014] 2154] 287% 
400 | 7441 856| 944|10 |105¢] 1214 |1254| 1384|1514|181412154)238 [3014 
: 100 | 534] 7441 734] 814] 834/10 |103¢] 1134] 1256] 1544|1734 |1876|25 
s 200 | 654| 8ig| 824] 93g|10  |1114|1174|1276| 1444] 1784|2084|215¢] 2884 
ie 300 | 714 884| 9956/1044 |1074|1214|1274|14 |1534|1874|22"</0384|3144 
a 400 | 756| 986 1044| 1034|115¢| 1314 |1354|1474| 1634 | 2014|2314|2474)33 
: 100 | 614] 7161 814] 854] 914|105¢|1076] 1174] 1384116 |1834|1974|263¢ 
iS 200 | 7 | 854) 934) 974|1054| 1214|1246| 1354] 1564|183¢|2114 22% |3014 
© | 300 | 75¢| 98411084|1034| 111411314 | 1354|1474| 1634120 |238¢|2474138 
“il 400 | Shel 926] 1034|113¢|1214 | 1414|1414|1584|1754|2144| 2434 | 261435 











‘“‘The above table has been constructed on the following basis: Allowing a 
loss of pressure of 14 oz. in the process of transmission through any length 
of pipe of any size as a standard, the increased friction due to lengthening 
the pipe has been compensated for by an enlargement of the pipe sufficient 
to keep the loss still at 44 0z. Thus if air under a pressure of 8 oz. is to be 
delivered by a No. 6 blower, through a pipe 100 ft. in length, with a loss of 
14 oz. pressure, the diameter of the pipe must be 1134 in. If its length is 
increased to 400 ft. its diameter should also be increased to 151% in., or if 
the pressure be increased to 12 oz. the pipe, if 100 ft. long, must be 1:5 in. 
in diameter, providing the loss of % oz. is not to be exceeded. This loss of 
14 oz. is to be added to the pressure to be maintained at the fan if the 
tabulated pressure is to be secured at the other end of the pipe.” 


Efficiency of Fans.—Much useful information on the theory and 
practice of fans and blowers, with results of tests of various forms, will be 
found in Heating and Ventilation, June to Dec. 1897, in papers by Prof. 
R. C. Carpenter and Mr. W.G. Walker. It is shown by theory that the 
volume of air delivered is directly proportional to the speed of rotation, 
that the pressure varies as the square of the speed, and that the horse- 
power varies as the cube of the speed. For a given volume of air moved 
the horse-power varies as the square of the speed, showing the great ad- 
vantage of large fans at slow speeds over small fans at high speeds deliver- 
- ing the same volume. The theoretical values are greatly modified by varia- 

tions in practical conditions. Prof. Carpenter found that with three fans 
running at a speed of 6200 ft. per minute at the tips of the vanes, and an air- 
pressure of 24 in. of water column, the mechanical efficiency, or the horse- 
power of the air delivered divided by the power required to drive the fan, 
ranged from 32% to 47%, under different conditions, but with slow speeds it 
was much less, in some cases being under 20%. Mr. Walker in experiments 
on disk fans found efficiencies ranging all the way from 7.4% to 43%. the size 
of the fans and the speed being constant, but the shape and angle of the 
blades varying. It is evident that there is a wide margin for improvements 
in the forms of fans and blowers, and a wide field for experiment to deters 
mine the conditions that will give maximum efficiency. 


| 


CENTRIFUGAL FANS. 521 


Centrifugal Ventilators for Mimes.—Of different appliances for 


| ventilating mines various forms of centrifugal machines having proved their 


efficiency have now almost completely replaced all others. Most if not all 
of the machines in use in this country are of this class, being either open- 
periphery fans, or closed, with chimney and spiral casing, of a more or less 
modified Guibal type. The theory of such machines has been demonstrated 
by Mr. Daniel Murgue in ‘‘ Theories and Practices of Centrifugal Ventilating 

achines,”’ translated by A. L. Stevenson, and is discussed in a paper by R. 
Van A. Norris, Trans, A. I. M. E. xx. 687. From this paper the following for- 
mule are taken: : 


Let a = area in sq. ft. of an orifice in a thin plate, of such area that its re- 
sistance to the passage of a given quantity of air equals the 
resistance of the mine; 

o = orifice in a thin plate of such area that its resistance to the pas- 
sage of a given quantity of air equals that of the machine; 
Q = quantity of air passing in cubic feet per minute; 
V = velocity of air passing through a in feet per second; 
V9 = velocity of air passing through o in feet per second; 
h = head in feet air-column to produce velocity V; 
ho = head in feet air-column to produce velocity Vo. 


Q=0.650V; V= 29h; Q=0.65a 2h; 
Q 


OS ae 
0.65 /2gh 


= equivalent orifice of mine; 


or, reducing to water-gauge in inches and quantity in thousands of feet per 
minute, 


wT 408O Lia pi. 
Cass Wie Q =0.650V9;  Vo= V2Ggho; Q = 0.650 V2gho3 
2 
o= e = equivalent orifice of machine, 


0.652 92g 


The theoretical depression which can be produced by any centrifugal ven- 
tilator is double that due to its tangential speed. The formula ‘ 


T2 v2 
ra 29 29’ 
in which Tis the tangential speed, V the velocity of exit of the air from the 
space between the blades, and H the depression measured in feet of air- 
column, is an expression for the theoretical depression which can’be pro- 
duced by an uncovered ventilator; this reaches a maximum when the air 
leaves the blades without speed, that is, V= 0,and H = T? + 2g. 

Hence the theoretical depression which can be produced by any uncovered 
ventilator is equal to the height due to its tangential speed, and one half- 
that which can be produced by a covered ventilator with expanding 
chimney. 

So long as the condition of the mine remains constant: 

The volume produced by any ventilator varies directly as the speed of 


‘rotation. 


The depression produced by any ventilator varies as the square of the 
speed of rotation. 

For the same tangential speed with decreased resistance the quantity of 
air increases and the depression diminishes. 

The following table shows a few results, selected from Mr. Norris’s paper, 
giving the range of efficiency which may be expected under different cir- 
cumstances. Details of these and other fans, with diagrams of the results 
are given in the paper. 


522 


Experiments on Mine-ventilating Fans, 












































+ isl n Hy qd ed oO FAS 
S.| og = z eu lea - ty titel. ales sae 
Be) 32) ag | “8/88 \Sel8 |, | 58) w.loeg 
Ze lo=| es |85| 88 l(ao8| 24/2 | Bs | asloge 
Ssl\pe1 2s Be |ou wag Ya | Be ae a ha 
sy] oR = Olas l2e"| Fe] '4]/ 8° | aslgok 
.|82|28| 25 | 9% | 88 Repl 25 | 9%) 33 | Se ees 
a] os | Ee, BR 25 7 Sd o S bl B cs a ae nD 
BA LG. thie. |.) 6° om m. | 48ja le 
{ 84 | 5517 | 286,684 | 2818 | 3040 | 4290 | 1.80 | 67.13} 88.40|75.9 |) o 
A 100 | 6282 | 336,862 | 3369 | 38040 | 5393 | 2.50 |132.70)155.43/85.4 3 
111 | 6973 | 347,396 | 3130 | 3040 | 5002 | 3.20 |175.17/209.64/83.6 on 
123 | 7727 | 394,100 | 3204 | 3040 | 5100 | 3.60 |223.56/295.21/75.7 || > 
B ; 100 | 6282 | 188,888 | 1889 | 1520 | 3007 | 1.40 | 41.67| 97.99/42.5 |) <4 
1380 | 8167 | 274,876 | 2114 | 1520 | $866 | 2.00 | 86.63/194.95)44.6 | 22 
C ; 59 | 3702 | 59,587 | 1010 | 1520 | 1610 | 1.20 | 11.27] 16.76/67.83 
83 | 5208 | 82,969 | 1000 | 1520 | 1593 | 2.15 | 27.86] 48.54/57.38 
D 40 | 3140 | 49,611 | 1240 | 3096 | 1580 | 0.87 | 6.80] 13.82/49.2 | 382 
70 | 5495 | 187,760 | 1825 | 3096 | 2507 | 2.55 | 55.35) 67.44/82.07 
50 | 2749 | 147,282 | 2944 | 1522 } 53856 | 0.50 | 11.60) 28.55)/40.63 
B 69 | 3793 | 205,761 | 2982 | 1522 | 5451 | 1.00 | 32.42) 45.98/70.50| 83 
96 | 5278 | 299,600 | 3121 | 1522 | 5676 | 2.15 |101.50)120.64/84.10 
200 | 7540 | 183,198} 666) 746 | 1767 | 83.35 | 70.30/102.79/68.40| 26.9 
F 200 | 7540 | 180,809 | 904 | 746 | 2398 | 3.05 | 86.89/129.07\67.30| 38.3 
200 | 7540 | 209,150 | 1046 | 746 | 2774 | 2.80 | 92.50)150.08.61.70} 46.3 
f 10} 785 | 28,896 | 2890 | 3022 | 3680 | 0.10 | 0.45) 1.30/35. 
20 | 1570 | 57,120} 2856 | 3022 | 3637 | 0.20] 1.80) 3.70/49. 
| 25 | 1962 | 66,640 | 2665 | 3022 | 3399 | 0.29 | 2.90) .6.10/48. 
30 | 2355 | 73,080 | 2486 | 8022 | 3103 | 0.40] 4.60) 9.70/47. 52 
G 85 | 2747 | 94,080 | 2688 | 8022 | 3425 | 0.50 | 7.40) 15.00/48. 
40 | 3140 | 112,000 | 2800 | 3022 | 3567 | 0.70 | 12.30) 24.90/49. 
50 | 3925 | 182,700 | 2654 | 3022 | 8381 | 0.90 | 18.80) 38.80/48. 
60 | 4710 | 173,600 | 2893 | 3022 | 3686 | 1.35 | 36.90) 66.40/55. 
-70 | 5495 | 203,280 } 2904 | 3022 | 3718 | 1.80 | 57.70/107.10/54. 
80 | 6280 | 222,820 | 2779 } 3022 | 3540 | 2.25 | 78.80/152.60)52. 
Type of Fan. Diam. Width. No. Inlets. Diam. Inlets, 
A. Guibal, double...............«. 20 ft. 6 ft. 4 8 ft. 10 in. 
B. Same, only lefthand running. 20 6 4 roe C1) 
CeGuibal, scccce sss ales elelsitiouisss™ 20 6 2 Set 
DeGutbalisinyececcccse macnn. 25 8 1 11 6 
E. Guibal, double............... . 17% 4 4 8 
Me CApelisis PoC i eS. Pos 12 10 2 i 
G. Guibal...... $2 ESS Taba eee 25 8 1 12 





i Anexamination of the detailed results of each test in Mr. Norris’s table 
Jshows a mass of contradictions from which it is exceedingly difficult to draw 
any satisfactory conclusions. The following, he states, appear to be more 
or less warranted by some of the figures : 

1. Influence of the Condition of the Airways on the Fan.—Mines with © 
varying equivalent orifices give air per 100 feet periphery-motion of fan, 
within limits as follows, the quantity depending on the resistance of the 
mine: 


Equivalent Cu.Ft.Airper Aver- Equivalent Cu. Ft. Air per Aver- 
Orifice. 100 ft. Periphery- age.. Orifice. 100ft.Periphery- age. 
speed. speed. 
Under 20 sq. ft. 1100 to 1700 1300 60 to 70 3300 to 5100 4000 
20 to 8 1800 to 1800 1600 70 to 80 4000 to 4700 4400 
80 to 40 1500 to 2500 2100 80 to 90 8000 to 5600 4800 
40 to 50 2300 to 3500 2700 90 to 100 
50 to 60 2700 to 4800 3500 100 to 114 5200 to 6200 ~=—- 5700 


The influence of the mine on the efficiency of the fan does not seem to be 
very clear. Eight fans, with equivalent orifices over 50 square feet, give 


| CENTRIFUGAL FANS, 7 . §23 


efficiencies over 70%; four, with smaller equivalent mine-oriflces, give about 
the same figures ; while, on the contrary, six fans, with equivalent orifices of 
over 50 square feet, give lower efficiencies, as do ten fans, all drawing from 
mines with small equivalent orifices. 

It would seem that, on the whoie, large airways tend to assist somewhat 
in attaining large efficiency. 

2. Influence of the Diameter of the Fan.—This seems to be practically nil, 
the only advantage of large fans being in their greater width and the lower’ 
speed required of the engines. , 

3. Influence of the Width of a Fan.—This appears to be small as regards 
the efficiency of the machine ; but the wider fans are, as a rule, exhausting 
more air. 

4, Influence of Shape of Blades.—This appears, within reasonable limits, 
to be practically nil. Thus, six fans with tips of blades curved forward, 
three fans with flat blades, and one with blades curved back to a tangent 
with the circumference, all give very high efficiencies— over 70%. 

5. Influence of the Shape of the Spiral Casing.—This appears to be con- 
siderable. The shapes of spiral casing in use fall into two classes, the first 
presenting a large spiral, beginning at or near the point of cut-off, and the 
second a circular casing reaching around three quarters of the circumference 
of the fan, with a short spiral reaching to the evasée chimney, 

Fans having the first form of casing appear to give in almost every case 
large efficiencies. 

Fans that have a spiral belonging to the first class, but very much con- 
tracted, give only medium efficiencies. It seems probable that the proper 
shape of spiral casing would be one of such form that the air between each 
pair of blades could constantly and freely discharge into the space between 
the fan and casing, the whole being swept along to the evaséechimney. This 
would require a spiral beginning near the point of cut-off, enlarging by 
gradually increasing mcrements to allow for the slowing of the air caused by 
its friction against the casing, and reaching the chimney with an area suc 
that the air could make its exit with its then existing speed—somewhat less 
than the periphery-speed of the fan. ‘ 

6. Influence of the Shutter.—This certainly appears to be an advantage, as 
by it the exit area can be regulated to suit the varying quantity of air given 
by the fan, and in this way re-entries can be prevented. It is not uncommon 
to find shutterless fans into the chimneys of which bits of paper may be 
dropped, which are drawn into the fan, make the circuit, and are again 
ror out. This peculiarity has not been noticed with fans provided with 
shutters. Pad : 

7%. Influence of the Speed at which a Fan is Run.—It is noticeable that 
most of the fans giving high efficiency were running at a rather high 
periphery velocity. The best speed seems to be between 5000 and 6000 feet 
per minute. 

The fans appear to reacha maximum efficiency at somewhere about the 
speed eeu: and to decrease rapidly in efficiency when this maximum point: 
is passed. 

discussion of Mr. Norris’s paper, Mr. A. H. Storrs says: From the “ cu- 
bic feet per revolution ’’ and “‘ cubical contents of fan-blades,’’ as given in the 
table, we find that the enclosed fans empty themselves from one half to 
twice per revolution, while the open fans are emptied from one and threes 
quarter to nearly three times. This for fans of both types, on mines cover- 
ing the same range of equivalent orifices. One open fan, on a very. larg3 
orifice, was emptied nearly four times, whilea closed fan, on a still larger 
orifice, only shows one and one-half times. For the open fans the ‘‘ cubic 
feet per 100 ft. motion ’’ is greater, in proportion to the fan width and equiv- . 
alent orifice, than for the enclosed type. Notwithstanding this apparently 
free discharge of the open fans, they show very low efficiencies. 

As illustrating the very large capacity of centrifugal fans to pass air, if 
the conditions of the mine are made favorable, a 16-ft. diam. fan, 4 ft. 6 in. 
wide, at 130 revolutions, passed 360,000 cu. ft. per min., and another, of same 
diameter, but slightly wider and with larger intake circles, passed 500,000 cu, 
ft , the water-gauge in both instances being about 14 in. : 

T. D. Jones says: The efficiency reported in some cases by Mr. Norris is . 
larger than I have ever been able to determine by experiment. My own ex- 
periments, recorded in the Pennsylvania Mine Inspectors’ Reports from 1875 
to 1881, did not show more than 60% to 652, 


524 AIR, 


DISK FANS. 


Experiments made with a Blackman Disk Fan, ¢ ft. 
diam., by Geo. A. Suter, to determine the volumes of air delivered under 
various conditions, and the power required; with calculations of efficiency 
and ratio of increase of power to increase of velocity, by G. H. Babcock. 
(Trans. A. 8. M. E., vii. 547) : 




















=e at ‘ ‘ s e/a 
Bde sl 2 ob utah Seee-4 Ge Baten Gl semen 
E lsta..| 8a | S2 [sod l seb | ves BK lea’ | 24 
5) 2 ak me HOS ies n> Cue =& gia om fay 
eh ee dy | sw | ofS | ose | oF [9 S S 
| [Ss D =) = me DQ! | So: aaa 8 ee 
ep (588 | 8 [Fe | 35" | e5a | S5™ WE le. | 8° 
a 5 i oo fa fa fo | ea 
350 | 25,797 | 0.65 Dae 8 cs ainvec™ eaten > Morate ie, slo pigs > [koto te Peel species 1.682 
440" ae. ml cco l= were ce 1.257 1,262 | 3.523 | 5.4 ele 9553 
534 | 41,929 | 4.42 ania 1.186 1.287 843,24 neha sates 1.062 
Cl lms Ce (OO wandod teal cteveiere es 1.146 1.139 1.674, |00.090 altace 9358 
For|series}........ 1.749 1 8hae | 11 3140 a oe eee She's get 
840 | 20,372 | 0.76 Vale coalinsien =e oe 686 Be se -7110 
45381 120,000 fie Le OO tcstearecs 1.332 1.308 2618. 18.50.) as ave mm OU0e 
536 | 81,649 | 3.86 |....... 1.188 1.187 1,940.) 8586)|5 0.60 5205 
C2 OO ts Th Oat leecesce sla elOd 1.155 1.676 | 8.59 |......| 4802 
For|series]........| 1.761 1.794 8.518, |v Os08 «| veces o File testelereta 
340 9,983 | 1.12 O28 ese ph. cee ao weststotes|vecyniaiet> Bey deere tke tale eR OO 
430 | 13,017 | 3.17 0.47 1.265 1.804 2.837 | 3.93 | 1.95 .38046 
534 | 17,018 | 6.07 0.75 1.242 1.307 1.915 | 2.25 | 1.74 .3319 
570 | 18,649 | 8.46 0.87 1.068 1.096 1.894 | 3.63 | 1.60 .8027 
For|series|......-. 1.676 1.04 | 47.554. 18.24 11.80 jets. cee 
330 8,399 | 1.31 Qe 2G lizisve ents oii hore s cheress%sslie overele st pal iota sieeve ore Rreters . 2681 
437 | 10,071 | 3.27 0.45 1.324 1.199 8.142 | 6.81 | 3.06 -2188 
516 | 11,157 | 6.00 0.75 1.181 1.108 1.457 | 3.66 | 4.96 . 2202 
For |series|........ 1.563 1.329 4 D805 5 Bonleaitelleceereien 





Nature of the Kxperiments.—First Series: Drawing eir through 30 ft. of 

* 48-in. diam. pipe on inlet side of the fan. 
se gts Series: Forcing air through 80 ft. of 48-in. diam. pipe on outlet side 
of the fan. 

Third Series: Drawing air through 30 ft. of 48-in. pipe on inlet side of the 
fan—the pipe being obstructed by a diaphragm of ckeese-cloth. 

Fourth Series: Forcing air through 30 ft. of 48-in. pipe on outlet side of fan 
—the pipe being obstructed by a diaphragm of chevse-cloth. 

Mr. Babcock says concerning these experiments: The first four experi- 
ments are evidently the subject of some error, becazise the efficiency is such 
as to prove on an average that the fan was a source of power sufficient to 
overcome all losses and help drive the engine besides. The second series is 
less questionable, but still the efficiency in the first two experiments is larger 
than might be expected. In the third and fourth series the resistance of the 
cheese-cloth in the pipe reduces the efficiency largely, as would be expected. 
In this case the value has been calculated from the height equivalent to the 
water-pressure, rather than the actual velocity of the air. 

This record of experiments made with the disk fan shows that this kind of 
fan is not adapted for use where there is any material resistance to the flow 
of the air. In the centrifugal fan the power used is nearly proportioned to 
the amount of air moved under a given head, while in this fan the power re- 
quired for the same number of revolutions of the fan increases very mate- 
rially with the resistance, notwithstanding the quantity of air moved is at the 
same time considerably reduced. In fact, from the inspection of the third 
and fourth series of tests, it would appear that the power required is very 
nearly the same for a given pressure, whether more or less air be in motion. 
It would seem that the main advantage, if any, of the disk fan over the cen- 
trifugal fan for slight resistances consists in the fact that the delivery is the 
full area of the disk, while with centrifugal fans intended to move the same 
quantity of air the opening is much smaller. 


DISK FANS. 525 


It will be seen by columns 8 and 9 of the table thav cho power used ine 

creased much more rapidly than the cube of the velocity, as in centrifugal 

fans. The different experiments do not agree with each other, but a general 
average may be assumed as about the cube root of the eleventh power. 


Full and Three-quarter Housing Fans, (Buffalo Forge Co.) 
Capacities at different velocities and pressures. (See also table on p. 519.) 


Velocities in cubic feet per minute; Pres- 








Pulleys. sures in ounces at Fan Outlets. 
3654 ft. per 4482 ft. per 5175 ft. per 
Size of min, %oz. | min., 34 oz. min., 1 oz. 


Capac-} per | Capac-| per | Capac-|" per 


=) 
2 
a 
= 
Outlet. S 
S 
3 ¢ ¢ 
ra ity. |min, | %Y- | min. | JY- | min. 











rr) 
i>) 
s 
cy 
7] 8140] 492 | 9,900] 600; 11,440] 693 
11,470 | 462 | 13,950; 562 | 16,120] 650 
9} 16.280] 361 | 19,800] 441 | 22,880] 509 
10 | 213460] 303 | 26,100] 369 | 30,160] 426 
11} 27,750] 266 | 33,750] 3825 | 39,000] 376 
100 | 8714x3714 | 4534 | 16 | 12 | 34.410] 242 | 41,850] 294 | 48360] 340 
13 
14 
15 
16 
17 
1 
19 








q 
s 
A 
50 | 1814x1814 | 2434] 9 
60 | 2214 x 2214 | 2654 | 10 
70| 26 x26 | 3414 | 11 
12 

14 


43,540] 217 | 50,400} 265 | 58,240] 307 
49,580} 195 | 60,300} 243 | 69,680] 280 
58,460} 187 | 71,100] 227 | 82,160, 263 
67,710 | 172 | 82,350) 214 | 95,160) 248 
77,700 | 161 | 94,500] 196 | 109,200) 227 
160 | 5934 x 5934 | 7414 | 28 88,800 | 149 | 108,000} 181 | 124,800} 209 
170 | 6314 x 6314 | 79 30 100,270 | 140 1 121,950! 171 | 140,920) 197 
180 112,480 | 136 | 136,800 | 165 | 158,080} 191 


For 4 oz. pressure, speed 2584 ft. per minute, the capacity and the revolue 
tions are each one-half of those for 1 oz. pressure. : 


Efficiency cf Disk Fans.—Prof. A.B. W. Kennedy (Industries, Jan. 
37, 1890) made a series of tests on two disk fans, 2 and 3 ft. diameter, known 
as the Verity Silent Air-propeller. The principal results and conclusions 
are condensed below. f 

In each case the efficiency of the fan, that is, the quantity of air delivered 
per effective horse-power, increases very rapidly as the speed diminishes, 
50 that lower speeds are much more economical than higher ones. On the 
other hand, asthe quantity of air delivered per revolution is very nearly 
constant, the actual useful werk done by the fan increases almost directly 
with its speed. Comparing the large and small fans with about the same 
air delivery, the former (running at a much lower speed, of course) is much 
the more economical. Comparing the two fans running at the same speed, 
however, the smaller fan is very much the more economical. The delivery 
of air per revolution of fan is very nearly directly proportional to the area 
of the fan’s diameter. 

The air delivered per minute by the 3-ft. fan is nearly 12.5R cubic feet 
(RF being the number of revolutions made by the fan per minute), For the 
2-ft. fan the quantity is 5.7R cubic feet. For either of these or any other 
similar fans of which the area is A square feet, the delivery will be about 
1.84R cubic feet. Of course any change in the pitch of the blades might 
entirely change these figures. 

The net H.P. taken up is not far from proportional to the square of the 
number of revolutions above 100 per minute. Thus for the 3-ft. fan the net 


, (R— 100)2 ri .. (R— 100)2 
H.P. is 300.000? while for the 2-ft. fan the net H.P. is “1,000,000 * 


The denominators of these two fractions are very nearly proportional in- 
versely to the square of the fan areas or the fourth power of the fan diam- 
eters. The net H.P. required to drive a fan of diameter D feet or area 4 
square feet, at_a speed of R revolutions per minute, will therefore be ap- 

yroximatel DR — 100)? or A(R — 100)? 
i Y 47,000,000 10,400,000 

The 2-ft. fan was noiseless at all speeds, The 3-ft. fan was also noiseless 

up to over 450 revolutions per minute, 














526 AIR. 
Propeller, Propeller, 
2ft. diam. 8 ft. diam. 
Speed of fan, revolutions per minute. 750; 676 577) 576) 459} 873 
Net H.P. to drive fan and belt........ 0.42) 0.32) 0.227) 1.02] 0.575) 0.324 
Cubic feet of air per minute. - ....{ 4,183) 8,830) 3,410) 7,400] 5,800) 4,470 
Mean velocity of air in 38-ft. flue, “feet 
DEK IMULE paves aaais isis dak panto 593} 543] 482] 1,046} 820] 622 
Mean velocity of air in flue, same 
diameter as fan, ......+-...se-+- 4. Hac0), 12208 vf Sp cieb .oapaae selene 


Cu.ft.of air per min.per effective H.P. 9, 980] 11,970} 15,000) 7,250} 10,070) 13,800 
Motion given to air per rev. of fan, ft. 1.77; 1.81] 1.88] 1.82] 1.79] i.70 
Cubic feet of air per rev. of fan....... 5.58] 5.66] 5.90! 12.8 | 12.6 | 12.0 


POSITIVE ROTARY BLOWERS, (P.H.&F.M Roots.) 


Size number . 22s. 2...06s8s%6 . \&% % 1 2 3 4 5 6 v 
Cubic feet per revolution... “(984 114 3 3 5 . § 138 28 87 63 
00 250 225 200 17 150 125 100  %5 

ga om: Her minute, to to to to _ to to to to to 
a” Gite” Ay igh" 350 eid 275 250 225 200 175 150 125 


10 16 24 oo 47 90 80 
Furnishes blast for mie Cotto td sto lick wate £5 ‘S - 


Revolutions per minute for 
cupola, melting iron.... 


Size of cupola, inches, in- 


sid@ lining... 52... ss se 6. bo | 80 | WhOD lee to to 


ts «18 9 80 86 42 50 2 
wieste (het 00! (eG (427 E50 @ 1502: 53's 

-s 14 2% 38 4% 8 1216 17% 
Will melt iron per ee tons t to_! to 
svat 22 bPRB be4eg: ori 12 167 2076 

Horse-power required..... ae 2 38144 5146 8 11% 173% 
The amount of iron melted is pit on 30,000 cubic feet of air it A ig 
iron. The horse-power is for maximum speed and a pressure of 34 pound, 

ordinary cupola pressure, (See also Foundry Practice.) 


BLOWING-ENGINES. 


Corliss Horizontal Cross-compound Condensing 
Blowing-cnugines. (Philadelphia Engineering Works.) 




















Indicated Blasts |. <I , eldest 3 ap’ 
Horse-power. |p... | Cu. Ft.| pres- > pees r= ae | slic d| w=s 1,288 
teu, | per |, Free | sure |“ gO OF 21 oA Ela | Bao s 
15Exp.|13Exp.! min, |Air per| per |ajo sla s re S| Seth Bo Obes o5 
1251bs. | 1001bs. min. |sqin.,| 20) 25 Soal|S4| Bae |Bnke 
Steam.|Steam. Ibs.’ ft Fin raat A | < 

1,572 | 40 | 30,400) 1 35 | 44 | 9% | (2) 84| CO | 505,000 | 605,000 


2'280 | 60 | 45.600 

1,290 | 4@ | 30,400 

2,060 | 60 | 45,600 

1,050 40 | 30,400 
1,596 60 | 45,600 
1,340] 40 | 26,800 

1.980 | 60 | 39,600 

1,152 | 40 | 26,800 

1,702 | 60 | 39,600 

938 | 40 | 26,800 

1,386 | 60 | 39,600 

780 | 40 | 15,680 

1,175 | 60 { 23,500 

548 | 40 | 15,680 

822 | 60 | 23,500 


Vertical engines are built of the same dimensions as above, except that 
the stroke is 48 in. instead of 60, and they are run at a higher number of 
revolutions to give the same piston- speed and the same I. H. P. 


12 | 42 | 72 1(2) 84] 60 | 475,000 | 550,000 
10 | 82 | 60 |(2) 84] 60 | 355,000 | 436,000 
15 | 40 | 72 |(2)%8| 60 | 445,000 | 545,000 
(2) 78 | 60 } 425,000 | 491,000 
10 | 36 | 66 | (2) 78| 60 | 415,000 | 450,000 
15 | 384 | GO |(2) 72] 60 | 340,000 | 430,000 
10 | 28 | 50 |(2) 721 60 | 270,000 | 300,000 


tc cn 
rat 
wo 
co 
@ 
cd 
Oo 


‘STEAM-JET BLOWER AND EXHAUSTER. 527 


The calculations of power, capacity, efc., of blowing-engines are the same 
as those for air-compressors. They are built without any provision for 
cooling the air during compression. About 400 feet per minute is the usual 
Pen opeed for recent forms of engines, but with positive air-valves, which 

ave been introduced to some extent, this speed may be increased. The 
efficiency of the engine, that is, the ratio of the I.H.P. of the air-cylinder to 
that of the steam-cylinder, is usually taken at 90 per cent, the losses by 
friction, leakage, etc., being taken at 10 per cent. 


STEAM-JET BLOWER AND EXHAUSTER. 


A blower and exhauster is made by L. Schutte & Co., Philadelphia, on 
the principle of the steam-jet ejector. The following is a table of capacities: 





Diameter of Diameter of 





Quantity of |p; aah uantity of |; ae 
Size |Air per hour Pipes in inches. Size en per hour Pipes in inches. 
No. in No. in Se fa 
cubic feet. Stoainsl. Air. cubic feet. Gianni ataies 
000 1,000 us 1 5 80,000 214 5 
00 2,000 34 1144 6 86,000 214 6 
0 4,000 1 2 ve 42,000 6 
1 6,000 114 2144 8 48,000 3 if 
2 12,000 14 3 9 54,000 314 @ 
3 18,000 2 i} 384% 10 60,000 314 8 
4 24,000 2 4 


The admissible vacuum and counter-pressure, for which the apparatus is 
constructed, is up to a rarefaction of 20 inches of mercury, and a counter- 
pressure up to one sixth of the steam-pressure. 

The table of capacities is based on a steam-pressure of about 60 lbs., and 
a counter-pressure of about 8 lbs. With an increase of steam-pressure or 
decrease of counter-pressure the capacity will largely increase. 

Another steam-jet blower is used for boiler-firing, ventilation, and similar 
purposes where a low counter-pressure or rarefaction meets the require: 
ments, 

The volumes as given in the following table of capacities are under the 
supposition of a steam-pressure of 45 lbs, and a counter-pressure of, say, 
2 inches of water: 

















Cubic |Diameter|Diameter in Cubic | Diam. |Diameter in 
Size feet of of inches of— Size feet of of inches of — 
No Air Steam- No Air de- |Steam- 
delivered] pipe in * | livered | pipe in 
per hour.} inches, |Inlet |Disch. per hour} inches.| Inlet. |Disch. 
00 6,000 34 4 3 4 250,000] 1 17 14 
0 12,000 4 5 4 6 500,000} 114 | 24 20 
1 80,000 4% 8 6 8 | 1,000,000} 11% 82 2 
2 60,000 34 11 8 10 | 2,000,000; 2 42 | 36 
3: 125,000 1 14 10 








The Steam-jet as a Means for Ventilation.—Between 1810 
and 1850 the steam-jet was employed to a considerable extent for ventilat- 
ing English collieries, and in 1852 a committee of the House of Commons 
reported that it was the most powerful and at the same time the cheapest 
method for the ventilation of mines ; but experiments made shortly after- 
wards proved that this opinion was erroneous, and that furnace ventilation 
was less than half as expensive, and in consequence the jet was soon aban- 
dened as a permanent method of ventilation. 

For an account of these experiments see Colliery Engineer, Feb. 1890, 
The jet, however, is sometimes advantageously used as a substitute, for 
instance, in the case of a fan standing for repairs, or after an explosion, 
when the furnace may not be kept going, or in the case of the fan having 
been rendered useless. 


628 HEATING AND VENTILATION. © 


HEATING AND VENTILATION. 


Ventilation. (A. R. Wolff, Stevens Indicator, April, 1890.)—The pop- 
ular impression that the impure air falls to the bottom of a crowded room 
is erroneous. There is a constant mingling of the fresh air admitted with 
the impure air due to the law of diffusion of gases, to difference of temper- 
ature, ete. The process of ventilation is one of dilution of the impure eir 
by the fresh, and a room is properly ventilated in the opinion of the hygien- 
ists when the dilution is such that the carbonic acid in the air does not ex- 
ceed from 6 to 8 parts by volume in 10,000. Pure country air contains about 
4 parts CO, in 10,000, and badly-ventilated quarters as high as 80 parts. 

An ordinary man exhales 0.6 of a cubie foot of CO, per hour. New York 
gas gives out 0.75 of a cubic foot of COg for each cubic foot of gas burnt. 
An ordinary lamp gives out 1 cu. ft. of C0, per hour. An ordinary candle 
gives out 0.3 cu. ft. per hour. One ordinary gaslight equals in vitiating 
effect about 544 men, an ordinary lamp 134 men, and an ordinary candle 4 
map. 

To determine the quantity of air to be supplied to the inmates of an un- 
lighted room, to dilute the air to a desired standard of purity, we can estab- 
lish equations as follows: 


Let v = cubic feet of fresh air to be supplied per hour; 

vr = cubic feet of CO, in each 10,000 cu. ft. of the entering air: 

& = cubic feet of CO, which each 10,000 cu. ft. of the air in the room 

may contain for proper health conditions; 

n = number of persons in the room; 

.6 = cubic feet of CO, exhaled by one man per hour. 
aan + .6n equals cubic feet of CO. communicated to the room dur 
ing one hour. 

This value divided by v and multiplied by 10,000 gives the proportion of 

CO, in 10,000 parts of the air in the room, and this should equal R, the stan- 
dard of purity desired. Therefore 


Uxr 
pL seo +2"), bri eure eee @ «@ (1) 
6000 
If we place r at 4 and FR at 6, v = ~~ = 3000n, . oof 6.6 tebceeiniatey 


or the quantity of air to be supplied per person is 3000 cubic feet per hour. 

If the original air in the room is of the purity of external air, and the cubic 
contents of the room is equal to 100 cu. ft. per inmate, only 3000 — 100 = 2900 
cu. ft. of fresh air from without will have to be supplied the first hour to 
keep the air within the standard purity of 6 parts of CO, in 10,000. If the 
cubic contents of the room equals 200 cu. ft. per inmate, only 8000 — 200 = 2800 
cu. ft. will have to be supplied the first hour to keep the air within the 
standard purity, and so on. 

Again, if we only desire to maintain a standard of purity of 8 parts of 
carbonic acid in 10,000, equation (1) gives as the required air-supply per hour 


v= i = 1500n, or 1500 cu. ft. of fresh air per inmate per hour. 
Cubic feet of air containing 4 parts of carbonic acid in 10,000 necessary per 
person per hour to keep the air in room at the composition of 


parts of carbonic acid in 
8000 2000 1500 1200 1000 545 3875 cubic feet. 


Tf the original air in the room is of purity of external atmosphere (4 parte 
of carbonic acid in 10,000), the amount of air to be supplied the first hour, 
for given cubic spaces per inmate, to have given standards of purity not 
exceeded at the end of the hour is obtained from the following table; 


VENTILATION. 529 





Proportion of Carbonic Acid in 10,000 Parts of the Air, not to 
Cubic Feet be Exceeded at End of Hour, 


of 
Space 
in Room 6 
per 
Individual. 





7 8 9 10 

















8 | 2 


Cubic Feet of Air, of Composition 4 Parts of Carbonic Acid in 
10,000, to be Supplied the First Hour. 


100 2900 1900 1400 1100 900 445 275 
200 2800 1800 1300 1000 800 345 175 
300 27 1700 1200 900 700 245 5 
400 2600 1600 1100 800 600 145 None 
500 2500 1500 1000 400 500 ABS ne create 
600 2400 1400 900 | 600 400 None |....... 
%00 2300 1300 800 500 30 shemes asta teste 
800 2200 1200 700 400 LOO waliceeoncaalae ci aval; 
900 2100 1100 600 300 LOD el see sisieots laiecertss 
1000 2000 1000 500 200 NOn@ ii |sss002 ee eeweees 
1500 1500 500 None NOHO S| Soectticc occ seeslloccien cote 
2000 1000 None e@@-.-@@+ee0 . eothees eeeeorsees eeeeeeeore eeoeeeoeeos 
2500 500 . e@seeeeode eoaoeeee ee eeeeeeeoen eeoeerveoe e7@C@Gsee-fLesoeecree ee 








It is exceptional that systematic ventilation supplies the 3000 cubic feet 
per inmate per hour, which adequate health considerations demand. Large 
auditoriums in which the cubie*space per individual is great, and in which 
the atmosphere is thoroughly fresh before the rooms are occupied, and the 
occupancy is of two or three hours’ duration, the systematic air-supply may 
be reduced, and 2000 to 2500 cubic feet per inmate per hour is a satisfactory 
allowance. 

Hospitals where, on account of unhealthy excretions of various kinds, the 
air-dilution must be largest, an air-supply of from 4000 to 6000 cubic feet per 
inmate per hour should be provided, and this is actually secured in some 
hospitals. A report dated March 15, 1882, by a commission appointed to 
examine the public schools of the District of Columbia, says : 

‘*Tn each class-room not less than 15 square feet of floor-space should be 
allotted to each pupil. In each class-room the window-space should not be 
less than one fourth the floor-space, and the distance of desk most remote 
from the window should not be more than one and a half times the height of 
the top of the window from the floor. The height of the class-room should 
never exceed 14 feet. The provisions for ventilation should be such as to 
provide for each person in a class-room not less than 30 cubic feet of fresh 
air per minute (1800 per hour), which amount must be introduced and 
thoroughly distributed without creating unpleasant draughts, or causing any 
two parts of the room to differ in temperature more than 2° Fahr., or the 
maximum temperature to exceed 70° Fahr.”’ 

When the air enters at or near the floor, it is desirable that the velocity of 
inlet should not exceed 2 feet per second, which means larger sizes of 
register openings and fines than are usually obtainable, and much higher 
velocities of inlet than two feet per second are the rule in practice. The 
velocity of current into vent-flues can safely be as high as 6 or even 10 feet 
per second, without being disagreeably perceptible. 

The entrance of fresh air into a room is co-incident with, or dependent on, 
the removal of an equal amount of air from the room, The ordinary means 
of removal is the vertical vent-duct, rising to the top of the building. Some- 
times reliance for the production of the current in this vent-duct is placed 
solely on the difference of temperature of the air in the room and that of 
the external atmosphere; sometimes asteam coil is placed within the flue 
near its bottom to heat the air within the duct; sometimes steam pipes 
(risers and returns) run up the duct performing the same functions; or steam 
jets within the flue, or exhaust fans, driven by steam or electric power, act 
directly as exhausters; sometimes the heating of the air in the flue is ac- 
complished by gas-jets. 

The draft of such a duct is caused by the difference of weight of the 


530 HEATING AND VENTILATION. 


heated air in the duct, and a column of equal height and cross-sectional area 
of weight of the external air. 

Let d = density, or weight in pounds, of a cubic foot of the external air. 

Let d, = density, or weight in pounds, of a cubic foot of the heated air 
within the duct. 

Let h = vertical height, in feet, of the vent-duct. 

h(d@ — d,) = the pressure, in pounds per square foot, with which the air is 
forced into and out of the vent-duct. 

This pressure can be expressed in height of a column of the air of density 
within the vent-duct, and evidently the height of such column of equal 

« hid — d,) 
presssure would be; Qa oe Oe Fey et te* te "fe  s> Oe 8e me 6 cee (3) 
1 

Or, if t= absolute temperature of external air, and ¢; = absolute temper- 

ature of the air in vent-duct in the form, then the pressure equals 


h(t, — @) 
er ae eC) 


The theoretical velocity, in feet per second, with which the air would 
travels through the vent-duct under this pressure is 


vay / OE 28.02 4/E GRD | oe ee -O 


The actual velocity will be considerably less than this, on account of loss 
due to friction. This friction will vary with the form and cross-sectional 
area of the vent-duct and its connections, and with the degree of smooth- 
ness of its interior surface. On this account, as well as to prevent leakage 
of air through crevices in the wall, tin lining of vent-flues is desirable. 

The loss by friction may be estimated at approximately 50%, and so we find 
for the actual velocity of the air as it flows through the vent-duct : 


1 @ —d) : J (t,—2) 
v= y/ 2gh———, or, approximately, v = 4 / aaatom tnt e « (6) 


If V= velocity of air in vent-duct, in feet per minute, and the external air 
be at 32° Fahr., since the absolute temperature on Fahrenheit scale equals’ 
thermometric temperature plus 459.4, 


V = 240 “Mia? eee eee ees | 


from which has been computed the following table 


Quantity of Air, in Cubic Feet, Discharged per Minute 
through a Ventilating Duct, of which the_Cross-sec= 
tional Area is One Square Foot (the External Tempera- 
ture of Air being 32° Fahr.). 





— 


Excess of Temperature of Air in Vent-duct above that of 











Height of External Air, 
Vent-duct in 
feet. 
5° 10° |} 15°} 20°] 25°) 30° {| 50°} 100° | 150° 
10 “71 108] 1338] 153 171 188 | 242) 3842] 419 
15 94 133 162 188 210 230 297 419 514 
90 108 is 188 217 242 265 342 484 593 
25 121 171 210 242 271 297 383 541 663 
30 133 188 230 2°65 297 825 419 593 926 
35 143 203 248 286 820 351 453 640 %84 
40 153 217 265 806 842 3875 484 656 838 
45 162 | 230} 282) 3825) 3863] 898} 514] 476 | 889 
50 171 | 242; 2971 342) 883] 4191 541 278 | 937 


Multiplying the figures in above table by 60 gives the cubic feet of air dis- 
charged per hour per square foot of cross-section of vent-duct. Knowing 


~ wes. 


MINE-VENTILATION, 53 


the cross-sectional area of vent-ducts we can find the total discharge; or 
for a desired air-removal, we can proportion the cross-sectional area of 
vent-ducts required. 

Artificial Cooling of Air for Wentilation. (Hngineering 
News, July 7, 1892.)—A pound of coal used to make steam for a fairly effi- 
cient refrigerating-machine can produce an iactual cooling effect equal to 
that produced by the melting of 16 to 46 lbs. of ice, the amount varying 
with the conditions of working. Or, 855 heat-units per lb. of coal converted 
into work in the refrigerating plant (at the rate of 3 lbs. coal per horse- 
power hour) will abstract 2275 to 6545 heat-units of heat from the refriger- 
ated body. If we allow 2000 cu. ft. of fresh air per hour per person as suffi- 
cient for fair ventilation, with the air at an initial temperature of 80° F., its 
weight per cubic foot will be .0736 Ib.; hence the hourly supply per person 
will weigh 2000 x .0736 lb. = 147.2 lbs. To cool this 10°, the specific heat of 
air being 0.238, will require the abstraction of 147.2 x 0.288 x 10 = 350 heat- 
units per person per hour. 

Taking the figures given for the refrigerating effect per pound of coal as 
above stated, and the required abstraction of 350 heat-units per person per 
hour to have a satisfactory cooling effect, the refrigeration obtained from a 
pound of coal will produce this cooling effect for 2275 -- 350 = 644 hours with 
the least efficient working, or 6545 + 350 = 18.7 hours with the most efficient 
working. With ice at $5 per ton, Mr. Wolff computes the cost of cooling with 
ice at about $5 per hour per thousand persons, and concludes that thisis too 
expensive for any general use. With mechanical refrigeration, however, if 
we assume 10 hours’ cooling per person per pound of coal as a fair practical 
service in regular work, we have an expense of only 15 cts. per thousand 
persons per hour, coal being estimated at $2 per short ton. This is for fuel 
alone, and the various items of oil, attendance, interest, and depreciation on 
the plant, etc., must be considered in making up the actual total cost of 
mechanical refrigeration. 

Mine-ventilation—Friction of Air in Underground Pas-= 
sages,.—lIn ventilating a mine or other underground passage the resistance 
to be overcome is, according to most writers on the subject, proportional to 
the extent of the frictional surface exposed; that is, to the product lo of the 
length of the gangway by its perimeter, to the density of the air in circula- 
tion, to the square of its average speed, v, and lastly to a coefficient k, whose 
numerical value varies according to the nature of the sidesof the gangway 
and the irregularities of its course. 

The formula for the loss of head, neglecting the variation in density as 


; : ksv? , ; : 
unimportant, is p = pape which p = loss of pressure in pounds per square 


foot, s = square feet of rubbing-surface exposed to the air, v the velocity of 
the air in feet per minute, a the area of the passage in square feet, and k the 
coefficient of friction. W. Fairley; in Colliery Engineer, Oct. and Nov. 
1893, gives the following formule for all the quantities involved, using the 
same notation as the above, with these additions: h = horse-power of ven- 
tilation; 1 = length of air-channel; 0 = perimeter of air-channel; g = quan- 
tity of air circulating in cubic feet per minute; w= units of work, in foot- 
pounds, applied to circulate the air: w = water-gaugeininches. Then, , 


ksv?_ksv*qg_ ksv8 u_q 
p u pv =pu v 
u gp 5.2qw 


rs ORE ECAR) Sm 5.2w 
*""~ gut ~ svi sut+a = sv2-+a 


* 


532 HEATING AND VENTILATION. 





2 
10. vw=qp=vpa= caer 





= ksvt = 5.2qw = 33,000h, 


_ To find the quantity of air witha given horse-power and efficiency (e) of 


engine: 
; ne h X 33,000 X e 
p e 


The value of k, the coefficient of friction, as stated, varies according to 
the nature of the sides of the gangway. Widely divergent values have been 
given by different authorities (see Colliery Engineer, Nov. 1893), the most 
generally accepted one until recently being probably that of J. J. Atkinson, 
.0006000217, which is the pressure per square foot in decimals of a pound for 
each square foot of rubbing-surface and a velocity of one foot per minute. 
Mr. Fairley, in his ‘‘ Theory and Practice of Ventilating Coal-mines,” gives a. 
value less than half of Atkinson’s, or .00000001; and recent experiments by D. 
Murgue show that even this value is high under most conditions. Murgue’s 
results are given in his paper on Experimental Investigations in the Loss of 
Head of Air-currents in Underground Workings, Trans. A.I. M, E., 1893. 
vol. xxiii. 63. His coefficients are given in the following table, as determined 
in twelve experiments: 

Coefficient of Loss of 
Head by Friction. 
French. British. 


Straight, normal section...........e.s.- .00092  .000,000,00486 

Rock. Straight, normal section....... ........ .00094 .000,000,00497 
gangways. | Straight, large section.................. .00104  .000,000,00549 
Straight, normal section........ ... «+. -00122  .000,000,00645 

(Straight, normal section.. ............. .00030 .000,000,00158 

Brick-lined | Straight, normal section................ .00036  .000,000,00190 
arched Continuous curve, normal section...... -00062  .000,000,00328 
gangways. | Sinuous, intermediate section.......... -00051 = .009,000,00269 
Sinuous, small section........... Ps eis arate -00055  .000,000,00291 

: _ (Straight, normal section....... secseeees .00168 .000,000,00888 
Timbered’ J Straight, normal section........ ie [00144 |000,000.00761 
kangways. | Slightly sinuous, small section.......... .00238  .000,000,01257 


The French coefficients which are given by Murgue represent the height 
of water-gauge in millimetres for each square metre of rubbing-surface and 
a velocity of one metre per second. Toconvert them to the British measure 
of pounds per square foot for each square foot of rubbing-surface and a 
velocity of one foot per minute they have been multiplied by the factor of 
conversion, .000005283. For a velocity of 1000 feet per minute, since the loss 
of Tonal aoe as v2, move the decimal point in the coefficients six places to 
the right 


FANS AND HEATED CHIMNEYS FOR VENTILATION. 533 


Equivalent Orifice.—The head absorbed by the working-chambers 
of a mine cannot be computed a priori, because the openings, cross-pas- 
sages, irregular-shaped gob-piles, and daily changes in the size and shape of 
the chambers present much too complicated a network for accurate 
analysis. In order to overcome this difficulty Murgue proposed in 1872 the 
method of equivalent orifice. This method consists in substituting for the 
mine to be considered the equivalent thin-lipped orifice, requiring the same 
height of head for the discharge of an equal volume of air. The area of 
this orifice is obtained when the head and the discharge are known, by 
means of the following formule, as given by Fairley: 


Let Q = quantity of air in thousands of cubic feet per minute; 
w = inches of water-gauge; 
A = area in square feet of equivalent orifice. 


Then 
SPiN Ai at Peyote On 
= ; w = 0.1369 x (“). 


Motive Column or the Head of Air Due te Differences 
of Temperature, ete. (airley.) 
Let M@ = motive column in feet; 
T = temperature of upcast; 
J = weight of one cubic foot of the flowing air; 
t = temperature of downcast; 
D = depth of downcast. 


Then 
Li T—t 5.2 X w, a ; SxXM p 
PRTG) ok Op Rh Tent eS eat OR ee 
To find diameter of a round airway to pass the same amount of airas a 
square airway the length and power remaining the same: 
Let D = diameter of round airway, A = area of square airway; O= peri- 
5/ A® X 3.1416 
meter of square airway. Then D3= 78543 X O 


If two fans are employed to ventilate a mine, each of which when worked 
separately produces a certain quantity, which may be indicated by A and B 
then the quantity of air that will pass when the two fans are worked together 


will be V* + B83, (For mine-ventilating fans, see page 521.) 


Relative Efficiency of Fans and Heated Chimneys for 
Ventilation.—wW. P. Trowbridge, Trans. A. S. M. E. vii. 531, gives a theo- 
retical solution of the relative amounts of heat expended to remove a given 
volume of impure air by a fan and by achimney. Assuming the total effi- 
ciency of a fan to be only 1/25, which is made up of an efficiency of 1/10 for 
the engine, 5/1C for the fan itself, and 8/10 for efficiency as regards friction, 
the fan requires an expenditure of heat to drive it of only 1/38 of the amount 
that would be required to produce the same ventilation by a chimney 100 ft. 
high. For achimney 500 ft. high the fan will be 7.6 times more efficient. 

In all cases of moderate ventilation of rooms or buildings where the air 
is heated before it enters the rooms, and spontaneous ventilation is pro- 
duced by the passage of this heated air upwards through vertical flues, 
no special heat is required for ventilation; and if such ventilation be suffi- 
cient, the process is faultless as far as cost is concerned. This is a condition 
of things which may be realized in most dwelling-houses, and in many halls, 
schoolrooms, and public buildings, provided inlet and outlet flues of ample 
cross-section be provided, and the heated air be properly distributed. 

If a more active ventilation be demanded, but such as requires the small- 
est amount of power, the cost of this power may outweigh the advantages 
of the fan. There are many cases in which steam-pipes in the base of a 
chimney, requiring no care or attention, may be preferable to mechanical 
ventilation, on the ground of cost, and trouble of attendance, repairs, etc. 





it and Norris 4 = we See page 521, ante. 


Ww Ww 





* Murgue gives 4 = 


§34 HEATING AND VENTILATION. 


The following figures are given by Atkinson (Coll. Engr., 1889), showing 
the minimum depth at which a furnace would be equal to a ventilating- 
machine, assuming that the sources of loss are the same in each case, i.e., 
that the loss of fuel in a furnace from ‘the cooling in the upcast is equivalent 
to the power expended in overcoming the friction in the machine, and also 
assuming that the ventilating-machine utilizes 60% of the engine-power. The 
coal consumption of the engine per I.H.P. is taken at 8 lbs. per hour: 


Average temperature in upeast....... 100° F. 150° F, 200° F. 
Minimum depth for equa! economy... 960 yards. 1040 yards. 1130 yards. 


Heating and Wentilating of Large Buildings. (A. R. 
Wolff, Jour. Frank. Inst., 1893.)—The transmission of heat from the interior 
to the exterior of a room or building, through the walls, ceilings, windows, 
etc., is calculated as follows: 


S = amount of transmitting surface in square feet; 

t = temperature F. inside, tg = temperature outside; 

K = a Coefficient representing, for various materials composing buildings, © 
the loss by transmission per square foot of surface in British thers 
mal units per hour, for each degree of difference of temperature 
on the two sides of the material; 

Q = total heat transmission = SK (¢ ~— fo). 


This quantity of heat is also the amount that must be conveyed to the 
room in order to make good the loss by transmission, but it does not cover 
the additional heat to be conveyed on account of the change of air for pur- 
poses of ventilation, The coefficients X given below are those prescribed by 
jaw by the German Government in the design of the heating plants of its 
pubis buildings, and generally used in Germany for all buildings. They 

ave been converted into American units by Mr. Wolff, and he finds that 
they agree well with good American practice: 


Va.ue or K ror Eacu Square Foot or Brick WALI. 


Ce nt 4” = «gs 4977 16/790" 94’? 98" 30/7 367 40” 


K = 0.68 0.46 0.382 0.26 0.23 0.20 0.174 0.15 0.129 0.115 


1sq. ft., wooden-beam construction, ) ..........as flooring, K = 0.083 
planked over or ceiled, eta creeieinas as ceiling, K = 0.104 

1 sq. ft., fireproof construction, ' cecoce. ee aS flooring, K = 0.124 
floored over, 


1 sq. ft. single WINDOW tee cece tee eb tec cate cece eeeececerece = 1.030 
sq to single'Sky HBA ey eco sec cress cel ce tccr ce ccneenre ste mnhG aml enLG 
1 sq. ft. ; double; window ,s eve ce tieeils te iiseed tides obese dec tries ueiss 0.015 
1 sq. ft., double skylight..... ASHI A PSH OIG a Ora UEP 
LEBEN 1 ts COOL «25:0 :n9 5 ate cienle-sie'c ccm ccinmie'ere Sibmiacige eh at's ¢ a: t'e Coit een Re 


These coefficients are to be increased respectively as follows: 10% when the 
exposure is a northerly one, and winds are to be counted on as important 
factors; 10% when the building is heated during the daytime only, and the 
iocation of the building is not an exposed one; 30% when the building is 
heated during the daytime only, and the location of the building is exposed}; 
50% when the building is heated during the winter months intermittently, 
with long intervals (say days or weeks) of non-heating. 

The value of the radiating-surface is about as follows: Ordinary bronzed 
cast-iron radiating-surfaces, in American radiators (of Bundy or similar 
type), located in rooms, give out about 250 heat-units per hour for each 
square foot of surface, with ordinary steam-pressure, say 3 to 5 lbs. per sq. 
jn., and about 0.6 this amount with ordinary hot-water heating. 

Non-paiated radiating-surfaces, of the ordinary ‘‘ indirect’ type (Climax 
or pin surfaces), give out about 400 heat-units per hour for each square foot 
of heating-surface, with ordinary steam-pressure, say 3 to 5 lbs. per sq. in.; 
and about 0.6 this amount with ordinary hot-water heating. 

A person gives out about 400 heat-units per hour; an ordinary gas-burner, 
about 4800 heat-units per hour; an incandescent electric (16 candle-power) 
light, about 1600 heat-units per hour. 

The following example is given by Mr. Wolff to show the application of 
the formula and coefficients: 

Lecture-room 40 x 60 ft., 20 ft. high, 48,000 cubic feet, to be heated to 
69° F.; exposures as follows: North wall, 60 x 20 ft., with four windows 
each 14 x8 feet, outside temperature 0* F. Room beyond west wall and 


HEATING AND VENTILATING OF LARGH BUILDINGS. 53d 


Toom overhead heated to 69°, except a double skylight in ceiling, 14 x 24 ft., 
exposed to the outside temperature of 0°. Store-room beyond east wall at 
86°. Door 6 X 12ft. in wall. Corridor beyond south wall heated to 59°. 
Two doors, 6 X 12, in wall. Cellar below, temperature 36°, 

The following table shows the calculation of heat transmission: 


g| 











cay na a oat oes ee 
aa 2: 4! Calculation | ©3 |< Sy 
& Ef Kind of Transmitting as &| of Area of | of 7 Ex 
@ SD Surface, oe 2 preneeHng sAZ\2 g 5 
Oo su" urface, = pt 
is rahe Sal | & 
69° |Outside wall.......... cooee -| 30” | 63 KX 22 — 448) 938) 9 8,442 
69 |Four windows (single)...... 4x 8X 14] 448; 72 32,256 
33 |Inside wall (store-room)..... 36” | 42% 22 — 72) 852) 4 3,408 
Som | DOO 2. Sus ae tests Seceee 6 x 12 72) 19 1,368 
10 {Inside wall (corridor).......} 24/7 | 45x 22— %2| 918] 2 1,836 
POM D6or a ee aie sos 6X 12 21 5 360 
10 |Inside wall (corridor).......| 86/7 | 17% 22— 72} 302] 1 802 
10 DOOR. cccteancesecencecwess : 6 xX 12 Qe 5 360 
69 Roof....<c6< oce-ceeeeeeeosoe 82 X 42 — 336 1,008 10 10,080 
69 |Double skylight....0....00. 14 x 24 336 | 43 14,448 
33 BlOOP eReece eeeeceeoeeseee2ee0 62 X 42 2,604 4 10,416 
; 83,276 
Supplementary allowance, north outside wall, 10%.......... 844 
“ “¢ north outside windows, 102%..... 8,226 
87,346 
Exposed location and intermittent day or night use, 30%....| 26.204 
Potalthermal tinitS cn sae om cae eee cae: 113,550 


If we assume that the lecture-room must be heated to 69 degrees Fahr. in 
the daytime when unoccupied, so as to be at this tempezature when first 
persons arrive, there will be required, ventilation not being considered, and 
bronzed direct low-pressure steam-radiators being the heating media, about 
113,550 + 250 = 455 sq. ft. of radiating-surface. (This gives a ratio of about 
405 cu. ft. of contents of room for each sq. ft. of heating-surface.) 

If we assume that there are 160 persons in the lecture-room, and we pro- 
vide 2500 cubic feet of fresh air per person per hour, we will supply 160 x 


2500 = 400,000 cubic feet of air per hour (i.e., ome: over eight changes of 


48,000 — 
contents of room per hour). 

To heat this air from 0° Fahr. to 69° Fahr. will require 400,000 x 0.0189 x 
69 =: 521,640 thermal units per hour (0.0189 being the product of a weight of 
a cubic foot by the specific heat of air). Accordingly there must be provided 
521,640 =- 400 = 13804 sq. ft. of indirect surface, to heat the air required for 
ventilation, in zero weather, If the room were to be warmed entirely indi- 
rectly, that is, by the air supplied to room (including the heat to be conveyed 
to cover loss by transmission through walls, etc.), there would have to be 
conveyed to the fresh-air supply 521,640 +- 113,550 = 635,190 heat-units. This 
would imply the provision of an amount of indirect heating-surface of the 
** Climax * type of 635,190 + 400 = 1589 sq. ft., and the fresh air entering the 
room would have to be at a temperature of about 84° Fahr., viz., 69° = 


113,550 A 

400,000 0.0180" or a 15 = 84° Fahr. 

The above calculations do not, however, take into account that 160 per- 
sons in the lecture-room give out 160 < 400 = 64,000 thermal units per hour; 
and thax, say, 50 electric lights give out 50 x 1600 = 80,000 thermal units per 
hour; or, say, 50 gaslights, 50 x 4800 = 240,000 thermal units per hour. The 
presence of 160 people and the gas-lighting would diminish considerably the 
amount of heat required, Practically, it appears that the heat generated 
by the presence of 160 people, 64,000 heat-units, and by 50 electric lights, 
80,000 heat-units, a total of 144,000 heat-units, more than covers the amount 
of heat transmitted through walls, ete. Moreover, that if the 50 gaslights 
give out 240,000 thermal units per hour, the air supplied for ventilation must 
epter considerably below 69° Fahr., or the room will be heated to an 
unbearably high temperature. If 400,000 cubic feet of fresh air per hour 


536 HEATING AND VENTILATION, 


are supplied, and 240,000 thermal units per hour generated by the gas must 
be abstracted, it means that the air must, under these conditions, enter 


240,000 i - ‘ 
400,000 x .0189 = about 32° less than 84°, or at about 52° Fahr, Further- 


more, the additional vitiation due to gaslighting would necessitate a much 
larger supply of fresh air than when the vitiation of the atmosphere by the 
people alone is considered, one gaslight vitiating the air as much as five 
men. 

Various Rules for Computing Radiating=-surface.—The 
following rules are compiled from various sources, They are more in the 
nature of ‘‘rule-of-thumb”’ rules than those given by Mr. Wolff, quoted 
above, but they may be useful for comparison. 

Divide the cubic feet of space of the room to be heated, the square feet 
of wall surface, and the square feet of the glass surface by the figures 
given under these headings in the following table, and add the quotients 
together; the result will be the square feet of radiating-surface required. 
(F. Schumann.) 


SPacr, WALL AND Giass SURFACE wHIcH One Sqtars Foot of RADIATING 
SURFACE WILL HEAT. 





























£ 3 Exposure of Rooms. 
e nn 
& oe 5 All Sides. Northwest. Southeast. 
a ts een roger eo Ot ss 
8S |g 2. Os] Wall Glass Wall Glass Wall Glass 
= |$8|30| Surface, | Surface, Surface, | Surface, | Surface, { Surface, 
a ls 7 sq. ft. sq. ft. sq. ft. sq. ft. sq. ft. sq. ft. 
Once| 1] 190] 13.8 | 7 15.87 | 8.05 | 16.56 |. 8.4 
per 3 | 210 15.0 LOL 17.25 8.85 18.00 9.24 
hour.| 5 | 225) 16.5 8.5 18.97 Oke, 19.80 10.20 
Twicel 1] 75) 11.1 5.7 12.76 | 6.55 13.22 | 6.84 
per 3] 82 12.1 6.2 13.91 7.13 14.52 7.44 
hour.! 5} 90} 13.0 6.7 14.52 7.60 15.60 8.04 


EMISSION OF HEAT-UNTS PER SQUARE FOOT PER Hour FROM CAST-IRON PIPES 
oR RaniaTors. TEMP. oF AIR IN Room, 10° F. (F. Schumann.) 





By Radiation 





Mean Temperature of By Contact. By Raai.|___ 20d Contact. 
elie Pipe. Radia- e pie ri 
or, etc. gett ir Shot nye ir 
’ Air quiet. moving. Air quiet. moving. 


es | ee | | 


Hot water........ -140°} 55.51 92.52 59.63 115.14 152 15 








Briers Suess LOO?) 65-45 109.18 69.69 185.14 178.87 

yr eo ledoustes- 160°; 75.68 126.13 80.19 155.87 206.32 
i pei Mtercirtois iss: vie.0:s 170°} 86.18 143.30 91.12 177.30 234.42 
ai Se ferences eid O0C}, 96.93 161.55 102.15 199.43 264.05 
se eet aero onary 190°; 107.90 179.83 114.45 222,35 294.28 
ce ert hasicice: §- Sa 200°} 119.13 198.55 127.00 246.13 825 .55 
a ‘¢ or steam ..210°} 130.49 217.48 139.96 270.49 857.48 
Steamist. Ser eee 220°} 142.20 237.00 155.27 297.47 892.27 
eS beret eee sseeeDD.| 100,90 256.58 169.56 323.51 426.14 


sie My AOE Ge ye REPS 240°} 165.90 79.83 184.58 350.48 464.41 
Meee yecenatoimepon 178.00 296.65 200.18 878.18 496.81 
Oe, se Tat Samereos, 189.90 316.50 214.36 404.26 530.86 
GD Pht ee et 202. 7 337.83 233.42 436.12 571.25 
OO SU Sy menanted 80 358.85 251.21 466.51 610.06 
Lie SECO OME iit ialsiber deer 880.91 267.73 496.28 648.64 
sen re Ue ebe, Fit 300°} 240.85 401.41 279.12 519.97 680.53 


INDIRECT HEATING-SURFACE. 537 


RADIATING-SURFACE REQUIRED FOR DIFFERENT KINDS OF BUILDINGS. 


The Nason Mfg. Co.’s catalogue gives the following: One square foot of 
surface will heat from 40 to 100 cu ft. of space to 75° in — 10° latitudes. 
This range is intended to meet conditions of exposed or corner rooms of 
buildings, and those less so, as intermediate ones of « block. As a general 
rule, 1 sq. ft. of surface will heat 70 cu. ft. of air In outer or front rooms and 
100 cu. ft. in inner rooms. In large stores in cities, with buildings on each 
side, 1 to 100 is ample. The following are approximate proportions: 

One square foot radiating-surface will heat: 


In dwellings, In hall, stores, Inchurches, large 


schoolrooms, lofts, factories, auditoriums, 
offices, ete. etc. ete. 
By direct radiatian. .. 60 to 80 ft. 75 to 100 ft. 150 to 200 ft. 
By indirect radiation. 40 to 50 “ 50to 70 ‘* 100 to 140 “* 


Isolated buildings exposed to prevailing north or west winds should have 
® generous addition made to the heating-surface on their exposed sides. 

The following tule is given in the catalogue of the Babcock & Wilcox Co., 
and is also recornmended by the Nason Mfg. Co.: 

Radiating surface may be calculated by the rule: Add together the square 
feet of glass in the windows, the number of cubic feet of air required to be 
changed per minute, and one twentieth the surface of external wall and 
roof; multiply this sum by the difference between the required temperature 
of the room and that of the external air at its lowest point, and divide the 
product by the difference in temperature between the steam in the pipes 
and the required temperature of the room. The quotient is the required 
radiating-surface in square feet. 

Prof. R. C. Carpenter (Heating and Ventilation, Feb..15, 1897), gives the 
following handy formula for the amount of heat required for heating build- 
ings by direct radiation: 


h=>C+G+W, 


in which W = wall-surface, G = glass- or window-surface, both in sq. ft., 
C = contents of building in cu. ft., m= number of times the air must be 
changed per hour, and h = total heat units required per degree of difference 
of temperature between the room and the surrounding space. To heat the 
building to 70°F. when the outside temperature is 0°, 70 times the above 
quantity of heat will be required. Under ordinary conditions of pressure 
aud temperature 1 sq. ft. of steam-heating surface will supply 280 heat units 
per hour, and 1 sq. ft. of hot-water heating surface 175 heat units per hour. 
The square feet of radiating-surface required under these conditions will 
be R = 0.25h for steam-heating, and R = 0.4h for hot-water heating. Prof. 
Carpenter says that for residences it is safe to assume that the air of the 
principal living-rooms will change twice in an hour, that of the halls three 
times and that of the other rooms once per hour, under ordinary condi- 
tions. 

Overhead Steamepipes. (A. R. Wolff, Stevens Indicator, 1887.)— 
When the overhead system of steam-heating is employed, in which system 
direct radiating-pipes. usually 114 in. in diam., are placed in rows overhead, 
suspended upon horizontal racks, the pipes running horizontally, and side 
by side, around the whole interior of the building, from 2 to 3 ft. from the 
walls. and from 2 to 4 ft. from the ceiling, the amount of 144 in. pipe re- 
quired, according to Mr. C. J. H. Woodbury, for heating mills (for which 
use this svstem is deservedly much in vogue), isabout 1 ft. in length for 
every 96 cu. ft. of space. Of course a great range of difference exists, due 
to the special character of the operating machinery in the mill, both in re- 
spect to the amount of air circulated by the machinery, and also the aid to 
warming the room by the friction of the journals. 

Endirect Heating-surface.—J. H. Kinealy, in Heating and Ven- 
tilation, May 15, 1894, gives the following formula, deduced from results of 
experiments by C. B. Richards, W. J. Baldwin, J. H. Mills, and others, upon 
indirect heaters of various kinds, supplied with varying amounts of air per 
bour per square foot of surface: 


35.04 35.04 
. Sr T, = (Tp — T;) (0.369 + et) 4 T,, 


538 HEATING AND VENTILATION, 


N = cubic feet of air, reduced to 70° F., supplied to the heater per square 
foot of heating-surface per hour; 7, = temperature of the steam or water 
in the heater; 7, = temperature of the air when it enters the heater; 
T, = temperature of the air when it leaves the heater. 

As the formula is based upon an average of experiments made upon all 
sorts of indirect heaters, the results obtained by the use of the equation 


may in some cases be slightly too small and in others slightly too large, 


although the error will in no case be great. No single formula ought to be 
expected to apply equally well to all dispositions of heating-surface in in- 
direct heaters, as the efficiency of such heater can be varied between such 
wide limits by the construction and arrangement of the surface. 

In indirect heating, the efficiency of the radiating-surface will increase, 
and the temperature of the air will diminish, when the quantity of the air 
caused to pass through the coil increases. Thus 1 sq. ft. radiating-surface, 
with steam at 212°, has been found to heat 100 cu. ft. of air per hour from 
zero to 150°, or 300 cu. ft. from zero to 100° in the same time. The best re- 
sults are attained by using indirect radiation to supply the necessary venti 
lation, and direct radiation for the balance of the heat. (Steamn.) 

In indirect steam-heating the least flue area should be 1 to 1% sq. in. 
to every square foot of heating-surface, provided there are no long horizons 
tal reaches in the duct, with little rise. The register should have twice the 
area of the duct to allow for the fretwork. For hot-water heating from 25% 
to 30% more heating-surface and flue area should be given than for low- 
pressure steam. (Hngineering Record, May 26, 1894. 

Boiler Heating-surface Required. (A. R. Wolff, Stevens Indi- 
cator, 1887.)—When the direct system is used to heat buildings in which the 
street floor is a store, and the upper floors are devoted to sales and stock- 
rooms and to iight manufacturing, and in which the fronts are of stone or 
iron, and the sides and the rear of building of brick—a safe rule to follow is to 
supply 1 sq. ft. of boiler heating-surface for each 700 cu. ft., and 1 sq. ft. of 
radiating-surface for each 100 cu. ft. of contents of building. 

For heating mills, shops, and factories, 1 sq. ft. of boiler heating-surface 
should be supplied for each 475 cu. ft. of contents of building; and the same 
allowance should also be made for heating exposed wooden dwellings. For 
heating foundries and wooden shops, 1 sq. ft. of boiler heating-surface 
should be provided for each 400 cu. ft. of contents; and for structures in 
which glass enters very largely in the construction—such as conservatories, 
exhibition buildings, and the like—1 sq. ft. of boiler heating-surface should 
be provided for each 275 cu. ft. of contents of building. 


When the indirect system is employed, the radiator-surface and the boiler 


capacity to be provided will each have to be, on an average, about 25% more 
than where direct radiation is used. This percentage also marks approxi- 
mately the increased fuel consumption in the indirect system. 

Steam (Babcock & Wilcox Co.) has the following: 1 sq. ft. of boiler-surface 
will supply from 7 to 10 sq. ft. of radiating-surface, depending upon the size 
of boiler and the efficiency of its surface, as well as that of the radiating- 
surface. Small boilers for house use should be much larger proportionately 
than large plants. Each horse-power of boiler will supply from 240 to 360 
ft. of 1-in. steam-pipe, or 80 to 120 sq. ft. of radiating-surface. Cubic feet 
of space has little to do with amount of steam or surface required, but is a 
convenient factor for rough calculations. Under ordinary conditions 1 
horse-power will heat, approximately, in— 


Brick dwellings, in blocks, as in cities... .... 15,000 to 20,000 cu. ft. 
‘* stores ts + sie sees ceo oe 00005 15,0005 ace 


‘“« dwellings, exposed all round........... 10,000 ‘* 15,000 §§ 
“mills, shops, factories, etc.............. 7,000 ‘* 10,000 ‘ 
Wooden dwellings, exposed....... i Reade code 28 3° 7,000, *€710:000K, at® 
Foundries and wooden shops..... » sw 3 000,000 «f A000.) 58 


Exhibition buildings, largely glass, etc....... 4,000 ** 15,000 ** 


Steam-consumption in Car-heating. 
C., M. & St, Paut Rattway Tests. (Engineering, June 27, 1890, p. 764.) 
Water of Condensation 


Outside Temperature. Inside Temperature, per Car per Hour. 
_ it 70 lbs, 
4 


85 
10 7 100 


EE ——————— 


a 


REGISTERS AND COLD-AIR DUCTS, 


539 


Internal Diameters of Steam Supply-mains, with Total 
Resistance equal to 2 inches of Water-column.* 


Steam, Pressure 10 lbs. per square inch above atm., Temperature 239° F. 


5 /Q21 


4 


Radiating- 
surface 


= length of mains in feet; h 








where d = internal diameter in inches; 


= 9.2 cubic feet of steam per minute per 100 sq. ft. of radiating-surface $ 
159.3 feet head of steam to produce flow. 


Internal Diameters in inches for Lengths of Mains from 1 ft. to 600 ft. 





} 
80 ft. |100 ft.|200 ft. |300 ft.|}400 ft.|600 ft, 


1 ft. | 10 ft. } 20 ft. | 40 ft. | 60 ft. 

sq.ft.| inch.| inch.| inch.| inch.} inch.| inch.j inch.| inch.| inch.| inch.| inch, 
1] 0.075) 0.119) 0.1386] 0.157] 0.170) 0.180] 0.189] 0.216] 0.234] 0.248) 0.270 

10{ 0.19 | 0.30 | 0.84 } 0.39 | 0.43 45 | 0.47 .54 | 0.59 | 0.62 | 0.68 
20} 0.25 | 0.39 | 0.45 | 0.52 | 0.56 | 0.60 | 0.62 } 0.72 | 0.78 | 0.82 | 0.89 
40; 0.33 | 0.52 | 0.60 | 0.69 | 0.74 | 0.79 | 0.82 | 0.95 | 1.03 | 1.09 | 1.18 
60} 0.39 | 0.61 | 0.71 | 0.81 | 0.87 | 0.93 } 0.97 | 1.11 | 1.21 | 1.28] 1.39 
80} 0.43 | 0.68 | 0.79 | 0.90 | 0.98 | 1.04 } 1.09 | 1.25 | 1.385 | 1.43 | 1.55 
100 | 0.47 | 0.75 | 0.86 | 0.99 | 1.07 | 1.14 | 1.19 | 1.36 | 1.48 | 1.57 | 1.70 
200} 0 62 | 0.99 | 1.14 | 1.30 | 1.41 } 1.50 | 1.57 | 1.80 | 1.95 | 2.07 | 2.24 
300! 0.73 { 1.16 | 1.34 |] 1.53 | 1.66 | 1.76 | 1.84 | 2.12 | 2.30 | 2.43 | 2.64 
400 | 0.82 | 1.30 | 1.50 | 1.72 | 1.86 | 1.98 | 2.07 | 2.37 | 2.57 | 2.73 | 2.96 
500 | 0.90 | 1.43 | 1.64 | 1.88 | 2.04 | 2.16 | 2.26 | 2.60 | 2.81 | 2.98 | 3.23 
600 | 0.97 | 1.53 | 1.76 | 2.03 } 2.20 | 2.33 { 2.43 | 2.79 | 3.03 | 3.21 | 3.48 
800} 1.09 } 1.72 | 1.98 | 2.27 } 2 46 | 2.61 | 2.73 | 3.13 | 3.40 | 8.60 | 3.90 
1,000 | 1.19 | 1.88 | 2.16 | 2.48 | 2.69 | 2.85 | 2.98 | 3.43 | 3.71 | 3.94 | 4.27 
1,200 | 1.28 | 2.04 | 2.33 | 2.67 { 2.90 | 3.07 | 3.21 | 3.68 | 4.00 | 4.23 | 4.59 
1,400 | 1.36 | 2.15 | 2.47 | 2.84 | 3.08 | 3.26 |] 3.41 { 3.92 | 4.25 | 4.50 | 4.88 
1,600 | 1.43 | 2.27 | 2.61 | 3.00 | 3.25 | 3.44 | 3.60 | 4.13 | 4.49 | 4.75 | 5.15 
1,800 | 1.50 | 2.388 | 2.74 |] 3.14 | 8.41 | 3.61 | 3.78 | 4.341 4.70 | 4.98 | 5.40 
2,000 | 1.57 | 2.48 | 2.85 | 3.28 | 3.55 | 3.76 | 3.93 | 4.52 } 4.90 | 5.19 | 5.68 
3,000 | 1.84 | 2.92 | 3.386 | 3.85 | 4.18 | 4.43 | 4.63 | 5.32 | 5.77 | 6.11 | 6.63 
4,000 1 2.07 | 3.28 | 3.76 | 4.82 | 4.69 | 4.96 | 5.19 | 5.96 | 6.47 | 6.85 | 7.44 


* From Robert Briggs’s paper on American Practice of Warming Buildings 
by Steam (Proc. Inst. C. E., 1882, vol. Ixxi). 3 
For other resistances and pressures above atmosphere multiply by the 


respective factors below : 
Watercol.. Gin. 12in. 24in. | Press. ab. atm. Olbs. 3lbs. 30lbs. 60 lbs. 
Multiply by 0.8027 0.6988 0.6084 | Multiply by 1.023 1.015 0.973 0.948 


Registers and Cold-air Ducts for Indirect Steam Heating. 
~-The Locomotive gives the following table of openings for registers and 
cold-air ducts, which has been found to give satisfactory results. The cold- 
air boxes should have 114 sq. in. area for each square foot of radiator suface, 
and never less than 34 the sectional area of the hot-air ducts. The hot-air 
ducts should have 2 sq. in. of sectional area to each square foot of radiator 


surface on the first floor, and from 114 to 2 inches on the second floor. 








Heating Surface i ly. Fi Size Cold oe 
in Stacks, Cold-air Supply, First Floor. Revision. Bol Ae y, 
inches inches inches 

30 square feet 45 square inches = 5by 9 9 by 12 4 by 10 
A0 sais i 60 i) ope = 6by 10 10 by 14 4 by 14 
50 maiies Be % se ed = 8by 10 10 by 14 5 by 15 
60: Le s¢ 90 ve “* 6 = 69 by 10 12 by 15 6 by 15 
Ope sf 108 * “« ss 9by 12 12 by 19 6 by 18 
80%) goss M 120 WY ce. _.= 10 by 12 12 by 22 8 by 15 
90» a58 Uh. 135 ee “ = 11 by 12 14 by 24 9 by 15 
100 =“ ty 150 oe se = 12 by 12 16 by 20 12 by 12 


The sizes in the table approximate to the rules given, and it will be found 
that they will allow an easy flow of air and a full distribution throughout the 


’ room to be heated. 


540 HEATING AND VENTILATION. 


Physical Properties of Steam and Condensed Water, 
under Conditions of Ordinary Practice in Warming by 
Steam. (Briggs.) 





! { Steam-pressure j above atm...] Ibs. 0 3 10 380 60 
Al) per square neh} totals ne Ibs. | 14.7 | 17.7 | 24.7 | 44.7 | 74.7 « 
¥ Temperature of steam..........] Fahbr. | 212° | 222° | 239° | 274° | 307° 
C)Temperature of air............. Fahr, | 60° | 60 60° 16025) 9608 
D|Difference = B—C....,. .....-. Fahr. | 152° | 162° | 179° | 214° | 247° 

1 Heat given out per minute per 
E 

















100 sq. ft. of radiating-sur- units | 456 | 486 | 537 | 642 | 741 
face =Dx3 
Latent heat of steam...........- Fahr. | 965° { 958° | 946° | 921° | S98° 





F 
G| Volume of 1 lb. weight of steam] cu. ft. | 26.4 | 22.1 | 16.2 | 9.24 | 5.70 
H 
J 














Weight of 1 cubic foot of steam! Ib. |0.0380)0.0452 0.0618)0.1082/0.1752 
Volume Q of steam per minute ; 

to give out ps cu. ft.| 12.48} 11.21) 9.20 | 6.44 | 4.70 
=EXG+-F. 


ee f 





Weight of 1 cubic foot of con- 
Ercan water at tempera-| > Ibs, | 59.64/ 59.51, 59.05) 58.07] 57.03 
ture 

Volume of condensed water to 
cu. ft 


< 














L return fe boiler per minute .|0.0079|0.0085 0.0096)0.0120/0.0144 
JxXH-+K, } 
Head of § steam equivalent to 
M 12 inches meron eene feet | 1569 | 1817 | 955.5) 586.7| 325.5 
STEAM-SUPPLY MAINS. 
n/{ to assumed 2 inches water-|\ feet | 061.5) 219.5] 159.3] 89.45] 54.25 


column for producing steam 
flow 9, = M+ 6, 


| Head h of steam, equivalent 
Priternal "diameter d of tube* 


for flow @ when l=. 1 foot,| ¢ inch | 0.484) 0.481) 0.474) 0.461] 0.449 


P 
R Do. do. when 1 = 100 feet, inch | 1.217) 1.207] 1.190) 1.158] 1.128 
S|Ratios of values of d. ratio | 1.023) 1.015|/1.000| 0.973) 0.948 


—— | S| | | 





WATER-RETURN MaINs. 
Head h assumed at 14-inch 
foot 





water-column for producing 

full-bore water-flow Q, 
U a gears diameter d of tube* t inch 

for flow Q@whenl= 1 foot, 0.147) 0°151] 0.158] 0.173} 0.186 
v Do. do. whenl = 100 feet,| inch | 0.368] 0.379] 0.398 0.434] 0.468 
WiRatios of valuesof d... ...... ratio | 0.926] 0.952/1.000| 1.092] 1.176 


0.0417/0.0417)0.0417)0.0417|0.0417 





ea 
* Pp, R, U, V are each determined from the formula d = 0.sar44/ S 2 


Size of Steam Pipes for Steam Heating. (See also Flow of 
Steam in Pipes.)—Sizes of vertical main pipes. Direct radiation. (J. R. 
Willett, Heating and Ventilation, Feb., 1894.) 

Diameter of pipe, inches. 1 14 1, 2 2% 344 5 6 
Sq. ft. of radiator surface 40 70 110 (220 3606 580 810 1110 2000 3000 


A horizontal branch pipe for a given extent of radiator surface should be 
one size larger than 4 vertical pipe for the same surface. 
The Nason Mfg. Co. gives the peor ins: 
Diameter of Mae Ty ao rele 14 14 2 2% $8 8% 
Radiator surface ct ft. (maximum). 125 200 500 1000 1500 2500 
When mains and surfaces are very much above the boiler the pipes need 
not be as large as given aboves uuder very favorable circumstances and 


HEATING A GREENHOUSE BY STEAM. 541 


conditions a 4-inch pipe may supply from 2000 to 2500 sq. ft. of surface, a 6- 
inch pipe for 5000 sq. ft., and a 10-inch pipe for 15,000 to 20,000 sq. ft., if the 
distance of run from boiler is not too great. Less than 114-inch pipe should 
not be used horizontally in a main unless for a single radiator connection. 

Steam, by the Babcock & Wilcox Co., says: Where the condensed water 
is returned to the boiler, or where low pressure of steam is used, the diame- 
ter of mains leading from the boiler to the radiating-surface should be 
equal in inches to one tenth the square root of the radiating-surface, mains 
included, in square feet. Thus a 11-inch pipe will supply 100 square feet of 
surface, itself included. Return-pipes should be at least 34 inch in diame- 
ter, and never less than one half the diameter of the main—longer returns 
requiring larger pipe. A thorough drainage of steam-pipes will effectually 
prevent all cracking and pounding noises therein. 

A. R. Wolff’s Practice.—Mr, Wolff gives the following figures showing his 
nresent practice (1897) in proportioning mains and returns. They are based 
on an estimated loss of pressure of 2% for a length of 100 ft. of pipe, not in- 
cluding allowance for bends and valves\see p. 678). For longer runs divide 
the thermal units given in the table by 0.1 /length in ft. Besides giving the 
thermal units the table also indicates the amount of direct radiating surface 
which the steam-pipes can supply, on the basis of an emission of 250 thermal 
units per hour for each square foot of direct radiating surface. 

Size of Pipes for Steam Heating. 




















bo = g]2 lbs. Pressure|5 lbs. Pressure ra (Sec 2lbs. Pressure 5 lbs. Pressure 
ro f 5 Mis © aU Cine ea] - 5 iad “MM tof ae °M ‘ ° 
BsSSys » -0|we ss rojacO PS QS Sle psi /coe .|e sock i; 
A |sSyslesclsssslsscq- |° |s5e2\see so esses 
In. JInje Sem @2 |e eblp 224in. jie eG Fee? eo fel ee 
1 1 9 36 15 60 5 | 34 930 SYP Nistal 6200 
114) 1 18 72 30 120 § 6 | 34%} 1500 | 6000) 2500 | 10000 
114) 14 30 120 50 200 8 7 2250 | 9000) 3750 | 15000 
2 11% 70 280 120 480 # 8 | 4 8200 | 12800; 5400 } 21600 
214) 2 132 528 220 880 # 9 | 446) 4450 | 17800; 7500 | 30000 
3 | 214) 225 900 375 | 1500 $10 | 5 5800 | 23200) 9750 | 39000 
314| 214; 330 | 1320 550 | 2200 § 12 | 6 9250 | 37000, 15500 | 62000 
4 |3 480 | 1920 800 | 3200 § 14 | 7 13500 | 54900) 23000 | 92000 
414] 3 690 | 2760 | 1150 | 4600§ 1618 19000 | 76000' 382500 {130000 


7a liserage tae POI A Ne CON gl ae Nag a ea ML Ga ag Seah Ss ead as cal Ee aap ae 
Heating a Greenhouse by Steam.—Wm. J. Baldwin answers a 
question in the American Muchinist as below: With five pounds steam- 
pressure, how many square feet or inches of heating-surface is necessary to 
heat 100 square feet of glass on the roof, ends, and sides of a greenhouse 
in order to maintain a night heat of 55° to 65°, while the thermometer out- 
side ranges at from 15° to 20° below zero; also, what boiler-surface is neces- 
sary ? Which is the best for the purpose to use—2” pipe or 114” pipe ? 
Ans.—Reliable authorities agree that 1.25 to 1.50 cubic feet of air in an 
enclosed space will be cooled per minute per sq. ft. of glass as many degrees 
as the internal temperature of the house exceeds that of the air outside. 
Between + 65? and — 20° there will be a difference of 85°, or, say, one cubic 
foot of air cooled 127.5° F. for each sq ft. of glass for the most extreme 
condition mentioned. Multiply this by the number of square feet of 
glass and by 60, and we have the number of cubic feet of air cooled 1° per 
hour within the building or house. Divide the number thus found by 48, and 
it gives the units of heat required, approximately. Divide again by 953, 
and it will give the number of pounds of steam that must be condensed from 
a pressure and temperature of five pounds above atmosphere to water at 
the same temperature in an hour to maintain the heat. Each square foot 
of surface of pipe will condense from 4% to nearly 1% lb. of steam per hour, 
according as the coils are exposed or well or poorly arranged, for which 
an average of 44 1b. maybetaken. According to this. it will require 3 sq. ft. 
of pipe surface per lb. of steam to be condensed. Proportion the heating- 
surface of the boiler to have about one fifth the actual radiating-surface, if 
you wish to keep steam over night, and proportion the grate to burn not 
more than six pounds of coal per sq. ft. of grate per hour. With very slow 
combustion, such as takes place in base-burning boilers. the grate might be’ 
proportioned for four to five pounds of coal per hour. It is cheaper to make 
coils of 114’ pipe than of 2/’, and there is nothing to be gained by using 2’ 
pipe unless the coiis are very long. The pipes in a greenhouse should be 


542, HEATING AND VENTILATION. 


\ 


under or in front of the benches, with every chance for a good circulation 
of air. ‘‘ Header” coils are better than ‘‘return-bend”’ coils for this purpose. 

Mr. Baldwin’s rule may be given the following form: Let H = heat-units 
transferred per hour, 7 = temperature inside the greenhouse, ¢ = tempera- 
ture outside, S = sq. ft. of glass surface; then H = 1.58(T — t) x 60+ 48 
= 1.875S(7 — t). Mr. Wolff’s coefficient K for single skylights would give 
HAH =1.118S(T — t). 

Heating a Greenhouse by Hot Water.—W. M. Mackay, of the 
Richardson & Boynton Co., in a lecture before the Master Plumbers’ Asso- 
ciation, N. Y., 1889, says: I find that while greenhouses were formerly 
heated by 4-inch and 38-inch cast-iron pipe, on account of the large body of 
water which they contained, and thesupposition that they gave better satis- 
faction and a more even temperature, florists of long experience who 
have tried 4-inch and 3-inch cast-iron pipe, and also 2-inch wrought-iron 
pipe for a number of years in heating their greenhouses by hot water, 
and who have also tried steam -heat, tell me that they get better satisfaction, 
greater economy, and are able to maintain a more even temperature with 2- 
inch wrought-iron pipe and hot water than by any other system they have 
used. They attribute this result principally to the fact that this size pipe 
contains less water and on this account the heat can be raised and lowered 
quicker than by any other arrangement of pipes, and a more uniform tem- 
perature maintained than by steam or any other system, 


HOT-WATER HEATING. 
(Nason Mfg. Co.) 


There are two distinct forms or modifications of hot-water apparatus, de- 
pending upon the temperature of the water. 

In the first or open-tank system the water is never above 212° tempera- 
ture, and rarely above 200°. This method always gives satisfaction where 
the surface is sufficiently liberal, but in making it so its cost is considerably 
greater than that for a steam-heating apparatus. 

In the second method, sometimes called (erroneously) high-pressure hot- 
water heating, or the closed-system apparatus, the tank is closed. If it is 
provided with a safety-valve set at 10 lbs. itis practically as safe as the open- 
tank system. 

Law of Velocity of Flow.—The motive power of the circulation 
in a hot-water apparatus is the difference between the specific gravities of 
the water in the ascending and the descending pipes. This effective pressure 
is very smail, and is equal to about one grain for each foot in height for each 
degree difference between the pipes; thus, with a height of 12’ in ‘‘up”’ pipe, 
and a difference between the temperatures of the up and down pipes of 8°, 
the difference in their specific gravities is equal to 8.16 grains on each square 
inch of the section of return-pipe, and the velocity of the circulation is pro-- 
portioned to these differences in temperature and height. 

To Calculate Velocity of Flow.—Thus, with a height of ascend- 
ing pipe equal to 10’ and a differeuce in temperatures of the flow and return 
pipes of 8°, the difference in their specific gravities will equal 81.6 grains, or 
-+- 7000 = .01166 lbs., or X 2.31 (feet of water in one pound) = .0269 ft., and by 


the law of falling bodies the velocity will be equal to 8 4.0269 = 1.312 ft. per 
second, or X 60 = 78.7 ft. per minute. In this calculation the effect of frice- 
tion is entirely omitted. Considerable deduction must be made on this 
account. Even in apparatus where length of pipe is not great, and with 
pipes of larger areas and with few bends or angles, a large deduction for 
friction must be made from the theoretical velocity, while in large and 
complex apparatus with small head, the velocity is so much reduced by 
friction that sometimes as much as from 50% to 90% must be deducted to ob- 
tain the true rate of circulation. 

Main flow-pipes from the heater, from which branches may be taken, are 
to be preferred to the practice of taking off nearly as many pipes from the 
heater as there are radiators to supply. 

It is not necessary that the main flow and return pipes should equal in 
capacity that of all their branches. The hottest water will seek the highest 
level, while gravity will cause an even distribution of the heated water if the 
surface is properly proportioned. ; 

It is good practice to reduce the size of the vertical mains as they ascend, 
say at the rate of one size for each floor. 

As with steam, so with hot water, the pipes must be unconfined to allow 





HOT-WATER HEATING, 


543 


for expansion of the pipes consequent on having their temperatures ine 


creased. 


An expansion tank is requ‘red to keep the apparatus filled with water, 
which latter expands 1/24 of its bulk on being heated from 40° to 212°, and 
the cistern must have capacity to hold certainly this increased bulk. It is 
recommended that the supply cistern be placed on level with or above the 
highest pipes of the apparatus, in order to receive the air which collects in 
the mains and radiators, and capable of holding at least 1/20 of the water 


in the entire apparatus, 


Approximate Proportions of Radiating=-surfaces to 
Cubic Capacities of Space to be Heated. 








In Dwellings, 
School-rooms, 
Offices, etc. 


One Square Foot of Ra- 
diating-surface will 
heat with— 


High temperature di- 
rect hot-water radi- 
ALIONL: Lee mamas we eA 

Low temperature di- 
rect hot-water radi- 
ation 

High temperature in= |) 
direct hot-water ra- 30:00 60st 
diation ( 

Low temperature in- 
direct hot-water ra- 
CLL ACIOU baer 


sé 


30 to 50 ‘* 


wees eer ere se sees 


20 to 40 ‘* ** 


50 to 70 cu. ft. 


In Halls, Stores, 
Lofts, Facto- 
ries, etc. 


65 to 90 cu. ft. 


66 


35 to 65 ‘* 


35 to 75 ** 


6e 


25 to 50 “ 





In Churches, 
Large Audito- 
riums, etc. 


130 to 180 cu. ft. 
70 to 180 ‘ 
70 to 150 § 


50 to 100 ** 


Diameter of Main and Branch Pipes and square feet of coil 
surface they will supply, in a low-pressure hot-water apparatus (212°) for 
direct or indirect radiation, when coils are at different altitudes for direct 
radiation or in the lower story for indirect radiation: 





. 1S S 
Ba | 32 
ASS Direct Radiation. Height of Coil above Bottom of Boiler, 
oo {ts in feet. 
21 4S 
Ey eae 
a 0 10 20 30 40 50 60 70 80 90 100 
sq. ft.|sq. ft.|sq. ft.'sq. ft.'sq ft./sq. ft.|sq. ft./sq. ft.|sq. ft./sq. ft./sq. ft. 
34 ‘ 49 50 as 52 53 55 57 59 61 63 65 68 
1 89 92 95 98 101 103 108 112 116 121 
14 140 144 149 153 158 161 169 175 182 189 
1% 202 209 214 222 228 | 235 243 202 261 271 
2 359 370 880 393 405 413 433 449 465 483 
26 561 ne | 595 613 | 633 { 643] 678) 701 02 755 
3 807 | 8385 | 856 | 888 912} 941 974 | 1009 | 1046 1086 
344 1099 | 1132 | 1166 | 1202 | 1241 | 1283 | 1827 | 1374 | 1425 1480 
4 1486 | 1478 | 1520 | 1571 | 1621 | 1654 | 1783 | 1795 | 1861 1933 
44g 1817 | 1871 | 1927 | 1988 | 2052 | 2120 | 2193 | 227 2356 | 2445 
5 2244 | 2309 | 2376 | 2454 | 2531 | 2574 | 2713 | 2805 | 2907 3019 
6 8228 | 3341 | 3424 | 3552 | 3648 | 3763 | 3897 | 4036 | 4184 | 4344 
q 4396 | 4528 | 4664 | 4808 | 4964 | 5132 | 5308 | 5496 | 5700 | 5920 
8 5744 | 5912 | 6080 | 6284 | 6484 | 6616 | 6932 | 7180 | 7444 7735 
9 7268 | 7484 | 7708 | 7952 | 8208 | 8482 | 877 9088 | 9424 9780 
10 8976 | 9236 | 9516 | 9816 10124 |10296 |10852 }11220 111628 | 12076 
11 10860 |11180 }11519 11879 |12262 |12666 |13108 |13576 |14078 | 14620 
12 12912 |13364 |13696 14208 {14592 |15052 |15588 |16144 |16736 | 17376 
13 15169 |15615 116090 |16591 {17126 |17697 |18307 |18961 |19683 | 20420 
14 17584 118109 |18656 19232 {19856 /20528 |21282 |21984 [22800 | 23680 
15 20195 |20789 121419 22089 }22801 23561 |243873 |25244 }26179 | 27168 
16 22978 |23643 |24320 25136 25936 126464 |27728 [28720 129776 | 30928 











544 HEATING AND VENTILATION. 


; The best forms of hot-water-heating boilers are proportioned about as 
ollows: , 


1 sq. ft. of grate-surface to about 40 sq. ft. of boiler-surface,. 
LISS boiler- ‘°° a Bese Fe radiating-surface. 
1 66 66 grate- ce 66 900 ee be 66 6 


Rules for Hot-water Heating.—J. L. Saunders (Heating and 
Ventilation, Dec. 15, 1894) gives the following: Allow 1 sq. ft. of radiating 
surface for every 3 ft. of glass surface, and 1 sq. ft. for every 30 sq. ft. of 
wall surface, also 1 sq. ft. for the following numbers of cubic feet of space 
in the several cases mentioned. 


In dwelling-houses: Libraries and dining-rooms, first floor.. 35 to 40 cu ft. 


Reception halls, first floor..............-. 40 to 50 ‘ 
Stair halls, SOMES OWES etc teat Ate ates 40 to baa st 
Chambersiaboveyste se tiie. thierceee 50 to=65,5" °° 

Libraries, sewing-rooms, nurseries, etc., 

ADOVE ATSULOOL: siete cic Cee Ales oie /cieke te 45) COM Meee 
Bath-rooms...... Soins Nocuate syice 2 ans stemeacte 80 to 40 ‘* “* 
Public-school rooms) ..1..0) 23 dcveieas'se 00's 5000000 0eiesee si) sani O00 LOBOO MAT 
MICOS iis Laneh es Fe te ee ars Bests aenks aaa at wile biga teenies we aaet OlCOM@Cgmen ¢ 
Factories and stores.............6. Ratiie Solio mite teeta settee os 65 to, Satie °° 
Assembly halls and churches..................e006 Pe ee dade 90 to 150 ‘“* “ 


To find the necessary amount of indirect radiation required to heaia room: 
Find the required amount of direct radiation according to the foregoing 
method and add 50%, This if wrought-iron pipe coil surface is used; if cast- 
iron pin indirect-stack surface is used it is advisable to add from 70% to 802. 

Sizes of hot-air flues, colu-air ducts, and registers for indirect work.— 
Hot-air flues, first floor: Make the net internal area of the flue equal to 
34 sq. in. to every square foot of radiating surface in the indirect stack. Hot- 
air flues, second floor: Make the net internal area of the flue equal to 9 sq. in. 
to every square foot of radiating surface in the indirect stack. 

Cold-air ducts, first floor: Make the net internal area of the duct equal 
to 54 sq. in. to every square foot of radiating surface in the indirect stack. 
Cold air ducts, second floor: Make the net internal area of the duct equal 
to 14 sq. in. to every square foot of radiating surface in the indirect stack. 

Hot-air registers should have their net area equal in full to the area of the 
hot-air flues. Multiply the length by the width of the register in inches ; 34. 
of the product is the net area of register. 

Arrangement of Mains for Hot-water Heating. (W. M. 
Mackay, Lecture before Master Plumbers’ Assoc., N. Y., 1889 )—There are 
two different systems of mains in general use, either of which, if properly 
placed, will give good satisfaction. One is the taking of a single large-flow 
main from the heater to supply all the radiators on the several floors, with a 
corresponding return main of the same size. The other is the taking of a 
number of 2-inch wrought-iron mains from the heater, with the same num- 
ber of return mains of the same size, branching off to the severai radiators 
or coils with 144-inch or 1-inch pipe, according to the size of the radiator or 
coil. A 2-inch main will supply three 114-inch or four 1-inch branches. and 
these branches should be taken from the top of the horizontal main with a 
nipple and elbow, except in special cases where it is found necessary to retard 
the flow of water to the near radiator, for the purpose of assisting the circu- 
lation in the far radiator ; in this case the branch is taken from the side of 
the herizontal main. The flow and return mains are usually run side by side, 
suspended from the basement ceiling, and should have a gradual ascent from 
the heater to the radiators of at least 1 inch in 10 feet. It is customary, and 
an advantage where 2-inch mains are used, to reduce the size of the main at 
every point where a branch is taken off. 

The single or large main system is best adapted for large buildings ; but 
there is a limit as to size of main which it is not wise to go beyond—gener- 
ally 6-inch, except in special cases. 

The proper area of cold-air pipe necessary for 100 square feet of indirect 
radiation in hot-water heating is 75 square inches, while the hot-air pipe 
should have at least 100 square inches of area. There should be a damper in 
the cold-air pipe for the purpose of controlling the amount of air admitted ta 
the radiator, depending on the severity of the weather, 


BLOWER SYSTEM OF HEATING AND VENTILATING. 546 


THE BLOWER SYSTEM OF HEATING AND 
VENTILATING. 


The system provides for the use of a fan or blower which takes its supply 

of fresh air from the outside of the buiding to be heated, forces it over 
steam coils, located either centrally or divided up into a number of indepen- 
dent groups, and then into the several ducts or flues leading to the various 
»70oms. The movement of the warmed air is positive, and the delivery of 
the air to the various points of supply is certain and entirely independent 
of atmospheric conditions. For engines, fans, and steam-coils used with the 
blower system, see page 519, 

Experiments with Radiators of 60 sq. ft. of Surface. 
(Mech. News, Dec., 1893.)—After having determined the volume and tem- 
perature of the warm air passing through the flues and radiators from 
natural causes, a fan was applied to each flue, forcing in air, and new sets of 
measurements were made. The results showed that more than two and one- 
third times as much air was warmed with the fans in use, and the falling off 
in the temperature of this greatly increased air-volume was only about 12.6%. 
The condensation of steam in the radiators with the forced-air circulation 
also was only 6624% greater than with natural-air draught. One of the 
several sets of test figures obtained is as follows ; 

. Natural Foresd- 
Draught air 
in Flue. Circulation, 


Cubic feet of air per minute..... Lies § ihe de Ma weisten Nese cbyaay | SPRY 
Condensation of steam per minute in ounces......... 11.7 19.6 
Steam pressure in radiator, pounds.............eee0 
Temperature of air after leaving radiator.... ....... 143° 124° 

“ ‘s ** before passing through radiator. 61° 61° 
Amount of radiating surface in square feet.......... 60 60 
Sizevof flue in both-casesicas 5: son. - -s-cclewiociers «ite eseeee 12 x 18 inches. 


There was probably an error in the determination of the volume of air in 
these tests, as appears from the following calculation. (W.K.) Assume 
that J lb. of steam in condensing from 9 lbs. pressure and cooling to the tem- 
perature at which the water may have been discharged from the radiator 
gave up 1000 heat-units, or 62.5 h. u. per ounce; that the air weighed .076 Ib. 
per cubic foot, and that its specific heat is .238. We have 


Natural Forced 
Draught. Draught. 
Heat given up by steam, ounces x 62.5.............. = {31 1225 HAW. 
Heat received by air, cu. ft. x .076 x diff. of tem. x .238 = 673 1399 s* 


Or, in the case of forced draught the air received 14% more heat than the 
steam gave out, which isimpossible. Taking the heat given up by the steam 
as the correct measure of the work done by the radiator, the temperature 
of the steam at 237°, and the average temperature of the airin the case of 
natural draught at 102° and in the other case at 93°, we have for the tem- 
perature difference in the two cases 135° and 144° respectively; dividing 
these into the heat-units we find that each square foot of radiating surface 
transmitted 5.4 heat-units per hour per degree of difference of temperature, 
in the case of natural draught, and 8.5 heat-units in the case of forced 
draught (= 8.5 & 144° = 1224 heat-units per square foot of surface). 

In the Women’s: Homceopathic Hospital in Philadelphia, 2000 feet of 
one-inch pipe heats 250,000 cubic feet of space, ventilating as well; this 
equals one square foot of pipe surface for about 350 cubic feet of space, or 
less than 3 square feet for 1000 cubic feet. The fan is located in a sepa- 
rate building about 100 feet from the hospital, and the air, after being heated 
to about 135°, is conveyed through an underground brick duct with a loss of 
only five or six degrees in cold weather. (H.I. Snell, Trans. A. S. M. E vix. 106. 

Heating a Building to 70° F. Inside when the Outside 
Wemperature is Zero.—lIt is customary in some contracts for heating 
to guarantee that the apparatus will heat the interior of the building to 70° 
in zero weather. As it may not be practivable to obtain zero weather for 
the purpose of a test, it may be difficult to prove the performance of the 
guarantee, E.E. Macgovern, in Engineering Record, Web. 3, 1894, gives a 
calculation tending to show that a test may be made in weather of a higher 
temperature than zero, if the heat of the interior is raised above 70°. The 
higher the temperature of the rooms the lower is the efficiency of the radi- 
pting-surface, since the efficiency depends upon the difference between the 


546 HEATING AND VENTILATION. | 


temperature inside of the radiator and the temperature of theroom. He 
concludes that a heating apparatus sufficient to heat a given building to 70* 
in zero weather with a given pressure of steam will be found to heat the 
same building, steam-pressure constant, to 110° at 60°, 95° at 50°, 82° at 40°, 
and 74° at 32°, outside temperature. The accuracy of these figures, however 
has not been tested by experiment. 

The following solution of the question is proposed by the author. It gives 
results quite different from those of Mr. Maegovern, but, like them, lacks ex- 
perimental confirmation. 


Let S = sq. ft. of surface of the steam or hot-water radiator; 
W = sq. ft. of surface of exposed walls, windows, etc.; 
Ts = temp. of the steam or hot water, 7, = temp. of inside of building 
* or room, 7’) = temp. of outside of building or room; 
a = heat-units transmitted per sq. ft. of surface of radiator per hour 
/ per degree of difference of temperature; 
- b= average heat-units transmitted per sq. ft. of walls per hour, per 
degree of difference of temperature, including allowance for 
ventilation. 


It is assumed that within the range of temperatures considered Newton’s 
law of cooling holds good, viz., that it is proportional to the difference of 
temperature between the two sides of the radiating-surface. 


Then aS(Ts — T;) = bW(T,— Ty). Let ia = Cs then 
Ts +. OT, Ts = T; 
Ts — T, = CT, — T); Ps ee 
If T, = 70, and 7) = 0,C= aa, 
Let Ts = 140°, 213.52, 308°; 
Then C= 1, 2.05, 3.4, 
From these we derive the following: 
Temperature of Outside Temperatures, 75. 
Steam or stot -— 20° — 10° 0° 10° 20° 30° 40° 
Water, 7's. Inside Temperatures, 7. 
140° 60 65 70 75 80 85 90 
213.5 56.6 63.3 70 76.7 83.4 90.2 96.9 
308 54.5 62.3 70 EMA 85.5 93.2 100.9 


Heating by Electricity.—If the electric currents are generated by 
a dynamo driven by a steam-engine, electric heating will prove very expen- 
sive, since the steam-engine wastes in the exhaust-steam and by radiation 
about 90% of the heat-units supplied toit. In direct steam-heating, with a 
good boiler and properly covered supply-pipes, we can utilize about 60% of 
the total heat value of the fuel. One pound of coal, with a heating value of 
13,000 heat-units, would supply to the radiators about 13,000 x .60 = 7800 
heat-units. In electric heating, suppose we have a first-class condensing- 
engine developing 1 H.P. for every 2 lbs. of coal burned per hour. 
This would be equivalent to 1,980,000 ft.-lbs. + 778 = 2545 heat-units, or 1272 
heat-units for 1lb. of coal. The friction of the engine and of the dynamo and 
the loss by electric leakage, and by heat radiation from the conducting 
wires, might reduce the heat-units delivered as electric current to the elec- 
tric radiator, and these converted into heat to 50% of this, or only 636 heat- 
units, or less than one twelfth of that delivered to the steam-radiators in 
direct steam-heating, Electric heating, therefore, will prove uneconomical 
unless the electric current is derived from water or wind power, which would 
otherwise be wasted. (See Electrical Engineering.) 


WRIGHT OF WATER. BAN 


WATER. 


Expansion of Water.—The following table gives the relative vol- 
umes of water at different temperatures, compared with its volume at 4° C. 
according to Kopp, as corrected by Porter. 








Cent. | Fahr, |Volume.} Cent. | Fahr. Volume. Cent. | Fahr. | Volume. 








ee —. 


4° 89.1°| 1.00000 35° 95° | 1.00586 70° 158° {| 1.02241 
5 41 1.00001 40 104 | 1.00767 75 167 1: 

10 50 1.00025 45 113 | 1.00967 80 176 1,02872 
15 59 1.00083 50 122 | 1.01186 85 185 1.08213 
20 68 1.00171 55 1381 | 1.01423 90 194 1.03857 
25 C7 1.00286 60 140 | 1.01678 95 203 4.03943 
30 86 1.00425 65 149 { 1.01951 100 212 1.04832 














Weight of 1 cu. ft. at 39.19 F. = 62.4245 Ib. + 1.04332 = 59.833, weight of 1 cu. 
ft. ati 212° F. 


Weight of Water at Different Temperatures.—The weight 
of water at maximum density, 39.1°, is generaliy taken at the figure given 
by Rankine, 62.425 lbs. per cubie foot. Some authorities give as low as 
62.879. The figure 62.5 commonly given is approximate. The highest 
authoritative figure is 62.425. At 62° F, the figures range from 62.291 to 62.360. 
The figure 62.355 is generally accepted as the most accurate. 

At 32° F. figures given by different writers range from 62.379 to 62.418. 
Clans gives the latter figure, and Hamilton Smith, Jr., (from Rosetti,) gives 

416, 

Weight of Water at Temperatures above 212° K.—Porter 
(Richards’ ‘‘Steam-engine Indicator,” p. 52) says that nothing is known 
about the expansion of water above 212°. Applying formule derived from 
experiments made at temperatures below 212°, however, the weight and 
volume above 212° may be calculated, but in the absence of experimental 
data we are not certain that the formule hold good at higher temperatures. 

Thurston, in his ‘*‘ Engine and Boiler Trials,” gives a table from which we 
take the following (neglecting the third decimal place given by him) : 





WM v2} mn wW 

. L:3 ‘ rE ‘ 23 He a3 e 23 
3 ef 2 rs} ° =O 3 . a) H joe P ° me) 
~ Gal oss bf | ose & fal oss be Eat uss x &| #3 
Deed) notin as Diary el Wot 4S Oe A Os TOs} i Pas Dy .| Sys 
RE ol ToS PRE | So f SE Ml eS PSR Moe Pee YES 
BSc] S29 550 | Sag R55| cad JESS| SES JESS] S28 
a - a = gS Ee a = a 











PP Pe Sh 
=D Ors Co oo 
Sain a=) 

Or 

(i) 

f=) 

“N 

or 

at 

o 

PS 

ie) 

~ 





480} 50.448 550] 47.52 





Box on Heat gives the following : 
Temperature F........ 212° 250° 300° 350° 400° 450° 500° 600° 
Lbs. per cubic foot.... 59.82 58.85 57.42 55,94 54.34 52.70 51.02 47.64 


At 212° figures given by different writers (see Trans, A. S. M. E., xiii. 409) 
range from 59.56 to 59.845, averaging about 59.77. os 2B 


548 


WATER, 


Weight of Water per Cubic Foot, from 382° to 212° F., and heat- 


units per pound, reckoned above 382° F.: 


The following table, made by in- 


terpolating the table given by Clark as calculated from Rankine’s formula, 
with corrections for apparent errors, was published by the author in 1884, 


Trans. A. S. M. E., vi. 90. 


(For heat units above 212° see Steam Tables.) 




















no ° Ne 
ms |} S°qs es 
we BG Oe Fissd 
eas] ESS le os 
MES] 2 Fes Fws 8 
Dae| S$ FREcloaL 
®o 
e otic FE 
62.42) 0. %8 62.2 
62.42) 1. 63 62.24 
G2T4ceos 80 62.23 
62.42) 3. 81 62.2 
62.42] 4. 82 62.21 
62.42) 5. 83 62.20 
62.42] 6. 84 62.19 
6242 ate 85 62.18 
62.42] 8. 86 62.17 
62.42) 9. 87 62.16 
62.42) 10. 88 62.15 
62.42] 11. 89 62.14 
62.42] 12, 90 62.13 
62.42) 13. 91 62. 
62.42) 14, 92 Dalal 
62.42] 15. 93 62.10 
62.41] 16. 94 62.09 
62.41) 17. 95 62.08 
62.41] 18. 96 62.07 
62.41} 19. 97 62.0 
62.40) 20. 98 62.0 
62.40] 21.01 99 62.03 
62.40] 22.019 100 62.02 
62.39) 238.018 101 62.01 
62.39} 24.018 102 62.00 
62.39] 25.018 103 61.99 
62.38] 26.019 104 61.97 
62.38] 27.018 105 61.96 
62.37] 28.019 106 61.9. 
62.387] 29.018 797 61.93 
62.36) 30.019 108 61.92 
62.36) 31.019 109 61.91 
62.55} 32.019 110 61.89 
62.34) 83.019 111 61.88 
62.34| 84.029 112 61.86 
2.38] 85.028 113 61.85 
62.33] 86.02% 114 61.83 
2.32] 37.028 115 61.82 
2.31] 38.028 116 61.80 
62.31) 89.028 117 61.78 
62.30} 40.02§ 118 61.77 
62.29) 41.028 119 61.75 
62.28) 42.038 12 61.74 
62.28} 43.038 121 61.72 
62.27) 44.039 122 61.7 
62.26! 45.038 




















hee : 

wl 2 fSe 0885] 8 

Cl + =m Wee oc} 

() @ SS Dies to 3 

ae o OHPd Cas) Oo 

ci - es) 
61.68) 91.169 168 | 60.81|186.44 
61.67] 92.178 169 | 60.79/137.45 
61.65) 93.178 170 | 60.77/138.45 
61.63) 94.179 171.| 60.75)139.46 
61.61) 95.188 172 | 60.78)140.47 
61.60) 96.188 173 | 60.70)141.48 
61.58) 97.198 174 | 60.68/142.49 
1.56) 98.199 175 | 60.66)143.50 
.54] 99.208 176 | 60.64/144.51 
.52|100.208 177 | 60.62/145.52 
.51/101.219 178 | 60.59)146.52 
.49}102.21 179 | 60.57)147.53 
.47)103.228 180 | 60.55)148.54 
.45/104.228 181 | 60.53/149.55 
.43/105.23 182 | 60.50)150.56 
.41}106.239 183 | 60.48)151.57 
.89|107.24 184 | 60.46/152.58 
.87}108.25f 185 | 60.44/153.59 
.86/109.258 186 | 60.41)154.60 
.384/110.269 187 | 60.39/155.61 
82}111.268 188 | 60.87)156.62 
.80)/112.27 189 | 60.34/157.62 
.28)1138.288 190 | 60.32)158.64 
.26/114.289 191 | 60.29/159.65 
.24)115.298 192.| 60.27)160.67 
-22)116.298 193 | 60.25)161.68 
.20}117.8 194 | 60.22/162.69 
.18}118.31f 195 | 60.20/163.70 
16}119.31§ 196 | 60.17/164.71 
14)120.382§ 197 | 60.15|165.72 
-12/121.33§ 198 | 60.12/166.73 
.10)122.3388 199 | 60.10,167.74 
.08/123.384§ 200 | 60.07/168.75 
.06/124.359 201 | 60.05)169.77 
.04/125.3858 202 | 60 02)/170.78 

.02}126.36— 203 | 60.00)171.% 

.00)127.3879 204 | 59.97/172.80 
60.98}128.378 205 | 59.951173.81 
60.96}129.389 206 | 59.92)174.83 
60.94)130.398 207 | 59.89)175.84 
60.92}131.40g 208 | 59.87)176.85 
60.90\132.419 209 | 69.84)177.86 
60.87)133.419 210 | 59.82!178.87 
60.85/1384.4z9 211 | 59.79|179.89 
60.838/135.43— 212 | 59.76)180.90 








Comparison of Heads of Water in Feet with Pressures in 
Various Units, 


One foot of water at 39°.1 Fahr. 


Ld 66 66 
td os 6s 
te be cs 


fs 


é 773.84 


62.425 lbs. on the square foot; 
0.4335 lbs, on the square inch 3 
0.0295 atmosphere; 

0.8826 inch of mercury at 32°; 


feet of air at 82° and 
atmospheric pressure; 


One Ib. on the square foot 
One 1b. on the square inch wiaiaent se 
One atmosphere of 29.922 inches of mercury.... 
One inch of mercury at 32°.1 
One foot of air at 32 deg., and one atmosphere.. 
One foot of average sea-WAter.... see cesee. coos 
at 62° F. se@ee Sees eseeeeeesceaeses 
Se Gata sawed 
One inch of water at 62°F... 
One pound of water on the square inch at 62° F. 
One ounce of water on the square inch at 62° F. 


One foot of water 
ee ee ee oe 


PRESSURE OF WATER. 


» at 39°.1 Pann? . 43 acs 


a eo ee) 


. = 0.5774 ounce 


549 


0.01602 foot of water; 
feet of water; 


oe 
“a 


oe 
ace 


66 
6 
o6 


1.026 foot of pure water; 

62.355 lbs. per sq. foot; 
U,43602 ib. per sq. inch; 
0.036085 Ib. per sq. inch; 
2.8094 feet of water. 
1.732 inches of water. 


Pressure in Pounds per Square Inch for Different Heads 


of Water. 


-At 62° F. 1 foot head = 0,483 lb. per square inch, .4383 x 144 = 62.852 Ibs. 
per cubic foot. 


Head, feet. 





1 





0.433) 0.866) 1.299 

4.330] 4.763) 5.196) 5.629 
8.660) 9.093} 9.526) 9.959 
12.990)13.423)13.856/14.289 
17.820/17.753/18.186)18.619 
21 .650)22.083)22.516/22.949 
25.980} 26 413/26. 846/27 .279 
30.310)30.743) 31 .176)31 .609 
34.640}35 .073/35.506/35.939 


2 





3 





6.062] 6.495 
10 392}10.825 
14,722/15.155 
19.052)19.485 
23. 382/23 .815 
27.712)28.145 
32.042|32.475 
36 .372|36.805 


38.970}39 403/39 .836/40.269/40.702/41.135 








6.928 
11.258 
15.588 
19.918 
24.248 
28.578 
32.908 
37.238 





41.568 


16.021 
20.351 


24.681/25.114/25.547 
29.011/29.444/29. 877 
33.341/33.774/34.207 
37.671/38. 104/38 .537 


——— | —__ | ee | Lf [| 


1.732] 2.165} 2.598] 3.031] 3.464) 3.897 
7.3861] 7.794) 8.227 
11.691)12.124)12.557 


16.454}16.887 
20 .784)21 217 


42.001}42. 436/42 .867 


Head in Feet of Water, Corresponding to Pressures in 
Pounds per Square Inch, 


1 Ib, per square inch = 2.30947 feet head, 1 atmosphere = 14.7 lbs. per sq. 
inch = 33.94 ft. head. 


Pressure. 


a 





0 


1 


2.309) 4.619 
23 .0947/25.404'27.714 
46 .1894'48.499 50.808 
69 .2841/71.594, 73.903 
92.3788 94.688 96.998 
115.4735 117.78) 120.09 


138.5682, 140.88 
161.6629 163.97 
184.7576 187.07 


hei ig May 





143.19 
166.28 
189.38 


30.023 32.3383 
53.118 55.427 
76.213 78.522 
99.307 101.62 
122.40 124.71 
145.50 147.81 
168.59 170.90 
191.69 194.00 








34.642 
57.737 
80.831 
103.98 
127.02 
150 12 
173 21 
196.31 


seep oiar yokes pee 





36. 952 
60.046 
83.141 
106.24 
129.33 
152.42 
175.52 
198.61 





16.166 
39.261 
62.356 
85.450 
108.55 
131.64 
154.73 
177.83 
200.92 


221.71 rat 02 





nO | | | | | LU 


6.928 9.238/11.547)13.857 


18.476 
41.57 

64.665 
87.760 
110.85 
1383.95 
157.04 
1180.14/182.45 
203 .23)205.54 
pias ee 


— 


20.785 
43.880 
66.975 
90.069 
113.16 
136.26 
159.35 








Pressure of Water due to its Weight.—The pressure of still 
water in pounds per square inch against the sides of any pipe, channel, or 
vessel of any sliape whatever is due solely to the “‘head,”’ or heivht of the 
level surface of the water above the point at which the pressure is con- 
sidered, and is equal to .43302 lb. per square inch for every foot of head, 
or 62.355 lbs. per square foot for every foot of head (at 62° F.). 

The pressure per square inch is equal in all directions, downwards, up- 
wards, or sideways, and is independent of the shape or size of the containing 


vessel, 


The pressure against a vertical surface, as a retaining-wall, at anv point 
is in direct ratio to the head above that point, increasing from 0 at the level 


surface to a maximum at the bottom. 


The total pressure against a vertical 


strip of a unit’s breadth increases as the area of a right-angled triangle 


550 | WATER, 


whose perpendicular represents the height of the strip and whose base 
represents the pressure on a unit of surface at the bottom; that is, it in- 
creases as the square of the depth. The sum of all the horizontal pressures 
is represented by the area of the triangle, and the resultant of this sum is 
equal to this sum exerted at a point one third of the height from the bottom. 
(The centre of gravity of the area of a triangle is one third of its height.) 

The horizontal pressure is the same if the surface is inclined instead of 
vertical. 

(For an elaboration of these principles see Trautwine’s Pocket-Book, or 
the chapter on Hydrostatics in any work on Physics. For dams, retaining- 
walls, etc., see Trautwine.) 

The amount of pressure on the interior walls of a pipe has no appreciable 
effect upon the amount of flow. 

Buoyancy.—When a body is immersed in a liquid, whether it float or 
sink, it is buoyed up by a force equal] to the weight of the bulk of the liquid 
displaced by the body. The weight of a floating body is equal to the weight 
of the bulk of the liquid that it displaces. The upward pressure or buoy- 
ancy of the liquid may be regarded as exerted at the centre of gravity of 
the displaced water, which is called the centre of pressure or of buoyancy. 
A vertical line drawn through it is called the axis of buoyancy or of flota- 
tion. Ina floating body at rest a line joining the centre of gravity and the 
centre of buoyancy is vertical, and is called the axis of equilibrium. When 
an external force causes the axis of equilibrium to lean, if a vertical line be 
drawn upward from the centre of buoyancy to this axis, the point where it 
cuts the axis is called the metacentre. If the metacentre is above the centre 
of gravity the distance between them is called the metacentric height, and 
the body is then said to be in stable equilibrium, tending to return to its 
original position when the external force is removed. 

Boiling-point.—Water boils at 212° F. (100° C.) at mean atmospheric 
pressure at the sea-level, 14.696 lbs. per square inch. The temperature at 
which water boils at any given pressure is the same as the temperature of 
saturated steam at the same pressure. For boiling-point of water at other 
pressure than 14,696 lbs. per square inch, see table of the Properties of 
Saturated Steam. 

The Boiling-point of Water may be Raised.—When water 
is entirely freed of air, which may be accomplished by freezing or boiling, 
the cohesion of its atoms is greatly increased, so that its temperature may 
be raised over 50° above the ordinary bcoiling-point before ebullition takeg 
place. It was found by Faraday that when such air-freed water did boil 
the rupture of the liquid was like an explosion. When water is surrounded 
by a film of oil, its boiling temperature may be raised considerably above 
its normal standard. This has been applied as a theoretical explanation in 
the instance of boiler-explosions. 

The freezing-point also may be lowered, if the water is perfectly quiet, to 
— 10° C., or 18° Fahrenheit below the normal freezing-point. (Hamilton ' 
Smith, Jr., on Hydraulics, p. 18.) The density of water at 14° F.is .99814, itg 
density at 39°. 1 being 1, and at 32°, .99987. 

-Freezing=-point.—Water freezes at 32° F. at the ordinary atmospheric 
pressure, and ice melts at thesame temperature. In the melting of 1 pound 
of ice into water at 32° F. about 142 heat-units are absorbed, or become 
latent: and in freezing 1 lb. of water into ice a like quantity of heat is given 
out to the surrounding medium. 

Sea=water freezes at 27° F. Theiceisfresh. (Trautwine.) 

Kee and Snow. (From Clark.)—1 cubic foot of ice at 32° F. weighs 
57.50 lbs.; 1 pound of ice at 32° F. has a volume of .0174 cu. ft. = 80.067 cu. in. 

Relative volume of ice to water at 32° F., 1.0855, the expansion in passing 
into the solid state being 8.55%. Specific gravity of ice = 0.922, water at 
62° F. being 1. : 

At high pressures the melting-point of ice is lower than 82° F., being at 
the rate of .0133° F. for each additional atmosphere of pressure 

The specific heat of ice is .504, that of water being 1. 

1 cube foot of fresh snow, according to humidity of atmosphere: 5 Ibs. to 
12 Ibs. 1 cubic foot of snow moistened and compacted by rain: 15 lbs. to 
50 lbs. (Trautwine). 

Specific Heat of Water. (From Clark’s Steam-engine.)—Calcu- 
lated by means of Regnault’s formula, c = 1 + 0.00004¢ + 0.000000972, in 
which c is the specific heat of water at any temperature ¢ in centig: ade des 
grees, the specific heat at the freezing-point being 1. : 





THE IMPURITIES OF WATER. 





a 


or 
Ou 
— 

















Hh fe = ¢ p o $3 rf ' “| » © = ap] . 

Tempera- is no | OL BIS oo af Tempera- o ee eg $ 8 sors eos eI 
tures. (A283) H58 |BSeof tures. Fash) es jes ao 
4°29) 828 Coe Sg) 22) 628 (leg 

Sass) B28 isse s Sa58| 228 les. £ 

Cent.|Fahr. Beas) oe \ZaR% Cent.|Fahr. Baas) San SO 83 
0° 32° 0.000, 1.0000 120° | 248° | 217.449) 1.0177 | 1.0067 
10 50 18.004, 1.0005 | 1.0002 | 130 | 266 | 235.791/ 1.0204 | 1.0076 
20 68 36.018; 1.0012 | 1.0005 9 140 | 284 | 254.187) 1.0232 | 1.0087 
30 86 54.047) 1.0020 | 1.0009 J 150 | 802 | 272.628) 1.0262 | 1.0097 
40 104 72.090; 1.0030 | 1.0013 § 160 | 320 | 291.132) 1.0294 | 1.0109 
50 122 90.157) 1.0042 | 1.0017 § 170 | 3838 | 309.690 1.0328 | 1.0121 
60 140 | 108.247) 1.0056 | 1.0028 — 180 | 356 | 828.320/ 1.0364 | 1.0133 
7 158 | 126.378} 1.0072 | 1.0030 § 190 | 374 | 847.004) 1.0401 | 1.0146 
80 176 | 144.508) 1.0089 | 1.0085 @ 200 | 3892 | 865.760] 1.0440 | 1.0160 

90 194 | 162.686) 1.0109 | 1.0042 fF 210 | 410 | 384.588} 1.0481 | 1.0174 ° 
100 212 | 180.900) 1.0130 | 1.0050 § 220 | 428 | 403.488) 1.0524 | 1.0189 
1 230 / 199.152) 1.0153 | 1.0058 § 230 | 446 | 422.478) 1.0568 | 1.0204 








Compressibility of Water.—Water is very slightly compressible. 
its compressibility is from .000040 to .000051 for one atmosphere, decreasing 
with increase of temperature. For each foot of pressure distilled water will 
be diminished in volume .0000015 to .0000013. Water is so incompressible 
that even at a depth of a mile a cubic foot of water will weigh only about 
half a pound more than at the surface. 


THE IMPURITIES OF WATER. 
(A. E, Hunt and G. H. Clapp, Trans. A. I. M. E. xvii. 338.) 


Commercial analyses are made to determine concerning a given water: 
(1) its applicability for making steams; (2) its hardness, or the facility with 
which it will ‘‘form a lather” necessary for washing; or (8) its adaptation 
to other manufacturing purposes. 

At the Buffalo meeting of the Chemical Section of the A. A. A.S. it was de- 
cided to report all water analyses in parts per thousand, hundred-thousand, 
and million. 

To convert grains per imperial (British) gallons into parts per 100,000, di- 
vide by 0.7. To convert parts per 100,000 into grains per U.S. gallon, mul- 
tiply by 7/12 or .583. 

The most common commercial analysis of water is made to determine its 
fitness for making steam. Water containing more than 5 parts per 100,000 
of free sulphuric or nitric acid is liable to cause serious corrosion, not only 
of the metal of the boiler itself, but of the pipes, cylinders, pistons, and 
valves with which the steam comes in contact. 

The total residue in water used for making steam causes the interior lin- 
ings of boilers to become coated, and often produces a dangerous hard 
scale, which prevents the cooling action of the water from protecting the 
metal against burning. 

Lime and magnesia bicarbonates in water lose their excess of carbonic 
acid on boiling, and often, especially when the water contains sulphuric 
acid, produce, with the other solid residues constantly being formed by the 
evaporation, a very hard and insoluble scale. A larger amount than 100 
parts per 100,000 of total solid residue will ordinarily cause troublesome 
seale, and should condemn the water for use in steam-boilers, unless a 
better supply cannot be obtained. 

The following is a tabulated form of the causes of trouble with water for 
steam purposes, and the proposed remedies, given by Prof. L. M. Norton. 


CAUSES OF INCRUSTATION. 


1. Deposition of suspended matter. 

2. Deposition of deposed salts from concentration. ' 

3. Deposition of carbonates of lime and magnesia by boiling off carbonic 
acid, which holds them in solution, 


552 WATER. 


4. Deposition of sulphates of lime, because sulphate of lime is but slightly 
soluble in cold water, less soluble in hot water, insoluble above 270° F. 
5. Deposition of magnesia, because magnesium salts decompose at high 


temperature. 


6. Deposition of lime soap, iron soap, etc., formed by saponification of 


grease. 


MEANS FOR PREVENTING INCRUSTATION. 


1. Filtration. 
2. Blowing off. 


8. Use of internal collecting apparatus or devices for directing the cir- 


culation. 
4. Heating feed-water. 


5. Chemical or other treatment of water in boiler. 


6. Introduction of zinc into boiler. 


”. Chemical treatment of water outside of boiler. 


TABULAR VIEW. 


Troublesome Substance. Trouble. 
Sediment, mud, clay, etc. Incrustation. 
Readily soluble salts. y 
Bicarbonates of lime, magnesia, “fh 

iron. 
Sulphate of lime. *! | 
serie and sulphate of magne- ‘ Ganrosiony { 
Carbonate of soda in large re J: 
amounts, t Priming. / 
Acid (in mine waters). Corrosion. 
Dissolved carbonic acid and C F 
oxygen. orrosion, 
: - Corrosion or 
Grease (from condensed water). ' oni 
Priming, $ 


Organic matter (sewage). 


corrosion, or 
incrustation. 


J 


Remedy or Palliation. 
Filtration; blowing off. 


Blowing off. 


Heating feed. Addition of 
caustic soda, lime, or 
magnesia, ete. 

Addition of carb. soda, 
barium hydrate, ete, 
Addition of carbonate of 

soda, ete. 


Feed milk of lime to the 
boiler, to form a thin in- 
ternal coating. 


Different cases require dif- 


ferent remedies. Consult 
aspecialist on the subject. 


The mineral matters causing the most troublesome boiler-scales are bicar- 
honates and sulphates of lime and magnesia, oxides of iron and alumina, 


and silica. 


The analyses of some of the most common and troublesome 
boiler-scales are given in the following table: 


Analyses of Boiler=-seale. (Chandler.) 
Sul- Per- Car- 
phate | Mag- | gilica, | Oxide | Water, | bonate 
of nesia ‘ of 1 of 
Lime Tron. Lime 
N.Y.C.&H.R.Ry., No. 1) 74.07 9.19 | 0.65 0.08 1.14 14.7 
4S a oe INOS E71 OT! /aeeeeeten 1.76 3. SRS eee ee 
AG oC st No. 3} 62.86 18.95 | 2.60 0.92 128 12.62 
$s ee Mis INOme4 8538.05 | ataecee S179 Oh, PORE, Se OCCA cece ee 
ee ss cS INO 18846683 || 9. ae Oe GeeM Le Boe oe ; Be 
et ‘S RG Nore 6880.80!) Slat aera, 1.08 2.44 26.93 
ss se oe INO pet) 4.95 2.61 EUG 1.08 0.63 86.25 
Jy as ce No. 8} 0.88 2.84 | 0.65 0.36 0.15 93.19 
ss oe My NOM Ole 810 bis. c ccce 2.92 wp lisicnietemte sive uberis 
a a Md No. 10} 30.07 8.24 





THE IMPURITIES OF WATER. 553 


Analyses in Parts per 100,000 of Water giving Bad 
HResults in Steame-boilers,. (A. E. Hunt.) 








Oy, i) ter) 
S| bee g 
Ot oem (} 
His jam : A = 
salss sis s 8 
oa Ory B o a ~~ TM 
HOl--a D =] S a 
Sy /Se el o = , ° 
Sslesi Bl sl2i¢ a] © 
Bslssi4)2) 8) 8 3/8/38 
[= mM col = t=] e ~) 
82/82/23 /2/S/3/8)&/ 2] s 
As ag Bie lalol|s&lo}]4] 5 
Coal-mine water...........-. 110] 25 | 119) 39] 890] 590] 780) 30 | 640]...... 
MEV Ol Ls Gy cds sett ticicae 151] 38 | 190) 48] 360} 990] 38] 21] 30] 13810 
BDF EN Sue th5-..4 low eubek meeonne 75| 89 | 95] 120] 310] 21! 75/10] 80} 36 
Monongahela River......... 130] 2t | 161) 33] 210} 38) 70]....]... re llarerercrete 
- ee aoe 80| 70 | 94} 81] 219} 210) 90]....}....]...... 
SS Pa Wie wted ease 82/ 82 | 61/ 204) 98] 190] 38]... ] .2.1...... 
Allegheny R., near Oil-works| 30] 50 | 41! 68] 890] 42] 23]....].... ae 











Many substances have been added with the idea of causing chemical 
action which will prevent boiler-scale. As a general rule, these do more 
harm than good, for a boiler is one of the worst possible places in which to 
carry on chemical reaction, where it nearly always causes more or less 
corrosion of the metal, and is liable to cause dangerous explosions. 

In cases where water containing large amounts of total solid residue is 
necessarily used, a heavy petroleum oil, free from tar or wax, which is not 
acted upon by acids or alkalies, not having sufficient wax in it to cause 
saponification. and which has a vaporizing-point at nearly 600° F., will give 
the best resultsin preventing boiler-scale. Its action is to form a thin 
greasy film over the boiler linings, protecting them largely from the action 
of acids in the water and greasing the sediment which is formed, thus pre- 
venting the formation of scale and keeping the solid residue from the 
evaporation of the water in such a plastic suspended condition that it can 
be easily ejected from the boiler by the process of ‘‘ blowing off.’? If the 
water is not blown off sufficiently often, this sediment forms into a ** putty” 
that will necessitate cleaning the boilers. Any boiler using bad water should 
be blown off every twelve hours. 

Hardness of Water.—The hardness of water, or its opposite quality, 
indicated by the ease with which it will form a lather with soap, depends 
almost altogether upon the presence of compounds of lime and magnesia. 
Almost all soaps consist, chemically, of oleate, stearate, and palmitate, of 
an alkaline base, usually soda and potash. The more lime and magnesia in a 
sample of water, the more soap agiven volume of the water will decompose, 
so as to give insoluble oleate, palmitate, and stearate of Jime and magnesia, 
and consequently the more soap must be added to a gallon of water in order 
that the necessary quantity of soaapmay remain in solution to form the lather. 
The relative hardness of samples of water is generally expressed in terms 
of the number of standard soap-measures consumed by a gallon of water in 
yielding a permanent lather. 

The standard soap-measure is the quantity required to precipitate one 
grain of carbonate of lime. 

It is commonly reckoned that one gallon of pure distilled water takes one 
soap-measure to produce a lather. Therefore one is deducted from the 
total number of soap-measures found to be necessary to use to produce a 
lather in a gallon of water, in reporting the number of soap-measures, or 
‘‘degrees ’ of hardness of the water sample. In actually making tests for 
hardness, the ** miniature gallon,’’ or seventy cubic centimetres, is used 
rather than the inconvenient largeramount. The standard measureis made 
by completely dissolving ten grammes of pure castile soap (containing 60 per 
cent olive-oil) in a litre of weak alcohol (of about 35 per cent alcohol). This 
yields a solution containing exactly sufficient soap in one cubic centimeter 
of the solution to precipitate one milligramme of carbonate of lime, or, in 
other words, the standard soap solution is reduced to terms of the ‘ minia- 
ture gallon’’ of water taken. i 

If a water charged with a bicarbonate of lime, magnesia, or iron is boiled, 


“4 


554 WATER. 


it will, on the excess of the carbonic acid being expelled, deposit a consid: 
erable quantity of the lime, magnesia, or iron, and consequently the water 
will be softer. The hardness of the water after this deposit of lime, after 
long boiling, is called the permanent hardness and the difference between it 
and the total hardness is called temporary hardiness. 

Lime salts in water react immediately on soap-solutions, precipitating the 
oleate, palmitate, or stearate of lime at once. Magnesia salts, on the con- 
trary, require some considerable time for reaction. They are, however, 
more powerful hardeners; one equivalent of magnesia salts consuming as 
much soap as one and one-half equivalents of lime. 

The presence of soda and potash salts softens rather than hardens water. 
Each grain of carbonate of lime per gallon of water causes an increased 
expenditure for soap of about 2 ounces per 100 gallons of water. (Hng’g. 
News, Jan. 31, 1885.) 

Purifying Feed=-water for Steam-boilers. (See also Incrus- 
tation and Corrosion, p. 716.)—When the water used for steam-boilers cone 
tains a large amount of scale-forming material it is usually advisable to 
purify it before allowing it to enter the boiler rather than to attempt the 

revention of scale by the introduction of chemicals into the boiler. Car- 
Bonatbe of lime and magnesia may be removed to a considerable extent by 
simple heating of the water in an exhaust-steam feed-water heater or, still 
better, by alive-steam heater. (See circular of the Hoppes Mfg..Co., Spring- 
field, O.) When the water is very bad it is best treated with chemicals— 
lime, soda-ash, caustic soda, etc.—in tanks, the precipitates being separated 
by settling or filtering. For a description of several systems of water 
purification see a series of articles on the subject by Albert A. Cary in Eng’g 
Mag., 1897. £ 

Mr, W. B. Coggswell, of the Solvay Process Co.’s Soda Works in Syracuse, 
N. Y., thus describes the system of purification of builer feed-water in use 
at these works (Trans, A.S. M. E., xiii. 255): 

For purifying, we use a weak soda liquor, containing about 12 to 15 grams 
Na,.Cos per litre. Say 144 to 2 M$ (or 397 to 530 gals.) of this liquor is run 
into the precipitating tank. Hot water about 60° C. is then turned in, and 
the reaction of the precipitation goes on while the tank is filling, which re- 
quires about 15 minutes. When the tank is full the water is filtered through 
the Hyatt (4), 5 feet diameter, and the Jewell (1), 10 feet diameter, filters in 
380 minutes. Forty tanks treated per 24 hours. 


Charge of water purified at once....,........... 35 M8, 9.275 gallons. 
Soda in purifying reagent.......,eceesseseeees-e 1D kgs. NagCOg. 
Soda used per 1,000 gallons... ................208 38.5 lbs, 


A sample is taken from each boiler every other day and tested for deg. 
Baumé, soda and salt. If the deg. B. is more than 2, that boiler is blown ta 
reduce it below 2 deg. B. 

The following are some analyses given by Mr. Coggswell: 














Lake Seale 
Water, Mud from Scale from fannd 
Hyatt Boilers > 
STARS Pew iter tube a 
litre. : Pump. 
Calcium sulphate...........-. 261 8.70 51.24 10.9 
Calcium chloride............. «186 WR 20 eee ene be Seek eee ee - 
Calcium carbonate.......... 091 63.37 19.76 87. 
Magnesium carbonate........ .015 1.11 5. 2iae ie hieee eickh 
Magnesium ehloride.......... O87" ecient. & Cecio’ oe. eanileaete aes = 
Salt NaC. 7. set cer tate. 568°) SHDN. ceteares Tay nS \tese Te é 
Silica..... YRSTHER Bae UE. Cae SCR ERE 15.17 2.29 8 
Iron and aluminum oxide....]............ 3.75 1.10 1:2 
TPOtEII ORR Ee 1.270 7.10 99.74 99.9 





Softening Hard Water for Locomotive Use.—A water-soft- 
ening plant in operation at Fossil, in Western Wyoming, on the Union Pa- 
cific Railway, is described in Lng’g News, June 9, 1892, It is the invention 


FLOW OF WATER. 555 


of Arthur Pennell, of Kansas City. The general plan adopted is to first dis- 
solve the chemicals in aclosed tank, and then connect this to the supply main 
so that its contents will be forced into the main tank, the supply-pipe being 
so arranged that thorough mixture of the solution with the water is ob- 
tained. A waste-pipe from the bottom of the tank is opened from time to 
time to draw off the precipitate. The pipe leading to the tenderis arranged 
to draw the water from near the surface. 

A water-tank 24 feet in diameter and 16 feet high will contain about 46,600 
gallons of water. About three hours should be allowed for this amount of 
water to pass through the tank to insure thorough precipitation, giving a 
permissible consumption of about. 15,000 gallons per hour. Should more 
than this be required, auxiliary settling-tanks should be provided. 

The chemicals added to precipitate the scale-forming impurities are so- 
dium carbonate and quicklime, varying in proportions according to the rela- 
tive ‘proportions of sulphates and carbonates in the water to be treated. 
Sufficient sodium carbonate is added to produce just enough sodium sulphate 
to combine with the remaining lime and magnesia sulphate and produce 
glauberite or its corresponding magnesia salt, thereby to get rid of the 
sodium sulphate, which produces foaming, if allowed to accumulate. 

For a description of a purifying plant established by the Southern Pacific 
R. R. Co. at Port Los Angeles, Cal.. see a paper by Howard Stillmann in 
Trans, A. S. M. E., vol. xix, Dec. 1897. 


HYDRAULICS_FLOW OF WATER. 


Formule for Discharge of Water though Orifices and 
Weirs.—Ffor rectangular or circular orifices, with the head measured from 
centre of the orifice to the surface of the still water in the feeding reservoir. 


Q=C 2gH » a. e ° e e e e e ° ° ° ° (1) 


For weirs with no allowance for inereased head due to velocity of approach: 


O= C% 29H x LH, ° e ° e e e e e e e (2) 


For rectangular and circular or other shaped vertical or inclined orifices; 
formula based on the proposition that each successive horizontal layer of 
water passing through the orifice has a velocity due to its respective head: 


Q = cL% 2g X ( VHb3 — Ht’). » 2. 6 © (3) 
For rectangular vertical weirs: 
Q = c% V2gH X Lh. ee © © © © © @ © @ (4) 


Q = quantity of water discharged in cubic feet per second; C = approxi- 
Le ee for formulas (1) and (2); c =correct coefficient for (3) 
an ). 

Values of the coefficients c and C are given below. 

g = 32.16; /2g = 8.02; H = head in feet measured from centre of orifice 
to level of still water; Hb = head measured from bottom of orifice; Ht = 
* head measured from top of orifice; h = H, corrected for velocity of ap- 

4 Va? 
proach, Va, = A+ 3 2g 

Flow of Water from Orifices,—The theoretical velocity of water 
flowing from an orifice is the same as the velocity of a falling body which 


has fallen from a height equal to the head of water, = /2gH. The actual 
velocity at the smaller section of ths vena contracta is substantially the 
same as the theoretical, but the velocity at the plane of the orifice is 
C W/2gH, in which the coefficient C has the nearly constant value of .62. The 
smallest diameter of the vena contracta is therefore about .79 of that of the 
orifice. If C’be the approximate coefficient = .62, and c the correct coeffi- 


; @ = area in square feet; Z = length in feet. 


556 HYDRAULICS, 


cient, the ratio c varies with different ratios of the head to the diametez 


of the vertical orifice, or to ek Hamilton Smith, Jr., gives the following: 


D 

H 
For D= 5 875 1 1.5 2. 2.5 5. 10. 

£ = .9604 .9849 .9918  .9965 .9980  .9987  .9997 i. 
For vertical rectangular orifices of ratio of head to width W: 

H Fi 
For y= 5 6 8 1 1.5 2. 3. 4, Donic 

g = .9428 .9657 .9823 .9890 .9953 .9974 .9988 .9993 .9996 .9998 


For H + Dor H + W over 8, C =, practically. 


Weisbach gives the following values of c for circular orifices in a thin wall. 
H = measured head from centre of orifice. 











H tt. 
D ft. taeda 
066 33 82 2.0 3.0 45, 340. 
033} 711] Sf 665 637 628 | 641 632 600 
“066 "629 "621 
10 "622 614 
13 614 "607 





For an orifice of D = .033 ft. and a well-rounded mouthpiece, H being the 
effective head in feet, 


H = .066 1.64 11.5 56 338 
c = .959 967 975 ~=—- . 994 994 


Hamilton Smith, Jr., found that for great heads, 312 ft. to 336 ft., with con- 
verging mouthpieces, c has a value of about one, and for small circular 
orifices in thin plates, with full contraction, c = about .60. Some of Mr, 
Smith’s experimental values of c for orifices in thin plates discharging into 
air are as follows. All dimensions in feet. 


Circular, in steel, D = 020, | c= 16495 16298 6264 


: : ie H= .18 586 1.74 2.73 3.5 
Circular, in brass, D = 050, 4 Ee a 0525 6265 6113 "607 6060 : 6061 
a : ‘ss = 4 900 1.7% 0 ei 
Circular, in brass,D = .100,| 2 = g39 “6155 16096 16042 "6088 © 16025 
Circular, in iron, D = 100, 4 ites ana ! at he tt one 
: fe H= .313 87 1.79 2.81 3.70 4.63 
Square, in brass, .05  .05, { ce 6410 6238 1st 6127 3 6113 : 609% 
5 = 8 wg re 
moquarenin prdas,»\0 2-10, 1 c= 16292 16189 26084 "6076 26060 "76055 
Rectangular, in brass, ; H= .261 COLT Pt 1A 2 OLS 3.75 4.70 
LL = 800, Wa=.050.......1 c= .647 -6280 .6203 .6180 .6176 .6168 


For the rectangular orifice, L, the length, is horizontal. 

Mr. Smith, as the result of the collation of much experimental data of 
others as well as his own, gives tables of the value of c for vertical orifices, 
with, full contraction, with a free discharge into the air, with the inner face 
of the plate, in which the orifice is pierced, plane, and with sharp inner 
corners, so that the escaping vein only touches these inner edges. These 
tables are abridged below. The coefficient c is to be used in the formule (3} 
and (4) above. For formule (1) and (2) use the coefficient C round from the 


values of the ratios - above. 


HYDRAULIC FORMULA. 557 


Values of Coefficient c for Vertical Orifices with Sharp 


Edges, Full Contraction, and Free Discharge into 
ir. (Hamilton Smith, Jr.) 


> 





Square Orifices, Length of the Side of the Square, in feet. 





Head from 
Centre of 
Orifice H. 








4 -643) .637] .628] .621] .616] .611 

6 | .660) .645) .636} .630} .623] .617] .613] .610] .605/ .601] .598] .596 
Aa -648} .636] .628} .622) .618) .613) .610| .608] .605] .603] .601] .600) .599 
0 





-632| .622) .616} .612) .609| .607| .606} .606] .605] .605| .604] .603) .603 
-623]) .616) .612) .609) .607) .605) .605) .605] .604] .604] .603] .602] .602 
10 -616) .611) 608} .606) .605) .604) .604] .603] .603] .603] .602) .602) .601 
20. .606] .605} .604) .603) .602) .602| .602| .602] .602) .601} .601] .601] .600 
100.(?)} .599] .598]} .598] .598] .598] .598] .598] .598] .598] 598] .598] .598] .598 


Circular Orifices. Diameters, in feet. 





1 .644} .631| .623) .617, .612} .608) .605| .603), .600} .598) .595] .593] .591 
2, .632) .621] .614) .610) .607) .604) .601} .600) .599) .599) .597| .596) .595 
4. -623) .614] .609; .605) .603) .602) .600) .599) .599) .598) .597) .597| .596 
6. -618) .611| .607| .604| .602| .600, .599} .599) .598) .598) .597| .596| .596 
0. .611| .606) .603| .601| .599) .598| .598) .597) .597) .597| .596) .596] .595 

20. -601| .600] .599| .598) .597| .596) .596) .596| .596) .596) .596) .595) .594 

50.(?)| .596} .596) .595| .595) .594) .594) .594) .594) .594) .594) .594) .593) .593 
190.(?)| .593' .593°..592° .592) .592' 592) .592' 592! .592' .592' .592! .592! .592 











HYDRATLIC FORMULZE.—FLOW OF WATER IN 
OPEN AND CLOSED CHANNELS. 


Flow of Water in Pipes.—The quantity of water discharged 
through a pipe depends on the ‘‘head;”’ that is, the vertical distance be- 
tween the level surface of still water in the chamber at the entrance end of 
the pipe and the level of the centre of the discharge end of the pipe; 
also upon the length of the pipe, upon the character of its interior surface 
as to smoothness, and upon the number and sharpness of the bends: but 
it is independent of the position of the pipe, as horizontal, or inclined 
upwards or downwards. 

The head, instead of being an actual distance between levels, may be 
caused by pressure, as by a pump, in which case the head is calculated as a 
vertical distance corresponding to the pressure 1 lb. per sq. in. = 2.309 ft. 
head, or 1 ft. head = .433 lb. per sq. in. ° 

The total head operating to cause flow is divided into three parts: 1. The 
velocity-head, which is the height through which a body must fall in vacuo 
to acquire the velocity with which the water flows into the pipe = v? + 2g, in 
which v is the velocity in ft. per sec. and 2g = 64.32; 2. the entry-head. that 
required to overcome the resistance to entrance to the pipe. With sharp- 
edged entrance the entry-head = about 1% the velocity-head; with smooth 
rounded entrance the entry-head is inappreciable; 3. the friction-head, due 
to the frictional resistance to flow within the pipe. 

In ordinary cases of pipes of considerable length the sum of the entry and 
velocity heads required scarcely exceeds 1 foot. In the case of long pipes 
with low heads the sum of the velocity and entry heads is generally so small 
that it may be neglected. 

General Formula for Flow of Water in Pipes or Conduits, 


Mean velocity in ft. per sec. = c {//mean hydraulic radius X slope 
Do. for pipes running full = c / x slope, 





‘n which c is a coefficient determined by experiment. (See pages 559-564.) 


558 HYDRAULICS, 


area of wet cross-section 
wet perimeter, 


In pipes running full, or exactly half full, and in semicircular open cham 
nels running full it is equal to 14 diameter. 

The slope = the head (or pressure expressed as a head, in feet) 

-- length of pipe measured in a straight line from end to end. 

In open channels the slope is the actual slope of the surface, or its fall per 
unit of length, or the sine of the angle of the slope with the horizon. 

Chezy’s Formula: v = cV7Vs = cVrs; r = mean hydraulic radius, 
$s z slope = head + length, v = velocity in feet per second, all dimensions 
in feet. 

Quantity of Water Discharged. —If Q = discharge in cubic feet 

. per second and a@ = area of channel, Q = av = ac Vrs. 

a Yr is approximately proportional to the discharge. It is a maximum at 
308°, corresponding to 19/20 of the diameter, and the flow of a conduit 19/20 
full is about 5 per cent greater than that of one completely filled. 


The mean hydraulic radius = 


Table giving Fall in Feet per Mile, the Distance on Slope 
corresponding to a Fall of 1 Ft., and also the Values 
of s and /s for Use in the Formula v=c /7rs, 


s= H-~L= sine of angle of slope = fall of water-surface (#), in any dis- 
tance (ZL), divided by that distance. 











Fallin | Slope, | Sine of Fallin | Slope, | Sine of 

Feet | 1 Foot | Slope, V/s. Feet | 1 Foot | Slope, V's. 

per Mi. in s. per Mi. in Ss. 

0.25 |} 21120 .00004:73 -006881 17 810.6 | .0032197 | .056742 
-30 17600 - 0000568 -007538 18 293.3 -0034091 .058588 
-40 18200 .0000758 - 008704 19 277.9 -0035985 -059988 
50 10560 0000947 .009731 20 264 © -0037879 061546 
.60 8800 .0001136 -010660 22 240 -0041667 -064549 
- 702 7520 -0001330 -011582 24 220 -0045455 -067419 
2805 6560 .0001524 -012347 26 203.1 -0049242 -070173 
.904 | 5840 .0001712 -013085 28 188.6 | .0053030 072822 

1. 5280 .0001894 -0138762 30 176 -0056818 075378 

1.25 4224 0002367 015386 35.20} 150 .0066667 | .081650 

1.5 3520 .0002841 .016854 40 132 -0075758 087039 

1.75 8017 -0008314 018205 44 120 .0083333 | .091287 

ee 2640 . 0003788 -019463 48 110 .0090909 - 095346 

2.25 2347 0004261 .020641 52.8 | 100 .010 

2.5 2112 0004785 -021760 60 88 -01136386 -1066 

2.75 1920 .0005208 -022822 66 80 0125 111803 

3. 1760 .0005682*}  .028837 70.4 15 .0183333 | .115470 

3.20 1625 .0006154 - 024807 80 66 -0151515 123091 

3.5 1508 .0006631 .025751 88 60 .0166667 1291 

3.75 1408 -0007102 .026650 96 55 -0181818 134839 

4 1320 .0007576 -027524 105.6 50 -02 141421 

5 1056 .0009470 -0307738 120 44 0227273 150756 

6 880 -0011364 03371 132 40 025 .158114 

if 754.3 | .0013257 036416 160 33 .0303080 174077 

8 660 .0015152 - 038925 220 24 - 0416667 204124 

9 586.6 | .0017044 .041286 § 264 20 .05 223607 

10 528 -0018939 -043519 330 16 - 0625 B45) 

11 443.6 | .0020833 045648 440 12 . 0833333 288675 
12 440 0022727 -047673 528 10. ot ,316228 
18 406.1 |} .0024621 .04962 660 8 0125 .008053 
14 877.1 | .0026515 -051493 § 880 6 -1666667 | .408248 
15 352 . 0028409 0538 1056 5 <e .447214 
16 330 .0030303 | 055048 § 1820 4 225 5 


a a ee a EY Fa GRE? 


HYDRAULIC FORMULA. 559 


# 


Values of {/r for Circular Pipes, Sewers, and Conduits of 
: different Diameters, : 


area 








+ = mean hydraulic depth = atten 14 diam. for circular pipes run 
ning full or exactly half full. 
‘Diam., Vr Diam., Vr Diam., Vr Diam., pF 
ft. in. | in Feet. J ft-in- | in Feet. { ft- im. | in Feet, J ft in. | in Feet. 
PF 36 088 2 107 4 6] 1.061 9 1.500 
4 -102 Zine “e G22 4 7 1.070 9543 1,521 
34 3126 2 2 736 4 8] 1.080 9 6] 1.541 
1 -144 248 750 4 9 1.089 95,99 1.561 
14 .161 2 4 764 4 10] 1.099 10 1.581 
1% 197 2 5 PYM is 4 11] 1.109 10 38] 1.601 
134 “191 2:56 790 5 1.118 10 6] 1.620 
2 204 ed Me 804 5 61 1.127 10% 29 1.639 
244 228 2-05 817 Bie 2 1.137 Il 1,658 
3 Ss! 24,9 829 I70 1.146 eines 1.67 
4 .290 ie i) 842 5 4 7.155 a hl A, 1.696 
5 823 2,11 854 Be 1.164 Tie 19 1.714 
6 . 3854 3 866 DOG ol. tts 12 1.782 
7 382 St efit Ss silk “ipod led den PPS 17750 
8 408 Hy aR .890 5 81] 1.190 12) 6s 216403 
9 .433 By o -901 Saint 1.199 tao 9 1.785 
10 456 3.4 913 5 10°)" 1.208 18 1.803 
11 479 5 ail 924 le teat 13 3] 1.820 
1 -500 38 6 935 6 1.225 13 6 1.837 
Ti .520 Ss Sitienti 946 Gao, ate cor 14 1.871 
ie .540 tinier! 957 Bay Gere 275 14 ~'6)| 1,904 
1 3 559 Bette) .968 Ge Os re te 209 15 1.936 
1 4 O77 3 10 909 is 1.323 15 6| 1.968 
1 5 -595 aioe uh 990 is type) 1.346 16 2. 
toeG .612 4 13 Ce) Patel 109 16 e462 2. 0a 
ao Wt 629 4 1 1.010 ial a dee Nes 17 2.061 
1es8 646 4 2 1.021 8: 1.414 17 6] 2.091 
1 9 661 a. 3 1.031 8 381] 1.4386 18 2.121 
110 677 4 4 1.041 Ge oe et 408 19 2.180 
1 11 .692 4 5 1.051 8 9] 1.479 20 2.236 


Values of the Coefficient c. (Chiefly condensed from P. J. Flynn 
on Flow of Water.)—Almost all the old hydraulic formulee for finding the 
mean velocity in open and closed channels have constant coefficients, and are 
therefore correct for only a small range of channels. They have often been 
found to give incorrect results with disastrous effects. Ganguillet and Kut- 
ter thoroughly investigated the American, French, and other experiments, 
and they gave as the result of their labors the formula now generally known 
as Kutter’s formula. There are so many varying conditions affecting the 
flow of water, that all hydraulic formule are only approximations to the 
correct result, Saad 
- When the surface-slope measurement is good, Kutter’s formula will give 
results seldom exceeding 714% error, provided the rugosity coefficient of the 
formula is known for the site. For small open channels D’Arcy’s and 
Bazin’s formule, and for cast-iron pipes D’Arcy’s formule, are generally 
accepted as being approximately correct. , 

Kutter’s Formula for measures in feet is 


[ woot oh 1.6 f+ OOREF | i 
x Vrs, 


= pu eee eee eee 
00281 Teo f 
ete So Syn 


in which v = mean velocity in feet per second ; 7 = - = hydraulic mean 


g 
Pp 


560 HYDRAULICS. 


depth in feet = area of cross-section in square feet divided by wetted perim- 
eter in lineal feet ; s = fall of water-surface (h) in any distance (1) divided 


by that distance, = - = sine of slope; n = the coefficient of rugosity, de- 


pending on the nature of the lining or surface of the channel. If we let the 
first term of the right-hand side of the equation equal c, we have Chezy’s 


formula, vy =c Vrs =c X Vr X Vs. 

Values ofr in Kutter’s Formula.—tThe accuracy of Kutter’s for- 
mula depends, in a great measure, on the proper selection of the coefficient 
of roughness n. Experience is required in order to give the right value to 
this coefficient, and to this end great assistance can be obtained, in making 
this selection, by consulting and comparing the results obtained from ex- 
periments on the flow of water already made in different channels. 

In some cases it would be well to provide for the contingency of future 
deterioration of channel, by selecting a high value of n, as, for instance, 
where a dense growth of weeds is likely to occur in small channels, and also 
where channels are likely not to be kept in a state of good repair. 

The foliowing table, giving the value of n for different materials, is com- 
piled from Kutter, Jackson, and Hering, and this value of n applies also in 
each instance, to the surfaces of other materials equally rough, 


VALUE OF 1 IN KUTTER’S FORMULA FOR DIFFERENT CHANNELS. 


n = .009, well-planed timber, in perfect order and alignment ; otherwise, 
perhaps .01 would be suitable. 

_ n= .010, plaster*in pure cement; planed timber ; glazed, coated, or en- 
nee stoneware and iron pipes ; glazed surfaces of every sort in perfect 
order. 

-n = .011, plaster in cement with one third sand, in good condition ; also for 
iron, cement, and terra-cotta pipes, well joined, and in best order. 

a n = .012, unplaned timber, when perfectly continuous on the inside ; 
umes. 

n = .013, ashlar and well-laid brickwork ; ordinary metal; earthen and 
stoneware pipe in good condition, but not new ; cement and terra-cotta pipe 
not well jointed nor in perfect order , plaster and planed wood in imperfect 
or inferior condition ; and, generally, the materials mentioned with n = .010, 
when in imperfect or inferior condition. : 

n = .015, second class or rough-faced brickwork ; well-dressed stonework ; 
foul and ‘slightly tuberculated iron ; cement and terra-cotta pipes, with im. 
perfect joints and in bad order ; and canvas lining on wooden frames. 

n = .017, brickwork, ashlar, and stoneware in an inferior condition ; tu- ~ 
berculated iron pipes ; rubble in cement or plaster in good order ; fine gravel, 
well rammed, 4% to % inch diameter ; and, generally, the materials men- 
tioned with = .018 when in bad order and condition. 

n = .020, rubble in cement in an inferior condition ; coarse rubble, rough 
set in a normal condition; coarse rubble set dry ; ruined brickwork and 
masonry ; coarse gravel well rammed. from 1 to 14% inch diameter ; canals 
with beds and banks of very firm, regular gravel, caremaly trimmed and 
rammed in defective places ; rough rubble with bed partially covered with 
silt and mud ; rectangular wooden troughs, with battens on the inside two 
inches apart ; trimmed earth in perfect order. 

n = .0225, canals in earth above the average in order and regimen. 

n = .025, canals and rivers in earth of tolerably uniform cross-section ; 
slope and direction, in moderately good order and regimen, and free from 
stones and weeds. 

n = .0275, canals and rivers in earth below the average in order and regi-. 
men. 

_ n = .080, canals and rivers in earth in rather bad order and regimen, hav- 
ing stones and weeds occasionally, and obstructed by detritus. 

a = .085, suitable for rivers and canals with earthen beds in bad order and 
regimen, and having stones and weeds in great quantities. 

n = .65, torrents encumbered with detritus. 

Kutter’s formula has the advantage of being easily adapted to a change 
in the surface of the pipe exposed to the flow of water, by a change in the 
value of n. For cast-iron pipes it is usual to use n = .013 to provide for the 
future deterioration of the surface. aw ©. 

Reducing Kutter’s formula tothe form v=eX Vr X Vs, and taking n, the 
coefficient of roughness in the formula = .011, .012, and .013, and s = .001, we 
nee the following values of the coefficient c for different diameters of 
conduit. 


HYDRAULIC FORMULA. 561 


Values ore in Formula v=c x //r X {’s for Metal Pipes and 
Moderately Smooth Conduits Generally. 


By Kurrrer’s ForRMULA (s = .001 or greater.) 





Diameter. |n= .011)n = .012}n = .013§ Diameter. |n = .011]n = .012/2 = .013 











fin C= (Or ft. = c= C= 
0 1 TAY Reece || ste oeeiae 7 152.7% | 189.2 127.9 

2 61. Bufo Se |s caren 8 155.4 141.9 130.4 

4 FR Soa SN el Mg ee 4 Ae 9 BY Sr 144.1 132.7 

6 4 ad 69.5 10 159.7 | 146 134.5 
1 105.7 94.6 85.3 11 161.5 147.8 186.2 
1 6 116.1 104.3 94.4 12 163 149.3 Toe 
2 123.6 1123 101.1 14 165.8 | 152 140.4 
3 133.6 120.8 110.1 16 168 154.2 142.1 
4 140.4 12-4 ia Ges 18 169.9 156.1 144.4 
> 145-4 132.3 Ip Lal 20 171.6 oy wif 146 
6 149.4 136.1 124.8 ff 


For circular pipes the hydraulic mean depth r equals 4 of the diameter. 

According to Kutter’s formula the value of c, the coefficient of discharge, 
-is the same for all slopes greater than 1 in 1000; that is, within these limits 
cis constant. We further find that up toa slope of 1 in 2640 the value of c 
is, for all practical purposes, constant, and even up toa slope of 1 in 5000 
the difference in the value of c is very little. This is exemplified in the 
following : 
Value of c for Different Values of /7r and s in Kutter’s 

Formula, with n= .013. 


V=CeVrxKys. 





Slopes. 
1 in 1000 1in 2500 | 1in 3333.3 | 1im5000 | 1in 10,000 
6 OF Bc bath da ieast Aoki SAO Ad AAW dat 88545 vu liomacingass 
1 116.5 115.2 114.4 113.2 109.7 
2 142.6 142.8 143.0 143.1 143.8 





The reliability of the values of the coefficient of Kutter’s formula for . 
pipes of less than 6 in. diameter is considered doubtful. (See note under 
table on page 564.) 

Values of c for Earthen Channels, by Kutter’s Formula, 
for Use in Formula v = c¢ //7rs. 





























Coefficient of Roughness, Coefficient of Roughness, 
= 0225: i=. 035% 
Vr in feet. Vr in feet. 
0.4 1.0 1.8 2.5 4.0 2.5 4.0 
Slope,lin| c c C1. .e c “ c c 
1000 85.7 | 62.5 | 80.8 | 89.2 | 99.9 59.3 | 69.2 
1250 35.5 | 62.3 | 80-3 | 89.3 | 100.2 59 4 | 69.4 
1667 35.2 | 62.1 | 80.3 | 89.5 | 100.6 59.5 | 69.8 
2500 34.6 | 61.7 | 80.3 | 89.8 | 101.4 59.7 | 70.4 
3333 34. 61.2 | 80.3 | 90.1 | 102.2 59.9 } 71.0 
5000 33. 60.5 |} 80.8 | 90.7 | 108.7 ; 60.4 | 72.2 
7500 81.6 | 59.4 | 80.3 | 91.5 | 106.0 2 60.9 | 73.9 
10000 80.5 | 58.5 | 80.3 | 92.3 | 107.9 35. 60.5 | %5.4 
15840 28.5 | 56.7 | 80.2 | 93.9 | 112.29 16.2 | 84.3 | 51.6 | 62.5 | 78.6 
20000 _| 97.4 | 85.7 | 80.9 | 94.8 | 115.00 15.6 | 38.8 | 51.5 | 63.1 | 80,6 


562 HYDRAULICS. 


Mr. Molesworth, in the 22d edition of his ‘‘ Pocket-book of Engineering 
Formule,” gives a modification of Kutter’s formula as follows: For flow in 


cast-iron pipes, v = c rs, in which 
181 + ot 


-026 ~ 00281)" 
1475 (41.04 


c= 


in which d = diameter of the pipe in feet. 
(This formula was given incorrectly in Molesworth’s 21st edition.) 


Molesworth’s Formula.—v = /krs, in which the values of k are 
as follows: 





Values of k for Velocities. 





Nature of Channel. 





Less than More than 

4 ft. per sec. 4 ft. per sec, 
Brickwork. c..cesc es MMe sein SESE 8800 8500 
PUA Voile cde cre siete cicbaels piget iat lemis ee 86,55 7200 6800 
SLIDE Gia, Gels ice oiets, a vis.ele erste aiee eat be 6400 5900 
Rough, with bowlders............... 5300 4700 


In very large channels, rivers, etc., the description of the channel affects 
the result so slightly that it may be practically neglected, and k assumed = 
from 8500 to 9000. 

Flynn’s Formula.—Mr. Flynn obtains the following expression of 
the value of Kutter’s coefficient for a slope of .001 and a value of n = .018; 


ca 183,72 
1+ (41x 
ge a) 


The following table shows the close agreement of the values of c obtainea 
from Kutter’s, Molesworth’s, and Flynn’s formule: 


Diameter. Slope. Kutter, Molesworth. Flynn, 
6 inches lin 40 71.50 71.48 69.5 
6 inches 1 in 1000 69.50 69.79 69.5 
4 feet Jin 400 117. ahh ee 116.5 
4 feet 1 in 1000 116.5 116.55 116.5 
8 feet lin 700 130.5 130.68 130.5 
8 feet 1 in 2600 129.8 129.93 130.5 


Mr. Flynn gives another simplified form of Kutter’s formula for use with 
different values of n as follows: 


K 


as n <as 
is 1+ (14.41 x —2) Vrs. 
Vr 


In the following table the value of K is given for the several values of n: 


OO I — — —— | O_O 
————<<—<——_ | — | 


.009 | 245.63 § .012 | 195.83 § .015 | 165.44 f .018 | 145.03 § .02 
-010 | 225.51 0138 | 183.72 § .016 | 157.6 # .019 | 139.73 “One 136.73 
011 | 209.05 § .014 | 187.77 J .017 | 150.94 | .020 | 124.96 | .0295| 194.9 


If in the application of Mr. Flynn’s formula given above within the limits 


of m as given in the table, we substitute for n, KK. and Vr thei 1 
have a simplified form of Kutter’s formula, ~~ Vr their va Si 


HYDRAULIC FORMULA. 563 


For instance, when n = .011, and d = 3 feet, we have 


209.05 us! 

GS fmt nae BA AS 1nd eed 
O11 Vrs. 
1+ (44.41 x “G55 


Bazin’s Formule: : 
For very even surfaces, fine plastered sides and bed, planed planks, etc., 


v =4/1 -+ ,0000045( 10.16 +3) x Vrs. 


For even surfaces such as cut-stone, brickwork, unplaned planking, mortar, 
ete. : 


1 ae, 
es VA 1 -+ .000018( 4.354 + ~) x Vrs. 


For slightly uneven surfaces, such as rubble masonry : 


v= 4/3 + ,00006( 1.219 ao *) xX Vrs. 


For uneven surfaces, such as earth: 


v= /2 00085 ( 0.2438 +4- *) xX Vrs. 


A modification of Bazin’s formula, known as D’Arcy’s Bazin’s: 


bts 1000s 
- .08534r + 0.35 


For small channels of less than 20 feet bed Bazin’s formula for earthen 
channels in good order gives very fair results, but Kutter’s formula is super- 
seding it in almost all countries where its accuracy has been investigated. 

The last table on p. 561 shows the value of c, in Kutter’s formula, for a wide 
range of channels in earth, that will cover anything likely to occur in the 
ordinary practice of an engineer. 


D°’Arcy’s Formula for clean iron pipes under pressure is 
rs % 


00000162 


C= —_—_———_ 
00007726 +- F 


Flynn’s modification of D’Arcy’s formula is 
_ (1552560 \2 
' =(3 i) X Vrs 
in which d = diameter in feet. 


_D’Arey’s formula, as given by J. B. Francis, 0.E., for old cast-iron pipe. 
lined with deposit and under pressure, is : 


re 144d2s ) 
~ \100sa(i2a Fi 7 ° 


Flynn’s modification of D’Arcy’s formula for old cast-iron pipe is 


FS Vas 








564 HYDRAULICS. 


For Pipes Less than 5 inches in Diameter, coefficients (c) 
in the formula v = c Yrs, from the formula of D’Arcy, Kutter, and Fanning. 









5 Kutter, | Fanning, 
erat hs on for for Clean 
alte oe tb Ola argn 


inches| Pipes. | 3 — ‘091 Pipes. 


: Kutter, | Fanning 

Diam. | D’Arcy for ° |for um 
i ’ or for Clean 
in j|for Clean nm = .011 Tron 


inches.| Pipes. | 3 — ‘991 Pipes 








% 59.4 32. 90.7 58.8 92.5 
04 65.7 36.1 92.9 61.5 94.8 
34 n4.5 42.6 96.1 66. 

1 80.4 47.4 80.4 98.5 £01 96.6 
114 84.8 51.9 101.7 "7.4 103.4 
144 88.1 55.4 88. 103.8 82.9 





Mr. Flynn, in giving the above table, says that the facts show that the co- 
efficients diminish from a diameter of 5 inches to smaller diameters, and it 
is a safer plan to adopt coefficients varying with the diameter than a con- 
stant coefficient. No opinion is advanced as to what coefficients shoulc be 
used with Kutter’s formula for small diameters. he facts are simply 
stated, giving the results of well-known authors. 

Older Formulz,.—tThe following are a few of the many formule for 
flow of water in pipes given by earlier writers. As they have constant coef- 
ficients, they are not considered as reliable as the newer formule. 


Prony, v= 97 Vrs — .08; 
dh 


Eytelwein, v= 504 or v= 108 Yrs — 0.13; 


1+ 50d’ 


ant divers é a Ves 
Hawksley, v= 48 / ta Neville, v = 140 //rs - 11 Yrs. 


In these formule d = diameter in feet; h = head of water in feet; 1 = 
length of pipe in feet; s = sine of slope = 7 * = mean hydraulic depth, 


= area + wet perimeter = < for circular pipe. 


Mr. Santo Crimp (Hng’g, August 4, 1893) states that observations on flow 
in brick sewers show that the actual discharge is 33% greater than that cal- : 
culated by Eytelwein’s formula. He thinks Kutter’s formula not superior 
to D’Arcy’s for brick sewers, the usual coefficient of roughness in the 
former, viz., .013, being too low for large sewers and far too small in the case 
of small sewers. 

D’Arcy’s formula for brickwork is 


V29 


o= = 
ne 


rss NY = a(t +2); a@ = .0087285; B= .229663. 


VELOCITY OF WATER IN OPEN CHANNELS. 


Irrigation Canals,—The minimum mean velocity required to prevent 
the deposit of silt or the growth of aquatic plants is in Northern India 
taken at 14 feet per second. It is stated that in America a higher velocity 
is required for this purpose, and it varies from 2 to 314 feet per second. The 
maximum allowable velocity will vary with the nature of the soil of the 
bed. .A sandy bed will be disturbed if the velocity exceeds 3 feet per 
second. Good loam with not too much sand will bear a velocity of 4 feet 
per second, The Cavour Canal in Italy, over a gravel bed, has a velocity of 
about 5 per second. (Flynn’s ‘‘Trrigation Canals.°’) 

Mean Surface and Bottom Velocities,—According to the for- 
mula of Bazin, 


VY = Umax ~ 25.4 Vrs; vs vb + 10,87 Vrs, 


VELOCITY OF WATER IN OPEN CHANNELS. 565 


-. vb = v — 10.87 7s, in which v = mean velocity in feet per second, 
ymax = maximum surface velocity in feet per second, vb = bottom velocity 
in feet per second, r = hydraulic mean depth in feet = area of cross-section 
in Square feet divided by wetted perimeter in feet, s = sine of slope. : 

The least velocity, or that of the particles in contact with the bed, is 
almost as much less than the mean velocity as the greatest velocity is 
greater than the mean. 

Rankine states that in ordinary cases the velocities may, be taken as bear- 
ing to each other nearly the proportions of 2, 4) ana 5. In wery slow cur- 
rents they are nearly as 2, 3, and 4. t SRS ew 2 Me Vie ‘ 

Safe Bottom and Mean Velocivies.--Ganguillet’ & Kutter give 
the following table of safe bottom and mean velocity in channels, calculated 





from the formula v = vb + 10.87 Vrs: ne FS wit’ eietiy 
ooo Ee 
Safe Bottom Veloce | Mean Velocity v, 
Material of Channel. ‘ity vb,in feet. | » in feet per 
per.segonid,. >| , , second, 
Soft brown earth ....... sihe hierdie cakes 0.249 ° 0.328 
SO hy lORM ose Seer. esee toadiaiceaten 0.499 0.656 
SEUNG peers he arare Ae eyes eb atare eleyete sbeie ed iten's 1.000 1.312 
Gravel SUITS Ae) Mase Hwee Oke 1.998 2.625 
Reb blesk regi. A. wecmprathadesaninnece aac. a 2.999 3.938 
Broken stone, flint ..... Hes Bone orstebowr ee 4.003 5.579 
Conglomerate, soft slate. ............ 4.988 6.564 


Sorawiiedwock:. a2... se beret. chkebeees 6.006 8.204 
Hard EOC Hae Pet oss ck eke iys 








Ganguillet & Kutter state that they are unable for want of observations 
to judge how far these figures are trustworthy. They consider them to be 
rather disproportionately small than too large, and therefore recommend 
them more confidently. 

Water flowing at a high velocity and carrying large quanties of silt is very 
destructive to channels, even when constructed of the best masonry. 

Resistance of Soils to Erosion by Water.—W. A. Burr, Eng’g 
News, Feb. 8, 1894, gives a diagram showing the resistance of various soils to 
erosion by flowing water. 

Experiments show that a velocity greater than 1.1 feet per second will 
erode sand, while pure clay will stand’a velocity of 7.35 feet per second. 
The greater the proportion of clay carried by any soil, the higher the per- 
missible velocity. Mr. Burr states that experiments have shown that the line 
describing the power of soils to resist erosion is parabolic. From his dia- 
eam the following figures are selected representing different classes of 
soils: 


Pure sand resists erosion by flow of.......- . 1.1 feet per second. 
Sandy Soll 1otiGlayae onyclae ttn, ate wate tee tee ae ee Re 
Sandy Joam: 40¢;claye.!.u s2.ccdecomhes.e #3, 25) 3B a> St 43 
Loamiy, Soil, 65¢:clayy ss... 0.1. 4acne. de tee Sila Sy 
Clay, loam. 85% clay... ....+c.. Abe at Git Marat Al 4.8 t ei 
Agricultural clay, 95% clay... .. ...tsseume sie Oxo hi MS 
OLA ij tiiceaeae Se auhtcc) abd seen ee: 7.35 * 


Abrading and Transporting Power of Water.—Prof. J. 
LeConte, in his *‘ Elements of Geology,” states : 

The erosive power of water, or its power of overcoming cohesion, varies as 
the square of the velocity of the current. 

The transporting power of a current varies as the sixth power of the ve- 
locity. * * * If the velocity therefore be increased ten times, the transport- 
ing power is increased 1,000,000 times. A current running three feet per 
second, or about two miles per hour, will bear fragments of stone of the 
size of a hen’s egg, or about three ounces weight. A current of ten miles an 
hour will bear fragments of one and a half tons, and a torrent of twenty 
miles an hour will carry fragments of 100 tons. 

The transporting power of water must not be confounded with its erosive 
power. ‘The resistance to be overcome in the one case is weight, in the 
other, cohesion ; the latter varies as the square : the former as the sixth 
power of the velocity. 

In many cases of removal of slightly cohering material, the resistance is a 


566 HYDRAULICS. 


mixture of these two resistances, and the power of removing material will 
vary at some rate between v2 and v§. 

Baldwin Latham has found that in order to prevent deposits of sewage silt 
in small sewers or drains, such as those from 6 inches to 9 inches diameter, 
a mean velocity of not less than 3 feet per second should be produced. 
Sewers from 12 to 24 inches diameter should have a velocity of not less than 
214 feet per second, and in sewers of larger dimensions in no case should the 
velocity be less than 2 feet per second. 

The specific zravity of the materials has a marked effect upon the mean 
velocities necessary to: move them. T. E. Blackwell found that coal of a 
sp. gr. of 1.26 was moved vy a current of from 1.25 to 1.50 ft. per second, 
while stones of a sp. gr. of 2.42. to 3.00 required a velocity of 2.5 to 2.75 ft. per 
second. . © , 

Chailly gives. the following forraula for finding the velocity required to 
moverounded stones or shingle: 

4 v = 5.67 Vag, 
in which v= veiovtity: of water in feet per second. a = average diameter in 
feet of the body te be moved, ¢ = its specific gravity. : 

Geo. Y. Wisner, Hig’g News, Jan 10, 1895, doubts the general accuracy of 
statements made by many authorities concerning the rate-of. flow of a cur- 
rent and the size of particles which different velocities will move. He says: 

The scouring action of any river, for any: given rate of current, must be an 
inverse function of the depth. The fact that some engineer has found that 
a given velocity of current on some stream of unknown depth will move 
sand or gravel has no bearing whatever on what may be expected of cur- 
rents of the same velocity in streams of greater depths. In channels 3 to 5 
ft. deep a mean velocity of 3 to 5 ft. per second may produce rapid scouring, 
while in depths of 18 ft. and upwards current velocities of 6 to 8 ft. per 
second often have no effect whatever on the channel bed. 

Grade of Sewers,.—The following empirical formula is given in Bau- 
meister’s ‘‘ Cleaning and Sewerage of Cities,’’ for the minimum grade for a 
sewer of clear diameter equal to d inches, and either circular or oval in 
section ; io 

Minimum grade, in per cent, 5d + 50" 

As the lowest limit of grades which can be flushed, 0.1 to 6.2 per cent may 
be assumed for sewers which are sometimes dry, while 0.3 per cent is allow- 
able for the trunk sewers in large cities. The sewers should run dry as 
rarely 2% possible. 

HRelution of Diameter of Pipe to Quantity Discharged.— 
In many cases which arise in practice the information sought is the diame-. 
ter necessary to supply a given quantity of water under a given head. The 
diameter is commonly taken to vary as the two-fifth power of the dis- 
charge. This is almost certainly too large. Hagen’s formula, with Prof. 


Ae : P sts 
Unwin’s coefficients, gived =c “y}) 
L 


are in feet and cubic feet per second. 

Mr. Thrupp has proposed a formula which makes d vary as the .383 power 
of the discharge, and the formula of M. Vallot,a French engineer, makes d 
vary as the .375 power of the discharge. (Mngineering.) 





, where c = .239 when d and Q 


FLOW OF WATER—EXPERIMENTS AND TABLES. 


Whe Flow of Water through New Cast-iron Pipe was 
measured by S. Bent Russell, of the St. Louis, Mo., Water-works. The 
pipe was 12 inches in diameter, 1631 feet long, and laid on a uniform 
grade from end to end. Under an average total head of 3.36 feet the flow 
was 43,200 cubic feet in seven hours; under an average head of 3.37 feet the 
flow was the same; under an average total head of 3.41 feet the flow was 
46,700 cubic feet in 8 hours and 35 minutes. Making allowance for loss 
of head due to entrance and to curves, it was found that the value of ¢ in 


the formula v = ¢ /7s was from 88 to 93. (Eng’g Record. April 14, 1894, 


Flow of Water in a 20-inch Pipe 75,000 Feet Long.—A 
comparison of experimental data with calculations by different formule is 


FLOW OF WATER—EXPERIMENTS AND TABLES. 56, 


given by Chas. B. Brush, Trans. A. 8. C. E., 1888. The pipe experimented 
with was that supplying the city of Hoboken, N. J. 


REsvULTS OBTAINED BY THE HACKENSACK WATER COMPANY, FROM 1882-1887, 
IN PuMPING THROUGH A 20-IN. CAST-IRON Matin 75,000 Feet Lone. 
Pressure in Ibs. per sq. in. at pumping-station; 

95 100 105 110 115 120 125 130 


Total effective head in feet; 
55 66 qq 89 100 112 128 185 


Discharge in U. S. gallons in 24 hours, 1 = 1000; 
2,848 38,165 8,354 3,566 8804 8904 4,116 4,255 


Actual velocity in main in feet per second : 
2.00 2.24 2.36 2.52 2.68 2.76 2.92 8.00 


Cost of coal consumed in delivering each million gals. at given velocities . 
$8.40 $8.15 $8.00 $8.10 -$830 $860 $9.00 $9.60 


Theoretical discharge by D’Arcy’s formula: 
2,743 8,004 38,244 38,488 38699 8,918 4,102 4,297 


Velocities in Smooth Czrst-iron Water-pipes from 1 Foot 
to 9 Feet in Diameter, on Hydraulic Grades of 0.5 
Foot to 8 Feet per Mile; with Corresponding Values 


ofcin V=cYrs. (D.M. Greene, in Eng’g News, Feb. 24, 1894.) 




















~ : = 
o> 5 os Hydraulic Grade; Feet per Mile =h. 
3 4/Sa 8 
oma $4 Ao 
As|zs his 08 1.0 1.5 2.0 3.0 4.0 
D.| r. |s=0.0000947 | 0.0001894| 0.0002841] 0.003788] 0.0005682| 0.0007576 
1. lo.o55 | V= 0.4542 0,667 0.8356 | 0.9803] 1.2877 | 1.4402 
- 10. 54 c= 92.7 97.0 99.1 100.7 103.0 104.7 
a. los §| 7=, 0.7859] 1.0798 | 1.8516 | 1.5856 | 1.9857 | 2.3204 
- 10-5 4) ¢= 106.6 | 110.9 113.4 115.2 117.9 119.7 
3. lo.rnh | V = ..0-9733] 1.4298 | 1.7906 | 2.1017} 2.6306 | 8.0860 
- 10.754) = 115.5 | 119.9 122.6 24.4 127.5 198.5 
a. lto S$ | V= ..1-1883] 1.7456 | 2.1861 | 2.5645 | 3.2116 | 3.7676 
- [i ; c= 122.1 | 126.8 129.7 131.8 | 184.7 136.9 
ical bead = 1.3872} 2.03791 2.5521} 2.9939| 3.7498 | 4.3983 
- fi. c=: 127.5 | 182.4 135.5 137.6 140 142.9 
ge. lis $| V=..1-5742| 2.8126 | 2.8961 | 3.8075 | 4.2548 | 4 9918 
- fi. ; c= 132.1 | 137.8 140.3 142.6 145.8 48.1 
». lead | Vx.) -T518| _ 25796 | 8.2280] 8.7809] 4.7850 | 5.5546 
xs { ce = 185.9 | 141.4 146.0 46.8 5 152.5 
s. leo $| V= .1-9218] 2.8284 | 3.5358} 4.1479] 5.1945 | 6 0936 
- [?- } c= 139.7 | 1451 148.4 150.7 154.1 156.5 
“ees = 2.0854, 3.0638} 3.8368] 4.5010] 5.6368 | 6.6125 
9. [2.2 ; c= 142.9 | 148.4 151.7 154.2 157 160.1 





The velocities in this table have been calculated by Mr. Greene’s modifi- 
cation of the Chezy formula, which modification is found to give results 
which differ by from 1.29 to — 2.65 per cent (average 0.9 per cent) from very 
earefully measured flows in pipes from 16 to 48 inches in diameter, on grades 
from 1.68 feet to 10.296 feet per mile, and in which the velocities ranged 
from 1.577 to 6.195 feet per second. The only assumption made is that the 
modified formula for V gives correct results in conduits from 4 feet to 9 
feet in diameter, as it is known to do in conduits less than 4 feet in diameter. 

Other articles on Flow of Water in long tubes are to be found in Eng’g 
News as follows: G. B. Pearsons, Sept. 23, 1816; E. Sherman Gould, Feb. 16, 
23, March 9, 16, and 23, 1889; J. L. Fitzgerald, Sept. 6 and 13, 1890; Jas. Duane, 
Jan. 2, 1892; J. T. Fanning, July 14, 1892; A. N. Talbot, Aug. 11, 1892. 


568 HYDRAULICS. 


Flow of Water in Circular Pipes, Sewers, etc., Flowing 
Full, Based on Kutter’s Formula, with n= .013. 


Discharge in cubic feet per second. 





Slope, or Head Divided by Length of Pipe. 




















Diam- 
eter 
1in 40} 1 in 70 |1 in 100 |1 in 200 |1 in 300 /1 in 400 |1 in 500 |1 in 600 

5 in. 456 344 288 204 166 0144 137 .118 
6 “ 162 .576 482 3841 278 241 280 19% 
! Ca 1.17 .889 744 526 430 .872 305 304 
Biss 1.70 1.25 1.08 2765 624 54 516 441 
g s¢ 2.387 1.79 1.50 1.06 868 ayes) tal 613 
Slope ....| 1 in 60 1 in 80 Lin 100 }1 in 200 |1 in 300 be 1 in 500 |1 in 600 
10 in. 2.59 2.24 2.01 1.42 1.16 1.0 90 82 
10h OF 3,389 2.94 2.63 1.86 1 52 le 21 1.17 1.07 
72) °* 4.32 3.74 3.35 2.387 1.93 1.67 1.5 1.37 
TOASS 5.38 4.66 4.16 2.95 2.40 2.08 1.86 140 
14h 6.60 5.72 5.15 3.62 2.95 2.57 2.29 2.09 
Slope....{ 1 in 100}1 in 200 |1 in 800 |1 in 400 }1 in 500 |1 oe eu 1 in 700 |1 in 800 
15 in, 6.18 4.37 8.57 3.09 2.77 2.34 2.19 
16 ‘* 7.8 5.22 4.26 3.69 8.30 3 “Ot 2.79 2.61 
18 ‘* 10.21 @.22 5.89 5.10 4.56 4.17 3.86 3.61 
20 * 13.65 9.65 7.88 6.82 6.10 5.57 5.16 4.83 
ae Ge 0 12.52 | 10.22 8.85 7.92 428 6.69 6.26 
Slope... {1 in in “200 1 in 400 |1 in 600 {1 in 800 |1 in 1000}1 in 1250)1 in 1500/1 in 1800 
2 ft. 15.88 | 11.23 9.17 7.94 4.10 6.35 5.80 5.29 


2ft.2in.| 19.73 | 18.96 } 11.389 9.87 8.82 7.89 7.20 6.58 
24 | 24.15} 17.07 | 13894] 12.07} 10.80 9.66 8.82 8.05 
26 | 29.08] 20.56 | 16.79 | 14.54] 18.00} 11.63 | 10.62 9.69 
28% | 84.71 | 24.54] 20.04] 17.85 | 15.52 | 18.88 | 12.67] 11.57 
Slope ....{1 in 500/1 in 750 |1 in 1000|1 in 1250/1 in 1500/1 in 1750/1 in 2000)1 in 2500 
2ft.10in.| 25.84 | 21.10 | 18.27) 16.34 | 14.92) 13.81 | 12.92] 11.55. 
eae’ 80.14 | 24.61 | 21.381} 19.06 | 17.40} 16.11 | 15.07 | 18.48 
8 ‘* Qin. | 34.90 | 28.50 | 24.68 | 22.07 | 20.15 | 18.66 | 17.45] 15.61 
Bist |S 40.08 | 82.72 | 28.84] 25.85 | 23.14] 21.42 | 20.04! 17.98 
a *<6 ie 45.66 | 87.28 | 82.28] 28.87 | 26.386 | 24.40] 22.88 ee 41 
Slope....{1 in 500 1 in 750/1 in 1000}1 in 1250/1 in 1500}1 in 1750/1 in 2000 lin in 2500 
3 ft. Sin, 51.74 | 42.52 | 86.59 | 82.72 | 29.87 |} 27.66 | 25.87 | 28.14 
810 ** | 58.36) 47.65 | 41.27] 86.91 | 33.69 | 31.20 | 29.18 | 26.10 








4% 65.47 | 53.46 | 46.30] 41.41 } 37.80 | 84.50 |] 32.74 | 29.28 
4°46 in2} 8957 73.28 | 63.47 | 56.76 | 51.82 { 47.97 | 44.88} 40.14 
Bis 118.9 97.09 | 84.08} 75.21} 68.65] 63.56 | 59.46] 53.18 








Slope ....]1 in 750)1 in 1000/1 in 1500|1 in 2000/1 in 2500}1 in 3000/1 in 3500/1 in 4000 
5ft.6in.| 125.2 | 108.4 88.54°| 76.67 | 68.58 | 62.60 | 57.96 | 54.21 


er toyes | 18627 | 111.6 96.66 | 86.45] 78.92 | %3.07 | 68 35 
6 “© 6s: } 195'0>) 168.8 | 187.9 | 119.4 | 106.8 97.49 | 90.26 | 84.43 
Ore 237.7 | 205.9 | 168.1 | 145.6 (180.2 | 118.8 | 110.00 | 102.9 


7° 6S | 285.8 | 247.1 | 201.7 | 174.7 | 156.3 | 142.6 | 182.1 | 123.5 


eee | ee ) | 








er | ee | 





_ 


Slope....{1 in 1500)1 in 2000)1 in wis 1 in 8000}1 in 8500}1 in =e 1 in 4500/1 in 5000 


8 ft. 239.4 | 207.3 | 195.4 ) 169.38 } 156.7 | 146.6 } 188.2 / 131.1 
8 “ Gin.} 281.1 | 248.5 | 217.8 | 198.8 | 184.0 | 172.2 | 162.3 | 154.0 
9 ** 827.0 | 283.1 | 258.3 | 2381.2 | 214.0 | 200.2 |} 188.7 | 179.1 
9 6 * | 376.9 | 826.4 | 291.9 | 266.5 | 246.7 | 230.8 { 217.6 | 206.4 
10 ‘* 431.4 | 873.6 | 384.1 |! 3805.0 1 282.4 | 264.2 | 249.1 | 266.3 





For U.S. gallons multiply the figures in the table by 7.4805. 
For a given diameter the quantity of flow varies as the square root of tho 
sine of the slope. From this principle the flow for other slopes than those 


FLOW OF WATER IN CIRCULAR PIPES, ETC. 569 


given in the table may be found. Thus, what is the flow for a pipe 8 feet 
diameter, slope 1in 125? From the table take Q = 207.3 for slope 1 in 2000, 
The given slope 1 in 123 is to 1 in 2000 as 16 to 1, and the square root of this 
ratio is4to1. Therefore the flow required is 207.3 x 4 = 829.2 cu. ft. 


Circular Pipes, Conduits, etc., Flowing Full. 


Values of the factor ac Vr in the formula (Ge vare: Vr x V's correspond~ 
ing to different values of the coefficient of roughness, 1. (Based on Kutter’s 
formula.) 





Value of ac Vr. 


Diam. 


— eee 


ft. in.|} n= .010. | m= .011. | a= .012. | n = .013. | n = .015. |n = .017, 








6.906 6.0627 5.3800 4.8216 3.9604 3.329 


6 
9 21.25 18.742 16.708 15.029 12.421 10.50 
1 46.93 41.487 37.149 33.497 27.808 23.60 
1 3 86.05 (6.347 68.44 61.867 51.600 43.93 
1 6 141.2 125.60 112.79 102.14 85.496 72.99 
ss) 214.1 190.79 171.66 155.68 130.58 111.8 
2 307.6 274.50 247 33 224.63 188.77 164 
2 3 421.9 377.07 340.10 809.23 260.47 223.9 
2 6 559.6 500.78 452.07 411.27 847.28 299.3 
ao 922.4 647.18 584.90 532.76 451.23 388.8 
3 911.8 817.50 739.59 674.09 570.90 493.3 
3 3 1128.9 1013.1 917.41 836.69 709.56 613.9 
38 6 1374.7 1234.4 1118.6 1021.1 866.91 750.8 
38 9 1652.1 1484.2 1345.9 1229.7 1045 906 
4 1962.8 1764.3 1600.9 1463.9 1245.3 1080.7 
4 6 2682.1 2413.3 2193 2007 1711.4 1487.3 
5 8543 3191.8 2903.6 2659 2272.7 1977 
5 6 4557.8 4111.9 8742.7 8429 2934.8 2557.2 
6 5731.5 5176.3 4713.9 4322 3702.3 3232.5 
6 6 7075.2 6394.9 5825.9 5339 4588.3 4010 
7 8595.1 7774.3 7087 6510 5591.6 4893 
7 6 | 10296 9318.3 8501.8 7814 6717 5884, 2 
8 12196 11044 10083 9272 7978.3 6995.3 
8 6| 14298 12954 11832 10889 9377.9 8226.3 
9 16604 15049 13751 12663 10917 9580.7 
9 6] 19118 7338 15847 14597 12594 11061 
10 21858 19834 18134 16709 14426 1267 
10 6] 24823 22534 20612 18996 16412 14434 
11 28020 25444 23285 21464 18555 16333 
11 6] 31482 28593 26179 24139 2087S 18395 
12 35156 81987 29254 26981 23352 20584 
12 6] 89104 85529 82558 30041 26012 22938 
13 43307 89358 86077 33301 28859 25451 
138 6) 47751 43412 89802 3E752 31860 28117 
14 52491 47739 43773 40432 3507 80965 
14 6] 57496 52308 47969 44322 38454 83975 
15 62748 57103 52382 48413 42040 37147 
16 74191 67557 62008 57343 49823 44073 
17 86769 79050 72594 67140 58387 51669 
18 100617 91711 84247 (7932 67839 60067 
19 115769 105570 . 96991 §9759 78201 69301 
20 132133 12057 110905 102559 89423 79259 


Flow of Water in Circular Pipes, Conduits, etc., Flowing 
under Pressure. 


Based on D’Arcy’s formule for the flow of water through cast-iron pipes. 
With comparison of results obtained by Kutter’s formula, with n = .013. 
{Condensed from Flynn on Water Power.) 


Values of a, and also the values of the factors c Vr and ac Yr for use 10 
the formule Q=av; v=cVrx Ys, and Q= ac Vrx Vs 


570 


Q = discharge in cubic feet per second, a = area in square feet, v = veloc 
ity in feet per second, » = mean hydraulic depth, 14 diam. for pipes running 
full, s = sine of slope. 


(For values of 4/3 see page 558.) 


HYDRAULICS. 








Clean Cast-iron Old Cast-iron Pipes 


Size of Pipe. 




















Pipes. Value of Lined with Deposit. 
ac Vr by 
d=idiam.) 2°" |. Bor For Dis- tee or For 
in square Velocity,| charge, when | Velocity, | Discharge, 
ft. in feet. c Vr acVr. |n=.013.| cYVr- ac Yr. 
8% 00077 5.251 .00403 3.532 .0027 
1 .00136 6.702 00914 4.507 .00613 
34 00307 9.309 .02855 6.261 01922 
1 .00545 | 11.61 .06334 7.811 04257 
14 .00852 | 13.68 11659 9.255 07885 
144 001227 | 15.58 «19115 # 10.48 - 12855 
134 -01670 | 17.32 228936 11.65 . 19462 
2 02182 | 18.96 .41357 12.75 021824 
216 -0341 21.94 374786 14.76 .90321 
3 0491 24.63 1.2089 16.56 .81333 
4 20873 29.37 2.5630 19.75 1.7246 
5 136 83.54 4.5610 22.56 3.0681 
6 0196 37.28 7.3068 4.822; 25.07 4.9147 
vg 267 40.65 10.852 27.34 7.2995 
8 .849 43.7 15.270 29.43 10.271 
9 2442 46.73 20.652 15.03 31.42 13.891 
10 0545 49.45 26.952 83.26 18.129 
11 2660 52.16 34.428 35.09 23.158 
1 785 54.65 42.918 23.50 86.75 28.867 
1438 1,000 59.34 63.435 39.91 42.668 
1 4 1,396 63.€7 88.886 42.83 59.788 
1 6 1,767 67.75 119.72 102,24 45.57 80.531 
1 8 2.182 71.71 156.46 48 .34 105.25 
2 10 2.640 75.32 198.83 50.658 133.74 
2 3,142 78.80 247.57 424.03 52.961 166.41 
2 2 3.687 82.15 302.90 55.258 203.74 
2 4 4.276 85.39 365.14 57.436 245.60 
2° 6 4,909 §8 .39 433.92 411.37 59.455 291.87 
DP} 5.585 91.51 511.10 61.55 843.8 
2 10 6.305 94.40 595.17 63.49 400.3 
3 7.068 97.17 686.76 674.09 €5.385 461.9 
3.2 7.875 99.93 786.94 67.21 529.3 
3 ea 8.726 102.6 895.7 69 602 
3 6 9.621 105.1 1011.2 102f.1 70.7% 680.2 
SCS 10.559 107.6 1136.5 72.40 764.5 
3 10 11.541 110.2 1271.4 4.10 855.2 
4 12.566 112.6 1414.7 1463.9 5.73 951.6 
4 8 14,186 116.1 1647.6 78.12 1108.2 
4 6 15.904 119.6 1901.9 2007 80.43 1279.2 
4 9 17.721 122.8 2176.1 82.20 1456.8 
5 19,636 126.1 2476.4 2659 84.83 1665.7 
5 3 21.648 129.3 2799.7 86.99 1883 .2 
5 6 23.758 132.4 3146.3 8429 89.07 2116.2 
5 9 25.967 185.4 3516 91.08 2365 
6 28 274 138.4 3912.8 4322 93.08 2681.7 
6 6 33.183 144.1 4782.1 5339 96.93 3216.4 
7 38.485 149.6 5757.5 6510 100.61 8872.5 
(eG 44.179 154.9 6841.6 7814 104.11 4601.9 
8 50.266 160 8043 9272 107.61 5409.9 
8 6 56.745 163 9364.7 10889 111 \ 6299.1 
9 63.617 169.8 10804 12663 114.2 9267.3 
9 6 70.882 174.5 12370 14597 | 117.4 8320.6 
10 78.540 179.1 14066 16709! 120.4 9460.9 


FLOW OF WATER IN CIRCULAR PIPES, ETC, 





Size of Pipe. 


d= diam. 


fi) in, 


Clean Cast-iron 
Pipes. 


Value of 

- Vr by 

Be utter’s 

mr oat ce For For Dis- |Formula, 

Velocity,! charge, when 
square 2S 

feet. c ac Vr nm = 013 
86.590 183.6 15893 18996 
95.033 187.9 17855 21464 
103.869 192.2 19966 24139 
113.098 196.3 22204 26981 
122.719 200.4 24598 30041 
132.733 204.4 27134 33301 
143.139 208.3 29818 867352 
153.938 212.2 32664 40432 
165.130 216.0 35660 44322 
176.715 219.6 38807 48413 
188.692 223.3 42125 52753 
201.062 226.9 45621 57343 
213.825 230.4 49273 62132 
226.981 233.9 58082 67140 
240.529 237.3 57074 72409 
254.470 240.7 61249 77932 
283 .529 247.4 70154 89759 
814.159 253.8 79736 102559 


571 


—? 


Old Cast-iron Pipes 
Lined with Deposit. 





For For 
Velocity, | Discharge, 
c Vr ac Yr. 
123.4 10690 
126.3 12010 
129.3 13429 
132 14935 
134.8 16545 
187.5 18252 
140.1 20056 
142.7 21971 
145.2 23986 
147.7 26108 
150.1 28385 
152.6 30686 
155 83144 
157.3 35704 
159.6 38389 
161.9 41199 
166.4 47186 
170.7 53633 


Flow of Water in Circular Pipes from % inch to 12 inches 
Diameter. 


Based on D’Arcy’s formula for clean cast-iron pipes. 


Q=ace Vr Vs. 





Value of on 


ac Yr. 


eee ee ee | eee 


.00403 
.00914 
.02855 
.06334 
-11659 
619115 
28936 
41357 
74786 
1.2089 
2.5630 
4.5610 
7.3068 
10.852 
15.270 
20.652 
26.952 
34.428 
42.918 


in, 


244 


OO Wt Or CO 


eh 
or 





.00127 
00289 
.00903 
-02003 
03687 
-06044 
-09140 
13077 
.23047 
88225 
-81042 
1.4422 
2.3104 
3.4314 
4.8284 
6.5302 
8.5222 


13.571 


2936 _|_.1581 [| .1291 | .1118 


Value of 7s =| _.3162 


ee | 


1 in 10.}1 in 20.|1 in 40.]1 in 60.)1 in 80. 








lin 
100. 


Slope, or Head Divided by Length of Pipe. 


lin 
150. 





Quan|tity in | cubic |feet pler sec/ond. 


.00090 
00204 
00638 
.01416 
.02607 
04274 
.06470 
.09247 
- 16722 
27031 
.57309 
1.0198 


.00064 
00145 
00251 
01001 


"72109 


1.6388 |1.1552 
2.4265 11.7157 
3.4143 |2.4141 
4.6178 |3.2651 
6.0265 |4.2611 
10.886 |7.6981 |5.4431 
9.5965 |6.7853 





.00052| .00045 
.00118) .00102 
-00369) .00319 
.00818) .00708 
.01505) .01303 
.02468) .02137 
.03736) .03235 
.05389| .04624 
09655) .08361 
15607) .18515 
.33088] .28654 
-58882| .50992 
94331] .81690 
1.4110 |1.2132 
1.9713 |1.7072 
2.6662 |2.3089 
3.4795 |3.0132 
4.4447 |3.8491 


.00040 
00091 
00286 
00633 
.01166 
01912 
02894 
04136 
07479 
12089 
-25630 
»45610 
73068 

1 “0852 
1.5270 
2.0652 
2.6952 


a a | Oe | 


1 


.00033 
00075 
. 00233 
.00517 
- 00952 
.01561 
-02363 
038377 
.06106 
.09871 
. 20927 
.37241 
. 59660 
. 88607 


lin 
200. 





.00028 
- 00065 
-00202 
00448 
-00824 
.01352 
02046 
02927 
05288 
.08548 
. 18123 
82251 
.51666 


. 16734 


1.2468 1.0797 
1.6862 11.4603 
2.2006 11.9058 
3.4428 |2.8110 |2 4344 
5.5407 |4.7982 |4.2918 |8.5043 |3.0347 





08165] .07 


07071 


572 HYDRAULICS, 








Slope, or Head Divided by Length of Pipe, 

Value of Dia. 
ac Yr. in. lin | lin | 1in | Jin | 1in | lin | 1in 
1 in 250.) 300, | 350. | 400. | 450. | 500. | 550. | 600. 











ed - 











-00403 34] .00025} .00023} .00022} .00020) .00019) .00018] .00017| .00016 
-00914 14; .00058} .00053} .00049} .00046} .00043; .00041} .00039| .00037 
02855 34| .00181] .00165) .00153) .00143) .00134) .00128) .00122) .00117 
-063384 | 1 .00400} .00366;} .00339] .00317) .00298) .00283} .00270} .00259 
.11659 | 124) .00737) .00673) .00623] .00583] .00549) .00521) .00497| .00476 
19115 | 134) .01209) .01104, .01022)} .00956/ .00901| .00855} .00815] .00786 
.28936 | 134] .01830) .01671| .01547) .01447] .01363) .01294] .01234] .01181 
41357 | 2 .02615) .02388] .02211] .02068} .01948) .01849] .01763, .01688 
74786 | 244) .04730) .04318] .03997) .03739] .03523) 08344) .03189) .03053 
‘1.2089 3 .07645) .06980} .06462| .06045! .05695) .05406; .05155) .04935 











2.5630 4 . 16208) .14799] .18699| .12815] .12074| .11461) .10929) .10463 

4.5610 5 .28843) .26335] .243879] .22805] .21487) .20397) .19448) .19620. 

7.3068 6 -46208} .42189] .39055| .36534| 34422) .82676/ .31156) .29830 
10.852 7 68628] .62660] .58005) .54260] .51124} .48530) .46273) .44303 
15.270 8 .96567| .88158] .81617) .76350) .71936) .68286) .65111) .62340 


20.652 9 4 1.3060 |1.1924 |1.1038 41.0326 | .97292} .92356} .88060) .84310 
26.952 10 | 1.7044 |1.5562 |1.4405 {1.38476 |1.2697 1.2053 |1.1492 |1.1003 
34.428 11 | 2.1772 [1.9878 |1.8402 {1.7214 }1.6219 |1.5396 }1.4680 |1.4055 
42.918 12 | 2.7141 |2.4781 12.2940 /2.1459 |2.0219 {1.9193 ]1.8300 |1.7521 


or 
fer) 




















Value of /s = | .06324] .05774| .05345 05 | .04711] .04472] .042641 .04082 
For U. S. gals. per sec., multiply the figures in the table by...... 7.4805 
6G 6 ‘6 min. 66 se ts 66 ecccce 448.83 
“8 cons hear 6s 66 66 “ epee 26929.8 
we 46 & 8% 94 hi ve 6s 6 « C ac re i. 646315. 


For any other slope the flow is proportional to the square root of the 
slope ; thus, flow in slope of 1 in 100 is double that in slope of 1 in 400, 


Flow of Water in Pipes from 34 Inch to 12 Inches 
Diameter for a Uniform Velocity of 100 Ft. per Min. 








Diameter Area Flow in Cubic |Flow in U. S.| Flow in U. §S. 
in in Feet per Gallons per | Gallons per 

Inches. Square Feet. Minute. Minute. Hour. 
36 00077 0.077 57 34 
44 -00136 0.136 1.02 61 
34 00307 0.307 2.30 138 

1 -00545 0.545 4.08 245 
14 -00852 0.852 6.38 383 
14% .01227 1.227 9.18 551 
134 01670 1.670 12.50 750 
2 .02182 2.182 16.32 979 
214 0341 3.41 25.50 1,530 
8 .0491 4.91 36.72 2,203 
4 0873 8.73 65.28 3,917 
5 0136 13.6 102.00 6,120 
6 196 19.6 146.88 8,813 
7 267 26.7 199.92 11,995 
8 2349 84.9 261.12 15,667 
9 442 44.2 330.48 19,829 
10 545 54.5 408.00 24,480 
11 660 66.0 493.68 29,621 
12 0785 78.5 587.52 35,251 





Given the diameter of a pipe, to find the quantity in gallons it will deliver, 
the velocity of flow being 100 ft. per minute. Square the diameter in inches 
and multiply by 4.08. 


LOSS OF HEAD. 573 


If Y = quantity in gallons per minute and d = diameter in inches, then 
_ d? X .7854 x 100 x 7.4805 


U 2 
Q a = 4.0842, 
4 
For any other velocity, V’, in feet per minute, Q’ = 4.08027 = .0408d?V'’. 


Given diameter of pipe in inches and velocity in feet per second, to find 
discharge in cubic feet and in gallons per minute, 


, a2 X .7854 X v xX 60 
Sho 144 
= .82725 x 7,4805 or 2.448d2v U. S. gallons per minute. 


= 0.82725d2v cubic feet per minute. 


To find the capacity of a pipe or cylinder in gallons, multiply the square 
of the diameter in inches by the length in inches and by .0034._ Or multiply 
the square of the diameter in inches by the length in feet and by .0408, 


Q= Saeee = ,0034d22 (exact) .0034 x 12 = .0408. 


LOSS OF HEAD. 


The loss of head due to friction when water, steam, air, or gas of any kind 
flows through a straight tube is represented by the formula 


h= oOue. whence v = CEB he 
d 2g’ iv Sfidied 


in which 2 = the length and d@ = the diameter of the tube, both in ‘eet; v = 
velocity in feet per second, and f is a coefficient to be determined by experi 
ment. According to Weisbach, f = .00644, in which case 


64.4 hd 
“Tin 50, and v= 50, > 


which is one of the older formule for flow of water (Downing’s), Prof. Un- 
win says that the value of f is possibly too small for tubes of small bore, 
and he would put f = .006 to .01 for 4-inch tubes, and f = .0084 to .012 for 2- 
inch tubes. Another formula by Weisbach is 


-01716\ 2 2 


rae (0148 a wrens = 


Rankine gives ‘ 
j= .005( + ea 7° 


From the general equation for velocity of flow of water v=c Vr Vs, = 





3 
for round pipes c (/% m we have vy? = og ‘ and h = et , in which 


c is the coefficient c of D'Arcy’s, Bazin’s, Kutter’s, or other formula, as found 
by experiment. Since this coefficient varies with the condition of the inner 
surface of the tube, as well as with the velocity, it is to be expected that 
values of the toss of head given by different writers will vary as much as those 
of quantity of flow. Twotables for loss of head per 100 ft. in length in pipes 
of different diameters with different velocities are given below. The first 
is given by Clark, based on Ellis’ and Howland’s experiments; the second is 
from the Pelton Water-wneel Co.’s catalogue, based on Cox’s formula, see 
p. 575, with the divisor 1000 instead of 1200, as it is for riveted steel pipe, 
The loss of head as given in these two tables for any given diameter and 
velocity differs considerably. Either table should be used with caution and 
the results compared with the quantity of flow for the given diameter and 
head as given in the tables of flow based on Kutter’s and D’Arcy’s formulee. 


iy ees HYDRAULICS. 


Relative Loss of Head by Friction for each 100 Feet 
Length of Clean Cast-iron Pipe. 


(Based on Ellis and Howland’s experiments.) 





Diameter of Pipes in Inches. 








Velocit RSENS) is a 
nfet [Sa ]s|efr]se]e»]o,n| x 
Second. a 


Loss of Head in Feet, per 100 Feet Long. 
Feet | Feet | Feet | Feet | Feet | Feet | Feet | Feet | Feet | Feet: 
of of of of of of of of of | of 
Head|Head |Head | Head|Head|Head|Head|Head |Head | Head 





Loss of Hiead in Pipe by Friction.— Loss of head by friction in _ 
each 100 feet in length of different diameters of pipe when discharging the 
following quantities of water per minute (Pelton Water-wheel Co.) : 














i Inside Diameter of Pipe in Inches. 

2 1 2 8 a BPRS 

i.) 

md ce ue se] te so) be 3 be Lo! we lS a 

eepge 1S (8 18 [eles & js 1a |eaie 

Sep el | es |e lee | “ail Solel eel meee 

S133 [es ) Ss | es) 63 | Bs) S38 | Bs [Ss les|s5 las 

§ on we wm 28 os 2a on Qs ne 2s = 28 

e che ae ite BF cha aa ite oe ba te a cle 
| 

Vik Q h Q h Q h Q hi @j;hi}Q 

2.0; 2.387) .65 } 1,185) 2.62 791} 5.89)  .503) 10.4 | .474) 16.3) .395) 23.5 

3.0} 4.89) .99 | 2.44 | 3.92 | 1.62} 8.83) 1.2 15.7 | .978| 24.5) .815| 35.3 

4.0} 8.20} 1.82 | 4.10 | 5.23 | 2.73 | 11.80) 2.05 | 20.9 [1.64 | 82.7/1.37 | 47.1 

5.0} 12.33) 1.65 | 6.17 | 6.54 | 4.11 | 14.70] 3.08 | 26.2 |2.46 | 40.9)2.05 | 58.9 

6.0) 17.23) 1.98 } 8.61 | 7.85 | 5.74 | 17.70) 4.31 | 81.4 |3.45 } 49.1]2.87 | 70.7 

7.0| 22.89) 2.31 |11.45 | 9.16 | 7.62 | 20.6 | 5.72 | 86.6 14.57 | 57.2/3.81 | 82.4 


(Continued on next page.) 
Flow of Water in Riveted Steel Pipes.—tThe laps and rivets 
tend to decrease the earrying capacity of the pipe. See paper on ‘New 
Formulas for Calculating the Flow of Water in Pipes and Channels,” 
by W. E. Foss, Jour. Assoc. Eng. Soc., xiii, 295. Also Clemens Herschel’s 
pook on ‘115 Experiments on the Carrying Capacity of Large Riveted Metal 
Conduits,’”? John Wiley & Sons, 1897. 


6 


LOSS OF HEAD. avo 





Inside Diameter of Pipe in Inches. 
ve j 8 9 : 10 i1 12 



































=| —— —_ | —-— 













2.0) .3838) 32.0) .296) 41.9) . 198] 94.2 
3.0} .698) 48.1) .611) 62.8) .544 

4.0) 1.175} 64.1) 1.027] 83.7) .913 

5.0) 1.76 | 80.2) 1.54 | 105 | 1.37 

6.0} 2. 2.15 | 125 

7.0 2.85 | 146 














13 16 18 20 
Veins ber Q;|;rA\Q{[ 2] Q 
2.0/ .183} 110 167 | .132] 212 | .119| 262 
3.0| 13751 166 251 | 271] 318 | 1245] 393 
4.0] 632} 221 335 | 456] 424 | 1410] 523 
5.01 19491 276 419 | .685| 530 | _617| 654 
6.0] 1.3: 502 | :957| 636 
7.01 1. 586 11.27 | 742 











Inside Diameter of Pipe in Inches. 
22 24 26 28 30 36 











Pelt the|) Onin hint On(haeteocli melo Me aAcleo 








0| .108| 816] .098 | 377 | .091 | 442] .084 | 513 | .079| 589) .066] 848 
O| .222] 475] .204 | 565 | .188} 663 | .174 | 770 | .163) 883) .135) 1278 
.0| .3873] 683) .842 | 754 | .815 | 885 | .298 | 1026 | .273) 1178] .228) 1697 
O| .561] 792} .513 | 942) .474 | 1106 | .440 | 1283 | .411] 1472) .842) 2121 
0, .782} 950 | .717 | 11381 | .662 | 1827 | .615 | 1539 | .574| 1767] 479) 2545 
‘0! 1.0401 1109 | .953 | 1319 | .879 | 1548 | .817 | 1796 | .762] 20611 2636] 2868 


EXAMPLE.—Given 200 ft. head and 600 ft. of 11-inch pipe, carrying 119 cubic 
feet of water per minute. To find effective head: In right-hand column, 
under 11-inch pipe, fina 119 cubic ft.; opposite this will be found the loss by 
friction in 100 ft. of length for this amount of water, which is .444. Multiply 
this by the number of hundred feet of pipe, which is 6, and we have 
2.66 ep bere is the loss of head. Therefore the effective head is 200 — 2.66 
= 197.34, 2 

EXPLANATION.—The loss of head by friction in pipe depends not only upon 
diameter and length, but upon the quantity of water passed through it. The» 
head or pressure is what would be indicated by a pressure-gauge attached 
to the pipe near the wheel. Readings of gauge should be taken while the 
water is flowing from the nozzle. 

To reduce heads in feet to pressure in pounds multiply by .433. To reduce 
pounds pressure to feet multiply by 2.309. 

Cox’s Formutla.—Weisbach’s formula for loss of head caused by the 
friction of water in pipes is as follows : 


Friction-head = {0.0144 + ee) L.vV2 


VV ) 5.3610 
where ZL = length of pipe in feet; 
V = velocity of the water in feet per second$ 
dad = diameter of pipe in inches. 
William Cox (Amer. Mach., Dec. 28, 1893) gives a simpler formula which 
gives almost identical results : Hi bertoys As 
A = friction-head in feet = ee. one ne tcemecly 


Hd 4V245 Sin 
V—2 
SA Oa i Sei 





\ 


576 HYDRAVLICK a Pa a 


2 —_ 
He gives a table by means of which the value of mie is at once 
obtained when V is known, and vice versa. 


4V245V —2 


VALUES OF 7800 











0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 


N 











.00588] .00695) .00813) .00938]) .01070} .01208} .01353, .01505) .01663) .01828 
02000} .02178} 02363] .02555) .02753) .02958| .0317G, .03388} .03613) .038845 
.04088; .04328) .04580| .04838) .05103] .05375] .05653) .05938) .06230) .06528 
06833 .07145| .07463) .07788} .08120| .08458} .08803, .09155) .09513) .09878 
.10250| .10628} .11013} .11405) .11803) .12208] .12620, .13038| .13463) .13895 
14383} .14778) 15280] .15688) .16153) .16625] .17108) .17588] .18080| . 18578 
19083] .19595) .20113] .20688] .21170) .21708] .22253) .22805} .22363) .23928 
.24500] .25078) .25663) .26255| .26853) .27458] .28070| .28688) .29313) .29945 
.30583| 31228) .31880) .32538]) .33203] .33875] .384553) .385238) .35930| .36628 
10| .87833) .88045) .38763] .389488) .40220] .40958) .41703) .42455) .43213) .438978 
11] .44750) .45528) .46313) .47105) .47903} .48708] .49520) .50338) .51163) .51995 
12| .52833) .53678] .54530} .55388) .56253) .57125) .58003) .58888) .59780] .60678 
13] .61583) .62495) .63413) .64338) .65270| .66208] .67153) .68105) .69063) .70U28 
14} .71000) .71978) .72963) .78955| .74953/ .75958] .76970| .77988) .79018) .80045 
15| .81083) .82128] .83180) .84288] .85303) .86375) .87453) .88538) .89630| .90728 
16] .91833] .92945] .94063) .95188) .96320) .97455} .98603) .99755|1.00913)1.02078 
17}1.08250)1 .04428)1 .05615)1 .06805)1 .08003}1 .09208)1.10420)1. 
18 )1.15333|1.16578!1.17830}1.19088)1.20353)1.21625)1.22903)1.24188)1.25480)1.2677 

19 }1.28(83)1 .29395]1.30713) 1.32038) 1.338370) 1.34708/ 1.36053) 1.37405) 1.38763/1.40128 

ibe 
is 


OMI Qos woe | 





2011.41500}1.42878)1 .44263/1 .45655)1.47053)1 . 48458} 1.49870, 1.51288) 1.52713}1.54145 
21 |1.55583/1 .57028) 1.58480) 1 .59938/1.61403)1.62875 ao a 65838) 1 .67330/1.68828 





The use of the formula and table is illustrated as follows: 
Given a pipe 5 inches diameter and 1000 feet long, with 49 feet head, what 
will the discharge be? f 
If the velocity V is known in feet per second, the discharge is 0.382725d2” 
cubic foot per minute. 
By equation 2 we have 
4V?F +5V—2 Hd 49x 5 Achy 
1200 SDs a 1000 crpeeapile 
whence, by table, V = real velocity = 8 feet per second. 
The discharge in cubic feet per minute, if V is velocity in feet per second 
and d diameter in inches, is 0.382725d2V, whence, discharge 
= 0.82725 25 x 8 = 65.45 cubic feet per minute. 


The velocity due the head, if there were no friction, is 8.025 4/H = 56.1%5 
feet per second, and the discharge at that velocity would be 


0.82725 x 25 x 56.175 = 460 cubic feet per minute, 


Suppose it is required to deliver this amount, 460 cubic feet, at a velocity 
of 2 feet per second. what diameter of pipe will be required and what will be 
the loss of head by friction? 


On: 460 . 
d = diameter = ae a BC eee f 
ve X 0.82725 (3 X 0.32725 W708 5 inches 


Having now the diameter, the velocity, and the discharge, the friction-head 

is calculated by equation 1 and use of the table; thus, 
EB4V2+5vV—2 1000 5 20 Si 
GP 1200 = 26.5 % 0:02 = se-= = 0.75 foot, 

thus leaving 49 — 0.75 = say 48 feet effective head applicable to power-pro- 
ducing purposes. 

Problems of the loss of head may be solved rapidly by means of Cox’s 
Pipe Computer, a mechanical device on the principle of the slide-rule, for 
sale by Keuffel & Esser, New York. 


11638]1.12863}1.14095 . 


LOSS OF HEAD. : 577 


Frictional Heads at Given Rates of Discharge in Clean 
Cast-iron Pipes for Each 1000 Feet of Length, 


(Condensed from Ellis and Howland’s Hydraulic Tables.) 






















4-inch 6-inch 8-inch 10-inch 12-inch } 14-inch 
Pipe. Pipe. Pipe. Pipe. Pipe. Pipe. 

Dap) | ms ity Cees Diba ur taki o |" 3 S's | oe 
Ses|p2|el] ee) eh | e2] s2] be | Sis2] see2] 22 
Gee es | Ss lah Saal oe leah Se neces ent stow 
-O-| SEI ED |] Se(/syz leg} su] 88] scio8i szlssi sd 
O25 2) 2S/e5/ 23 | 25) 2s) so | S385) Sse.) Ss 
.64 59 .28 willl 16 04 DO) OREO Cr Ollie en, 

Dees) 32.01 on, 232 .32 .10 .20} .04) .14 02} .10} .02 

tata | cast) bs alae ype keis! 64 -29 o41} = 311) 628) 05); 3211 19.08 

3.83] 16.05} 1.70} 2.28 .96 .60 -61) .22) 48) .10) 81} .05 

Bell SoS |e seer ler onoelcllecc| a. Ol 82 |).8-30) 1.50 ls 16| 9 42) OS 

6.37| 43.47] 2.84) 6.00} 1.60) 1.52) 1.02] .54) .71] .24) .52) .12 

7.66] 62.20} 38.40}° 8.52] 1.91] 2.13) 1.23) .75) .85] .82) .63! .16 

8.94} 84.26] 3.97) 11.48) 2.23) 2.85) 1.43] .99) .99| .43] .73) 21 
10.21}109.68) 4.54! 14.89] 2.55) 8.68) 1.63) 1.27/1.18 54) .83) .27 
12.77/170.53] 5.67) 23.01] 3.19] 5.64) 2.04) 1 93/1.42] .81]1.04) .40 
15.32/244.76| 6.81) 32.89) 3.83) 8.038) 2.45) 2.72)1.70] 1.14/1.25] .55 
17.87/332.36] 7.94) 44.54] 4.47) 10.838) 2.86) 3.66)1.98} 1.52/1.46] .73 

BCE Rl st oto of 9.08) 57.95) 5.09] 14.05} 3.27) 4.73)2.27] 1.96]1.67| .94 

sce Bld bo tt 10.21) 73.12} 5.74) 17.68) 3.68) 5.93)2.55) 2.45/1.88] 1.17 

fatyerss| gree hee 11 35) 90.05] 6.38) 21.74] 4.08] 7.28/2.84] 3.00/2.08] 1.43 

Seca ial te cearee 13.61]129.20| 7.66] 31.10] 4.90)10.38/8.40) 4.26/2.50) 2.02 

MNS |e ots § 15 88/175.38| 8.94] 42.13] 5.72)14.02)'3.97| 5.74/2 91] 2.7% 
cewece[esee ce] 18.15/228 62) 10.21) 54.84) 6.53)18.22)4.54] 7.44/3.33) 3.51 

PSH et Beebaan 20, 42/288 .90) 11.47) 69.22) 4.35)22.96 5.11!) 9.36/38.75) 4.41 

eee cale@es ceil ee. 00/000. 22012277 | Corel Se Lr eS. eD TOT O04 Tl beat 

i Oa BA RASA | GR 15.96/132.70| 10.21/43.87)7.09)17.82/5.21] 8.35 

ee co llae coe tseteay ieee iis |nessnieltnmemaden colle. Oc OOL ep dol Goal heos 

Etec Pee We cersias Mica sees Mane ae lehahersbilisereeee lh eee aa AMO Cloanaie beOO 
EE a ALS ET EEE PR BBE TOE 2 FSGS EEL PE EI RRS TE RGIS 





16-inch 
Pipe. 


18-inch 20-inch 24-inch 30-inch | 36-inch 
Pipe. Pipe. Pipe. Pipe. Pipe. 


per Minute. 
Velocity in 
ft. per sec. 
head, feet. 
Velocity in 
ft. per sec 
head, feet 
Velocity in 
ft. per sec. 
head, feet. 
Velocity in 
ft. per sec. 
head, feet. 
Velocity in 
ft. per sec. 
head, feet. 
Velocity in 
ft. per sec. 
head, feet. 


Friction- 
Friction- 
Friction- 
Friction- 
Friction- 
Friction- 


a0 
oo 
= OO 
Sg 
Os 
~O 
WM 2 
ae 
Pp 


























——_ | ———— | —— | | 


3000 | 4.79| 6.19} 3.78! 3.48] 3.06] 2.09} 2.13! .87/1.36] .30] .95] (13 
3500 | 5.59| 8.371 4.41] 4.70] 3.57] 2.81] 2.48] 1.16/1.59] .40/1.10 ? 
4000 | 6.38] 10.87] 5.04] 6.09] 4.08 3.64] 2.84] 1.50/1.82! .52/1.26; .22 
4500 | 7.18] 13.70] 5.67] 7.67] 4.59] 4.58] 3.19] 1.88/2.04| .64/1.42] .27 
5000 | 7.98] 16.85} 6.30) 9.43] 5.11] 5.62) 3.55] 2.31/2.27] .7811.58] 33 
BOG dae aah een aK} 7.57| 18.491 6.13] 8.03] 4.26] 3.28/2.721 1.1111.89] .46 
000 st a ORR Sa 7.15 10.86) 4.96) 4.43/3.18] 1.49/2 21] .@2 

rs weaheyee fee dc. -} 5 267|'5.7513.63] 11. 98120521 wt RO 
9000 ate | 6.38| 7.25/4.08] 2.43/2 84! 1.00 
10000 Ms ve eee|eeee]4.54] 2.98/3.15! 1.23 


ee oo 


ee ee 


ses wale woece 


578 HYDRAULICS, 


Effect of Bends and Curves in Pipes.—Weisbach’s rule for 
‘ : e r\3 tran: 2 ; 
bends: Loss of head in feet = | -131 + 1.847 (3) | ms 644 x 580° in which 7 


= internal radius of pipe in feet, R = radius of curvature of axis of pipe, ¥ 


= velocity in feet per second, and a = the central angle, or angle subtended. 


by the bend. 

Hamilton Smith, Jr., in his work on Hydraulics, says: The experimental 
data at hand are entirely insufficient to permit a satisfactory analysis of 
this quite complicated subject; in fact, about the only experiments of value 
are those made by Bossut and Dubuat with small pipes. 

Curves.—If the pipe has easy curves, say with radius not less than 5 
diameters of the pipe, the flow will not be materially diminished, provided 
the tops of all curves are kept below the hydraulic grade-line and provision 
be made for escape of air from the tops of all curves. (Trautwine.) 

Hydraulic Grade-lime.—In a straight tube of uniform diameter 
throughout, running full and discharging freely into the air, the hydraulic 
grade-line is a straight line drawn from the discharge end to a point imme- 
diately over the entry end of the pipe and at a depth below the surface 
equal to the entry and velocity heads. (Trautwine.) 


In a pipe leading from a reservoir, no part of its length should be above 
the hydraulic grade-line. 


Flow of Water in House-service Pipes. 


Mr. E. Kuichling, C.E., furnished the following table to the Thomson 
Meter Co.: 


















































s Discharge, or Quantity capable of being delivered, in 
‘3 Cubic Feet per Minute, from the Pipe, 
hy Sc under the conditions specified in the first column. 
Ronkition e 22 
Discharge. DG 2 Nominal Diameters of Iron or Lead Service-pipe in 
SES Inches, 
o 25 
a %| 4% | % 1 144} 2 3 4 6 
30 | 1.10 | 1.92 | 8.01 | 6.13 | 16.58] 38.34] 88.16/173.85|444.63_ 
nee 35) 40 | 1.27 | 2.92 | 3.48 | 7.08 | 19.14] 38.50/101 .80|200.75|513.42 
eet 0 50 | 1.42 | 2.48 | 3.89 | 7.92 | 21.40] 43.04/113.82/224 .44/574.02 
service- 60 | 1.56 | 2.71 | 4.26 | 8.67 | 23.44] 47.15]124.68/245.87|/628.81 
pee no] 7 | 1.74 | 3.03 | 4.77 | 9.70 | 26.21] 52.71|189.39|/274.89/703.03 
ae 100 | 2.01 | 3.50 | 5.50 |11.20 | 30.27) 60.87/160.96/317.41|811.79 
pressure.| 439 | 2.29 | 3.99 | 6.28 12.77 | 34.51] 69.40/188.52/361.91 |925.58 
Th h 0 | 0.66 | 1.16 | 1.84 | 3.78 | 10.40] 21.30] 58.19/118.13/317.23 
ToOdeot | 40 | 0.77 | 1.84 | 2.12 | 4.36 | 12.01) 24.59) 67.19)136.41/366.30 
/Teevol) 50 | 0.86 | 1.50 | 2.37 | 4.88 | 13.43] 27.50| 75.13/152.51/409.54 
service- 60 | 0.94 | 1.65 | 2.60 | 5.34 | 14.71] 30.12] 82.30)167.06/448.63 
Bacar % | 1.05 | 1.84 | 2.91 | 5.97 | 16.45] 33.68) 92.01/186.78|/501.58 
aCe 100 | 1.22 | 2.13 | 3.36 | 6.90 | 18.99] 38.89|106.24/215.68|579.18 
pressure. / 139 | 1.39 | 2.42 | 3.83 | 7.86 | 21.66] 44.34/121.14/245.91|660.36 
Through. | 380 | 0.55 | 0.96 | 1.52 | 8.11 | 8.57] 17.55] 47.90) 97.17/260.56 
100feetof| 40 | 0.66 | 1.15 | 1.81 | 3.72 | 10.24] 20.95] 57.20/116.01/311.09 
service- O | 0.75 | 1.81 | 2.06 | 4.24 | 11.67] 23.87] 65. 18/132.20|354.49 
pipe and | 60 | 0.83 | 1.45 | 2.29 | 4.70 | 12.94] 26.48] 72.28)146.61/393.13 
15 feet 5 | 0.94 | 1.64 | 2.59 | 5.82 | 14.64] 29.96] 81.79|165.90/444.85 
vertical | 100 | 1.10 | 1.92 | 3.02 | 6.21 | 17.10] 35.00] 95.55/198.82/519.72 
rise. 130 + 1.26 | 2.20 | 8.48 | 7.14 | 19.66] 40.23/109.82 222.75/597.31 
Through 30 | 0.44 | 0.77 | 1.22 | 2.50 | 6.80) 14.11] 38.63] 78.54/211.54 
100feetof| 40 | 0.55 | 0.97 | 1.53 |] 3.15 | 8.68] 17.79] 48.68] 98.98'266.59 
service- 50 :| 0.65 | 1.14 } 1.79 | 3.69 | 10.16] 20.82] 56.98 115.87/312.08 
pipe, and] 60 | 0.73 | 1.28 | 2.02 | 4.15 | 11.45] 28.47] 64.22/130.59 351.73 
30 feet 7% | 0.84 | 1.47 | 2.82 | 4.77 | 18.15] 26.95] 73.76/149.99, 403.98 
vertical | 100 | 1.00] 1.74 | 2.75 | 5.65 | 15.58] 31.93) 87.38'177.67,478.55 
rise. 130 | 1.15 | 2.02 | 3.19 } 6.55 | 18.07] 87.02/101 .33/206.04/554.96 














a 


| 


#IRE-STREAMS. 59 


In this table it isassumed that the pipe is straight and smooth inside; that 
the friction of the main and meter are disregarded; that the inlet from the 
main is of ordinary character, sharp, not flaring or rounded, and that the 
outlet is the full diameter of pipe. The deliveries given will be increased if, 
first, the pipe between the meter and the main is of larger diameter than the 
outlet; second, if the main is tapped, say for 1-inch pipe, but is enlarged 
from the tap to 1144 or 114 inch; or, third, if pipe on the outlet is larger than 
that on the inlet side of the meter. The exact details of the conditions given 
are rarely met in practice; consequently the quantities of the table may be 
expected to be decreased, because the pipe is liable to be throttled at the 
joints, additional bends may interpose, or stop-cocks may be used, or the 

ck-pressure may be increased. : 

Air=-bound Pipes.—aA pipe is said to be air-bound when, in conse- 
quence of air being entrapped at the high points of vertical curves in the 
line, water will not flow out of the pipe, although the supply is higher than 
the outlet. The remedy is to provide cocks or valves at the high points, 
through which the air may be discharged. The valve may be made auto- 
matic by means of a float. 

Vertical Jets. (Molesworth.)—H = head of water, h = height of jet, 
d = diameter of jet, K = coefficient, varying with ratio of diameter of jet 
to head; then h = KH. 

If H= dx 3800 _~_—-600 1000 1500 1800 2800 3500 4500, 

K= - 9 85 8 rif 6 5 .25 

Water Delivered through Meters. (Thomson Meter Co.).—The 
best modern practice limits the velocity in water-pipes to 10 lineal feet per 
second. Assume this as a basis of delivery, and we find, for the several sizes 
of pipes usually metered, the following approximate results: 


Nominal diameter of pipe in inches: 
34 56 34 1 1% 2 3 4 6 
Quantity delivered, in cubic feet per minute, due to said velocity: 
0.46 Beer 185 8.25 eee lode eda seek lac 


Prices Charged for Water in Different Cities (National 
Meter Co,): 


Average minimum price for 1000 gallons in 163 places............. 9.4 cents. 
is maximumiait iS Vt oe 4s SEE eon c gs ten Ore ee 
Extremes, 2144 cents to........... BSE RS CR. Rk Oe. ca San ARORA 
FIRE-STREAMS. 


Discharge from Nozzles at Different Pressures, 
(J. T. Fanning, Am. Water-works Ass’n, 1892, Hng’g News, July 14, 1892.) 








* P Horizon- : Friction 
Nozzle eters as tal Pro- | Gallons | Gallons a aaah per 100 
diam., aeonin iw y jection of per per 24 ft. Hos ft. Hose, 
HIEW ye ft : pat i Streams,} minute. | hours. 1b a Net 
: ft. ‘ Head, ft. 
1 ‘s 46.5 59.5 203 292 298 103% 24.776 
1 80 59.0 67.0 230 831,200 13.00 31.10 
1 90 79.0 76.6 267 884.500 17.70 40,7 
1 100 130.0 88.0 811 447.900 22.50 54.14 
114 70 44.5 61.3 249 358,520 15.50 35.71 
114 80 55.5 69.5 281 401,700 19.40 44.70 
144 90 72.0 78.5 324 466,600 25.40 58.52 
144 100 103.0 89.0 376 541,500 33.80 77.88 
1144 70 43.0 66.0 306 440.613 Oo i 52.42 
14 80 53. 92.4 843 493.900 28.40 65.43 
144 90 68.5 81.0 888 /)58,800 35.90 82.71 
14 100 93.0 92.0 460 662,500 ay Ae 86.98 
134 70 41.5 77.0 368 530,149 82.50 - 74.88 
138 80 5D %4.4 410 590,500 40.00 92.16 
134 90 65.5 82.6 468 674.000 51.40 118.43 
134 100 88.0 92.6 540 997.700 72.00 165.89 





580 HYDRAULICS. 


Friction Losses in Hlose.—In the above table the volumes of 
water discharged per jet were for stated pressures at the play-pipe. 

In providing for this pressure due allowance is to be made for friction 
1OReee in ance hose, according to the streams of greatest discharge which are 
to be used. 

The loss of pressure or its equivalent loss of head (h) in the hose may be 


found by the formula h = Oe aad: 


In this formula, as ordinarily used, for friction per 100 ft. of 214-in. hose 
there are the following constants: 244 in. diameter of hose d = .20833 ft.; 
length of hose / = 100 ft., and 2g = 64.4. The variables are: v = velocity in 
feet per second; 2 = loss of head in feet per 100 ft. of hose; m = a coeffi- 
cient found by experiment ; the velocity v is found from the given dis- 
charges of the jets through the given diameter of hose. 


Head and Pressure Losses by Friction in 100 -ft. 
Lengths of Bubber-lined Smooth 2\4-in. Hose. 


Gallons per 





Discharge | Velocity | Coefficient, Heed Lost,| Pressure 
m. t. 








per minute, |per second, Lost, lbs. 24 hours. 
gallons. ft. per sq. in. 
200 13.072 00450 22.89 9.93 288,000 
250 16.388 00446 35.55 15.43 360,000 
300 18.858 00442 46.80 20.31 432,000 
347 21.677 00439 61.53 26.70 499,680 
350 22.873 00439 68.48 29.7 504,000 
400 26.144 00436 88.83 38.55 576,000 
450 29.408 00434 111.80 48.52 648,000 
500 32.675 00432 137.50 59.67 720,000 
520 33.982 - 00431 148.40 64.40 748,800 





These frictions are for given volumes of flow in the hose and the veloci- 
ties respectively due to those volumes, and are independent of size of 
nozzle. The changes in nozzle do not affect the friction in the hose if there 
is no change in velocity of flow, but a larger nozzle with equal pressure at 
the nozzle augments the discharge and velocity of flow, and thus materially 
increases the friction loss in the hose. 

Loss of Pressure (p) and Head (h) in BRubber-lined 
ao On 2o-in. Hose may be tound approximately by the formule 
apa ie qd 
P = 415005 1801d5 
pounds per square inch; 27 = length of hose in feet; qg = gallons of water 
discharged per minute: d = diam. of the hose in inches, 24% in.; h = friction- 

head in feet. The coefficient of d® would be decreased for rougher hose. 

The loss of pressure and head for a 11é-in. stream with power to reach a 
height of 80 ft. is, in each 100 ft. of 214-in. hose, approximately 20 Ibs., or 45 
ft. net, or, say, including friction in the hydrant, 4% ft. loss of head for each 
foot of hose. 

If we change the nozzles to 114 or 13g in. diameter, then for the same 80 ft. 
height of stream we increase the friction losses on the hose to approxi- 
‘mately 3% ft. and 1 ft. head, respectively, for each foot-Jength of hose. 

These computations show the great difficulty of maintaining a high 
stream through large nozzles unless the hose is very short, especially for a. 
gravity or direct-pressure system. 

This single 11é-in. stream requires approximately 56 lbs pressure, equiva- 
lent to 129 ft. head, at the play-pipe, and 45 to 50 ft. head for each 100 ft. 
length of smooth 244-in. hose, so that for 100, 200,and 300 ft. of hose we 
must have available heads at the hydrant or fire-engine of 179, 229, and 279 
ft., respectively. If we substitute 114-in. nozzles for same height of stream 
we must have available heads at the hydrants or engine of 193, 259, and 325 
ft., respectively, or we must increase the diameter of a portion at least of 
the long hose and save friction-loss of head. 

Rated Capacities of Steam Wire-engimes, which is perhaps 
one third greater than their ordinary rate of work at fires, are substantially 
as follows: ; 

3d size, 550 gals. per min., or 792,000 gals. per 24 hours, 
2d ‘* 700 ‘* sd 1,008,000 + . 
1st * 900 ‘ Wy 1,296,000 se “ 
1 ext., 1,100 “ ie 1,584,000 $8 - 


andh = ,in which p = pressure lost by friction, in 


THE SIPHON. 581 


Pressures required at Nozzle and at Pump, with Quantity 
and Pressure of Water Necessary to throw Water 
Various Distances through Different-sized Nozzles= 
using 24-inch Rubber Hose and Smooth Nozzles. 


(From Experiments of Ellis & Leshure, Fanning’s ‘‘ Water Supply.) 


Size of Nozzles. 1 Inch. 11g Inch. 














Pressure at nozzle, lbs. per sq. in....... 40; 60; 80 
* Pressure at pump or hydrant with 

100 ft. 244-inch rubber hose............ 48| 73) 97 
Gallons PerimMIMUtED ¢ ai scisec o> ciaacleiee sie 155| 189) 219 
Horizontal distance thrown, feet..... ..| 109} 142) 168 
Vertical distance thrown, feet........... 79| 108] 131 

Size of Nozzles. 114 Inch. 13g Inch. 

Pressure at nozzle, lbs. per sq. in........ 40} 60} 80] 100} 40) 60; 8&0; 100 
* Pressure at pump or hydrant with 

100 feet 21-inch rubber hose.......... 61] 92) 123] 154) 71) 107] 144} 180 
Gallons! periminutere: occ sc cuss «sacle nee 242) 297) 842) 383) 293] 358] 413] 462 
Horizontal distance thrown, feet........ 118] 156} 186) 207) 124] 166] 200) 224 
Vertical distance thrown, feet........... 82} 115] 142) 164! 85| 118] 146) 169 


* For greater length of 214-inch hose the increased friction can be ob- 
tained by noting the differences between the above given ‘‘ pressure at 
nozzle’ and ‘‘ pressure at pump or hydrant with 100 feet of hose.” For 
instance, if it requires at hydrant or pump eight pounds more pressure 
than it does at nozzle to overcome the friction when pumping through 100 
feet of 214-inch hose (using 1-inch nozzle, with 40-pound pressure at said 
nozzle) then it requires 16-pounds pressure to overcome the friction in 
‘forcing through 200 feet of same size hose. 


Decrease of Flow due to Increase of Lengeth of Hose. 
(J. R. Freeman’s Experiments, Trans. A. S. C. E. 1889.)—If the static pres- 
sure is 80 lbs. and the hydrant-pipes of such size that the pressure at the hy- 
drant is 70 lbs., the hose 24% in. nominal diam., and the nozzle tl in. diam., 
the height of effective fire-stream obtainable and the quantity in gallons per 


minute will be; 
Best Rubber- 


Linen Hose. lined Hose, 
Height, Gals. Height, Gals. 
feet. per min. feet... _ per min; 
With 50 ft. of 2l4-in. hose...... AM 261 81 282 
S081 O56" ES i Sea tlerte: Maren: 42 184 61 229 
$61.00 So ce bec AN a sh 2 146 46 152 


With 500 ft. of smoothest and best rubber-lined hose, if diameter be 
exactly 214 in., effective height of stream will be 39 ft. (177 gals.); if diameter 
be lg in. larger, effective height of stream will be 46 ft. (192 gals.) 


THE SIPHON. 


The Siphon is a bent tube of unequal branches,"open at both ends, and 
is used to convey a liquid from a higher to a lower level, over an intermedi- 
ate point higher than either. Its parallel branches being in a vertical plane 
and plunged into two bodies of liquid whose upper surfaces are at different 
levels, the fluid will stand at the same level both within and without each 
branch of the tube when a vent or small opening is made at the bend. If 
the air be withdrawn from the siphon through this vent, the water will rise 
in the branches by the atmospheric pressure without, and when the two 
columns unite and the vent is closed, the liquid will flow from the upper 
reservoir as long as the end of the shorter branch of the siphon is below the 
surface of the liquid in the reservoir. 

If the water was free from air the height of the bend above the supply 
level might be as great as 33 feet, 


582 HYDRAULICS, 


If A = area of cross-section of the tube in square feet, H =: the differenca 
in level between the two reservoirs in feet, D the density of the liquid in 
pounds per cubic foot, then ADH measures the intensity of the force which 


causes the movement of the fluid,and V= /2gH = 8.02 WH is the theoretica. 
velocity, in feet per second, which is reduced by the loss of head for entry 
and friction, as in other cases of flow of liquids through pipes In the case 
of the difference of level being greater than 33 feet, however, the velocity of 
the water in the shorter Jeg is Jimited to that due to a height of 33 feet, or 
that due to the difference between the atmospheric pressure at the entrance 
and the vacuum at the bend. 

Leicester Allen (Am. Mach., Nov. 2, 1893) says: The supply of liquid to a 
siphon must be greater than the flow which would take place from the dis- 
charge end of the pipe, provided the pipe were filled with the liquid, the 
‘ supply end stopped, and the discharge end opened when the discharge end 
is left free, unregulated, and unsubmerged. 

To illustrate this principle, let us suppose the extreme case of a siphon 
having a calibre of 1 foot, in which the difference of level, or between the 
point of supply and discharge, is 4 inches. Let us further suppose this 
siphon to be at the sea-level, and its highest point above the level of the 
supply to be 27 feet. Also suppose the discharge end of this siphon to be un- 
regulated, unsubmerged. It would be inoperative because the water in the 
longer leg would not be held solid by the pressure of the atmosphere against 
it, and it would therefore break up and run out faster than it could be re- 
placed at the inflow end under an effective head of only 4 inches. 

Long Siphons.—Prof. Joseph Torrey, in the Amer. Machinist, 
describes a long siphon which was a partial failure. 

The length of the pipe was 1792 feet. The pipe was 3 inches diameter, and 
rose at one point 9 feet above the initial level. The final level was 20 feet 
_ below the initial level. No automatic air valve was provided. The highest 
point in the siphon was about one third the total distance from the ponu and 
nearest the pond. At this point a pump was placed, whose mission was to 
fill the pipe when necessary. This siphon would flow for about two hours 
and then cease, owing to accumulation of air in the pipe. When in full 
operation it discharged 4314 gallons per minute. The theoretical discharge 
from such a sized pipe with the specified head is 5514 gallons per minute. 

Siphon om the Water-supply of Mount Vernon, N. WY. 
(Eng’q News, May 4, 1893.)—A 12-inch siphon, 925 feet long, with a maximum 
lift of 22.12 feet and a 45° change in alignment, was put in use in 1892 by the 
New York City Suburban Water Co., which supplies Mount Vernon, N.Y. . 

at Ge summit the siphon crosses a supply main, which is tapped to charge 
the siphon. ; 

The air-chamber at the siphon is 12 inches by 16 feet long. <A 14-inch tap 
and cock at the top of the chamber provide an outlet for the collected air. 

It was found that the siphon with air-chamber as desc.ibed would run 
until 125 cubie feet of air had gathered, and that this took place only half as 
soon with a 14-foot lift as with the full lift of 22.12 feet. The siphon will 
operate about 12 hours without being recharged, but more water can be 
gotten over by charging every six hours. It can be kept running 23 hours 
out of 24 with only one man in attendance. With the siphon as described 
above it is necessary to close the valves at each end of the siphon to 
recharge it. 

It has been found by weir measurements that the discharge of the siphon 
before air accumulates at the summit is practically the same as through a 
straight pipe. 


MEASUREMENT OF FLOWING WATER. 


Piezometer.—lIf a vertical or oblique tube be inserted into a pipe con- 
taining water under pressure, the water will rise in the former, and the ver- 
tical height to which it rises will be the head producing the pressure at the 
point where the tube is attached. Such a tube is called a piezometer or 
pressure measure, If the water in the piezometer falls below its proper 
level it shows that the pressure in the main pipe has been reduced by an 
obstruction between the piezometer and the reservoir. If the water rises 
above its proper. level, it indicates that the pressure there has been in- 
creased by an obstruction beyond the piezometer. 

If we imagine a pipe fullof water to be provided with a number of pie- 
zometers, then a line joining the tops of the columns of water in them is 
the hydraulic grade-line. 


MEASUREMENT OF FLOWING WATER. © 583 


. Pitot Tube Gauge.—tThe Pitot tub> is used for measuring the veloc- 
ity of fluids in motion. It has been used with great success in measuring 
the flow of natural gas. (S. W. Robinson, Report Ohio Geol. Survey, 1890.) 
(See also Van Nostrand’s Mag., vol. xxxv.) It is simply a tube so bent that 
a short leg extends into the current of fluid flowing from a tube, with the 
plane of the entering orifice opposed at right angles to the direction of the 
current. The pressure caused by the impact of the current is transmitted 
through the tube to a pressure-gauge of any kind, such as a column of 
water or of mercury, or a Bourdon spring-gauge. From the pressure thus 
indicated and the known density and temperature of the flowing gas is ob- 
tained the head corresponding to the pressure, and from this the velocity, 
In a modification of the Pitot tube described by Prof. Robinson, there are 
two tubes inserted into the pipe conveying the gas, one of which has the 
plane of the orifice at right angles to the current, to receive the static pres- 
sure plus the pressure due to impact; the other has the plane of its orifice 
parallel to the current, so as to receive the static pressure only. These 
tubes are connected to the legs of a U tube partly filled with mercury, which 
then registers the difference in pressure in the two tubes, from which the 
velocity may be calculated. Comparative tests of Pitot tubes with gas- 
meters, for measurement of the flow of natural gas, have shown an agrees 
ment within 32. 

The Venturi Meter, invented by Clemens Herschel, and described in 
a pamphlet issued by the Builders’ Iron Foundry of Providence, R. 1., is 
named from Venturi, who first called attention, in 1796, to the relation be- 
tween the velocities and pressures of fluids when flowing through converging 
and diverging tubes, 

It consists of two parts—the tube, through which the water flows, and the 
heagn which registers the quantity of water that passes through the 

ube. 
._ The tube takes the shape of two truncated cones joined in their smallest 
diameters by a short throat-piece. At the up-streain end and at the throat 
there are pressure-chambers, at which points the pressures are taken, 

The action of the tube is based on that property which causes the small 
section of a gently expanding frustum of a cone to receive, without material 
resultant loss of head, as much water at the smallest diameter as is dis- 
charged at the large end, and on that further property which causes the 
pressure of the water flowing through the throat to be less, by virtue of its 
greater velocity, than the pressure at the up-stream end of the tube, each 
pressure being at the same time a function of the velocity at that point and 
of the hydrostatic pressure which would obtain were the water motionless 
within the pipe. 

The recorder is connected with the tube by pressure-pipes which lead to 
it from the chambers surrounding the up-stream end and the throat of the 
tube. It may be placed in any convenient position within 1000 feet of the 
tube. Itis operated by a weight and elockwork, 

The difference of pressure or head at the entrance and at the throat of the 
meter is balanced in the recorder by the difference of level in two columns 
of mercury in cylindrical receivers, one within the other. The inner carries 
a float, the position of which is indicative of the quantity of water flowing 
through the tube. By its rise and fall the float varies the time of contact 
between an integrating drum and the counters by which the successive 
readings are registered. 

There is no limit to the sizes of the meters nor the quantity of water that 
may be measured. Meters with 24-inch, 36-inch, 48-inch, and even 20-foot 
tubes can be readily made. 

Measurement by Venturi Tubes, (Trans. A.S.C. E., Nov., 1887, 
and Jan., 1888.)—Mr. Herschel recommends the use of a Venturi tube, in- 
serted in the force-main of the pumping: engine, for determining the quantity 
of water discharged. Such a tube applied to a 24-inch main has a total 
length of about 20 feet. At a distance of 4 feet from the end nearest the 
engine the inside diameter of the tube is contracted to a throat having a 
diameter of about 8 inches. A pressure-gauge is attached to each of two 
chambers, the one surrounding and communicating with the entrance or 
main pipe, the other with the throat. According to experiments made upon 
two tubes of this kind, one 4 in. indiameter at the throat and 12 in. at the en- 
trance, and the other about 36 in. in dizumeter at the throat and 9 feet at its 
entrance, the quantity of water which passes through the tube is very nearly 
the theoretical discharge through an o0))ening having an area equal to that 
of the throat, and a velocity which is that due to the difference in head shown 


584 HYDRAULICS, 


by the twogauges. Mr. Herschel states that the coefficient for these twa 
widely-varying sizes of tubes and for a wide range of velocity through the 
pipe, was found to be within two per cent, either way, of 98%. In other 
words, the quantity of water flowing through the tube per second is ex- 


pressed within two per cent by the formula W=0.98 X A X ¥2gh, in which 
A is the area of the throat of the tube, h the head, in feet, correspond- 
ing to the difference in the pressure of the water entering the tube and that 
found at the throat, and g = 32.16. 

Measurement of Discharge of Pumping-engines by 
Means of Nozzles. (Trans. A. S. M. E., xii. 575).—The measurement 
of water by computation from its discharge through orifices, or through the 
nozzles of fire-hose, furnishes a means of determining the quantity of water 
delivered by a pumping-engine which can be applied without much difficulty. 
John R. Freeman, Trans. A. S. C. E., Nov., 1889, describes a series of experi- 
ments covering a wide range of pressures and sizes, and the results showed 
that the coefficient of discharge for asmooth nozzle of ordinary good form 
was within one half of one per cent, either way, of 0.977; the diameter of 
the nozzle being accurately calipered, and the pressures being determined 
by means of an accurate gauge attached to a suitable piezometer at the base 
pf the play-pipe. 

In order to use this method for determining the quantity of water dis- 
charged by a pumping-engine, it would be necessary to provide a pressure- 
box, to which the water would be conducted. and attach to the box as many 
nozzles aS would be required to carry off the water. According to Mr. 
Freeman’s estimate, four 144-inch nozzles, thus connected, with a pressure 
of 80 lbs. per square inch, would discharge the full capacity of a two-and a- 
half-million engine. He also suggests the use of a portable apparatus with 
a single opening for discharge, consisting essentially of a Siamese nozzie, 
so-called, the water being carried to it by three or more lines of fire-hose. 

To insure reliability for these measurements, it is necessary that the shut-’ 
off valve in the force-main, or the several shut-off valves, should be tight, 
so that all the water discharged by the engine may pass through the nozzles. 


Flow through Rectangular Orifices, (Approximate, Seep. 556.) 


CuBpic Feet oF WATER DISCHARGED PER MINUTE THROUGH AN ORIFICE ONE 
IncH SQUARE, UNDER ANY HEAD OF WATER FROM 3 TO 72 INCHES. 
For any other orifice multiply by its area in square inches. 
Formula, Q/ = .624 V/h’’X a. Q/ = cu. ft. per min.; a = area in sq. in. 



























Pee! PEV =} PE To] Pel =} BSVie} Pee} rei} 

-|oo ~-|o0 oo -|OO -]ooO | OOD -|o0OD 
bio Pa} iS ee Shel gic ey Cleef SP haf sie he 
eal Salat ae eal mE etal Pea leetica) Peel ieee! ett ee 
BolQa SIS oloss OSES oles O12 Els C195 Ef O95 4g 
S52 os SFIS o. She AIS & AIS Re S=|S9 SAIS on 
158 i 8158 dh 51546 88s 1046 8 slo 8h 8156 Sie = (558 
8 | 1.12 § 13 | 2.20 2.90 # 33 | 3.47 38.95 # 53 | 4.39 § 63 | 4.78 
4} 1.27 § 14 | 2.28 2.97 F 34 | 3.52 4.00 8 54} 4.42 § 64 | 4.81 
5 | 1.40 § 15 | 2.36 8.038 § 35 | 3.57 4 05 § 55 | 4.46 § 65 | 4.85 
6 | 1.52 § 16 | 2.48 3.08 § 36 | 3.62 4.09 § 56 | 4.52 § 66 | 4.89 
Gai vl O44m La pneeol 3.14 § 37 | 3.67 4.12 9 57 | 4.55 § 67 | 4.92 
8 | 1.75 $18 | 2.58 3.20 § 38 | 3.72 4.18 § 58 | 4.58 § 68 | 4.97 

9/ 1.84 719 | 2.64 8.25 § 39 | 3.77 4.21 § 59 | 4.63 § 69 | 5.00 
10 | 1.94 § 20 } 2.71 3.31 # 40 | 3.81 4.27 § 60 | 4.65 § 70 | 5.03 
11 |. 2.038 § 2112.78 3.36 § 41 | 3.86 4.30 § 61 | 4.72 § 71 | 5.07 
12 | 2.12 7 22 | 2.84 8.41 § 42 | 3.91 4.34 § 62 | 4.74 # 72 | 5.09 





Co EG EG ARS Go aPC OEE F=E pee IS or TS meme pee 

Wreasurement of an Open Stream by Velocity and Cross- 
section.—Measure the depth of the water at from 6 to 12 points across 
the stream at equal distances between. Add all the depths in feet together 
and divide by the number of measurements made; this will be the average 
depth of the stream, which multiplied by its width will give its area or cross- 
section. Multiply this by the velocity of the stream in feet per minute, and 
the result will be the discharge in cubic feet per minute of the stream. 

The velocity of the stream can be found by laying off 100 feet of the bank 
and throwing a float into the middle, noting the time taken in passing over 
the 100 ft. Do this a number of times and take the average ; then, dividing 


MEASUREMENT OF FLOWING WATER. 585 


this distance by the time gives the velocity at the surface. As the top of the 
stream flows faster than the bottom or sides—the average velocity being 
about 83% of the surface velocity at the middle—it is convenient to measure 
a distance of 120 feet for the float and reckon it as 100. 


\\ 


/ 


SSS 


fy 
\ 





Fig. 130. 


Miners? Inch Measurements. (Pelton Water Wheel Co.) 

The cut, Fig. 180, shows the form of measuring-box ordinarily used, and the 
following table gives the discharge in cubic feet per minute of a miner’s inch 
of water, as measured under the various heads and different lengths and 
heights of apertures used in California, 


Openings 2 Inches High. Openings 4 Inches High. 





Lene 

re) 

Opening | Head to} Headto| Headto| Head to | Head to Head to 
in Centre, | Centre, | Centre, Centre, Centre, Centre, 


inches. | 5 inches.| 6 inches.| 7 inches.| 5 inches. 6 inches. 7 inches. 








Cu. ft. Cusit: Cu. ft. Cu. ft. Cu. ft. Cu. ft. 

4 1.348 1.473 1.589 1.320 1.450 1.50 
6 1.355 1.480 1.596 1.336 1.47 1.595 
8 1.359 1.484 1.600 1.344 1.481 1.608 
10 1.361 1.485 1.602 1.349 1.487 1.615 
12 1.363 1.487 1.604 1.352 1.491 1.620 
14 1.364 1.488 1.604 1.354 1.494 1.623 
16 1.365 1.489 1.605 1.356 1.496 1.626 
18 1.365 1°489 1.606 1.357 1.498 1.628 
20 1.365 1.490 1.606 1.359 1.499 1.630 
22 1.366 1.490 1.607 1.359 1.500 1.631 
24 1.366 1.490 1.607 1.360 1.501 1a ey 
26 1.366 1.490 1.607 1.361 1.502 1.633 
28 1.367 1.491 1.607 1.361 1.503 1.634 
80 1.367 1.491 1.608 1.362 1.503 1.635 
40 1.367 1.492 1.608 1.363 1.505 1.637 
50 1.368 1.4938 1.609 1.364 1.507 1.639 
60 1.368 1.493 1.609 1.365 1.508 1.640 
a 1.368 1.493 1.609 1.365 1.508 1.641 
80 1.368 1.433 1.609 1.366 1.509 1.641 
90 1.369 1.493 1.610 1.366 1.509 1.641 
100 1.369 1.494 1 610 1.366 1.509 1.642 


Nots.—The apertures from which the above measurements were obtained 


586 | HYDRAULICS, 


i 


were through material 114 inches thick, and the lower edge 2 inches above 
the bottom of the measuring-box, thus giving full contraction. ’ 

Flow of Water Over Weirs. Weir Dam Measurement. 
(Pelton Water Wheel Co.)—Place a board or plank in the stream, as shown 


We 
SSS 


z) 
S 





Fig. 131. 


in the sketch, at some point where a pond will form above. The length of 
the notch in the dam should be from two to four times its depth for small 
quantities and longer for large quantities. The edges of the notch should 
be bevelled toward the intake side, as shown. The overfall below the notch 
should not be less than twice its depth. [Francis says a fall below the crest 
equal to one-half the head is sufficient, but there must be a free access of 
air under the sheet.] 

In the pond, about 6ft. above the dam, drive a stake, and then obstruct the 
water until it rises precisely to the bottom of the notch and mark the stake 
at this level. Then complete the dam so as to cause all the water to flow 
through the notch, and, after time for the water to settle, mark the stake 
again for this new level. If »referred the stake can be driven with its top 
precisely level with the bottom of the notch and the depth of the water be 
measured with a rule after the water is flowing free, but the marks are pre- 
ferable in most cases. The stake can then be withdrawn; and the distance 
between the marks is the theoretical depth of flow corresponding to the 
quantities in the table on the following page. 


Francis’s Formulse for Weirs. 


As given by As modified by 
Francis, Smith. 
Weirs with both end contractions be 3 hy,# 
~ tSHDDIeseed aig was foe eas ss +s t @ = 3.38/h 3.20(2 +9 dn 


Weirs with one end contraction _ 99 3 3 
suppressed......... ME Taltte shies s t Q = 8.830 — .1h)h 8.290h 


h 
Weirs with full contraction....... Q = 3.330 — .2nynt 8.20(1 = vn 


The greatest variation of the Francis formule from the values of c given by 
Smith amounts to 314%. The modified Francis formule, says Smith, will give 
results sufficiently exact, when great epee os is not required, within the 
limits of h, from .5 ft. to2 ft., 2 being not less than 3 h. 


MEASUREMENT OF FLOWING WATER. 587 


Q = discharge in cubic feet per second, / = length of weir in feet, h =effec- 
tive head in feet, measured from the level of the crest to the level of still 
water above the weir. 

If Q’ = discharge in cubic feet per minute, and l’/ and h’/are taken in 


3 
inches, the first of the above formule reduces to Q’ = 0.4l’h’2.. From this 
formula the following table is calculated. The values are sufficiently accu- 
rate for ordinary computations of water-power for weirs without end con- 
traction, that is, for a weir the full width of the channel of approach, and 
are approximate also for weirs with end contraction when Z = at least 10h, 
but about 6% in excess of the truth when / = 4h, 


Weir Table. 


GivinG CuBic FEET OF WATER PER MINUTE THAT WILL FLOW OVER A W&IR 
ONE INCH WIDE AND FROM 1g TO 20% INCHES DEBP. 


For other widths multiply by the width in inches. 


t 


Win. | Yin. | 3in.; Win. | Sin. | Kin. | % in. 








n. eu. ft. cu. ft. | cu. ft. | cu. ft. | cu. ft. | cu. ft. | cu. ft. | cu. ft. 
0 .00 .O1 208 -09 14 19 -26 «02 
1 .40 47 OD .64 03 82 .92 1.02 
2 idle 1.28 1,385 1.46 1.58 1.70 1.82 1.95 
3 2.07 2101 2.34 2.48 2.61 2.76 2.90 8.05 
4 3.20 Bob) 8.50 3.66 3.81 8.97 4.14 4.30 
5 4.47 4.64 4.81 4,98 Delo D.oo 5.51 5.69 
6 5.87 6.06 6.25 6.44 6.62 6.82 7.01 21 
ti 7.40 7.60 7.80 8.01 8.21- 8.42 8.63 8.83 
8 9.05 9.26 9.47 9.69 9.91 10.13 10.35 | 10.57 
9 10.80 11.02 14.25 11.48 TRG 11.94 1a 12.41 
10 12.64 12.88 13.12 13.36 13.60 13.85 14.09 14.34 
11 14.59 14.84 15.09 15 34 15.59 15.85 16.11 16.36 
12 16.62 16.88 | 17.15 | 17.41 1060 -)  1%294 1821 18.47 
13 18.74 19.01 19.29 | 19.56] 19.84] 20.11 20.39 | 20.67 
14 20.95 21.23 21.51 21.80 22.08 QBI3¢ 22.65 22.94 
15 23.28 23.52 23.82 24.11 24.40 R407 25.00 25.30 
16 25.60 25.90 26.20 26.50 26.80 27.11 27.42 27.92 
ly 28.03 28 34 28.65 28.97 29.28 29 59 29.91 380.22 
18 30.54 SOLS IE Oletoaieol DO leak. 82) aoe. 1 bale e264 CalmesencO 
19 o0.12 33.45 Spit 384.11 84.44 3400 85.10 35.44 
20 SOot 36.11 36.45 36.7 Stele 37.46 37.80 38.15 





For more accurate computations, the coefficients of flow of Hamilton 
Smith, Jr., or of Bazin should be used. In Smith’s hydraulics will be found 
a zollection of results of experiments on orifices and weirs of various shapes 
mace by many different authorities, together with a discussion of their 
several formule. (See also Trautwine’s Pocket Book.) q 

Bazin’s Experiments.—M. Bazin (Annales des Ponts et Chaussées, 
Oct., 1888, translated by Marichal and Trautwine, Proc. Engrs. Club of Phila., 
Jan., 1890), made an extensive series of experiments with a sharp-crested 
weir without lateral contraction, the air being admitted freely behind the 
falling sheet, and found values of m varying from 0.42 to 0.50, with varia- 
tions of the length of the weir from 1934 to 7834 in., of the height of the crest 
above the bottom of the channel from 0.79 to 2.46 ft., and of the head from 
1,97 to 23.62 in. From these experiments he deduces the following formula ; 


Q =[ 0.425 of 0.(5o 7) | LH 29H, 


in which Pis the height in feet of the crest of the weir above the bottom of 
the channel of approach, Z the length of the weir, H the head, both in feet, 
and Q the discharge in cu. ft. per sec. This formula, says M. Bazin, is en- 
tirely practical where errors of 2% to 3% are admissible. The following 
table is condensed from M. Bazin’s paper : 


Hod WATER-POWER. 


VALUES OF THE COEFFICIENT m IN THE ForMULA G@ = mLH V3qH, FOR A 
SHARP-CRESTED WEIR WITHOUT LATERAL CONTRACTION ; THE AIR BEING 
ADMITTED FREELY BEHIND THE FALLING SHEET. 





Height of Crest. of Weir Above Bed of Channel. 




















Head, 
H. 
Feet ...0.66 | 0.98} 1.31) 1.64) 1.97) 2.62 8.28) 4.92} 6 56) @ 
Inches 7.87 | 11.31] 15.75] 19.69] 23.62/81 .50| 89.88. 59.07|78.76| 
Ft. | In. m n m m mim m mi\m m 
.164] 1.97 .458 0.453] 0.45110.450) 0.449|0.449] 0.449 0.448/0.448] 0.4481 
.230! 2.76 0.455 0.448) 0.445] 0.443] 0.442/0.441] 0.440, 0.440/0.439) 0.4891 
295] 3.54 0.457 0.447) 0.442| 0.440] 0.488)0. 436) 0.436 0.435/0. 434) 0.4840 
094!) 4.72 0.462 0.448) 0.442] 0.438] 0.486)0.433] 0.432! 0.430]0.430) 0.4291 
-525| 6.30 0.471 0.453] 0.444] 0.438] 0.485/0.431} 0.429) 0.427/0.426| 0.4246 
656) 7.87 9.480 0.459] 0.447| 0.440] 0. 486/0. 431} 0.428] 0.425/0.423) 0.4215 
087) 9.45 0.488 0.465) 0.452) 0.4441 0.4388/0. 432] 0.428) 0.424)0.422/ 0.4194 
-919)11.02 0.496 0.472) 0.457|0.448] 0.441/0. 433) 0.429) 0.424/0. 422) 0.4181 
1.050)12.601... e000 ©. 2--|0.478) 0.462)0. 452] 0.44410. 436] 0.480) 0.42410.421] 0.4168 
TeUSLT 4 icess eee ese fe 483] 0.46710.456} 0.448)0.438}0 482) 0.42410.421/ 0.4156 
1.312]15.'75] coc seecee cee} 0.489] 0.47210.459] 0.451/0.440)0 483) 0.424)/0.421] 0.4144 
1.444]17.32}. oi ny 494| 0.476(0.463] 0.454|0.442| 0.435) 0.425/0.421) 0.4134 
1.575)18.90 weal temante 0.480|0.467|0.457/0.444! 0.436) 0.425/0.421/ 0.4122 
1.706/20.47] . 22. ccccccccee| oe-+(0.483/0.470)0.460/0.446! 0.438, 0.426/0.421/ 0.4112 
1.837 |22.05]. .cccccccesse:| oes s(0.487/0.478] 0.463/0.448] 0.439) 0.427/0. 421) 0.4101 
TE969 S862 eee es cee clean eel Ocd9010. 4760. 466/0.451\0.441) 0.427/9. 421] 0.4092 











A comparison of the results of this formula with those of experiments, 
says M. Bazin, justifies us in believing that, except in the unusual case of a 
very low weir (which should always be avoided), the preceding table will 
give the coefficient m in all cases within 1%; provided, however, that the ar- 
rangements of the standard weir are exactly reproduced. It is especially 
important that the admission of the air behind the falling sheet be a Henan 
assured. If this condition is not complied with, m may vary within muc 
lg limits. The type adopted gives the least possible variation in the 
coefficient, 


W ATER-POWER. 


Power of a Fall of Water—Efficiency.—The gross power of 
a fall of water is the product of the weight of water discharged in a unit of 
time into the total head. i.e., the difference of: vertical elevation of the 
upper surface of the water at the points where the fall in question begins 
and ends. The term ‘‘ head” used in connection with water-wheels is the 
difference in height from the surface of the water in the wheel-pit to the 
surface in the pen-stock when the wheel is running. 

If Q@ = cubic feet of water discharged per second, D = weight of a cubio 
foot of water = 62.36 lbs. at 60° F., H = total head in feet; then 


DQH = gross power in foot-pounds per second, 
and DQH + 550 =.1134QH = gross horse-power. 


, 
If Q’ ig taken in cubic feet per minute, H.P. = ee ORG ao 86 
9 


A water-wheel or motor of any kind carnot utilize the whole of the head 
H, since there are losses of head at both the entrance to and the exit from 
the wheel. There are also losses of energy due to friction of the water in 
its passage through the wheel. she ratio of the power developed by the 
wheel to the gross power of the fall is the efficiency of the wheel. For 75% 


efficiency, net horse-power = .00142Q’H = 


001899'H. 


"108 ° 


MILL-POWER. 589 


A head of wate: van be made use of in one or other or we ru1luw'ng ways 
viz. : 

1st. By its weight, as in the water-balance and overshot-wheel. 

2d. By its pressure, as in turbines and in the hydraulic engine, hydraulie 
press, crane, ete. 

3d. By its impulse, as in the undershot- wheei, and in the Pelton wheel. 

4th. By a combination of the above. 

Horse-power of a Running Stream.—The gross horse-power 
is, H. P. = QH & 62.86 + 550 = .1134QH, ip which ¢ is the discharge in cubie 
feet per second actually impinging on the float or bucket, aud A = theoret- 

3 
ical head due to the velocity of the stream = eat ow , in which v is the 
velocity in feet et second. If Q be taken in cubic feet per minute, 
H.P. = .001890’Z. 

Thus, if the’floats of an undershot-wheel driven by a current alone be 5 
feet > 1 foot, and the niles of stream = 21C ft. per minute, or 314 ft. per 
sec., of which the theoretical head is .19 ft.. Q@ = 5 sq. ft. x 210 = 1050 cu. ft. 
per minute; H = .19ft.; H. P. = 1050 « .19 «.00189 = .377 H. P. 

The wheels would realize only about .4 of this power, on account of friction 
and slip, or .151 H.P., or about .03 H.I. per square foot of float, which is 
equivalent to 88 sq. ft. of float per H.P. 

Current Motors.—A cu:rent motor could only utilize the whole power 
of a running stream if it could take all the relocity out of the water, so that 
it would leave the floats or buckets with no velocity at all; or in other words, 
it would require the backing up of the whole volume of the stream until the 
actual head was equivalent to the theoretical head due to the velocity of the 
stream. As but a small fraction of the velocity of the strean: can be taken 
up by a current motor, its efficiency is very small. Current motors may be 
used to obtain small amounts of power from large streams, but for large 
powers they are not practicable. 

Horse=power of Water Flowing in a Tube.—tThe head due to 


the velocity is = ; the head due to the pressure is =e the head due to actual 
height above the datum plane is h feet. The total head is the sum of these = 
5 +h+ a in feet, in which v = velocity in feet per second, f = pressure 
in Ibs. per sq. ft., w = weight of 1 cu. ft. of water = 62.36 lbs. Ifp = pres- 
sure in Ibs. per sq. in., aate 2.309p. In hydraulic transmission the velocity 


and the height above datum are usually small compared with the pressure- 
head. The work or energy of a given quantity of water under pressure = 
its volume in cubic feet x its pressure in lbs. per sq. ft.; or if Q@ = quantity 
in cubic feet per second, and p = pressure in lbs. per square inch, W = 


144nQ, and the H. P. = ae x= 2618pQ. 


Maximum Efficiency of a Long Conduit.—A. L. Adams and 
R.C.Gemmell (Hng’g News, May 4, 1893), show by mathematical analysis that 
the conditions for securing the maximum amount of power through a long 
couduit of fixed diameter, without regard to the economy of water, is that 
the draught from the pipe should be such that the frictional loss in the pipe 
will be equal to one third of the entire static head. 

Wthl-Power.—A ‘“mill-power”’ is a unit used to rate a water-power for 
the purpose of renting it. The value of the unit is differentin different 
localities. The following are examples (from Emerson): 

Holyoke, Mass.—Each mill-power at the respective falls is declared to be 
the right during 16 hours in a day to draw 38 cu. ft. of water per second at 
the upper fall when the head there is 20 feet, or a quantity proportionate to 
the height at the falls. This is equal to 86.2 horse-power as a maximum, 

Lowell, Mass.—The right to draw during 15 hours in the day so much water 
as shall give a power equal to 25 cu. ft. a second at the great fall, when the 
fall there is 80 feet. Equal to 85 H. P. maximum. : 

Lawrence, Mass.—The right to draw during 16 hours in a day so much 
water as shall give a power equal to 30 cu. ft. per second when the head is 
25 feet. Equal to 85 H.P. maximum. ; 

Minneapolis, Minn.—30 cu. ft. of water per second with head of 22 feet, 
Equal to 74.8 H.P. As ; 

Manchester, N. H.—Divide 725 by the number of feet of fall minus 1, and 





590 WATER-POWER, _ 


the quotient will be the trumber of cubic feet per second in that fall. For 20 
feet fall this equals 38.1 cu. ft., equal to 86.4 H. P. maximum. 

Cohoes, N. Y.—‘‘ Mill-power ”? equivalent to the power given by 6 cu. ft. 
per second, when the fall is 20 feet. Equalto 13.6 H. P., maximum, 

Passaic, N. J.—Mill-power: The right to draw 814 cu. ft. of water per sec., 
fall of 22 feet, equal to 21.2 horse-power. Maximum rental $700 per year for 
each mill-power = $33.00 per H. P. 

The horse-power maximum above given is that due theoretically to the 
weight of water and the height of the fall, assuming the water-wheel to 
have perfect efficiency. It should be multiplied by the efficiency of the 
wheel. say 75% for good turbines, to obtain the H. P. delivered by the wheel. 

Value of a Water-power.—In estimating the value of a water- 
power, especially where such value is used as testimony fora plaintiff whose 
water-power has beer diminished or confiscated, it is a common custom for 
the person making such estimate to say that the value is represented by a 
sum of money which, when put at interest, would maintajn a steam-plant 
of the same power in the same place. 

Mr. Charles T. Main (Trans. A. S. M. E. xiii. 140) points out that this sys- 
tem of estimating is erroneous; that the value of a power depends upon a 
great number of conditions, such as location, quantity of water, fall or head, 
uniformity of flow, conditions which fix the expense of dams, canals, founda 
tions of buildings, freight charges for fuel, raw materials and finished prod. 
act, ete. He gives an estimate of relative cost of steam and water-pewer 
for a 500 H. P. plant from which the following is condensed: 

The amount of heat required per H. P. varies with different kinds of busi- 
ness, but in an average plain cotton-mill, the steam required for heating and 
slashing is equivalent to about 25% of steam exhausted from the high- 
pressure cylinder of a compound engine of the power required to run that 
mill, the steam to be taken from the receiver. 

The coal consumption per H. P. per hour for a compound engine is taken 
at 134 lbs. per hour, when no steam is taken from the receiver for heating 
Fe eae aa gross consumption when 25% is taken from the receiver ig 
about 2. Se 


%5% of the steam is used as in a compound engine at 1.75 Ibs. = 1.81 lbs. 
Pay ite tee *“* high-pressure ‘* 8.00 lbs. = .75 ** 


2.06 $* 
The running expenses per H. P. per year are as follows $ 
2.06 lbs. coal per hour = 21.115 lbs. for 1044 hours or one day = 6503.42 
Ibs. for 308 days, which, at $3.00 per long ton = 


Attendance of boilers, one man @ $2.00, and one man @ $1.25 = 2 00 
oe 66 engine, 06 be 66 $3.50. 2 16 
Oil, waste, and supplies. 80. 


The cost of such a steam-plant in New England and vicinity of 500 
H. P. is about $65 per H. P. Taking the fixed expenses as 4% on 
engine, 5% on boilers, and 2% on other portions, repairs at 2%, in- 
terest at 5%, taxes at 114% on 34 cost, an insurance at 14% on exposed 
portion, the total average per cent is about 1214, or $65 xX le = 8.13 


Gross cost cf power and low-pressure steam per H. P, $21 80 


Comparing this with water-power, Mr. Main says: *' At Lawrence the cost 
of dam and canals was about $650,000, or $65 per H. P.. The cost per H. P. 
of wheel-plant from canal to river is about $45 per H. P. of plant, or about 
$65 per H. P. used, the additional $20 being caused by making the plant 
large enough to compensate for fluctuation of power due to rise and fall of 
river. The total cost per H. P. of developed plant is then about $130 per H. P. 
Placing the depreciation on the whole plant at 2%, repairs at 1%, interest at 
5%, taxes and insurance at 1%, or a total of 9%, gives: 


Fixed expenses per H. P. $130 x .09 = $11 70 
Running “* 68 (Estimated) 200 


$13 70 


“To this has to be added the amount of steam required for heating pur- 
poses, said to be about 25% of the total amount used, but in winter months 
the consumption is at least 3714%. It is therefore necessary to have a boiler 
plant of about 37142 of the size of the one considered with the steam-plant, 





TURBINE WHEELS. 591 


costing about $20 x .375 = $7.50 per H. P. of total power used, The ex: 
pense of running this boiler-plant is, per H. P. of the the total plant per year: 


Fixed expenses 1214% on $7.50,......cec-cccsevccecccseseres.s $0.94 
Coal 


See eeSS SOTHO HOSS HSHOHEHHF HOHE. 281 SHOHFHOSFOE DEH SHOSEBHEDOOOOS 8.26 


PDO tc crcccseiccrareesels 6 cenisibeig cea ce Oeste Meee th eee ate 1.23 





Total See +-Seesss S8esSSSeeseSeteoesesesee BH2088 8808 $5.43 


Making a total cost per year for water-power,with the auxiliary boiler plant 
$13.70 + $5.43 = $19.18 which deducted from $21.80 make a difference in 
favor of water-power of $2.67, or for 10,000 H. P.a saving of $26,700 per 
year. 

‘‘It is fair to say,’’ says Mr. Main,“ that the value of this constant power is 
a sum of money which when put at interest will produce the saving; or if 6% 
is a fair interest to receive on money thus invested the value would be 
$26.700 +- .06 = $445,000.” 

Mr. Main makes the following general statements as to the value ofa 
water-power ; ‘‘ The value of an undeveloped variable power is usually noth- 
ing if its variation is great, unless it is to be supplemented by a steam-plant. 
It is of value then only when the cost per horse-power for the double-plant 
is less than the cost of steam-power under the same conditions as mentioned 
for a permanent power, and its valuecan be represented in the same man- 
ner as the value of a permanent power has been represented. 

** The value of a developed power is as follows; If the power can be run 
cheaper than steam, the value is that of the power, plus the cost of plant, 
less depreciation. If it cannot be run as cheaply as steam, considering its 
cost, etc., the value of the power itself is nothing, but the value of the plant 
is such as could be paid for it new, which would bring the total cost of run- 
ning down to the cost of steam-power, less depreciation.” 

Mr. Samuel Webber, Iron Age, Feb. and March, 1893, writes a series of 
articles showing the development of American turbine wheels, and inci- 
dentally criticises the statements of Mr. Main and others who have made 
comparisons of costs of steam and of water-power unfavorable to the latter, 
Hesays: ‘* They have based their calculations on the cost of steam, on large 
compound engines of 1000 or more H. P. and 120 pounds pressure of steam 
in their boilers, and by careful 10-hour trials succeeded in figuring down 
steam to a cost of about $20 per H. P., ignoring the well-known fact that its 
average cost in practical use, except near the coal mines, is from $40 to $50. 
In many instances dams, canals, and modern turbines can be all completed 
for a cost of $100 per H. P.; and the interest on that, and the cost of attend- 
ance and oil, will bring water-power up to but about $10 or $12 per annum; 
and with a man competent to attend the dynamo in attendance, it can 
probably be safely estimated at not over $15 per H. P.” 


TURBINE WHEELS. 


Proportions of Turbines.—Prof. De Volson Wood discusses at 
length the theory of turbines in his paper on Hydraulic Reaction Motors, 
Trans. A. S. M. E. xiv. 266. His principal deductions which have an imme- 
diate bearing upon practice are condensed in the following ; 


Notation. 
Q = volume of water passing through the wheel per second, 
h, = head in the supply chamber above the entrance to the bucksta, 
hg = head in the tail-race above the exit from the buckets, 
2, = fall in passing through the buckets, 
H=h,+ 2, — hg, the effective head, 
“, = coefficient of resistance along the guides, 
Mg = coefficient of resistance along the buckets, 


7, = radius of the initial rim, 
r radius of the terminal rim, 
v velocity of the water issuing from supply chamber, 


v, = initial velocity of the water in the bucket in reference to the bucket, 
q = terminal velocity in the bucket, 

= angular velocity of the wheel, 

= terminal angle between the guide and initial rim = CAB, Fig. 1382, 

¥1 = angle between the initial element of bucket and initial rim = EAD, 

Ya = GFT, the angle between the terminal rim and terminal element of 
the bucket. 

= eb, Fig. 183 = the are subtending one gate opening, 


592 WATER-POWER, 


a, = the arc subtending one bucket at entrance. (In practice a, is larget 
than a, 

Ag Be the arc subtending one bucket at exit, 

K = bf, normal section of passage, it being assumed that the passages 
and buckets are very narrow, 

k, = bd, initial normal section of bucket, 

= gi, terminal normal section, 

wr, = velocity of initial rim, 

= velocity of terminal rim, 
HFI, angle between the terminal rim and actual direction of the 


ll 





Oo 
Fre. 182. Fie. 183, 


Three simple systems are recognized, 7, < r9q,called outward flow; 1; > 19, 
called inward flow; 7, = rg, called parallel flow. The first and second may 
be combined with the third, making a mixed system, 

Value of yq (the quitting angle).—The efficiency is increased as y_, de- 
creases, and is greatest for yg = 0. Hence, theoretically, the terminal ele- 
ment of the bucket should be tangent to the quitting rim for best efficiency. 
This, however, for the discharge of a finite quantity of water, would 
require an infinite depth of bucket. In practice, therefore, this angle must 
have a tinite value. The larger the diameter of the termina! rim the smaller 
may be this angle for a given depth of wheel and given quantity of water 
discharged. In practice y, is from 10° to 20°. 

In a wheel in which all the elements except yg are fixed, the velocity of 
the wheel for best effect must increase as the quitting angle of the bucket 
decreases. 

Values of a-4-y, must be less than 180°, but the best relation cannot be © 
determined by analysis. However, since the water should be deflected from 
its course as much as possible from its entering to its leaving the wheel, the 
angle a for this reason should be as small as practicable. 

In practice, a cannot be zero, and is made from 20° to 30°. 

The value r,; = 1.4rg makes the width of the crown for internal flow about 
the same as for r, =", /\% for outward flow, being approximately 0.8 of the 
external radius, 

Values of », 1nd wq.—The frictional! resistances depend upon the construc- 
tion of the wheel as to smoothness of the surfaces, sharpness of the angles, 


TURBINe WHEELS, 693 


regularity of the curved parts, and also upon the speed it fs run. These 
values cannot be definitely assigned beforehand, but Weisbach gives for 
good conditions wy = Mg = 0.05 to 0.10. 

They are not necessarily equal, and », may be from 0.05 to 0.0%5, and ps 
from 0.06 to 0.10 or even larger, 

Values of y, must be less than 180° — a, 

To be on the safe side, y, may be 20 or 30 degrees less than 180°—2a, giving 


¥, = 180° — 2a —25 (say) = 155 — 2a. 


Then if a = 30°, y, = 95°. Some designers make y, 90°; others more, and 
still others less, than that amount. Weisbach suggests that it be less, so 
that the bucket will be shorter and friction less. This reasoning appears to 
be correct for the inflow wheel, but not for the outflow wheel. In the Tre- 
mont turbines, described in the Lowell Hydraulic Experiments, this angle 
is 90°, the angle a 20°, and yz_ 10°, which proportions insured a positive 
pressure in the wheel. Fourneyron made y, = 90°, and a from 30° to 33°, 
which values made the initial pressure in the wheel near zero. 

Form of Bucket.—The form of the bucket cannot be determined analytic- 
ally. From the initial and terminal directions and the volume of the water 
flowing through the wheel, the area of the normal sections may be found. 

The normal section of the buckets will be: 


Ka 2; k=; ee 


v UY i) ‘ 
The depths of those sections will be: ' 
cadets spptllad Win hye = penile | 
Nan ire! vaso. siny, 9 ajsiny,. 


The changes of curvature and section must be gradual, and the general 
form regular, so that eddies and whirls shall not be formed. For the same 
reason the wheel must be run with the correct velocity to secure the best 
effect. In practice the buckets are made of two or three arcs of circles, 
mutually tangential. ’ 

The Value of w.—So far as analysis indicates, the wheel may run at any 
speed; but in order that the stream shall flow smoothly from the supply 
chamber into the bucket, the velocity V should be properly regulated. 

If wy = Mg = 0.16, rg 7, = 1.40, a = 25°, yy = 90°, yo = 12°, the velocity of 
the initial rim for outward flow will be for maximum efficiency 0.614 of the 
velocity due to the head, or wr, = 0.614 29H. 


The velocity due to the head would be /2yH = 1.414 VgH. 

For an inflow wheel for the case in which 1,2 = 2792, and the other dimen 
sions as given above, wr; = 0.682 29H. 

The highest efficiency of the Tremont turbine, found experimentally, was 
0.79375, and the corresponding velocity, 0.62645 of that due to the head, and 
for all velocities above and below this value the efficiency was less. 

In the Tremont wheel a = 20° instead of 25°, and yg = 10° instead of 12°. 
These would make the theoretical efficiency and velocity of the wheel some. 
what greater. Experiment showed that the velocity might be considerably 
larger or smaller than this amount without much diminution of the efficiency. 

It was found that if the velocity of the initial (or interior) rim was not less 
than 44% nor more than 75% of that due to the fall, the efficiency was 75% or 
more. This wheel was allowed to run freely without any brake except its 
own friction, and the velocity of the initial rim was observed to be 


1.335 4/29H, half of which is 0.6675 29H, which is not far from the velocity 
giving maximum effect; that is tosay,when the gate is fully raised the coeffi- 
cient of effect is a maximum when the wheel is moving with about half its 
maximum velocity. 

Number of Buckets.—Successful wheels have been made in which the dis- 
tance between the buckets was as small as 0.75 of an inch, and others as 
much as 2.75 inches. Turbines at the Centennial Exposition had buckets 
from 41% inches to 9 inches from centre to centre. If too large they will not 
work properly. Neither should they be too deep. Horizontal partitions 
are sometimes introduced. These secure more efficient working in case the 
gates are only partly opened. The form and number of buckets for com: 
mercial purposes are chiefly the result of experience. 


594 WATER-POWER. 


Ratio of Radit.—Theory does not limit the dimensions of the wheel. In : 
practice, 


for outward flow, 19 + 7°, is from 1.25 to 1.503 
for inward flow, rg--7, is from 0.66 to 0.80. 


It appears that the inflow-wheel has a higher efficiency than the outward- 
flow wheel. The inflow-wheei also runs somewhat slower for best effect. 
The centrifugal force in the outward-flow wheel tends to force the water 
outward faster than it would otherwise flow ; while in the inward-flow wheel 
it has the contrary effect, acting as it does in opposition to the velocity in 
the buckets. 

It also appears that the efficiency of the outward-flow wheel increases 
slightly as the width of the crown is less and the velocity for maximum 
efficiency is slower ; while for the inflow-wheel the efficiency slightly in- 
creases for increased width of crown, and the velocity of the outer rim at the 
same time also increases. 

Efficiency.—The exact value of the efficiency for a particular wheel must 
be found by experiment. 

It seems hardly possible for the effective efficiency to equal, much less 
exceed, 86%, and all claims of 90 or more per cent for these inotors should be 
discarded as improbable. A turbine yielding from 75% to 80% is extremely 
good. Experiments with higher efficiencies have been reported. 

The celebrated Tremont turbine gave 7914% without the ‘ diffuser,” which 
might have added some 2%. A Jonval turbine (parallel flow) was reported 
as yielding 0.75 to 0.90, but Morin suggested corrections reducing it to 0.63 to 
0.71. Weisbach gives the results of many experiments, in which the effi- 
ciency ranged from 50% to 84%. Numerous experiments give # = 0.60 to 0.65, 
The efficiency, considering only the energy imparted to the wheel, will exe 
ceed by several per cent the efficiency of the wheel, for the latter will in- 
clude the friction of the support and leakage at the joint between the sluice 
and wheel, which are not included in the former; also as a plant the resist- 
ances and losses in the supply-chamber are to be still further deducted. 

The Crowns.—The crowns may be plane annular disks, or conical, or 
curved. If the partitions forming the buckets be so thin that they may be 
discarded, the law of radial flow will be determined bv the form of the 
crowns. If the crowns be plane, the radial flow (or radial component) will 
diminish, for the outward flow-wheel, as the distance from the axis increases 
=the buckets being full—for the angular space will be greater, 

Prof. Wood deduces from the formule in his paper the tables on page 595. . 

It appears from‘these tables: 1. That the terminal angle, a, has frequently 
been made too large in practice for the best efficiency. 

2. That the terminal angle, a, of the guide should be for the inflow less 
than 10° for the wheels here considered, but when the initial angle of the 
bucket is 90°, and the terminal angle of the guide is 5° 28’, the gain of effi- 
ciency is not 2% greater than when the latter is 25°. 

3..That the initial angle of the bucket should exceed 90° for best effect for 
outflow-wheels. ' 

4. That with the initial angle between 60° and 120° for best effect on inflow 
wheels the efficiency varies scarcely 12. 

5. In the outflow-wheel, column (9) shows that for the outflow for best 
effect the direction of the quitting water in reference to the earth should be 
nearly radial (from %6° to 97°), but for the inflow wheel the water is thrown 
forward in quitting. This shows that the velocity of the rim should some- 
what exceed the relative final velocity backward in the bucket, as shown in 
columns (4) and (5). 


6. In these tables the velocities given are in terms of /2gh, and the co- 
efficients of this expression will be the part of the head which would produce 
that velocity if the water issued freely. There is only one ease, column (5), 
where the coefficient exceeds unity, and the excess is so small it may be dis- 
earded; and it may be said that in a properly proportioned turbine with the 
conditions here given none of the velocities will equal that due to the head 
in the supply-chamber when running at best effect. 

7. The inflow turbine presents the best conditions for construction for 
producing a given effect, the only apparent disadvantage being an increased 
first cost due to an increased depth, or an increased diameter for producing 
a given amount of work. The larger efficiency should, howeve:, more than 
neutralize the increased first cost. 


595 


TURBINE WHEELS. 


. 




















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596 | WATER-POWER, 


Tests of Turbines.—Emerson says that in testing turbines itisarare 
thing to find two of the same size which can be made to do their best at the 
same speed. The best speed of one of the leading wheels is invariably wide 
from the tabled rate. It was found that a 54-in. Leffel wheel under 12 ft. 
head gave much better results at 78 revolutions per minute than at 90. 

Overshot wheels have been known to give 75% efficiency, but the average 
performance is not over 602%. 

A fair average for a good turbine wheel may be taken at 75%. In tests of 18 
wheels made at the Philadelphia Water-works in 1859 and 1860, one wheel 
gave less than 50% efficiency, two between 50% and 60%, six between 60% and 
70%, seven between 71% and 77%, two 82%, and one 87.77%. (Kmerson.) 

Tests of Turbine Wheels at the Centennial Exhibition, 
1876. (From a paper by R. H. Thurston on The Systematic Testing of 
Turbine Wheels in the United States, Trans. A. S. M. E., viii. 859.)—In 187@ 
the judges at the International Exhibition conducted a series of trials of 
turbines, Many of the wheels offered for tests were found to be more or 
less defective in fitting and workmanship. The following is a statement of 
the results of all turbines entered which gave an efficiency of over 75%, 
Seven other wheels were tested, giving results between 65% and 752. 


























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Maker’s Name, or Name the |°o |8a |@ Ete Se (ee, [am 
Wheel is Known By. Bosleudls ols ole ole dleag 
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RisdOnene cre sik aces ea bes cS O8 ts cg. NO6s20 82.4 isan ee 75. Sb eens 
National....... ve neeeceereces we 83.79 alee Coliseo oe 60209) | Mceeate. | eet eern et | eee 
Geyelin (single) {1.0 sede s ee Se oF CO-30 Paces tel ee wasdc css sets mea aeee A eateries 
Thos. Tait eocoeeoee ereee ceeeoeee 82.13 oe L ROY NL elos Bit 70.40 66.35 sooeere 55.00 
Goldie & McCullough. ......... | 81.21 ]......] 71.01 | 55.90] ......)...... secerne 
Rodney Hunt Mach. Co........} ¢8.70 | 71.66}...... 68.60 | 51.03}. .....7.. aie 
Tyler Wheel.....cccccccescssoe| 69.09 oo ee] 81.24 ] 79.92 | 67.23 | 69.59 1....66 
Geyelin (duplex),..... Seeks doch CROC RS waves [elooaleoll sects eile ober ee ance eee 
Knowlton & Dolanicce. secccee | 60c48 [C420 ec sep oc tees Oc-80 | oe aeee Seniee 
E. T. Cope & Sons......ccccoce| (6.94]...... GO02 Wile sc ails ce ents Iacctearee ieeroemee 
Barber & Harris......... secrete 60,10 [tGBsOa"[ ee eel ce siete 70.87 1 Tia | aes 
York Manufacturing Co.......| 75.70]...... 67,08)| 67257 862:06 12s sie ee es. 
W. F. Mosser & Co....... ....| 75.15 | 74.89 | 71.90 | 70.52 )...... 66.04}. 2.4. 


The limits of error of the tests, says Prof. Thurston, were very uncertain; 
they are undoubtedly considerable as compared with the later work done in 
the permanent flume at Holyoke—possibly as much as 4% or 5%, 

Experiments with ‘“ draught-vubes,’? or ‘‘ suction-tubes,” which were 
actually ‘‘ diffusers’ in their effect, so far as Prof. Thurston has analyzed 
them, indicate the loss by friction which should be anticipated in such 
cases, this loss decreasing as the tube increased in size, and increasing ag 
its diameter approached that of the wheel—the minimum diameter tried. 
It was sometimes found very difficult to free the tube from air completely, 
and next to impossible, during the interval, to control the speed with the 
brake. Several trials were often necessary before the power due to the full 
head could be obtained. The loss of power by gearing and by belting was 
variable with the proportions and arrangement of the gears and pulleys, 
length of belt, etc., but averaged not far from 30% for a single pair of bevel- 
gears, uncut and dry, but smooth for such gearing, and but 10% for the same 
gears, well lubricated, after they had been a short time in operation. The 
amount of power transmitted was, however, small, and these figures are 
probably much higher than those representing ordinary practice. Intro- 
ducing a second pair—spur-gears—the best figures were but little changed, 
although the difference between the case in which the larger gear was the 
driver, and the case in which the small wheel was the driver, was perceiv- 
able, and was in favor of the former arrangement, A single straight belt 
gave a loss of but 2% or 3%, & crossed belt 6% to 8%, when transmitting 14 


TURBINE WHEELS. BO" 


horse-power with maximum tightness and transmitting power. A ‘ quarter 
turn” wasted about 10% as a maximum, and a ‘‘ quarter twist’ about 5%. 

Dimensions of Turbines.—For dimensions, power, etc., of stand- 
ard makes of turbines consult the catalogues of different manufacturers. 
The wheels of different makers vary greatly in their proportions for any 
given capacity. 

The Pelton Water-wheel!.—Mr. Ross E. Browne (Eng’g News, Feb. 
20, 1892) thus owilines the principles upon which this water-wheel is 
constructed : 

The function of a water-wheel, operated by a jet of water escaping from 
a nozzle, is to convert the energy of the jet, due to its velocity, into useful 
work In order to utilize this energy fully the wheel-bucket, after catching 
the jet, must bring it to rest before discharging it, without inducing turbu- 
lence or agitation of the particles. 

This cannot be fully effected, and unavoidable difficulties necessitate the 
loss of a portion of the energy. The principal losses occur as follows: 
First, in sharp or angular diversion of the jet in entering, or in its course 
through the bucket, causing impact, or the conversion of a portion of the 
energy into heat instead of useful work. Second, in the so-called frictional 
resistance offered to the motion of the.water by the wetted surfaces of the 
buckets, causing also the conversion of a portion of the energy into heat 
instead of useful work, Third, in the velocity of the water, as it leaves the 
bucket, representing energy which has not been converted into work. 

Hence, in seeking a high efficiency: 1. The bucket-surface at the entrance 
should be approximately parallel tc the relative course of the jet, and 
the bucket should be curved in such 
amanner as to avoid sharp angular de- 
fiection of the stream. If, for example, 
a jet strikes a surface at an angle and 
is sharply deflected, a portion of the 
water is backed, the smoothness of the 
stream is disturbed, and there results 
considerable loss by impact and other- 
wise. The entrance and deflection in 
the Pelton bucket are such as to avoid Fia. 184, Fie. 135, 
these losses in the main. (See Fig. 186.) 

2. The number of buckets should be small, and the path of the jet in the 
bucket short; in other words, the total wetted surface should be small, as 
the loss by friction will be proportional to this. 

3. The discharge end of the bucket should be as nearly tangential to the 
wheel periphery as compatible with the clearance of the bucket which 
follows; and great differences of velocity in the parts of the escaping water 
should be avoided. In order to bring the water to rest at the discharge end 
of the bucket, it is shown, mathematically, that the velocity of the bucket 
should be one half the velocity of the jet. 

A bucket, such as shown in Fig. 135, will cause the heaping of more or less 
dead or turbulent water at the point indicated by dark 
shading. This dead water is subsequently thrown from 
the wheel with considerable velocity, and represents a 
large loss of energy. The introduction of the wedge in 
the Pelton bucket (see Fig. 184) is an efficient means of 
avoiding this loss. 

A wheel of the form of the Pelton conforms closely in 
construction to each of these requirements. 

In ate.. made by the proprietors of the [Idaho mine, 

Fig. 186. near Grass Valley, Cal., the dimensions and results were 

' as foll. vs: Main supply-pipe, 22 in. diameter, 6900 ft. 

Jong, with a head of 38614 feet above centre of nozzle. The loss by friction 

in the pipe was 1.8 ft., reducing the effective head to 384.7 ft. The Pelton 

wheel used in the test was 6 ft.in diameter and the nozzle was 1.89 in. 

diameter. The work done was measured by a Prony brake, and the mean 
of 13 tests showed a useful effect of 87.37. 

The Pelton wheel is also used as a motor for small powers. A test by 
M. E. Cooley of a 12-inch wheel,with a 34-inch nozzle, under 10t lbs. pressure, 
gave 1.9 horse-power. The theoretical discharge was .09385 cubic feet per 
second, and the cheoretical horse-power 2.45; the efficiency being 80 per 
cent. Two other styles of water-motor tested at the same time each gave 
efficiencies of 55 per cent. 








598 


WATER-POWER. 


Pelton Water-wheel Tables, (Abridged.) 
The smaller figures under those denoting the various heads give the 


spouting velocity of the water in feet per minute. 


ment is also based on the flow per minute. 





Size of 
Wheels, 


Head 
in ft. 


6 
in. 


12 
in. 


18 
in. 





18 
in. 


bay 


No.1] No. 2} No.3; No. 4 Nov5 


———— — «| ——— | ——_—_— 


.05} —.12)- 220 
{1.67} 3.91] 6.62 
684] 342] 228 


10) > 231. .88 
2.05) 4.79) 8.11 
8387) 418) 279 
.15). 385) 59 
5.53} 9.37 


2.00 
3043 .39|Revolutions..| 969} 484) 323 
.49} .84 


60 |Horse-power.} .21 
6.18]10.47 
541{ 361 


20 |Horse-power. 
Cubie feet.. 
2151.97 Revolutions.. 
80. |Horse-power. 
Cubic feet. ... 
2635.62/Revolutions.. 
40 |Horse-power. 
Cubie feet. ... 























Cubic feet. ...]2.64 
3402.61|/Revolutions.. |1083 
60 |Horse-power.} .28 
Cubie feet. ...|2.90 
8727 .37{ Revolutions.. |1185 
20 |Horse-power. 
Cubic feet. . 
4026.00 Revolutions.. 
80 |Horse-power. 
Cubic feet.... 
4303.99|Revolutions.. 














7.31/12.39 
640} 427 


1.00} 1.70 


1281 
43 
8.35 
1368 
90 |Horse-power.| .51 
Cubie feet. ...]3.55 

4565 .04| Revolutions. .]1452 
100 Horse-power.}| .60 
Cubic feet. ...(8.74] 8. 
4812.00) Revolutions.. {1530} 765 





























120 Horse-power. “99 1 84; 3.12 

Cubic feet..../4.10} 9.57/16.21 

5271.80] Revolutions..|1677} 838] 559 

140 |Horse-power.]| .99 "2.33 3.94 

. {Cubic feet. ..]4.43]10.384]17.53 

5693.65| Revolutions..}1812; 906) 604 

160 |Horse-power.|}1.22| 2.84 “4.82 
Cubic feet. ...}4.73]11.05 

6086 .74| Revolutions. .{1938| 969 


18.74 
646 
180 \Horse power.|1.45) 3.39 Be 
Cubic feet.. .j5.02)11.72 
6455.97) Revolutions, .|2049) 1024 


5.405 














<a | 





19.87 
683 
200 |Horse-power.}1.70| 3.97) 6.74 

Cubie feet. .}5.29)12.36/20. 294 

6805.17) Revolutions. .}2160] 1080) 720 


250 |Horse-power.|2.38) 5.56) 9:42 
Cubic feet. ...]5.92/13.82/23.42 
7608.44 Revolutions. .{2418] 1209] 8066 









































387 
11.72 
228 
69 
14.36 
279 


66 
20.83 
171 


1.22 
25.51 
209 


150} 2.64 
46.93} 83.82 
114 85 70 


2.76} 4.88 
57.44] 102.04 

189; 104 
4.24) 7.58 
66.36/107.84 

161; 121 
5.98} 10.60 
74.17)131.72 

180} 135 
7.84] 13.94 
81.25/144.32 


























1.06 
16.59 
823 


1.49 
18.54 
361 


1.96 
20.31 
895 


2.47 
21.94 

































































25 .59 
52/176. 75 
181 
29.93 
186.82 
191 





























89.41 
204.10 
209 
49.64 
220.44 
226 











SEE 


“453 "302 




















18.10) 40.77) 72. 
62.49]140. 74): 
513) 342 


21.20) 47.75] 84.81 
65 .87]148.35/263.49 
540] 860} 9270 216 
29.63] 66.74/118.54) 185.47 
73 .64)165.86}294.59) 460.91 
605} 403' 3802 241 














132.70 
412 25 














16.68 
41.46 
806 


The cubie-feet measure- 





























163.08 
562.96 
171 
191.00 
593.40 
180 


266.96 
663.45 
202 








POWER OF OCEAN WAVES, 599 


Pelton Water-wheel Tables.—Continued. 





a ae Bd bb 18 24 3 4 5 6 


Inge] Sia ity. in. in. ft. ft. ft. tf. 
No.1] No.2} No.3; No. 4 | No. 5 


300 |Horse-pow’r|3.13] 7.81]12.38| 21.93] 38.95) 87.73/155.83| 243.82] 350.94 
Gubie feet. ,|6.48|15.13]25.66| 45.42) 80.67/181 .691322.71| 504.91| 726.76 
8334.62|Revolutions |2652| 1326, 884, 884} 663) 442) 831] 265, 221 


| ee | | ———_ - ] - —_ 






Head Size of 
in ft. Wheels. 


—— | —__. 























—— | ——— | —- ———————_|- 


350 |Horse-pow’r|3.94] 9.21]15.61] 27.64] 49.09/110.56)196.38) 3807.25] 442.27 
Cubic feet...|7.00}16.35/27.71| 49.06) 87.14)196.25/348.57) 545.36) 785.00 
9002.43|/Revolutions |2865) 1482} 955] 955) 716) 477) 358 285 238 


———— | 











400 |Horse-pow’r|4.82]11.25/19.0 | 33.77) 59.98)135.08)239.94} 375.40) 540.35 
Cubic feet...|7.49]17.48/29 68) 52.45) 98.16/209.80/372.64] 583.02) 839.20 

9624.00) Revolutions |8063] 1532] 1021) 1021 765 510 3882 3806 255 
450 |Horse-pow’r 
Cubic feet... 

10207 .79|Revolutions 


























——_—— 





——— 








B.%5 13.48 22.76 40.29) 71.57)161.19)286.31) 447.95] 644.78 
7.94]15.54/31.42) 55.63) 98.81/222.52/395.24) 618.38) 890.11 
3249) 1624) 1083] 1083) 812} 541) 406 824 270 























500 |Horse-pow’r|6.74]15.73|26.66) 47.20) 83.83)188.80/3385.34| 524.66 “756.20 
Cubic feet... |8.37]19.54/33.12) 58.64/104.15/234.56/416.62) 651.83) 938.25 
10759.96|Revolutions |8426) 1713] 1142) 1142] 856) 571] 428 842 285 






























































600 |Horse-pow’r|....}.... eihesstecm 62.04|110.19}248.16/440.77| 689.63} 992.65 
Cubic feet...]....}...0.]-.---| 64.24/114.09/256.95/456.38} 714.05) 1027.80 
11786.94|Revolutions |....] ....].... 4) Ban 938 625 469 875 312 
650 |Horse-pow’r|....|..0..|..+.-| 69.95|124.25/279.82/497.01| 777.6211119.29 
Cubie feet...}...-]..«- A eb tia 66.86] 118.75)/267.44/475.02] 743.21/1069.77 

12268 .24|Revolutions |....|.... place ee LoOsi mo LOO ll usec 390 825 
700 |Horse-pow’r}....|..... hig .-.| 78.18]188.86)312.73)/555 46 “869.06 1250.92 


Cubic feet...]....]...-.].02.«| 69.38)123.23)277.54/492.95) 771.26) 1110.16 
12731 .34/Revolutions }....].....]. .-.} 1851] 1013) 675) 506 405 337 


——— | —__. 





| ee | | 
























































750 |Horse-pow’r|. ..|... .|.....| 86.70]154.00|346.831616.03| 963.82] 1387.34 
Cubic feet...|..._|.....|.....| 71.82|127.56]287.281510.25| 798.33/1149 13 
13178.19|Revolutions |....|....1..... 1399| 1049 699] 5241  419/ 349 
800 |Horse-pow’r|....|.... .....| 95.521 169.661382.09|678.66]1061.8111528.36 
Gubic feet...|....4...../.222.| 74/17/1381 74|296.70/526.99| 824.51/1186.81 
13610.40|Revolutions| ...!.....}..... 1444, 1083 G22l 542] 433] B61 
900 |Horse-pow’r|....|..... ....{113.98]202. 451455 .94|809.82| 1267 .0211823.76 
Guble teeticli oh tke 78_67|139.74]314.70|558.96| 874.53]1258.81 
14436.00|Revolutions |....|.....|..... 1532] liga] vecl S74| 4591 383 
1000 |Horse-pow’r|....{|.....|..-.. 133 .50/237.12/534.01/948.48 1483.97 2136.04 
Gubic feet...|. ..|...../.... 2) 82.93/147.301/331.721589.19| 921.83/1326.91 
15216.89|Revolutions |....].....|..... 1615] 1210} 807] 605 4e4{ 408 


THE POWER OF OCEAN WAVES. 


Albert W. Stahl, U.S. N. (Trans. A. S. M, E., xiii. 438), gives the following 
formule and table, based upon a theoretical discussion of wave motion: 

The total energy of one whole wave-length of a wave H feet high, L feet 
long, and one foot in breadth, the length being the distance between succes- 


sive crests, and the height the vertical distance between the erest and the 
2 
trough, is H = 8LH? (1 — 4.935 =) foot-pounds, 
The time required for each wave to travel through a distance equal v0 1ts 


own length is P= / a5 seconds, and the number of waves passing any. 


600 WATER-POWER. 


given point in one minute is N = ad = 60 . Hence the total energ’y 


of an indefinite series of such waves, expressed in horse-power per foot of 
breadth, is | 
EXN Hi? 
83000 L?7* 


By substituting various values for H + L, within the limits of such values 
actually occurring in nature, we obtain the following table of 





= 0320H?L(1 — 4,935 


ToTaL ENERGY OF DE&EP-SEA WAVES IN TERMS OF HORSE-POWER PER Foor 
oF BREADTH. 








ieee Length of Waves in Feet. 
ra mo 
eight o 
Waveas 25 50 @ | 100 150 200 [300 400 
50 .04 23 64 1.31 3.92 7.43 20.46 42.01 
40 -06 230 1.00 2.05 5.65 11.59 81.95 65.58 
30 cae .64 1.77 8.64 10.02 20.57 56.70} 116.38 
20 .25 1.44 3.96 8.13 21.7 45.¢8 120.70) 260.08 
15 42; 2.83 6.97 14.3 39.438 80.94 223.06} 457.89 
10 .98 5.53 15.24 31.29 86.22 | 177.00 487.75) 1001.25 
5 38.380 | 18.68 51 48 105.68 | 291.20 | 597.78 | 1647.°1| 3381.60 


The figures are correct for trochoidal deep-sea waves only, but they give 
a close approximation for any nearly regular series of waves in deep water 
and a fair approximation for waves in shallow water. 

The question of the practical utilization of the energy which exists in 
ocean waves divides itself into several parts: 

1. The various motions of the water which may be utilized for power 
purposes. 

2. The wave motor proper. That is, the portion of the apparatus in direct 
contact with the water, and receiving and transmitting the energy thereof ; 

ogether with the mechanism for transmitting this energy to the machinery 
for utilizing the same. 

. Regulating devices, for obtaining a uniform motion from the irregular 
and more or less spasmodic action of the waves, as well as for adjusting the 
apparatus to the state of the tide and condition of the sea. 

4, Storage arrangements for insuring a continuous and uniform output of 
power during a calm, or when the waves are comparatively small. 

The motions that may be utilized for power purposes are the following: 
1. Vertical rise and fall of particles at and near the surface. 2. Horizontal 
to-and-fro motion of particles at and near the surface. 3. Varying slope of 
surface of wave. 4. {mpetus of waves rolling up the beach in the form of 
breakers. 5. Motion of distorted verticals. All of these motions, except the 
jast one mentioned, have at various times been proposed to be utilized for 
power purposes; and the last is proposed to be used in apparatus described 
by Mr. Stahl. 

The motion of distorted verticals is thus defined: A set of particles, origi- 
nally in the same vertical straight line when the water is at rest, does not 
remain in a vertical line during the passage of the wave; so that the line 
connecting a set of such particles, while vertical and straight in still water, 
becomes distorted, as well as displaced, during the passage of the wave, its 
upper portion moving farther and more rapidly than its lower portion. 

Mr. Stahl’s paper contains illustrations of several wave-motors designed 
upon various principles. His conclusions as to their practicability is as fol- 
lows: ‘‘ Possibly none of the methods described in this paper may ever prove 
commercially successful; indeed the problem may not be susceptible of a 
financially successful solution. My own investigations, however, so far as I 
have yet been able to carry them, incline me to the belief that wave-power 
can and will be utilized on a paying basis.” 

Continuous Utilization of Tidal Power. (P. Decceur, Proce. 
Inst. C. E. 1890.)—In connection with the training-walls to be constructed ia 


PUMPS AND PUMPING ENGINES. 601 


the estuary of the Seine, it is proposed to construct large basins, by means 
of which the power available from the rise and fall of the tide could be util- 
ized. The methou pronosed is to have two basins separated by a bank rising 
above high water, within which turbines would be placed. The upper basin 
would be in communication with the sea during the higher one third of the 
tidal range, rising, and the lower basin during the lower one third of the 
tidal range, falling. If H be the range in feet, the level in the upper 
basin would never fall below ¥4H measured from low water, and the 
level in the lower basin would never rise above 44H. The available head 
varies between 0.53H and 0.80H, the mean value being 24H. If S square feet 
be the area of the lower basin, and the above conditions are fulfilled, a 
quantity 1/3SA cu. ft. of water is delivered through the turbines in the space 
of 914 hours. The mean flow is, therefore, SH + 99,900 cu. ft. per sec., and, 
the mean fall being 34H, the available gross horse-power is about 1/30S’77?, 
where S’ is measured in acres. This might be increased by about one third 
if a variation of levelin the basins amounting to 44H were permitted. But 
to reach this end the number of turbines would have to be doubled, the 
mean head being reduced to 14H, and it would be more difficult to transmit 
a constant power from the turbines. The turbine proposed is of an improved 
model designed to utilize a large flow with a moderate diameter. One has 
been designed to produce 300 horse-power, with a minimum head of 5 ft. 3 
in. at a speed of 15 revolutions per minute, the vanes having 13 ft. internal 
diameter. The speed would be maintained constant by regulating sluices. 


PUMPS AND PUMPING ENGINES. 


Theoretical Capacity of a Pump.—Let Q’ = cu. ft. per min.; 
G’ = Amer. gals. per min. = 7.4805Q’; d = diam. of pump in inches; 2 = 
stroke in inches; NV = number of single strokes per min. 





ity i (pee OF esters eos ee (OOO BAN IVa P= 
Capacity in cu. ft. per min. = Q 5a rae Okla -0004545.Nd215 
Capacity in gals. per min. G’ = * pap = .00384 Nd21; 
Capacity in gals. per hour ..... poh deeetaeds Suwa -cOtNGel, 
Diameter required for <i as “Q” J G’ 
given capacity per min. d = 46.9 WIC. 17.15 NN 


If v = piston speed in feet per min., d= 13.544/ & = 1054/2, 
v 


If the piston speed is 100 feet per min.: 
Ni = 1200, and d = 1.354 /Q’ = .495 V@’;_ _G’ = 4.08d? per min. 


The actual capacity will be from 60% to 95% of the theoretical, according to 
tlie tightness of the piston, valves, suction-pipe, ete. 


Wheoretical Horse-power required to raise Water toa 
given Height.—Horse-power = 


Volume incu. ft. per min. X pressure per sq. ft. | Weight x height of lift 
33,000 ot 33,000 


’= cu. ft. per min.; G’ = gals, per min.; W = wt. in lbs.; P = pressure 
in Ibs. per sq. ft.; p = pressure in lbs. per sq. in.; H = height of lift in ft.; 
W <= 62.369’. P= 144p, p = .488H, H = 2.309p, G’ = 7.48059’. 


/ / D , / 
Mp Cae ease OH. GH 


~ 33,000 33,000 ™~ 529.2 3958.7" 
pp = WH _ Q X 6236 x 2.209 _ Op _ _G’p 
~ 88,000 ~~ 33,000 229.2 0 4170405) 


For the actual horse-power required an allowance must be made for the 
friction, slips, etc., of engine, pump, valves, and passages. 


602 WATER-POWER. 


Depth of Suction.—Theoretically a perfect pump will draw water 
from a height of nearly 84 feet, or the height corresponding to a perfect 
vacuum (14.7 Ibs. x 2.309 = 33.95 feet); but since a perfect vacuum cannot be 
obtained, on account of valve-leakage, air contained in the water, and the 
vapor of the water itself, the actual height is generally less than 20 feet, 
When the water is warm the height to which it can be lifted by suction de- 
creases, on account of the increased pressure of the vapor. In pumping hot 
water, therefore, the water must flow into the pump by gravity. The fol- 
lowing table shows the theoretical maximum depth of suction for different 


temperatures, leakage not considered: | 
a 











Absolute Max. Absolute axt 
Pressure Vacuum Depth Pressure Vacuum Depth 
Temp. in Temp in f 
ofVapor, of of Vapor, oO 
: lbs. p ee of Suction, B. Ibs. p ree Suction, 
sq. in StCUry + fee sq. in Y+\ feet 
102.1 1 27.88 31.6 182.9 8 13.63 15.4 
126.3 2 25.80 29.3 188.3 9 11.60 nes ee, 
141.6 3 23.83 210 193.2 10 9.56 10.8) 
153.1 4 Alek 24.7 197.8 11 Vi152 8.5 
162.3 5 19.74 22.3 202.0 12 5.49 6.2 
LOR 6 17.70 20.0 205.9 13 3.45 3.9 
176.9 i 15.67 i heath 209.6 14 1.41 1.6 








Amount of Water raised by a Single-acting Lift-pump. 
—It is common to estimate that the quantity of water raised by a 
single-acting bucket-valve pump per minute is equal to the number of 
strokes in one direction: per minute, multiplied by the volume traversed by 
the piston in a single stroke, on the theory that the water rises in the pump 
only when the piston or bucket ascends; but the fact is that the column of 
water does not cease flowing when the bucket descends, but flows on con- 
tinuously through the valve in the bucket, so that the discharge of the 
pump, if it is operated at a high speed, may amount to nearly double that 
calculated from the displacement multiplied by the number of single strokes 
in one direction. 

Proportioning the Steam-cylinder of a Direct-acting 
Pump.—Let 

A =: area of steam-cylinder; a = area of pump-cylinder; 

D = diameter of steam-cylinder; qd = diameter of pump-cylinder; 

P= steam-pressure, lbs. per sq. in.; = resistance per sq. in. on pumps; 

H= head = 2.309p; p= .4000Ts 
work done in pump-cylinder 


pig eee es wae piInp = work done by the steam-cylinder® 








WGP wo HAP» 5. Pe a EP» ius (ope SA 
A= 7p 4= 3 D=ay/ 2s d=D SRE hE Ty Se 
A Pp 433 | A A 


—-= == pry TP —}3 = 10% = 1.732P — 
5 EP EP? HH = 2.309EP. re Ti = 15%, cock. a 

Eis commonly taken at 0,7 to 0.8 for ordinary direct-acting pumps. For 
the highest class of pumping-engines it may amount to 0.9. The steam- 
pressure Pis the mean effective pressure, according to the indicator-dia- 
gram; the water-pressure p is the mean total pressure acting on the pump 
plunger or piston, including the suction, as could be shown by an indicator- 
diagram of the water-cylinder. The pressure on the pump-piston is fre- 

uently much greater than that due to the height of the lift, on account of 
ee cHgD of the valves and passages, which increases rapidly with velocity 
19) Ow. ‘ 

Speed of Water through Pipes and Pump-passages,.— 
The speed of the water is commonly from 100 to 200 feet per minute. If 200 
feet per minute is exceeded, the loss from friction may be considerable. 


F F Sune: p gallons per minute 
The diameter of pipe required is 4.954 / volonity iuleeetiper minahes 


For a velocity of 200 feet per minute, diameter =.35 X gallons per min, 


PUMPS. - 603 


Sizes of Direct-acting Pumps.—The tables on this and the next 
page are selected from catalogues of manufacturers, as representing the 
two common types of direct-acting pump, viz., the single-cylinder and the 
duplex. Both types are now made by most of the leading manufacturers. 

The Deane Single Boiler-feed or Pressure Pump.—Suitable 
for pumping clear liquids at a pressure not exceeding 150 Ibs. 


<< , 
































Sizes. Capacity : sizes of Pipes. 
g{ permin. o vi 

i A 3 | | at Given g £ 

=| | lL et) Speed | (pails 

& at icewe Ie) q e ; o 
in, | eae xbheedl golwmi dads % | g | ® 
= g S) ‘ Oo} 4 = © ra aq To gj a Ke) 8 
al eth O are at anced ecto ee a shale 
2\|n E 3 |s n O pe) = n Bb he) Meet 
0 3 2 5 07} 150 10 | 29% 7 6 34 1314 1 
fo ote | 234 1 ed 09) 150°) 13-4 Babel © Ve 54} 114 | 4 
16] 4 oe S| 510) - 150.19. 15 | 83be | vig 1-461] 84 ea 
ay Pee Oe) 5 1 Std) 1504 B16 | B8ket| Sig) |= Sel] 984 Naa 
Yl 434] 8 5 | .15| 150] 22] 34 Bigite Beir 87 116 14 
3 5 344 a B25 125 31 | 48% 94 34 1 2 1% 
4 |, 56} 834) 7 PY 88 195 42 | 48k 1 Big Tg) 1) Re aie 
4yy| & 4i4| 8 | .49| 1290] 58) 5114] 12 1 16°03 1 ee 
5 7 44 10 69} 100 69 | 55 12 1 1g | 3 2 
6 Tg 10 85} 100 85 | 55 4 1 144 | 3 v 
64] 8 5 12 |1.02} 100 | 102] 63 | 14 1 14] 3. | 2 
% 10 6 12) lea?) 100 147 | 69 19 1% 2 4 4 
8 12 rG 12 |2.00; 100 200 | 69 19 2 24 | 5 4 
9 14 8 120 A206.) 100 261 | 69 21 2 24415 5 











The Beane Single Tank or Light-service Pump.—tThese 
pumps will all stand a constant working pressure of 75 lbs. on the water- 
cylinders. 






































Sizes. © Capacity A Sizes of Pipes. 
fa) per min ® ”) —— 
Pa + at Given a a 
o S Oo 
3 Sti : Speed 5 g : 
ae Glactmeaain aa neediae: gee ee 
! | 2 as & 
Spi ie Heer epee Mierke or ilear. |e a eto 
3 Pal ge = iS) =I S us| 3 aq D 9 
& Se) S zs 3 ® ‘a £ 4 = ae 
Be EW file | Cue er WAC teehee guerre |) Bl 4. no ae 
4 4 D 27 130 35 | 33 9144 4% 34 2 1% 
5 4 7 38 125 48 | 45146) 15 34 1 3 26 
ig |) Sle lia 72] 125 | 90] 45%) 15 vane 3 | 2h 
76g | Th 10 ae On 1107) 7.210 17 14 5 4 
8 6 12 1.46 100 146 67 2016 144 4 4 
6 7 12 2.00 | 100 | 200] 66 34 1 4 4 
8 a 12 2.00 100 200 | 67 2014 1 1% 5 4 
8 8 12 2.61 100 261 68 30 i 1% 5 5 
10 8 12 2.61 100 261 6814} 30 1% iy 5 5 
8 10 12 4,08 100 408} 68 | 2014 144 8 8 
10 | 10 12 | 4.08| 100] 408] 6814/3 114] 2 8 | 8 
12 10 12 4.08 100 408 | 64 24 2 24 8 8 
10 12 12 5.87 100 } 587] 6814; 380 1% 7 8 8 
12 12 12 5.87 10¢ 587 | 64 28144 2 246 8 8 
10 12 18 fe vi 616} 95 1 25 1g} 2 8 8 
12 12 18 path 7 616} 95 2815 2 216 8 alas 
12 14 18 12.00 70 | 840} 95 | 28% 2 244 8 8 
14 16 18 15.66 70 | 1095} 95 | 34 2 246} 12 | 10 
16 16 18 15.66 ui 1096 | 95 B4 2 244 12 10 
18 16 18 15.66 7 1096) 97 34 é 34 12 10 
16 18 24 26.42 50} 1821 .).115 | 40 2 24 14 12 
18 18 24 26.42 50} 1321 } 185 | 40 3 346 14 12 


604 WATER-POWER. 


Efficieney of Small Direct-acting Pumps.—Chas. E. Emery, 
in Reports of Judges or Philadelphia Kxhibition, 1876, Group xx., says: “Ex- 
periments made with steam-pumps at the American Institute Exhibition of 
1867 showed that average-sized steam-pumps do not, on the average, utilize 
more than 50 per cent of the indicated power in the steam-cylinders, the re- 
mainder being absorbed in the friction of the engine, but more particularly 
in the passage of the water through the pump. It may be safely stated 
that ordinary steam-pumps rarely require less than 120 pounds of steam 
per hour for each horse-power utilized in raising water, equivalent toa duty 
of only 15,000,000 foot-pounds per 100 pounds of coal.. With larger steam- 
pumps, particularly when they are proportioned for the work to be done, 
the duty will be materially increased.”’ 


The Worthington Duplex Pump. 
STANDARD SIZES FOR ORDINARY SERVICE. 















































bt ao. Sizes of Pipes for 
= SiS 
y ne we, a = 3o8 Short Lengths. 
ig a hy Saray mia =~ </To be increased as 
a 2 2. Qe ac ‘32%! length increases. 
Ss = uD = eZ SS ose 
Fa ace ois ete s or 
o | @ f5| =56S 5a eo 
: be SA, Le 242 == 
Ailes [si Lot see otter lee: 
$) 8 |S e8| 2:3 Dog | Bax 
n = & BO o> oe ® oe Aes é 6 3, 
he G4 RM Say S = ) La) wo 5 : 3. o 6, 
ty u o oO eal aan 2 weg] = : a, o 
® ® @ Md RAS Pas Of eR] a] 2 BO 
— + fa C06 a Ui oO - YX) ° 1 n [=| ~ 
2 | 2/8/88] Seg SSL |B heo tae | eal mee nate 
= a a o ~ 
a ulee! 12 | 22 oR 1 SS 1a oS) a ie aa aie 
A; A |H}A os es) =) N\A] wn =) 
3 2 3 .04) 100 to 250 8to 20) 2% | 3%] Ww) 14) 1 
4144 | 234] 4] .10}-100to200| 20to 40) 4 |%| 34] 2 114 
544 | 346| 5 .20} 100 to 200 40 to 80) 5 34 | 114) 246] 1% 
6 4 6 .33} 100 to 150 TOto 100) 55 |1 1144) 3 2 
| 4144] 6] .42| 100to150| 85to 125] 63 |1%12 | 4 3 
ThE | 5 6| .51] 100to 150 | 100to 150) 7 {1146/2 | 4 3 
714 | 416 | 10 69} %5to 125 | 100 to 170; 63 114 | 2 4 3 
9 514 | 10 93} 75 to125 |} 1385to 230) 7 2 216) 4 3 
10 6 10 i ARs 15 to 125 | 180 to 300) 8 2 24} 5 4, 
10 {f 10 1.66} 75to0 125 | 245 to 410} 9% {2 2146| 6 5 
12 7 10} 1.66] %5to125 | 245to 410} 9% |2% | 3 6 5 
14 fi 10 1.66} 75to 125} 245 to 410) 9% |2% | 3 6 5 
12 844 | 10 2.45} 75 to 125 | 365to 610} 12 26 | 3 6 5 
14 844 |10| 2.45] %5to 125] 365to 610) 12 |216/3 | 6 5 
16 8h_ | 10 2.45} 75 to 125 | 865 to 610) 12 214 | 3 6 5 
1814 8144 | 10| 2.45! T5to 5 | 365 to 610) 12 3 314) 6 5 
20 814 | 10 2.45} 5 to 125 | 365 to 610) 12 4 5 6 5 
12 1044} 10} 3.57) %5to125 | 530 to 890] 1414 |2%4 | 3 8 7 
14 10144 | 10) 3.57) %5to 125 | 580 to 890) 1414 [2% | 3 8 7 
16 1044 |} 10] 38.57) 5 to 125 | 580 to 890) 1414 |2%4 | 3 8 is 
1844 | 10144 | 10] 3.57) %5to 125} 5380 to 890) 1414 |3 3144) 8 i 
20 1044 | 10 3.57} 75 to 125 | 530to 890] 1444 |4 5 g q 
14 12 10} 4.89) %5 to 125 | 730 to 1220) 17 12144) 3 | 10 8 
pC  ie &4 10] 4.89) %5to125 | 730 to 1220) 17 216 | 3 10 8 
184% | 12 | 10] 4.89] %5to125/ 730to 1220] 17 {E 314| 10 8 
20 12 10 4.89} 75 to 125 | 730 to 1220) 17 4 5 10 8 
184 | 14 10 | 6.66] %5to125 | 990 to 1660) 1934 |3 314) 12 10 
20 i4 10 6.66] 75 to 122 | 990 to 1660) 1934 |4 5) 2 10 
ile 10 | 15} 5.10} 50to0100 | 510 to 1020) 14 {3 314| 8 ff 
20 12 15 7.34) 50to100 | 730 to 1460] 17 4 5 12 10 
20 15 15.) '1134750'Co 100: | 1145.t0. 2290) 21 aaeer a. -\|/- «1. sae faraeme 
25 15 15 | 11.47} 50 to 100 | 1145 to 2400 Pa Wn, 9 oc Sel RAIA EU ois Ge 





PUMPS. 605 


Speed of Piston.—A pisvon speed of 100 feet per minute is commonly 
assumed as correct in practice, but for short-stroke pumps this gives too 
high a speed of rotation, requiring too frequent a reversal of the valves. 
For long stroke pumps, 2 feet and upward, this speed may be considerably 
exceeded, if valves and passages are of ample area. 


Number of Strokes required to Attain a Piston Speed 
from 50 to 125 Feet per Minute for Pumps having 
Strokes from 3 to 18 Inches in Length, 














Ps 3 Length of Stroke in Inches, 
Cel te ea 
Pei | edie bathe’ Steaved: 8 fled” ited | Mts Sheds 
oes |” ; 
PS 2, Number of Strokes per Minute. 
50 200 150 120 100 |. 86 75 60 50 40 | 383 
55 220 165 132 110 94 82.5 66 55 44 | 37 
60 240 180 144 120 103 90 G2 60 48 | 40 
65 260 195 156 130 Vl 97.5 78 65 52 | 43 
70 280 210 168 140 120 105 84 70 56 | 47 
i 300 225 180 150 128 11255 90 (5) 60 | 50 
80 320 240 192 160 137 120 96 80 64 | 53 
85 340 255 204 70 146 N/A) 102 85 68 | 57 
90 360 27 216 180 154 135 108 90 721 60 
95 880 285 228 190 163 142.5 114 95 7 63 
100 400 300 240 200 171 150 120 100 80 | 67 
105 420 315 252 210 180 m hay (45) 126 , 105 84} 70 
110 440 330 264 220 188 165 132 110 88 | 73 
115 460 845 276 230 197 172.5 138 115 92°) .7 
120 480 360 288 240 206 180 144 120 96 | 80 
125 500 3875 300 250 214 187.5 150 125 100 | 83 


Piston Speed of Pumping-engines,. (Jobn Birkinbine, Trans. 
A. I. M. E., v. 459.)—1In dealing with such a ponderous and unyielding sub- 
stance as water there are many difficulties to overcome in making a pump 
work with a high piston speed. The attainment of moderately high speed 
is, however, easily accomplished. Well-proportioned pumping-engines of 
large capacity, provided with ample water-ways and properly constructed 
valves. are operated successfully against heavy pressures at a speed of 250 ft. 
per minute, without ‘‘thug,’’ concussion, or injury to the apparatus, and 
there is no doubt that the speed ean be still further increased. 

Speed of Water through Valves.—If areas through valves and 
water passages are sufficient to give a velocity of 250 ft. per min. or less, 
they are ample. The water should be carefully guided and not too abruptly 
defiected. (F,. W. Dean, Eng. News, Aug. 10, 1898.) 

Boiler-feed Pumps.—Practice has shown that 100 ft. of piston speed 
per minute is the limit, if excessive wear and tear is to be avoided. 

The velocity of water through the suction-pipe must not exceed 200 ft. 
per minute, else the resistance of the suction is too great. 

The approximate size of suction-pipe, where the length does not exceed 
25 ft. and there are not more than two elbows, may be found as follows: 

7/10 of the diameter of the cylinder multiplied by 1/100 of the piston speed 
in feet. For duplex pumps of small size, a pipe one size larger is usually 
employed. The velocity of flow in the discharge-pipe should not exceed 
500 ft. per minute. The volume of discharge and length of pipe vary so 
greatly in different installations that where the water is to be forced more 
than 50 ft. the size of discharge-pipe should be calculated for the particular 
conditions, allowing no greater velocity than 500 ft. per minute. The size of 
discharge-pipe is calculated in single-cylinder pumps from 250 to 400 ft. per 
minute. Greater velocity is permitted in the larger pipes. 

In determining the proper size of pump for a steam-boiler. allowances 
must be made for a supply of water sufficient to cover all the demands of 
engines, steam-heating, etc., up to the capacity of generator, and should not 
be calculated simply according to the requirements of the engine. In prac- 
tice engines use all the way from 12 up to 50, or more, pounds of steam per 
H.P. per hour when being worked up to capacity. When an engine is over- 
loaded or underloaded more water per H.P. will be required than when 
operating at its rated capacity. The average run of horizontal tubular’ 


606 WATER-POWER. 


boilers will evaporate from 2 to 3 lbs. of water per sq. ft. of heating-surface 
per hour, but may be driven up to 6 lbs. if the grate-surface is too large or 
the draught too great for economical working. 
Pump-Valves.—aA. F. Nagle (Trans. A. 8S. M. E., x. 521) gives a number 
of designs with dimensions of double-beat or Cornish valves used in large 
umping-engines, with a discussion of the theory of their proportions. The 
ollowing is a summary of the proportions of the valves described. 


SUMMARY OF VALVE PROPORTIONS. 








D hot ou ae 
> OD a8 Ssl os 
G SEPE gO S| ae 
2 ra @® = 
an Ee os oa]  F d 
Cae act a7) 4 
Location of Engine, 39 = e283 Sa S83 23 | ae 
a oe a 2] 5 a 2 
da| Be 82 |o88| 38 4 
3” OD PHB_q S86] C8a 














Providence high-ser- 
vice engine .......| 12 1c 1b: 16% | 877 Ibs. ‘Good 
peciied to 


Providence Cornish- 


engine......se6...-| 16 1.28 2 | 680 Good 
St. Louis Water Wks.| 16 1.86 6% | 250 Some noise 
Milwaukee * “ | 7 40 88 | 120 | { Somonoise.at 
Chicago <ohe 25 1.41 75 | 151 Noisy 
ae ae eS 15 1.31 85 | 140 G 
ée 6 CT} 
wood seats...... eoo| 15 1.16 94 | 132 * 
Chicago Water Wks. 8 .96 %5 | 151 - 


Mr. Nagle says: There is one feature in which the Cornish valves are 
necessarily defective, namely,the lift must always be quite large, unless great 
power is sacrificed to reduce it. It is undeniable that a smail lift is prefer- 
able to a great one, and hence it naturally leads to the substitution of 
numerous small valves for one or several large ones. To what extreme re- 
duction of size this view might safely lead must be left to the judgment of 
the engineer for the particular case in hand, but certainly, theoretically, we 
must adopt small valves. Mr. Corliss at one time carried the theory so 
far as to make them only 13g inches in diameter, but from 3 to 4 inches is 
the more common practice now. A small valve presents proportionately a 
larger surface of discharge with the same lift than a larger valve, so that 
whatever the total area of valve-seat opening, its full contents can be dis- 
charged with less lift through numerous small valves than with one large 
one. 

Henry R. Worthington was the first to use numerous small rubber valves 
in preference to the larger metal valves, These valves work well under ail 
ithe conditions of a city pumping-engine. A volute spring is generally used 
‘to limit the rise of the valve. 

In the Leavitt high-duty sewerage-engine at Boston (Am. Machinist, May 
31, 1884), the valves are of rubber, 34-inch thick, the opening in valve-seat 
being 134% X 444inches. The valves have iron face and back-plates, and 
form their own hinges. 


CENTRIFUGAL PUMPS, 


Relation of Height of Lift to Velocity.—The height of lift 
il aan only on the tangential velocity of the circumference, every tangen- 
tial velocity giving a constant height of lift—sometimes termed ‘head "— 
whether the pump is small or large. The quantity of water discharged is in 
proportion to the area of the discharging orifices at the circumference, or in 
proportion to the square of the diameter, when the breadth is kept the same, 
R. H. Buel (App. Cyc. Mech., ii, 606) gives the following: 

Let Q represent the quantity of water, in cubic feet, to be pumped per 
minute, h the height of suction in feet, h’ the height of discharge in feet, and 
d the diameter of suction-pipe, equal to the diameter of discharge-pipe, in 


CENTRIFUGAL PUMPS. 607 


| / Q 
e . 2 —_ a 5 oe Le 
feet; then, according to Fink, d = 0.36 V29h4 bh)’ g being the acce 


eration due to gravity, 

If the suction takes place on one side of the wheel, the inside diameter of 
the wheel is equal to 1.2d, and the outside to 2.4d. If the suction takes place 
at both sides of the wheel. the inside diameter of the wheel is equal to 0.85d, 
and the outside to 1.%d. Then the suction-pipe will have two branches, the 
area of each equal to half the area of d. The suction-pipe should be as short 
as possible, to prevent air from entering the pump. The tangential velocity 


of the outer edge of wheel for the delivery Q is equal to 1.25 W729 (h +h’) 
feet per second. 

The arms are six in number, constructed as follows: Divide the central 
angle of 60°, which incloses the outer edges of the two arms, into any num- 
ber of equal parts by drawing the radii, and divide the breadth of the wheel 
in the same manner by drawing concentric circles. The intersections of the 
several radii with the corresponding circles give points of the arm. 

In experiments with Appold’s pump, a velocity of circumference of 500 
ft. per min. raised the water 1 ft. high, and maintained it at that level 
without discharging any; and double the velocity raised the water to four 
times the height, as the centrifugal force was proportionate to the square 
of the velocity; consequently, 

500 ft. per min. raised the water 4 ft. without discharge. 
e ee 6 6 


2000 iT} 6s 06 66 $s 16 66 66 6s 
4000 (i) 66 ee 66 66 64 66 6 66 
The greatest height to which the water had been raised without discharge, 
{n the experiments with the 1-ft. pump, was 67.7 ft., with a velocity of 4153 
ft. per min., being rather less than the calculated height, owing probably to 
leakage with the greater pressure, A velocity of 1128 ft. per min. raised the 
water 514 ft. without any discharge, and the maximum effect from the 
power employed in raising to the same height 5144 ft. was obtained at the 
velocity of 1678 ft. per min., giving a discharge of 1400 gals. per min. from 
the 1-ft. pump. The additional velocity required to effect a discharge of 
1400 gals. per min., through a 1-ft. pump working at a dead level without an 
height of lift, is 550 ft. per min. Consequently, adding this number in eac 
case to the velocity given above, at which no discharge takes place, the fol- 
lowing velocities are obtained for the maximum effect to be produced in 
each case; 
1050 ft. per min., velocity for 1 ft. height of lift. 
1550 66 ob 74 66 4 66 6ée 66 


2550 be oe 66 66 16 66 66 66 
4550 66 66 66 66 64 66 66 66 
Or, in general terms, the velocity in feet per minute for the circumference 
of the pump to be driven, to raise the water to a certain height, is equal to 
550 + 500 height of lift in feet. 


Lawrence Centrifugal Pumps, Class B-—For Lifts from 








fartae > lane 
«| o5 {o23 | 9 | oa jo28 | 3S 
cel eet) Bowes ies ory Patines eae us Stare > |seul as 
SsiSa| So loSecleake| & mls) se losucl(*ak| & 
Se a 4722s o= ° SAIS Ss a® QA s plc ° 
SIS ES) OS (6 Se slaran| 8S Fosse) oS 18 easly gu} bw 
sm 2 es Ze he aR Eo Sh) 28) 2A po ME) 90 Eo 
A 8 


Ss 














EN 
wre 
wr 


700 | .386]} 1032 § 30] 30] 30 25000 \ 10.50) 20000* 


1 1 

1 1 

2 2 

3 3 dj : 

; 444 % 450 | .27 680 § 24 | 24] 24 18060 } 7.60} 9000* 
4 : 1200 | .65 | 1260 § 86 | 36] 36 35000 | 14.75] 22000* 





* Without base. 

The economical capacity corresponds to a flow not exceeding 10 ft. per 

second iu the delivery-pipe. Small pipes and high rate of flow cause a great 
loss of power. 


608 WATER-POWER. 


Size of Pulleys, Width of Belts, and Revolutions per 
Minute Necessary to Raise the Rated Quantity of Water 
to Different Heighis with Pumps of Class B. 








SEAR Bere 
2 bs | : o- yee Height in Feet and Revolutions per Minute. > A 
Seals lS g eo re) 
8 ze SE lEa|s ss ; : oa 
oiQ |= {= CPE OIE BT 10h AS hT8F 20 25! BOM ae Beet, 
114] 5 5] 3 70| 520 | 590} 665) 720; 885} 930) 1045 | 1125 | 1200 | 1% 
2 | 6 5] 4 100} 475 | 540} 605} 660) 765] 850} 955 | 1025 | 1100 | 2 
3 | 74} 7] 6 250) 435 | 500} 560} 610) 705} 790) 880 | 945 | 1000 | 3 
4 10 Gita % 450} 400 | 465} 520) 570) 655) 730} 815 | 880} 945 | 4 
5 |!4 | 11] 8 700} 355 | 410) 454) 595) 575] 640) 715 | 765 | 825 | 5 
6 |16 | 11] 9 {| 1200] 815 | 365} 400) 440) 510} 570) 6385 | 685 | 745 | 6 
8 [20 | 12] 10] 2000) 234 | 270] 300} 3830) 385) 425) 475 | 500 | 555 | 8 
10 (22 | 12] 10} 3000] 234 | 270) 300) 330) 885) 425) 47 500 | 555 /10 
12 |30 | 14] 12] 4200) 160 | 185) 200) 220) 255) 285) 318 | 340 | 360 12 
15 (36 | 16] 15 | 000; 140 | 165) 180} 198) 228) 255) 285 | 805 | 330 /15 
18 {40 | 16} 15 | 10000} 125 | 145) 160) 173} 200) 225) 250! 27 290 |18 
CE OO RBS, RAs econ 18000} 105 | 125) 185] 150] 170} 190) 214-7 280 | 250 \24 
BO aie vn | 88 ..-.{ 25000} 95 | 106} 118] 130) 148] 165) 185 | 204 7 25 (30 
ROM aes. | 35000} 95 | 106) 118} 130] 148) 165} 185 | 204 | 215 36 








Efficiencies of Centrifugal and Reciprocating Pumps.— 
W. O. Webber (Trans. A.'S. M. E., vii. 598) gives diagrams showing the 
relative efficiencies of centrifugal and reciprocating pumps, from which the 
following figures are taken for the different lifts stated : 


Lift, feet: 

2 5 10 15 20 2 30 35 40 50 60 80 100 120 160 200 240 280 
Efficiency reciprocating pump: 

so ee, 00 45.55) .617 266.68 71.75 67 182 685) 877.90 389" (BB ks 
Efficiency centrifugal pump: 

7507.56, 264.68 4.09. .661..001 025002500 40 scien «com Nain wenes nulNeer ns ue mann 

The term efficiency here used indicates the value of W. H. P. +I. H. P., 
or horse-power of the water raised divided by the indicated horse- power of 
the steam-engine,and does not therefore show the full efficiency of the pump, 
but that of the combined pump and engine. It is, however, a very simple 
way of showing the relative values of different kinds of pumping-engines 
having their motive power forming a part of the plant. 

The highest value of this term, given by Mr. Webber, is .9164 for a lift of 
170 ft., and 3615 gals. per min. This was obtained in a test of the Leavitt 
pumping-engine at Lawrence, Mass., July 24, 1879. 

With reciprocating pumps, for higher lifts than 170 ft., the curve of effi 
ciencies falls, and from 200 to 300 ft. lift the average value seems about 
.84. Below 170 ft. the curve also falls reversely and slowly, until at about 90 
ft. its descent becomes more rapid, and at 35 ft. .727 appears the best 
recorded performance. There are not any very satisfactory records below 
this lift, but some figures are given for the yearly coal consumption and 
total number of gallons pumped by engines in Holland under a 16-ft. lift, 
from which an efficiency of .44 has been deduced. 

With centrifugal pumps, the lift at which the maximum efficiency is ob- 
tained is approximately 17 ft. At lifts from 12 to 18 ft. some makers of 
large experience claim now to obtain from 65% to 70% of useful effect, but 
.613 appears to be the best done at a public test under 14.7 ft. head. 

The drainage-pumps constructed some years ago for the Haarlem Lake 
were designed to lift 70 tons per min. 15 ft., and they weighed about 150 
tons. Centrifugal pumps for the same work weigh only 5tons. The weight 
at aycentrifugal pump and engine to lift 10,000 gals. per min. 35 ft. high is 

onus, 

The pumps placed by Gwynne at the Ferrara Marshes, Northern Italy, in 
1865, are, it is believed, capable of handling more water than other set of 

umping-engines in existence. The work performed by these pumps is the 

ee of 2000 tons per min.—over 600,000,000 gals. per 24 hours—on a mean 
lift of about 10 ft. (maximum of 12.5 ft.). (See Engineering, 1876.) 
The efficiency of centrifugal pumps seems to increase as the size of pump 


DUTY TRIALS OF PUMPING-ENGINES. 609 


increases, approximately as follows: A 2/7 pump (this designation meaning 
always the size of discharge-outlet in inches of diameter), giving an effi- 
ciency of 38%, a 3/7 pump 45%, and a 4” pump 52%, a 5’ pump 60%, and a 6” 
pump 64% efficiency. 


Tests of Centrifugal Pumps, 
W. O. Webber, Trans. A. S. M. E., ix. 237. 





Heald | Heald | Heald | Berlin. 
An- An- An- 
Maker. : & & & Sehwartz- 
drews. | drews.| drews. Sisco. | Sisco. | Sisco. | kopff. 
SIZeaten te cw cess No. 9. | No. 9.} No. 9. } No. 10.} No. 10. | No. 10. No. 9. 
Diam. discharge.| 91¢”’ 91g” 91g’) 10” 10” 10” gi4”’ 
** suction... 934”” 934!) 9984/7) 12” 12/7 1277 10.3” 


(Gon ONG Seigler 26// 26//. 80.577} 30.5” | 30.5” 20.5/7 
Rev. per minute.} 191.9 | 195.5 | 200.5 | 188.3 | 202.7 | 213.7 500 
Galls. per minute|1513.12 {2023 82/2499 .33 |1673.37 }2044.9 |2371.67 | 1944.8 
Height in feet...:| 12.25 | 12.62) 138.08) 12.383 | 12.58 | 13.0 16.46 
Water H.P.......}. 4.69 6.47] 8.28 5.22 6.51 Ol et alec ar nalaa 
Dynam’eter H.P.| 10.09] 12.2] 14.88} 8.11 | 10.74] 14.02 11 
Efficiency........| 46.52 | 53.0] 57.57) 64.5 60.74 | 55.72 73.1 





Vanes of Centrifugal Pumps.—For forms of pump vanes, see 
paper by W. O. Webber, Trans. A.S. M. E., ix. 228, and discussion thereon 
by Profs. Thurston, Wood, and others. 

Whe Centrifugal Pump used as a Suction Dredge.—The 
Andrews centrifugal pump was used by Gen. Gillmore, U.S. A., in 1871, in 
deepening tbe channel over the bar at the mouth of the St. John’s River, 
Florida. The pump was aNo. 9, with suction and discharge pipes each 9 
inches diam. It was driven at 300 revolutions per minute by belt from an 
engine developing 26 useful horse-power. 

Although 200 revolutions of the pump disk per minute will easily raise 
3000 gallons of clear water 12 ft. high, through a straight vertical 9-inch 
pipe, 300 revolutions were required to raise 2500 gallons of sand and water 
11 ft. high, through two inclined suction-pipes having two turns each, dis- 
charged through a pipe having one turn. 

The proportion of sand that can be pumped depends greatly upon its 
specific gravity and fineness. The calcareous and argillaceous sands flow 
more freely than the silicious, and fine sands are less liable to choke the 
pipe than those that are coarse. When working at high speed, 50% to 55% of 
sand can be raised through a straight vertical pipe, giving for every 10 cubic 
yards of material discharged 5 to 5144 cubic yards of compact sand. With 
the appliances used on the St. John’s bar, the proportion of sand seldom 
exceeded 45%, generally ranging from 380% to 35% when working under the 
most favorable conditions. 

In pumping 2500 gallons, or 12.6 cubic yards of sand and water per minute 
there would therefore be obtained from 3.7 to 4.3 cubic yards of sand. Dur. 
ing the early stages of the work, before the teeth under the drag had been 
properly arranged to aid the flow of sand into the pipes, the yield was con- 
siderably below this average. (From catalogue of Jos. Edwards & Co., 
Mfrs. of the Andrews Pump, New York.) 


DUTY TRIALS OF PUMPING-ENGINES, 


A committee of the A. S. M. E. (Trans., xii. 530) reported in 1891 on a 
standard method of conducting duty trials. Instead of the old unit of 
duty of foot-pounds of work per 100 lbs. of coal used, the committee recom - 
mend a new unit, foot-pounds of work per million heat-units furnished by 
the boiler. The variations in quality of coal make the old standard unfit as 
a basis of duty ratings. The new unit is the precise equivalent of 100 Ibs. of 
coal in cases where each pound of coal imparts 10,000 heat-units to the 
water in the boiler, or where the evaporation is 10,000 + 965.7 = 10.355 lbs. of 
water from and at 212° per pound of fuel. This evaporative result is readily 
obtained from all grades of Cumberland bituminous coal, used in horizontal 
return ge boilers, and, in many cases, from the best grades of anthra- 
tite coa. 


610 WATER-POWER. 


The committee also recommend that the work done be determined by 
plunger displacement, after making a test for leakage, instead of by meas- 
urement of flow by weirs or other apparatus, but advise the use of such 
apparatus when practicable for obtaining additional data. The following 
extracts are taken from the report. When important tests are to be made 
the complete report should be consulted. 

The necessary data having been obtained, the duty of an engine, and other 
quantities relating to its performance, may be computed by the use of the 
following formule: 


Foot-pounds of work done 
number of heat-units consumed 


—APsp+s)xLXwNn 





4, Duty = x 1,000,000 


x 1,000,000 (foot- pounds), 


H 
ste a SQ Tad 
2. Percentage of leakage = Sark wX 100 (per cent), 


8, Capacity = number of gallons of water discharged in 24 hours 


_AXLXNX 7.4803X2%  AXLX NX 1.24675 


Dx 144 = D (gallons). 


4. Percentage of total frictions, 
A(P+p+s\XLXN 
is paeee ee D X 60 & 33,000 | oh 
= LHP. me 


—[,;- AC tet xLxNn 
=| As X M.E.P. X Ls X Ns 
or, in the usual case, where the length of the stroke and number of strokea 
of the plunger are the same as that of the steam-piston, this last formula 


becomes: AP 48) 
1 ‘ott eat ieee Slee De se 3 
Percentage of total frictions = [1 dsX MEP. |x 100 (per cent). 





|x 100 (per cent); 


In these formule the letters refer to the following quantities: 
A = Area, in square inches, of pump plunger or piston, corrected for area 
of piston rod or rods; 
P = Pressure, in pounds per square inch, indicated by the gauge on the 
force main; 
py = Pressure, in pounds per square inch, corresponding to indication of the 
vacuum-gauge on suction-main (or pressure-gauge, if the suction- 
pipe is under a head). The indication of the vacuum-gauge, in 
inches of mercury, may be converted into pounds by dividing it by 
2.0353 
s = Pressure, in pounds per square inch, corresponding to distance be- 
tween the centres of the two gauges. The computation for this 
pressure is made by multiplying the distance, expressed in feet, by 
the weight of one ctbic foot of water at the temperature of the 
pump-well, and dividing the product by 144; 
L = Average length of stroke of pump-plunger, in feet; 
N = Total number of single strokes of pump-plunger made during the trial; 
As = Area of steam-cylinder, in square inches, corrected for area of piston- 
rod. The quantity As x M H.P., in an engine having more than one 
cylinder, is the sum of the various quantities relating to the respec- 
tive cylinders; 
Ls = Average length of stroke of steam-piston, in feet; 
Ns = Total number of single strokes of steam-piston during trial; 
M.E.P. = Average meéan effective pressure, in pounds per square inch, 
measured from the indicator-diagrams taken from the steam-cylin- 


der; 
I.H.P. = Indicated horse-power developed by the steam-cylinder; 
C = Total number of cubic feet of water which leaked by the pump-plunger 
during the trial, estimated from the results of the leakage test; 
D = Duration of trial in hour's: 


DUTY TRIALS OF PUMPING-ENGINES. 611 


H = Total number of heat-units (B. T. U.) consumed by engine = weight of 
water supplied to boiler by main feed-pump xX total heat of steam 
of boiler pressure reckoned from temperature of main feed-water + 
weight of water supplied by jacket-pump xX total heat of steam of 
boiler-pressure reckoned from temperature of jacket-water + weight 
of any other water supplied x total heat of steam reckoned from its 
temperature of supply. The total heat of the steam is corrected for 
the moisture or superheat which the steam may contain. No allow- 
ance is made for water added to the feed water, which is derived 
from any source, except the engine or some accessory of the engine. 
Heat added to the water by the use of a fiue-heater at the boiler is 
not to be deducted. Should heat be abstracted from the flue by 
means of a steam reheater connected with the intermediate re- 
ceiver of the engine, this heat must be included in the total quantity 
supplied by the boiler. 

Leakage Test of Pump.—tThe leakage of an inside plunger (the 
only type which requires testing) is most satisfactorily determined by mak- 
ing the test with the cylinder-head removed. A wide board or plank may 
be temporarily bolted to the lower part of the end of the cylinder, so as to 
hold back the water in the manner of adam, and an opening made in the 
temporary head thus provided for the reception of an overflow-pipe. The 
piunger is blocked at some intermediate point in the stroke (or, if this posi- 
tion is not practicable, at the end of the stroke), and the water from the 
force main is admitted at full pressure behind it. The leakage escapes 
through the overflow-pipe, and it is collected in barrels and measured. The 
test should be made, if possible, with the plunger in various positions. 

In the case of a pump so planned thatit is difficult to remove the cylinder~ 
head, it may be desirable to take the leakage from one of the openings 
which are provided for the inspection of the suction-valves, the head being 
allowed to remain in place. 

Itis assumed that there is a practical absence of valve leakage. Exami- 
nation for such leakage should be made, and if it occurs, and it is found to 
be due to disordered valves, it should be remedied before making the plunger 
test. Leakage of the discharge valves will be shown by water passing down 
into the empty cylinder at either end when they are under pressure. Leak- 
age of the suction-valves will be shown by the disappearance of water which 
covers them. 

If valve leakage is found which cannot be remedied the quantity of water 
thus lost should also be tested. One method is to measure the amount of 
water required to maintain a certain pressure in the pump cylinder when 
this is introduced through a pipe temporarily erected, no water being al- 
lowed to enter through the discharge valves of the pump. 

Table of Data and Results.—In order that uniformity may be se- 
cured, itis suggested that the data and results, worked out in accordance 
with the standard method, be tabulated in the manner indicated in the fol- 
lowing scheme; 


DUTY TRIAL OF ENGINE, 


DIMENSIONS. 

JNUMbDeCHOMSteA MI - CyMNGCrs cenit ccene iemee its an ees sees fa telae 

ep pDiametenot sted al-Cy Niels ramet eee et cehe de ecicele ss oe . ins. 

3. Diameter of piston-rods of steam-cylinders...... ......00. «.- ins, 

4, Nominal stroke of steam-pistons....... eee Mee cis ors’ cin viel oucitts Tt 

5. Number of water=plun 2ers eee ee a oe etl. dalats ale «-0)'2:0'e' siete ole 

6. Diameter of plungers..?........ i) DAA SAREE DOE Tee Dieta ins. 

7, Diameter of piston-rods of water-cylinders........... fel eigialt Seaae ins. 

8. Nominal stroke of, plunvers.ceseeeess. ssc TMs s sitin'e. wats: arenes £t: 

9. Net area of steam-pistons........... RSS Gets. ona = cate rate oft (ole cette x . Sq. ins. 
10. Net area of plungers...... ....... Be see ere ec accla a sie ots earcre Neier » Sq. ins. 
11. Average length of stroke of steam-pistons during trial.......... Us 
12, Average length of stroke of plungers during trial ............. ft. 

(Give also complete description of plant.) 
TEMPERATURES. 
18. Temperature of water in pump-well..............-0-ecee00- o... degs, 


14. Temperature of water supplied to boiler by main feed-pump.. degs. 
15. Temperature of water supplied to boiler from various other 
BOULEGCES es sic... sis's's simile rere Pile cevicemecsvetsseevics stetalsfayela?e's\eeiv ais degs. 


512 WATER-POWER. 


FERED-WATER. 


16. Weight of water supplied to_boiler by main feed-pump........ Ibs. 
17. Weight of water supplied to boiler from various other sources. Ibs. 


18. Total weight of feed-water supplied from al! sources.......... . lbs. 
PRESSURES. 
19. Boiler pressure indicated by gauge............ pols Diets eeetets wins lbs, 
20. Pressure indicated by gauge on force main...............seeeee lbs. 
21. Vacuum indicated by gauge on suction Tail Ae ee ins. 
22, Pressure corresponding to vacuum given in preceding line..... lbs. 
£8. Vertical distance between the centres of the two gauges....... ins. 
24, Pressure equivalent to distance between the two gauges....... Ibs. 
MISCELLANEOUS DATA. 
OOM ULALION OL CELA mets arce crsrstestc are erates olclejcret siete oratatneets Be ocho siete fete 500 LER 
26. Total number of single ‘str okes duri ine trial oct og ntete eee 
27. Percentage of moisture in steam supplied to engine, or number 
of degrees of superheating .... 0.0... .20.ceeencecerese en seeas % or deg. 
28. Total leakage of pump during trial, determined from results of 
LOR AGE LOSE ye tciels, slays «Sey a0: ole eici ePnc yal Mekeaiclourtnseee se eoein ao uae heats lbs. 
29. Mean effective pressure, measured from diagrams taken from 
BECAIM-CYHMACIS 2. os cm aspects eis ae orng wll sia.s e¥e, s.agsjetalegapreletoiseconte M.H.P. 
: PRINCIPAL RESULTS 
OOM MDG Vectra en tater ai ciele cinctenteeits > Tae Hae ean s 2 Otel tale eet atte aes ft. Ibs. 
31. Percentage of leakage... BARNET GO DIOO COC ICCC Sa. aimee dd bie bac, 
32. Capacity... SAC SCOURS OAS Sa Aa blomcth: gals. 
33. Percentage of ‘total friction.. no a Aertee Uc cee bote eee hob SEs % 
ADDITIONAL RESULTS. 
34. Number of double strokes of steam-piston per minute ....... 
35. Indicated horse-power developed by the various steam- cylinders LeHieP: 
36. Feed-water consumed by the plant per hour..... .............. lbs, 
37. Feed-water consumed by the plant per indicated horse-power 
per hour, corrected for moisture in steam. ................. Ibs, 
38. Number of heat units consumed be indicated horse-power 
WO CTOMOE EAE es hee Me eeteieaste ieee oie al - Leake MOLES OED CIEE R REED BaTUE 
39. Number of heat units consumed per ‘indicated horse- power 
PCT WaOMRe | Bt Oo. Ra ae eee Ashe ed Re eee B.T,U.- 
40, Steam accounted for by indicator at cut-off and release in the 
-various steam-cylinders.. lbs. 
41. Proportion which steam accounted for by ‘indicator. bears to 
the feed-water consumption.... . .... eee ee eee a nce oHeN 
42. Number of double strokes of pump per minute sess: hice Re 
43. Mean effective pressure, measured from pump dilode potiok sais Hpiee 
44. Indicated horse-power exerted in pump-cylinders....... ...... I.H.P. 
45. Work done (or duty) per 100 lbs. of coal ............. c..eecccee ft. lbs. 


SAMPLE DIAGRAM TAKEN FROM STEAM-CYLINDERS. 
(Also, if possible, full measurement of the diagrains, embracing pressures 
at the initial point, cut-off, release, and compression ; also back pressure, 
and the proportions of the stroke completed at the various points noted.) 


SAMPLE DIAGRAM TAKEN FROM PUMP-CYLINDERS. 


These are not necessary to the main object, but it is desirable to give 
them. 
DATA AND RESULTS OF BOILER TEST. 
(In accordance with the scheme recommended by the Boiler-test Com- 
mittee of the Society.) 


VACUUM PUMPS-AIR-LIFT PUMP. 


The Pulsometer.—in the pulsometer the water is raised by suction 
into the pump-chainber by the condensation of steam within it, and is then 
forced into the delivery-pipe by the pressure of a new quantity of steam on 
the surface of the water. Two chambers are used which work alternately, 
one raising while the other is discharging. 

Test of a Pulsometer.—A test of a pulsometer is described by De Volson 
Wood in Trans, A. S. M. E. xiii, It had a 34-inch suction-pipe, stood 40 in. 
high, and weighed 695 lbs. 

The steam-pipe was 1 inch in diameter. A throttle was placed about 2 feet 


VACUUM PUMPS-——AIR-LIFT PUMP. 613 


from the pump, and pressure gauges placed on both sides of the throttle, 
and a mercury well and thermometer placed beyond the throttle. The wire 
drawing due to throttling caused superheating. 
The pounds of steam used were computed from the increase of the tem 
perature of the water in passing through the pump. 
Pounds of steam loss of heat = Ibs. of water sucked in x increase of temp. 
The loss of heat in a pound of steam is the total heat in a pound of satu- 
rated steam as found from ‘‘steam tables’ for the given pressure, plus the 
heat of superheating, minus the temperature of the discharged water ; or 


Ibs. water < increase of temp. 
H — 0.48¢ — 7. 
The results for the four tests are given in the following table: 


Pounds of steam = 








j Number of Test. 
Data and Results. 





il 2 3 4 
Strokes per minute ................ 71 60 Di 64 
Steam press.in pipe before throttl’g 114 110 127 104.3 
Steam press. in pipe after throttl’g 19 30 43.8 26.1 
Steam temp. after throttling,deg.F.| 270.4 27 309.0 270.1 
Steam am/’nt of superheat’g,deg.F. 3.1 3.4 17.4 1.4 
Steam used as det’d from temp.,lbs. 1617 931 1518 1019.9 
Water pumped; lbs... 20... 0003. 06s 404,786 186.362 228,425 | 248,05 
Water temp.before entering pump, 5.15 80.6 76.3 70.25 
Water tem p.yise Ol. yer. fottse lec 4.47 OO 7.49 4.55 
Water head by gauge on lift, ft.... 29.90 54.05 54.05 29.90 
Water head by gauge on suction... 12.26 12.26 19.67 19.67 
Water head by gauge, total (A).... 42.16 66.31 73.72 49.57 
Water head by measure, total (i) 32.8 57.80 66.6 41.66 
Coeff. of friction of plant (h) + (A) 0.77 0.877 0.911 0.889 
Efficiency of pulsometer........... 0.012 0.0155 0.0126 0.0138 
Effic. of plant exclusive of boiler... 0.6093) 0.0136 0.0115 0 0116 
Effic. of plant if that of boiler be 0.7 65 080 0.0081 





0.C0 0.0095 0.0 
Duty,if 1 lb.evaporates 10 ibs: water! 10,511,400} 13,391,000] 11,059,000] 12,036,300 


Of the two tests having the highest lift (54.05 ft.), that was more efficient 
‘which had the smaller suction (12.26 ft.), and this was also the most efficient 
of the four tests. But, on the other hand, the other two tests having the 
same lift (29.9 ft.), that was the more efficient which had the greater suction 
(19.67), so that no law in this regard was established. The pressures used, 
19, 80, 43.8, 26.1, follow the order of magnitude of the total heads, but are 
not proportional thereto. No attempt was made to determine what press- 
ure would give the best efficiency for any particular head. The pressure used 
was intrusted to a practical runner, and he judged that when the pump was 
running regularly and well, the pressure then existing was the proper one 
It is peculiar that, in the first test, a pressure of 19 lbs. of steam should pro- 
duce a greater number of strokes and pump over 50% more water than 26.1 
lbs., the lift being the same, as in the fourth experiment. 

Chas. E. Emery in discussion of Prof. Wood’s paper says, referring to 
tests made by himself and others at the Centennial Exhibition in 1876 (see 
Report of the Judges, Group xx.), that a vacuum-pump tested by him in 
1871 gave a duty of 4.7 millions; one tested by J. F. Flagg, at the Cinciinati 
Exposition in 1875, gave a maximum duty of 3.25 millions. Several vacuum 
and small steam-pumps, compared later on the same basis, were reported 
to have given duties of 10 to 11 millions. the steam-pumps doing no better 
than the vacuum-pumps. Injectors, when used for lifting water not re- 
quired to be heated, have an efficiency of 2 to 5 millions; vacuum-pumps 
vary generally between 3 and 10; small steam-pumps between 8 and 15; 
larger steam-pumps, between 15 and 30, and pumping-engines between 30 
and 140 millions. 

A very high record of test of a pulsometer is given in Eng’g. Nov, 24, 1893, 
p. 639, viz.: Height of suction 11.27 ft. ; total height of lift, 102.6 ft. ; hori- 
zontal length of delivery-pipe, 118 ft. ; quantity delivered per hour, 26,188 
British gallons. Weight of steam used per H. P. per hour, 92.76 lbs.; work 


614 WATER-POWER. 


done per pound of steam 21,845 foot-pounds, equal to a duty of 21,345,000 
foot-pounds per 100 lbs. of coal, if 10 lbs of steam were generated per 
pound of coal. 

The Jet-pump.—tThis machine works by means of the tendency of a 
stream or jet of fluid to drive or carry contiguous particles of fiuid along 
with it. The water-jet pump, in its present form, was invented by Prof, 
James Thomson, and first described in 1852, In some experiments on a 
small seale.as to the efficiency of the jet-pump, the greatest efficiency was 
found to take place when the depth from which the water was drawn by the 
suction-pipe was about nine tenths of the height from which the water fell 
to form the jet ; the flow up the suction-pipe being in that case about one 
fifth of that of the jet, and the efficiency, consequently, 9/10 xk 1/5 = 0.18, 
This is but a low efficiency; but it is probable that it may be increased by 
improvements in proportions of the machine. (Rankine, §. E. 

The Injector when used as a pump has a very low efficiency. (See 
Injectors, under Steam-boilers.) 

Air-lift Pump.—the air-lift pump consists of a vertical water-pipe 
with its lower end submerged in a well, and a smaller pipe delivering air 
into itat the bottom. The rising column in the pipe consists of air mingled 
with water, the air being in bubbles of various sizes, and is therefore lighter 
than a column of water of the same height; consequently the water in the 
pipe is raised above the level of the surrounding water. This method of 
raising water was proposed as early as 1797, by Loescher, of Freiberg, and 
was mentioned by Collon in lectures in Paris in 1876, but its first practical 
application probably was by Werner Siemens in Berlin in 1885. Dr. J. G. 
Pohle experimented on the principle in California in 1886, and U. 8S. patents 
on apparatus involving it were granted to Pohle and Hillin the same year. 
A paper describing tests of the air-lift pump made by Randall, Browne and 
Behr was read before the Technical Society of the Pacific Coast in Feb. 1890. 

The diameter of the pump-column was 3 in., of the air-pipe 0.9 in., and 
of the air-discharge nozzle 4 in. The air-pipe had four sharp bends and a 
length of 35 ft. plus the depth of submersion. 

The water was pumped from a closed pipe-well (55 ft. deep and 10 in. in 
diameter). The efficiency of the pump was based on the least work theo- 
retically required to compress the air and deliver it to the receiver. If the 
efficiency of the compressor be taken at 70%, the efficiency of the pump and 
Bonne RSS OF together would be %0% of the efficiency found for the pump 
alone. 

For a given submersion (h) and lift (£1), the ratio of the two being kept 
within reasonable limits, (H) being not much greater than (h), the efficiency 
was greatest when the pressure in the receiver did not greatly exceed the 
head due to the submersion. The smaller the ratio H +h, the higher wag 
the efficiency. 

The pump, as erected, showed the following efficiencies : 

For H+h= 0.5 1.0 1.5 2.0 
Efficiency = 50% 40% 30% 25% 

The fact that there are absolutely no moving parts makes the pump 
especially fitted for handling dirty or gritty water, sewage, mine water, 
and acid or alkali solutions in chemical or metallurgical works. 

In Newark, N. J., pumps of this type are at work having a total capacity 
of 1,000,000 gallons daily, lifting water from three 8-in. artesian wells. The 
Newark Chemical Works use an air-lift pump to raise sulphuric acid of 1.72° 
gravity. The Colorado Central Consolidated Mining Co., in one of its mines 
at Georgetown, Colo., lifts water in one case 250 ft., using a series of lifts. 

For a full account of the theory of the pump, and details of the tests 
above referred to, see Eng’g News, June 8, 1893. 


THE HYDRAULIC RAM, 


Efficiency.—The hydraulic ram is used where a considerable flow of 
water with a moderate fall is available, to raise a small portion of that flow 
to a height exceeding that of the fall. The following are rules given by 
Eytelwein as the results of his experiments (from Rankine): 

Let Q be the whole supply of water in cubic feet per second, of which q is 
lifted to the height h above the pond, and Q — q runs to waste at the depth 
H below the pond; L, the length of the supply-pipe, from the pond to the 
waste-clack ; D, its diameter in feet; then 


D= VG8Q; L=H+h+ 2x eteots 
Volume of air vessel = volume of feed pipe; 


THE HYDRAULIC RAM, 615 
e » 


: h h 
Efficiency, pert: = 1.12 ~ 0.2 a when “ does not exceed 20. 


or 


h h 
1+ (1 + na) nearly, when 74 does not exceed 12. 


D’Aubuisson gives ee = 1.42 — .28 y/ h 


H 
Clark, using five sixths of the values given hy D’Aubuisson’s formula,gives: 


Ratio of lift to fall..... 4 6 8 10 12 14 16 18 20 22 2% 26 ~ 
Efficiency per sent..... 72 61 52 44 37 31 2 19 14 9 4 O 


Prof. R. C. Carpenter (Hng’g Mechanics, 1894) reports the results of four 
tests of a ram constructed by Rumsey & Co., Seneca Falls. The ram was 
fitted for pipe connection for 114-inch supply and -inch discharge. The 
supply-pipe used was 1} inches in diameter, about 50 feet long, with 3 elbows, 
so that it was equivalent to about’65 feet of straight pipe, so far as resist- 
ance is concerned. Hach run was made with a different stroke for the waste 
or clack-valve, the supply and delivery head being constant; the object of 
the experiment was to find that stroke of clack-valve which would give the 
highest efficiency. 





Length of stroke, per cent......... Sa oser 100 80 60 46 
Number of strokes per minute. .........0.- 52 56 61 66 
Supply head, feet of water.................| 5.67 5.77 5.58 5.65 
Delivery head, feet of water...............] 19.75 | 19.75 | 19.75 | 19.75 


Total water pumped, pounds.........ssee.. 297 296 301 297.5 
Total water supplied, pounds...............] 1615 1567 1518 | 1455.5 
Efficiency, per cent........ Settee Tea 2 eo ®, G449 66 44.9 70 


The efficiency, 74.9, the highest realized, was obtained when the clack-valve 
travelled a distance equal to 60% of its full stroke, the full travel being 15/16 
of one inch. 

Quantity of Water Delivered by the Hydraulic Ram, 
(Chadwick Lead Works.)—From 80 to 100 feet conveyance, one seventh of 
supply from spring can be discharged at an elevation five times as high as 
the fall to supply the ram; or, one fourteenth can be raised and discharged 
say ten times as high as the fall applied. 

Water can be conveyed by a ram 3000 feet, and elevated 200 feet. The 
drive-pipe is from 25 to 50 feet long. 

The following table gives the capacity of several sizes of rams, the dimen- 
sions of the pipes to be used, and the size of the spring or brook to which 
they are adapted: 





Caliber of { Weight of Pipe (Lead), if Wrought 
Pipes. Iron, then of Ordinary Weight. 
Quantity OG ater ea er | ee an ay, 

Furnished per Discharge- 


























Size of |Min. by the Spring o eae . | pipe for 
Ram. | or Brook to which 2 vay eat | Baa tee ok over 50 ft. 
ea te g ‘I jor fall not} over 50 ft. a eae 
ewe - 2 | over 10 ft. rise, 100 ft. in 
A A height. 
Gals. per min. |inch.| inch.| per foot. | per foot. | per foot. 
No.2 34 to 2 34 3 2 lbs. 10 ozs. | 1 lb. 
Sad tig) St 4 1 VA euss 12.0) 1 \** dogs. 
“4 OTN 114 dniile 5“ 12.“ |1 * 40zs, 
$45 Gun %*.14 2 34 Siess 1lb4 * [2 
So. 12ih7 “25 6) 1 Ist ais 3.4 
a6 v4 20 6 40 2 114 13 66 38 66 4 66 
66 10 95 (i) "5 4 2 21 66 % 66 8 6¢ 


616 WATER-POWER. 


HYDRAULIC-PRESSURE TRANSIAISSION. 


Water under high pressure (700 to 2000 lbs. per square inch and upwards, 
affords a very satisfactory methed of transmitting power to a distance, 
especially for the movement of heavy loads at small velocities, as by cranes 
and elevators. The system consists usually of one or more pumps capable 
of developing the required pressure; accumulators, which are vertical cylin- 
ders with heavily-weighted plungers passing through stuffing-boxes in the 
upper end, by which a quantity of water may be accumulated at the pres- 
sure to which the plunger is weighted; the distributing-pipes; and the presses, 
cranes, or other machinery to ve operated. 

The earliest important use of hydraulic pressure probably was in the 
Bramah hydraulic press, patented in 1796. Sir W. G. Armstrong in 1846 was 
one of the pioneers in the adaptation of the hydraulic system to cranes. The 
use of the accumulator by Armstrong led to the extended use of hydraulic 
machinery. Recent developments and applications of the system are largely 
due to Ralph Tweddell, of London, and Sir Joseph Whitworth. Sir Henry 
Bessemer, in his patent of May 18, 1856, No. 1292, first suggested the use of 
hydraulic pressure for compressing steel ingots while in the fluid state. 

The Gross Amount of Energy of the water under pressure stored 
in the accumulator, measured in foot-pounds, is its volume in cubic feet X 
its pressure in pounds per square foot. The horse-power of a given quantity 

F Stem i 144pQ 
steadily flowing is H.P. = SED 
in cubic feet per second and p the pressure in pounds per square inch. 

The loss of energy due to velocity of flow in the pipe is calculated as fol- 
lows (R. G. Blaine, Hng’g, May 22 and June 5, 1891): 


ML .. j hgh 
According to D’Arcy, every pound of water loses Me times its kinetic 





= .2618pQ, in which Q is the quantity flowing 


energy, or energy due toits velocity, in passing along a straight pipe L feet 
in length and D feet diameter, where A is a variable coefficient. Hor clean 


cast-iron pipes it may be taken as A = .005 € + mo) or for diameter in 
inches = d, 


d= ¥% 1 2 3 4 5 6 tf 8 9 10 12 
A= .015 .01 .0075 .00667 .00625 .006 .00583 .00571 .00563 .00556 .0055 .00549 
AL v2 


The less of energy per minute is 60 x 62.36Q x 


.6363A L(H.P.)$ 

p3.D5 

diameter as above. p= pressure at entrance in pounds per square inch. 

Values of .6363A for different diameters of pipe in inches are: 
: 5 6 


D ay" and the horse< ~ 


, in which A varies with the 





power wasted in the pipe is W = 





=k 1 2 3 4 9 10 12 
-00954 .00636 .00477 .00424 .00398 .00382 .00371 .00363 .00358 .00353 .00350 .00345 


Efficiency of Hydraulic Apparatus.—The useful effect of a 
direct hydraulic plunger or ram is usually taken at 93%. The following is 
given as the efficiency of a ram with chain-and-pulley multiplying gear 
properly proportioned and well lubricated: 

Multiplying.... 2tol 4to1 6tol 8tol 10to1 12to1 14to1 16tol 
Efficiency %.... 80 %6 72 67 63 59 54 50 

With large sheaves, small steel pins, and wire rope for multiplying gear 
the efficiency has been found as high as 66% fora multiplication of 20 to 1. 

Henry Adams gives the following formula for effective pressure in cranes 
and hoists: 

f = accumulator pressure in pounds per square inch; 

m = ratio of multiplying power: 

E = effective pressure in pounds per square inch, including all allowances 


for friction; r ’ 
= P(.84 — .02m). 


_J. E. Tuit (Hng’g, June 15, 1888) describes some experiments on the fric- 
tion of hydraulic jacks from 344 to 135¢-inch diameter, fitted with cupped 
leather packings. The friction loss varied from 5.6% to 18.8% according to 
the condition of the leather, the distribution of the load on the ram, etc. 
The friction increased considerably with eccentric loads. With hemp pack- 
ing a plunger, 14-inch diameter, showed a friction loss of from 11.4% to 3.4%, 
the load being central, and from 15.0% to 7.6% with eccentric load, the per 
centage of loss decreasing in both cases with increase of load. 


| 


: 
: 


HYDRAULIC-PRESSURE TRANSMISSION. 617 


Thickness of Hydraulic Cylinders.—From a table used by Sir 
W. G. Armstrong we take the following, for cast-iron cylinders, for an in- 
terior pressure of 1000 lbs. per square inch: 


- Diam. of cylinder, inches... 2 4 6 8 10° 12 #16 #20 «624 


Thickness, inches.......... 0.832 1.146 1.552 1.875 2.222 2.578 3.19 3.69 4.11 
For any other pressure multiply by the ratio of that pressure to 1000. 


- These figures correspond nearly to the formula t = 0,175d +- 0.48, in which 


t = thickness and d = diameter in inches, up to 16 inches diameter, but for 
20 inches diameter the addition 0.48 is reduced to 0.19 and at 24 inches it 


disappears. For formule for thick cylinders see page 287, ante. 


Cast iron should not be used for pressures exceeding 2000 lbs. per square 
inch. For higher pressures steel castings or forged steel should be used. 
For working pressures of 750 lbs. per square inch the test pressure should 
be 2500 lbs. per square inch, and for 1500 lbs. the test pressure should not be 
less than 3500 Ibs. 

Speed of Hoisting by Hydraulic Pressure.—The maximum 
allowable speed for warehouse cranes is 6 feet per second; for platform 
cranes 4 feet per second; for passenger and wagon hoists, heavy loads, 2 
feet per second. The maximum speed under any circumstances should 
never exceed 10 feet per second. 

The Speed of Water Through Valves should never be greater 
than 100 feet per second. 

Speed of Water Through Pipes.—Experiments on water at 1600 
Ibs. pressure per square inch flowing into a flanging-machine ram, 20-inch 
diameter, through a 14-inch pipe contracted at one point to 14-inch, gave a 
velocity of 114 feet per second in the pipe, and 456 feet at the reduced sec- 
tion. Through a %-inch pipe reduced to 3-inch at one point the velocity 
was 213 feet per second in the pipe and 381 feet at the reduced section Ina 
4%-inch pipe without contraction the velocity was 355 feet per second. 

For many of the above notes the author is indebted to Mr. John Platt, 
consulting engineer, of New York. 

High-pressure Hydraulic Presses in Iron=-works are de- 
scribed by R. M. Daelen, of Germany, in Trans, A. I. M. E. 1892. The fol- 
lowing distinct arrangements used in different. systems of high-pressure 
hydraulic work are discussed and illustrated: 

1. Steam-pump, with fly-wheel and accumulator. 

2. Steam-pump, without fly-wheel and with accumulator. 

3. Steam-pump, without fly-wheel and without accumulator, 

In these three systems the valve-motion of the working press is operated 
fn the high-pressure column. This is avoided in the following: 

4, Single-acting steam-intensifier without accumulator. 

5. Steam-pump with fly-wheel, without accumulator and with pipe-circuit. 

6. Steam-pump with fly-wheel, without accumulator and without pipe- 
circuit. 

The disadvantages of accumulators are thus stated: The weighted plungers 
which formerly served in most cases as accumulators, cause violent shocks 
in the pipe-line when changes take place in the movement of the water, 
so that in many places, in order to avoid bursting from this cause, the pipes 
are made exclusively of forged and bored steel. The seats and cones of the 
metallic valves are cut by the water (at high speed), and in such cases only 
the most careful maintenance can prevent great losses of power. 

Hydraulic Power in London.—tThe general principle involved 
is pumping water into mains laid in the streets, from which service-pipes 
are carried into the houses to work lifts or three-cylinder motors when 
rotatory power is required. In some cases a small Pelton wheel has been 
tried, working snder a pressure of over 700 lbs. on the square inch. Over 55 
miles of hydraulic mains are at present laid (1892). 

The reservoir of power consists of capacious accumulators, loaded to a 
pressure of 800 lbs. per square inch, thus producing the same effect as if 
large supply-tanks were placed at 1700 feet above the street-level. The 
water is taken from the Thames or from wells, and all sediment is removed 
therefrom by filtration before it reaches the main engine-pumps. 

There are over 1750 machines at work, and the supply is about 6,500,000 
gallons per week. 

It is essential that the water used should be clean. The storage-tank ex- 
tends over the whole boiler-house and coal-store. The tank is divided, and 
& certain amount of mud is deposited here. It then passes through the sur- 
face condenser of the engines, and it is turned into a set of filters, eight in 
pumber, The body of the filter is a cast-iron cylinder, gontaining a layer of 


we 


618 WATER-POWER. 


granular filtering material resting upon a false bottom; under this is the dis 
tributing arrangement, affording passage for the air, and under this the real 
bottom of the tank. The dirty water is supplied to the filters from an over- 
head tank. After passing through the filters the clean effluent is pumped 
into the clean-water tank, from which the pumping-engines derive their 
supply. The cleaning of the filters, which is done at intervals of 24 hours, is 
effected so thoroughly in situ that the filtering material never requires to be 
removed. 

The engine-house contains six sets of triple-expansion engines. The 
cylinders are 15-inch, 22-inch, 36-inch xX 24-inch. Each cylinder drives a 
single plunger-pump with a 5-inch ram, secured directly to the cross-head, 
the connecting-rod being double to clear the pump. The boiler-pressure is 
150 lbs. on the square inch. Each pump will deliver 300 gallons of water per 
minute under a pressure of 800 lbs. to the square inch, the engines making 
about 61 revolutions per minute. This is a high velocity, considering the 
heavy pressure; but the valves work silently and without perceptible shock. 

The consumption of steam is 14.1 pounds per horse per hour. 

The water delivered from the main pumps passes into the accumulators, 
The rams are 20 inches in diameter, and have a stroke of 23 feet. They are 
each loaded with 110 tons of slag, contained in a wrought-iron cylindrical 
box suspended from a cross-head on the top of the ram. 

One of the accumulators is loaded a little more heavily than the other, so 
that they rise and fall successively; the more heavily loaded actuates a stops 
valve on the main steam-pipe. If the engines supply more water than is 
wanted, the lighter of the tworams first rises as far as it can go; the other 
then ascends, and when it has nearly reached the top, shuts off steam and 
checks the supply of water automatically. 

The mains in the public streets are so constructed and laid as to be per- 
fectly trustworthy and free from leakage, 

Every pipe and valve used throughout the system is tested to 2500 Ibs. per 
square inch before being placed on the ground and again tested to a reduced 
pressure in the trenches to insure the perfect tightness of the joints. The 
jointing material used is gutta-percha. 

The average rate obtained by the company is about 3 shillings per thou- 
sand gallons. The principal use of the power is for intermittent work in cases 
where direct pressure can be employed, as, for instance, passenger elevators, 
cranes, presses, warehouse hoists, etc. 

An important use of the hydraulic power is its application to the extin- 
guishing of fire by means of Greathead’s injector hydrant. By the use of 
these hydrants a continuous fire-engine is available. 

Wydraulic Riveting-machines.—Hydraulic riveting was intro- 
duced in England by Mr. R. H. Tweddell, Fixed riveters were first used about 
1868. Portable riveting-machines were introduced in 1872. 

The riveting of the large steel plates in the Forth Bridge was done by small 
portable machines working with a pressure of 1000 lbs. per square inch. In 
exceptional cases 3 tons per inch was used. (Proc. Inst. M. E., May, 1889.) 

An application of hydraulic pressure invented by Andrew Higginson, of 
Liverpool, dispenses with the necessity of accumulators, It consists of a 
three-throw pump driven by shafting or worked by steam, and depends 
partially upon the work accumulated in a heavy fly-wheel. The water in its 

‘passage from the pumps and back to them is in constant circulation at a 
very feeble pressure, requiring a minimum of power to preserve the tube of 
water ready for action at the desired moment, when by the use of a tap the 
current is stopped from going back to the pumps, and is thrown upon the 
piston of the tool to be set in motion. The water is now confined, and the 
driving-belt or steam-engine, supplemented by the momentum of the heavy 
fly-wheel, is employed in closing up the rivet, or bending or forging the ob- 
ject subjected to its operation. 

Hydraulic Forging.—In the production of heavy forgings from 
cast ingots of mild steel it is mines Hy) that the mass of metal should be 
operated on as equally as possible throughout its entire thickness. When 
employing a steam-hammer for this purpose it has been found that the ex- 
ternal surface of the ingot absorbs a large proportion of the sudden impact 
of the blow, and that a comparatively small effect only is produced on the 
central portions of the ingot, owing to the resistance offered by the inertia 
of the mass to the rapid motion of the falling hammer—a disadvantage that 
is entirely overcome by the slow, though powerful, compression of the 
hydraulic forging-press, which appears destined to supersede the steam- 
hammer for the production of massive steel forgings. 


HYDRAULIC-PRESSURE TRANSMISSION. 619 


In the Allen forging-press the force-pump and the large or main cylinder 
of the press are in direct and constant communication. There are no inter- 
mediate valves of any kind, nor has the pump any. clack-valves, but it 
simply forces its cylinder full of water direct into the cylinder of the press, 
and receives the same water, as it were, back again on the return stroke, 
Thus, when both cylinders and the pipe connecting them are full, the large 
ram of the press rises and falls simultaneously with each stroke of the 
pump, keeping up a continuous oscillating motion, the ram, of course, 
travelling the shorter distance, owing to the larger capacity of the press 
eylinder. (Journal lron and Steel Institute, 1891. See also illustrated article 
fn ‘* Modern Mechanism,” page 668.) 

For a very complete illustrated account of the development of the hy- 
draulic forging-press, see a paper by R. H. Tweddell in Proc. Inst. C. E., vol. 
exvii. 1893-4, 

Hydraulic Forging=-press.—A 2000-ton forging-press erected at 
the Couillet forges in Belgium is described in Eng. and M. Jour., Nov. 25, 1893. 

The press is composed essentially of two parts—the press itself and the 
compressor. The compressor is formed of a vertical steam-cylinder and a 
hydraulic cylinder. The piston-rod of the former forms the piston of the 
latter. The hydraulic piston discharges the water into the press proper. 
The distribution is made by a cylindrical balanced valve; as soon as the 
pressure is released the steam-piston falls automatically under the action of 
gravity. During its descent the steam passes to the other face of the piston 
to reheat the cylinder, and finally escapes from the upper end. 

When steam enters under the piston of the compressor-cylinder the pis- 
ton rises, and its rod forces the water into the press proper. The pressure 
thus exerted on the piston of the latter is transmitted through a cross-head 
to the forging which is upon the anvil. To raise the cross-head two small 
single-acting steam-cylinders are used, their piston-rods being connected to 
the cross-head; steam acts only on the pistons of these cylinders from below. 
The admission of steam to the cylinders, which stand on top of the press 
frame, is regulated by the same lever which directs the motions of the com- " 
pressor. The movement given to the dies is sufficient for all the ordinary 
purposes of forging. 

A speed of 30 blows per minute has been attained. A double press on the 
same system, having two compressors and giving a maximum pressure of 
6000 tons, has been erected in the Krupp works, at Hssen. 

The Aiken Intensifier. (Iron Age, Aug. 1890.)—The object of the 
machine is to increase the pressure obtained by the ordinary accumulator 
which is necessary to operate powerful hydraulic machines requiring very 
high pressures, without increasing the pressure carried in the accumulator 
and the general hydraulic system. 

The Aiken Intensifier consists of one outer stationary cylinder and one 
inner cylinder which moves in the outer cylinder and on a fixed or stationary 
hollow plunger. When operated in connection with the hydraulic bloom- 
shear the method of working is as follows: The inner cylinder having been 
filled with water and connected through the hollow plunger with the hydrau- 
lic cylinder of the shear, water at the ordinary accumulator-pressure is ad- 
mitted into the outer cylinder, which being four times the sectional area of 
the plunger gives a pressure in the inner cylinder and shear cylinder con- 
nected therewith of four times the accumulator-pressure—that is, if the ac- 
cumulator-pressure is 500 lbs. per square inch the pressure in the intensifier 
will be 2000 lbs. per square inch, 

Wydraulic Engine driving an Air-compressor and a 
Forging-hammer. (Jron Age, May 12, 1892.)\—The great hammer in 
Terni, near Rome, is one of the largest in existence. Its falling weight 
amounts to 100 tons, and the foundation belonging to it consists of a block 
of cast iron of 1000 tons. The stroke is 16 feet 434 inches; the diameter of 
the cylinder 6 feet 314 inches; diameter of piston-rod 1334 inches; total height 
of the hammer, 62 feet 4 inches. The power to work the hammer, as well as 
the two cranes of 100 and 150 tons respectively, and other auxiliary appli- 
ances belonging to it, is furnished by four air-compressors coupled together 
and driven directly by water-pressure engines, by means of which the air is 
compressed to 73.5 pounds per square inch. The cylinders of the water- 

ressure engines, which are provided with a bronze lining, have a 1334-inch 

ore. The stroke is 41734 inches, with a pressure of water on the piston 
amounting to 264.6 pounds per square inch, The compressors are bored out 
to 3144 inches diameter, and have 4734-inch stroke. Each of the four cylin- 
ders requires a power equal to 280 horse-power. The compressed air is de- 


620 FUEL. 


livered into huge reservoirs, where a uniform pressure fs kept up by means 
of a suitable water-column. i 

The Mydraulic Forging Plant at Bethlehem, Pa.,, is de- 
scribed in a paper by R. W. Davenport, read before the society of Naval 
Engineers and Marine Architects, 1893. It includes two hydraulic forging. 
presses complete, with engines and pumps, one of 1500 and one of 4500 tons 
capacity, together with two Whitworth hydraulic travelling forging-cranes 
and other necessary appliances for each press; and a complete fluid-compres- 
sion ‘plant, including a press of 7000 tons capacity and a 125 ton hydraulic 
travelling crane for serving it (the upper and lower heads of this press 
weighing respectively about 135 and 120 tons). 

A new forging-press has been designed by Mr. John Fritz, for the Bethle- 
hem Works, of 14,000 tons capacity, to be run by engines and pumps of 15,000 
horse-power. The plant is served by four open-hearth steel furnaces of a 
united capacity of 120 tons of steel per heat. 

Some References on Hydraulic Transmission.—Reuleaux’s 
**Constructor;” ‘ Hydraulic Motors, Turbines, and Pressure-engines,” G. 
Bodmer, London, 1889 ; Robinson’s ‘* Hydraulic Power and Hydraulic Ma- 
chinery,”’ London, 1888 ; Colyer’s *‘ Hydraulic Steam, and Han/d-power Lift- 
ing and Pressing Machinery,’’ London, 1881. See also Engineering (London), 
Aug. 1, 1884, p. 99, March 13, 1885, p. 262; May 22 and June 5, 1891, pp. 612, 
665 5 Feb. 19, 1892, p. 25; Feb. 10, 1893, p. 170. 


FUEL. 


Theory of Combustion of Solid Fuel, (from Rankine, some- 
what altered.)—The ingredients of every kind of fuel commonly used may 
be thus classed: (1) Fixed or free carbon, which is left in the form of char- 
coal or coke after the volatile ingredients of the fuel have been distilled 
away. These ingredients burn either wholly in the solid state (C to COg), or 
part in the solid state and part in the gaseous state (CO + O = CQg), the lat« 
ter part being first dissolved by previously formed carbonic acid by the re-- 
action COg + C = 200. Carbonic oxide, CO, is produced when the supply 
of air to the fire is insufficient. 

(2) Hydrocarbons, such as olefiant gas, pitch, tar, naphtha, etc., all ot 
which must pass into the gaseous state before being burned. 

If mixed on their first issuing from amongst the burning carbon with a 
large quantity of hot air, these inflammable gases are completely burned with 
a transparent blue flame, producing carbonic acid and steam. When mixed - 
with cold air they are apt to be chilled and pass off unburned. When 
raised to a red heat, or thereabouts, before being mixed with a sufficient 
quantity of air for perfect combustion, tney disengage carbon in fine pow- 
der, and pass to the condition partly of marsh gas, and partly of free hydro- 
gen; and the higher the temperature, the greater is the proportion of carbon 
thus disengaged. 

If the disengaged carbon is cooled below the temperature of ignition be- 
fore coming in contact with oxygen, it constitutes, while floating in the gas, 
smoke, and when deposited on solid bodies, soot. 

But if the disengaged carbon is maintained at the temperature of ignition. 
and supplied with oxygen sufficient for its combustion, it burns while float 
ing in the inflammable gas, and forms red, yellow, or white flame. The flame 
from fuel is the larger the more slowly its combustion is effected. The 
flame itself is apt to be chilled by radiation, as into the heating surface of a 
steam-boiler, so that the combustion is not completed, and part of the gas 
and smoke pass off unburned. 

(3) Oxygen or hydrogen either actually forming water, or existing in 
combination with the other constituents in the proportions which form water. 
Such quantities of oxygen and hydrogen are to left be out of account in deter- 
mining the heat generated by the combustion. If the quantity of water 
actually or virtually present in each pound of fuel is so great as to make its 
latent heat of evaporation worth considering, that heat is to be deducted 
from the total heat of combustion of the fuel. 

(4) Nitrogen, either free or in combination with other constituents. This 
substance is simply inert. 

(5) Sulphuret of iron, which exists in coal and is detrimental, as tending 
to cause spontaneous combustion. 

(6) Other mineral compounds of various kinds, which are also inert, and 
form the ash left after complete combustion of the fuel, and also the clinker 
or glassy material produced by fusion of the ash, which tends to chaxe the 
grate, 


FUEL. 621 


Total Heat of Combustion of Fuels, (Rankine.)—The follow- 
ing table shows the total heat of combustion with oxygen of one pound of 
each of the substances named in it, in British thermal units, and also in 
lbs. of water evaporated from 212°. It also shows the weight of oxygen re- 
quired to combine with each pound of the combustible and the weight of 
ab necessary in order to supply that oxygen. The quantities of heat are 
given on the authority of MM. Favre and Silbermann. 








Lbs. Oxy- Total Brit Evapora- 
. gen per |Lb. Air] 7904) STIL tive Power 
Combustible. lb. Com- |(about). ny ely from 212° 
bustible. rf F., lbs. 
ATV ATOLEM, SAS. +25 merrantaae nics sciatic 8 36 62,032 64.2 
Carbon imperfectly burned so as 
to make carbonic oxide..........| 144 6 4,400 4.55 
Carbon perfectly burned so as to 
make carbonic acid.....,........ 254 12 14,500 15.0 
OlCTANt- PAS. LD ste actress cea cc: 3 3/7 15 3/7 F 21,3844 22.1 
: Seale 2 rom 21,700) from 22h 
Various liquid hydrocarbons, 1 lb.]..........]...-.- { to 19'000/ to 20 


Carbonic oxide, as much as is made 
by the imperfect combustion of| +114 6 10,000 10.45 
1 lb. of carbon, viz., 244 lbs...... 


The imperfect combustion of carbon, making carbonic loxide, produces 
less than one third of the heat which is yielded by the complete combustion. 

The total heat of combustion of any compound of hydrogen and carbon 
is nearly the sum of the quantities of heat which the constituents would pro- 
duce separately by their combustion. (Marsh-gas is an exception.) 

In computing the total heat of combustion of compounds containing oxy- 
gen as well as hydrogen and carbon, the following principle is to be 
observed: When hydrogen and oxygen exist in a compound in the proper 
proportion to form water (that is, by weight one part of hydrogen to eight 
' of oxygen), these constituents have no effect on the total heat of combus- 
tion. If hydrogen exists ina greater proportion, only the surplus of hydro- 
gen above that which is required by the oxygen is to be taken into account. 

The following is a generalformula (Dulong’s) for the total heat of combus- 
tion of any compound of carbon, hydrogen, and oxygen: 

Let CO, H, and Obe the fractions of one pound of the compound, which 
consists respectively of carbon, hydrogen, and oxygen, the remainder being 
nitrogen, ash, and other impurities. Let h be the total heat of combustion 
of one pound of the compound in British thermal units. Then 


hes 14,500 § O+ 4.28( T— < l. 


The following table shows the composition of those compounds which are 
of importance, either as furnishing oxygen for combustion, as entering into 
the composition, or as being produced by the combustion of fuel: 











. Q 

SE wi 43 er neg 

Og2| #85 fgsc) §58 

Names. S2¢é SES ase ESS 

pee] fe Bs,| Se 

G°-s| Ese Pas] ESE 
WM IES. Sok wolee hee elatis eld nea ls.eelaeh ai Ean eee N77 +023 | 100 IN 79+ 021 

Water... 2 eee @eeeeses cee eeoe eees H,O (Bi +0 16 18 H2 +0 

Ammonia ........ # oem atau ele aha ae anne NH;|H38 +N14]/ 17 |H3 +N 

Carbonic Oxide........0.... seeeesees CO |} C12+016 | 28 C+0 
Oarbonic acide... :....<,.inaseepeameesapCOg | C124 O 32 44 C+02 
Olefiant gas........ 722.00 ese sermememiCrts | O.12 -- Hz 14 C+H2 
Marsh-gas or fire-damp............. .| CH, | C12+4+H4 16 C+H4 
Sulphurous acid............- ses vsesien | Ug) |S 82 + O 82 1964. he... sinicts ipa 
Sulphuretted hydrogen.... .........4. SH, | S8+H2 oY COARSE. 5) 

Sulphuret of.carbon....., ses ems SgC | S64+CR 46 Se ; 








622 FUEL. 


Since eacu ww. uf C requires 234 Ibs. of O to burnit to COq, and air contains 
23% of O, by weight, 234 + 0.23 or 11.6 lbs. of airare required to burn 1 Ib. of C. 

Analyses of Gases of Combustion.—The following are selected 
from a large number of analyses of gases froin locomotive boilers, to show 
the range of composition under different circumstances (@. H. Dudley, 
Trans. A. I. M. E., iv. 250): 


Test.{|CO,}CO}O | N 





A a 





.5] 81.6|No smoke visible, 

2.5/Old fire, escaping gas white, engine working hard. 
83 |Fresh fire, much black gas, Me oe Me 

2} 80.5/Old fire, damper closed, engine standing still. 

71 79.6] “* ** smoke white, engine working hard. 
.4| 82 |New fire, engine not working hard. 
4 

8 

5 


a 
oo 
OF 


= 
Sd GY 0 GO O05 COP CO 


82.6/Smoke black, engine not working hard. 
76.8} ‘* dark, blower on, engine standing still. 
81.5} ‘ white, engine working hard. 


1 
we aie SS 
Bw iB WOOoTOTo 


Co ry c 
eae ae 
oe w- 


In analyses on the Cleveland and Pittsburgh road, in every instance 
when the smoke was the blackest, there was found the greatest percentage 
of unconsumed oxygen in the product, showing that something besides the 
mere presence for oxygen is required to effect the combustion of the volatile 
carbon of fuels. 

J. C. Hoadley (Trans. A. S. M. E., vi. 749) found as the mean of a great 
number of aualyses of flue gases from a boiler using anthracite coal ¢ 


CO_, 13.103 CO, 0.30; O, 11.943 N, 74.66. 


The loss of heat due to burning C to CO instead of to CO, was 2.18%. The 
surplus oxygen averaged 113.8% of the O required for the C of the fuel, the 
average for different weeks ranging from 88.6% to 1372. 

Analyses made to determine the CO produced by excessively rapid firing 
gave results from 2.54% to 4.81% CO and 5.12 to 8.01% CO, ; the ratio of Cin 
the CO to total carbon burned being from 48.80% to 48.55%, and the number of 
pounds of air supplied to the furnace per pound of coal being from 33.2 ta 
19.3lbs. The loss due to burning C to CO was from 27.84% to 30.86 of the 
full power of the coal. 

Temperature of the Wire. (Rankine, S. E., p. 283.)—By temper. 
ature of the fire is meant the temperature of the products of combustion at 
the instant that the combustion is complete. The elevation of that temper- 
ature above the temperature at which the air and the fuel are supplied ta 
the furnace may be computed by dividing the total heat of combustion of 
one lb. of fuel by the weight and by the mean specific heat of the whole 
products of combustion, and of the air employed for their dilution under 
constant pressure. The specific heat under constant pressure of these prod 
ucts is about as follows: 

Carbonic-acid gas, 0.2173 steam, 04753 nitrogen (probably), 0.245; air, 
0.238; ashes, probably about 0.200. Using these data, the following results 
are obtained for pure carbon and for olefiant gas burned, respectively, first, 
in just sufficient air, theoretically, for their combustion, and, second, when 
an equal amount of air is supplied in addition for dilution. 


Products undiluted.} Products diluted. 











Fuel. Pllc ade pe oo en ma 
Olefiant Olefiant 
Carbon. Gael Carbon. Gaal 

Total heat of combustion, per lb...] 14,500 21,300 14,500 / 21,300 
Wt. of products of combustion, lbs. 13 16.43 25 31.86 
Their mean specific heat........ Sue Ove 0.257 0.238 0.248 
Specific heat X weight.............. 8.08 4.22 5.94 7.9 
Elevation of temperature, F........ 4580° 5050° 2440° 2710° 


(The above calculations are made on the assumption that the specific 
heats of the gases are constant, but they probably increase with the in- 
crease of temperature (see Specific Heat), in which case the temperature 
would be less than those above given. The temperature would be further 


CLASSIFICATION Of FUEL. 623 


feduced by the heat rendered latent by the conversion into steam of any 
watev present in the fuel.] 

Rise of Femperature in Combustion of Gases, (Eng’g 
March 12 and April 2, 1886.)—It is found that the temperatures obtained 
by experiment fall short of those obtained by calculation. Three theo- 
ries have been given to account for this: 1. The cooling effect of the 
sides of the containing vessel; 2. The retardation of the evolution of heat 
caused by dissociation; 3. The increase of the specific heat of the gases at 
very high temperatures. The calculated temperatures are obtainable only 
on the condition that the gases shail combine instantaneously and simulta- 
neously throughout their whole mass. This condition is practically impos- 
sible in experiments. The gases formed at the beginning of an explosion 
dilute the remaining combustible lgases and tend to retard or check the 
combustion of the remainder. 


CLASSIFICATION OF SOLID FUELS. 
Gruner classifies solid fuels as follows (Zng’g and M’g Jour., July, 1874): 


THO 
Ratio i «Proportion of Coke or 





Name of Fuel. Charcoal yielded b 
Fe 
or O-EN*; the Dry Pure Fuel 
H 
PUre COUUIOKE Ga es-g geod bos oak: see ee oe 8 0.28 @ 0.30 
Wood (cellulose and encasing matter),... ve 30 05 
Peat and fossil: fuel 02). oon ee eee hice 6@5 -35@ .40 
Lignite,t or brown Coal.........cce cece 5 -40@ .50 
IBILUIMINOUS COBNS loses cacicle sia:s <¢ sieccincletie 4@1 .50@ .90 
MATIUR EACLE Lt tices clasice co cscces cscs ose cue 1 @ 0.75 -90@ .92 
The bituminous coals he divides into five classes as below: 
l 
Elementary Propor- 
Composition, . ©| tionof | Nature 





Rare OF Type. O-LN* yielded | Appear- 
CG H O poe by Dis-| ance of 
% bs tilla- Coke, 
tion 





| |] eee ff 


1. Long flaming dry | |. asols.5@4.5/19.5@15| 4@3_ |0.80@.60 


coal, 

2. Long flaming fat 
or coking coals, 
or gas coals, 


3. Caking fat nits 


80@85|5.8@5 }14.2@10| s@2 | .60@.68 
friable. 


or blacksmiths’ 
coals, 


4, Short flaming fat 
or caking coals, 
coking coals, 


5. Lean or anthra- 
citic coals, t 90@93 


88@91|5.5@4.5] 6.5@5.5, 1 | .74@.82 


com- 
pact. 


4.5@4 Hee 1 | .82@.90 ener 


Melted; 
some- 
84@89/5 @4.5 }11 @5.5 2@1 .68@.74 what 


ent. 











* The nitrogen rarely exceeds 1 per cent of the weight of the fuel. 
+ Not including bituminous lignites, which resemble petroleums. 

. Rankine gives the following: The extreme differences in the chemical 
composition and properties of different kinds of coal are very great. The 
proportion of free carbon ranges from 30 to 93 per cent ; that of hydrocar- 
bons of various kinds from 5 to 58 per cent ; that of water, or oxygen and 
hydrogen in the proportions which form water, from an inappreciably 
small quantity to 27 per cent ; that of ash, from 114 to 26 per cent. 

The numerous varieties of coal may be divided into principal classes as 
follows: 1, anthracite coal; 2, semi-bituminous coal ; 3, bituminous coal ; 
4. long tlaming or cannel coal ; 5, lignite or brown coal, 


624 | FUEL. 


Diminution of H and 0 in Series from Wood to Anthracite , 
(Groves and Thorp’s Chemical Technology, vol, i., Fuels, p. 58.) 


Substance. Carbon. Hydrogen. Oxygen. 
WOOD VITIDPO. sateen teants coccnteecees 52.65 5.25 42.10 
Peat from Vuleaire...... alisiSroite cieeuetmetiieres 59.57 5.96 34.47 
Lignite from Cologne........... praise cecieitee 66.04 5.27 28.69 
Earthy brown coal ...............-e00. Adar: 73.18 5.88 21.14 
Coal from Belestat, secondary...... ..... 75.06 5.84 19.10 
Coal from Rive de Gier............ AN ciate eee 89.29 5.05 5.66 
Anthracite, Mayenne, transition formation 91.58 3.96 4.46 


Progressive Change from Wood to Graphite. 
(J. S. Newberry in Johnson’s Cyclopedia.) 


Lig- Bitumi- Anthra- Graph- 
Wood. Loss. nial LOSS. ous coal, LOSss: cite, . LOSS: ite. 


Carbon...... 49.1 18.65 30.45 12.35 18.10 385% 14.53 1.42 13.11 
Hydrogen... 63 3.25 3.05 1.85 1.20 0:93) ..0.27) 3.0.14 0.13 
Oxygen...... 44.6 24.40 20.20 18.13 2.07 1.382 0.65 0.65 0.00 


——e 


100.0 46.30 53.70 32.83 21.87 5.82 15.45 2.21 13.24 


Classification of Coals, as Anthracite, Bituminous, etc.— 
Prof. Persifer Frazer (Trans. A. I. M. E., vi, 430) proposes a elassifica- 
tion of coals according to their ‘‘ fuel ratio,’ that is, the ratio the fixed car- 
bon bears to the volatile hydrocarbon. 

In arranging coals under this classification, the accidental impurities, such 
as sulphur, earthy matter, and moisture, are disregarded, and the fuel con- 
stituents alone are considered. 








Carbon Fixed Volatile 
Ratio. Carbon. Hydrocarbon. 
I. Hard dry anthracite. 100 to 12 100. to 92.31% 0. to 7 69% 
II. Semi-anthracite...... 12to 8 92.31 to 88.89 7.69 to 11.11 
Ill. Semi-bituminous. ... 8to 5 88.89 to 83.33 pid 17 to 16267 
IV. Bituminous. ........ s 5to 0 83.33 to 0. 16.67 to 100 


It appears to the author that the above classification does not draw the 
‘line at the proper point between the semi-bituminous and the bituminous 
coals, viz., at a ratio of C + V.H.C. = 5, or fixed carbon 83.33%, volatile hy- 
drocarbon 16.67%, since it would throw many of the steam coals of Clearfield 
and Somerset counties, Penn., and the Cumberland, Md., and Pocahontas, 
Va., coals, which are practically of one class, and properly rated as 
semi-bituminous coals, into the bituminous class. The dividing line be- 
tween the semi-anthracite and semi-bituminous coals, C + V.H.C. = 8, 
would place several coals known as semi-anthracite in the semi-bituminous 
class. The following is propostd by the author as a better classification : 


Carbon Ratio. Fixed Carbon. VolsEeG: 
I. Hard dry anthracite.. 100 to 12 100 to 92.31% 0 to %.69% 
II. Semi-anthracite....... 12 to 7% 92.31 to 87.5 7.69to 12.5 
{IIl. Semi-bituminous...... to 3 87.5 to 75 12.5.2to. 25 
T Vee Bituiminousi.:......6%. 8to 0 05) to 0 25 to100 


Rhode Island Graphitic Anthracite,—A peculiar graphite is 
found at Cranston, near Providence, R. I. It resembles both graphite and 
anthracite coal, and has about the following composition (A. E. Hunt, Trans. 
A.I. M. E., xvii., 678): Graphitic carbon, 78%; volatile matter, 2.60%; silica, 
15.06%; phosphorus, .045%. It burns with extreme difficulty. 


ANALYSES OF COALS. 


Composition of Pennsylvania Anthracites, (Trans. A. I. 
M. E., xiv., 706.)—Samples weighing 100 to 200 lbs. were collected from lots 
of 100 to 200 tons as shipped to market, and reduced by proper methods to 
laboratory samples. Thirty-three samples were analyzed by McCreath, giv- 
ing results as follows. They show the mean character of the coal of the more 
important coal-beds in the Northern field in the vicinity of Wilkesbarre, in 
the Eastern Middle (Lehigh) field in the vicinity of Hazleton, in the Westerv 


ANALYSES OF COALS. 625 


Middle field in the vicinity of Shenandoah, and in the Southern field between 
Mauch Chunk and Tamaqua. 





pi Sos rs 
qa qe . oO. ad 2 oo & oO ~~ 
° O.. te a oe ; Ppt - 
ES es |e | 82 | ke | 2 |8)e8s3| Sr 
3m om B | es |) BS | 7 1B) o.s8 | my 
odglsd) 

2 | cas O 
ee ff ee | ae ee — 
Wharton.../EK, Middle | 8.71 3.08 86.40 | 6.22 | .58} 3.44 28.07 
Mammoth..|E. Middle 4.12 | 3.08 86.38 | 5.92 | .49 3.45 27:99 
Primrose ..|W. Middle | 3.54 | 38.72 81.59 |10.65 | .50| 4.36 21,93 
Mammoth .|W. Middle | 3.16 | 3.72 81.14 |11.08 } .90} 4.38 21.83 
Primrose F|Southern 3.01 4.13 87.98 | 4.88 | .50) 4.48 213382 
Buck Mtn..|W. Middle | 3.04 | 3.95 82.66 | 9.88 | .46] 4.56 20.93 
Seven Foot|W. Middle | 3.41 | 3.98 80.87 |11.23 | .51 4.69 20.82: 
Mammoth .|Southern 3.09 | 4.28 83.81 | 8.18 | .64 4.85 19.62 
Mammoth .|Northern 3.42 4.38 crinet? |i taeeab dh ot 5.00 19.00 


B. Coal Bed|Loyalsock | 1.30] 8.10 83.34 | 6.23 |1.03} 8.86 10.29 


The above analyses were made of coals of all sizes (mixed). When coal is 
screened into sizes for shipment the purity of the different sizes as regards 
ash varies greatly. Samples from oue mine gave results as follows: 


Screened Analyses. 
Nameof Through Over Fixed 
Coal. inches. inckes. Carbon. Ash. 
Heo ote cfc! 2.5 1.75 88.49 5.66 
Stove. ...c.ce- 1.75 1.25 83.67 10.17 
Chestnut...... 1.25 ais: 80.72 12.67 
Peale = ASO Ads: .50 79 05 14.66 
Buckwheat... 00 225 76.92 16.62 


Bernice Basin, Pa., Coals, 
Water. Vol. H.C. Fixed C. Ash. Sulphur. 
3.27 0.24 


Bernice Basin, Sullivan and on ee ee ih to 
Lycoming Cos.; range of 8.. } 197 8.56 89.39 9.34 1.04 


This coalis on the dividing-line between the anthracites and semi-anthra- 
cites, and is similar to the coal of the Lykens Valley district. 
More recent analyses (Trans. A. I. M. E., xiv. 721) give: 


Water. Vol. H.C. Fixed Carb. Ash. Sulphur. 
Working seam....... 065 9,40 83.69 5.34 0.91 
60 ft. below seam.... 3.67 15.42 71.34 8.97 0.59 


The first is a semi-anthracite, the second a semi-bituminous. 

Space Occupied by Anthracite Coal. (J.C. I. W., vol. iii..—The 
eubic contents of 2240 lbs. of hard Lehigh coal isa little over 36 feet ; an 
average Schuylkill W. A., 87 to 88 feet ; Shamokin, 38 to 39 feet; Lorberry, 
nearly 41. 

According to measurements made with Wilkesbarre anthracite coal from 
the Wyoming Valley, it requires 32.2 cu. ft. of lump, 33.9 cu. ft. broken, 
345 cu. ft. egg, 34.8 cu. ft. of stove, 35.7 cu. ft. of chestnut, and 36.7 cu. ft. 
of pea, to make one ton of coal of 2240 Ibs.; while it requires 28.8 cu. ft. of 
lump, 30.8 cu. ft. of. broken, 30.8 cu. ft. of egg, 31.1 cu. ft. of stove, 31.9 cu. 
ft of chestnut, and 32.8 cu. ft. of pea, to make one ton of 2000 Ibs. 

Composition of Anthracite and Semi-bituminous Coals. 
(Trans. A. I. M. E., vi. 430.)\—Hard dry anthracites, 16 analyses by Rogers, 
show a range from 94.10 to 82.47 fixed carbon, 1.40 to 9.53 volatile matter, 
and 4.50 to 8.00 ash, water, and impurities. Of the fuel constituents alone, 
the fixed earbon ranges from 98.53 to 89.63, and the volatile matter from 1.47 
to 10.37, the corresponding carbon ratios, or C -+ Vol. H.C. being from 67.02 
to 8.64. 

Semi-anthracites.—12 analyses by Rogers show a range of from 90.23 to 
"4.55 fixed carbon, 7.07 to 13.75 volatile matter, and 2.20 to 12.10 water, ash, 
and impurities. Excluding the ash, etc., the range of fixed carbon is 92.75 
to 84.42, and the volatile combustible 7.27 to 15,58, the corresponding carbon 
ratio being from 12.75 to 5.41, ; 


626 FUEL. 


Semi-bituminous Coals.—10 analyses of Penna. and Maryland coals give 
fixed carbon 68.41 to 84.80, volatile matter 11.2 to 17.28, and ash, water, and 
impurities 4 to 13.99. The percentage of the fuel constituents is fixed carbon 
79.84 to 88.80, volatile combustible 11.20 to 20.16, and the carbon ratio 11.41 to 
3.96. 


American Semi-bituminous and Bituminous Coals, 
(Selected chiefly from various papers in Trans, A. I. M. E.) 











Moisi- Fixed Sul- 
ure Ee Carbon Ash phur 

Penna. Semi-bituminous : . 
Broad Top, extremes of 5....... ; e ie oe tore ' He aa 


Somerset Co., extremes of 5..... ; 1,89 18.51 65.90 | 10.62 3°08 


Blair Co., average of Beh ee fe 1.07 26.7 60.7 9.45 2.20 
Cambria Co., average of 7, y a 

fower bed, B }....[ 0.74 | 21.21] 68.94] 7.51 | 1.98 
Cambria Co., 1, y 

chon React ' eis Mp 4s 1.14 | 17.18] 73.42] 6.58 | 1.41 
Cambria Co., South Fork, 1..... RES 15.51 78.60 |} 5.84 he 
Centre. Col tare 3. aes: aie hives 0.60 22 60 68.71 5.40 2.69 


Clearfield Co., average of 9, & , 
venenteeet beds Cu ' m uy 03.94 | 69.28] 4.62 | 1.42 
Clearfield Co., average of 8, 
lower bed, D. fore 0.81 21.10 | 74.08 3.36 0.42 


0. : : 
Clearfield Co., range of 17 anal.. Bie to to to to 


Bituminous : 
Jefferson Co., average of 26.... MAA | 82.53 | 60.99 | 3.76 1.00 


Clarion Co., average of 7........ oe 88.60 | 54.15 | 4.10 1.19 
PAV IUTISCROMS™ COs, dice tate ass sejetere ere: 1.18 42.55 | 49.69 | 4.58 2.00 
Connellsville Coal................ 1.26 30.10 | 59.61 |. 8.28 78 
Coke from Conn’ville (Standard) .49 0.01 | 87.46 | 11.82 .69 - 
Youghiogheny Coal. ........... 1.03 36.49 | 59.05 | 2.61 81 
Pittsburgh, Ocean Mine......... 28 89.09 | 57.383 | 3.380 seth 





The percentage of volatile matter in the Kittaning lower bed B and the 
Freeport lower bed D increases with great uniformity from east to west; thus’ 


Volatile Matter. Fixed Carbon. 
Clearfield Co, bed D............ 20.09 to 25.19 68.73 to 74.76 
Se pels, il eal = OR ecscicices see 22.56 to 26.13 64.37 to 69.63 
Clarion Co., SB acte eee 35.70 to 42.55 47.51 to 55.44 
66 Sgr Na DM ee ct ray 87.15 to 40.80 51.89 to 56.36 


Connelisville Coal and Coke, (Trans. A. I. M.E., xiii. 332.)— 
The Connellsville coal-field, in the southwestern part of Pennsylvania, is a 
strip about 3 miles wide and 60 miles in length. The mine workings are 
confined to the Pittsburgh seam, which here has its best development as to 
size, and its quality best adapted to coke-making. It generally affords 
from 7 to 8 feet of coal. 

The following analyses by T. T. Morrell show about its range of composi- 


tion: 
Moisture. Vol. Mat. Fixed C. Ash. Sulphur. Phosph’s, 
Herold Mine .... 1.26 28.83 60.79 8.44 .67 -013 
Kintz Mine....... 0.79 31.91 56.46 9.52 1.32 .02 


In comparing the composition of coals across the Appalachian field, in the 
western section of Pennsylvania, it will be noted that the Connellsville 
variety occupies a peculiar position between the rather dry semi-bituminous 
coals eastward of it and the fat bituminous coals flanking it on the west. 

Beneath the Connellsville or Pittsburgh coal-bed occurs an interval of 
from 400 to 600 feet of ‘* barren measures,’ separating it from the lower 
productive coal-measures of Western Pennsylvania, The following tableg 


ANALYSES OF COALS, 627 


show the gréat similarity in composition in the coals of these upper and 
lower coal-measures in the same geographical belt or basin. 


Analyses from the Upper Coal-measures (Penna.) ina 
Westward Order. 


Localities. Moisture. Vol. Mat. Fixed Carb. Ash. Sulphur. 
35 0.30 


IANtHPACTICS. <: -ac)e'o ue 1.35 3.45 89.06 5.81 
Cumberland, Md..... 0.89 15.52 74.28 9.29 0.71 
SALSHUNY PEA tccsen ae 1.66 22.35 68.77 5.96 1.24 
Connellsville, Pa..... (s.-.. 31.38 60.30 7.24 1.09 
Greensburg, Pa...... 1.02 33.50 61.34 8.28 0.86 
PRWAN SPA ce cca cles « 1.41 37.66 54.44 5.86 0.64 
Analyses from the aes Sic ie in a Westward 
rder. 

Localities. Moisture. Vol. Mat. Fixed Carb. Ash. Sulphur. 
ANthracite’ 3) 2.5.5.5 1.35 3.45 89.06 5.81 0 30 
Broad Tomsss. Sarath Ura 1SsiSme 73.34 6.69 1.02 
Bennington....... .. 1.40 27.23 61.84 6.93 2.60 
Johnstown..... rae ey Rees) 16.54 74.46 5.96 1.86 
Blairsville ....... aden Uo 24.36 62.22 7.69 4.92 
Armstrong Co...... 5 URIS 88.20 52.03 5.14 3.66 


Pennsylvania and Ohio Bituminous Coals. Variation 
im Character of Coals of the same Beds in different Dis- 
tricts.—From 50 analyses in the reports of the Pennsylvania Geological 
Survey, the following are selected. They are divided into different groups, 
and the extreme analysis in each group is given, ash and other impurities 
being neglected, and the percentage in 100 of combustible matter being 

alene considered. 
ee 


No. of | Fixed Vol. |Carbon 
Analyses] Carbon| H.C. | Ratio. 








Waynesburg coal-bed, upper bench....... 5 
Jefferson township, Greene Co..... .... 59.72 | 40.28 1.48 
Hopewell township, Washington Co.... 53.22 | 46.78] 1.13 
Waynesburg coal-bed, lower bench....... 9 
Morgan township, Greene Co..... .. ... 60.69 | 39.31 | 1.54 
Pleasant Valley, Washington Co........ 54.81 45.69 1.19 
Sewickley coal-bed... .. ...6.....0...000% 3 
Whitely Creek, Greene Co............... 64.39 | 35.61 1.80 
Gray’s Bank Creek, Greene Co. ...... 60780) |) +89765))) 152 
Pittsburgh coal-bed: H 
Upper bench, Washington Co........... ; ka ee as 
: 63.54 | 36.46 | 1.7 
Lower bench, O ON Mats isiase Satoteis 5 ae 49:03 | 1.04 
Main bench, Greene Cen... + ssislec see 3 ; eras fae ae 
Frick & Co., Washington Co., average . 66.44 | 33.56 | 1.98 
Lower bench, Greene Co... ........ ... 1 Beso) 420107 |) wld 
Somerset Co., semi-bituminous (showing t 8 79 7% 20 ner, 3.93 
decrease of vol. mat. to the eastward). Dean | 240D58i i a.Oa 
Beaver Coy We aastass as - Ghee cee eee a 
Diehl’s Bank, Georgetown............... 40.68 | 59.82 |} 0.68 
Bryan’s Bank, Georgetown.............. 62.57 7.43 | 1.66 
OHIO. 
Pittsburgh coal-bed in Ohio: 
Jeiferson™o., Ohio. ..25 lyse tee ae eee eae ares 1.59 
k 63.4 36.54 1.73 
Belmont Cog Ohio. j.\< ase isceete iene. ; 66.14 | 33.86] 1.95 
HarrisoniOa,, Ohio. ..:;..4 seb anenkee ss be 84 - meas ee 
i 60.92 | 389.08] 1.55 
Pomeroy Cox Ohio... .«...0sseeeaeee ae sl-: ; 62.38 | 37.67 165 





628 FUEL. 





Moisture. (Vol. Mat.| Fixed G.| Ash. | SU 








phur. 
OHIO. 
: 5.00} 32.80 58.15 | 9.05 | 0.44 
Hocking Ma cf. BR ae SHOOT Ane } "401 29.90 60.45 | 2.95 | 0.93 
ARYLAND. 
‘ ey ake pels: 72.70 | 6.40 | 0.78 
“alana ene aa Peer ata we i 1.23] 15/47 "3.51 1 9.09 0:70 
IRGINIA. : 
South of James River, 23 anal- ; good Ak 27 28 46.70 | 2.00 | 0.58 
yses, range Oo 2. 38.60 67.83 |15.76 | 2.89 
IAVerace Oluccouee sees 1.48} 32.24 58.89 | 7.72 | 1.45 
North of James River, eastern ; : es 18.60 71.00 |10.00 
outcrop 7 23.96 59.98 |14.28 
Sibiibulielor Natural Coke j eof 9.64 79.93 | 8.86 
samen 1.56} 14.26 Sl Gl wp esetaimones 
Western outcrop, 11 analyses, aay bald 21.33 54.97 | 3.35 
range to 30.50 70.80 |22.60 
Average of 11...........- 26.06 63.75 |10.06 
Pocahontas Flat-top* ) 0.52} 23.90 74.20 | B88sin0252 
(Castner & Curran’s Circular) 0.62) 18.48 (5.220 Seb8e| OL2s 
WEST VIRGINIA (New River.) é a nee 7 oo anes 
ae rom 0.% ; F 3 , 
Quinnimont,t 8 analyses ...... } ¥ 0 94 18.19 79/40 | 492 | 0°30 
29.59 69.00 1.07 
Nuttal burch tities caetle net. e ; 1.35] 25.35 70.67 | 2.10 | 0.08 
VIRGINIA and KENTUCKY. 
Big Stone Gap Field, 9 anal- ; from 0.80} 31.44 54.80 | 1.73 | 0.56 
yses, range to 2.01; 36.27 63.50 | 8.25 | 1.72 
KENTUCKY. . < 
; : f 1.26 sil : : : 
Pulaski Co., 3 analyses, range| "5" j"301 S944 | seca | 5.52 | 100 
a eo pers Co., 4 analyses, tated Oke a ey oe nt 
ange ‘ J 5 56 j 
Be Co., Eastern Ky., 37 an-/| {from aia roa Age ae po 
BLY SCS Vane Cera citlals sisielersts to é = f ; . OF 
Kentucky Cannel Coals,§ 5 an-/|§from..... 40.20|] |59.80 coke] 8.81 | 0.96 
BLYSCS; TANLE.. oe see eile (ON DAn 66.30I| }83.70 coke] 4.80 | 1.32 
TENNESSEE. from 10] 32.33 46.61 |16.94 | 3.87 
Scott Co., Range of several... { to 1.831 41.29 61.66 | 1.11 0.77 
Roane Co., Rockwood, ........ 1.75} 26.62 60.11 {11.52 | 1.49 
eee bon Mele Ae ae ey, ges oe res ; a 
arioniCo.. Htna. 2. ocshueee ce. 3.0 F 3 . 
Sewanee Co., Tracy City...... 1.60} 29.30 61.00 | 7.80 
Kelly ©o., Whiteside.......... 1.30} 21.80 4°20 meee 
GEORGIA. 
JOR (Cok. 47 ee eae beets 1.20) 23.05 60.50 |15.16 | 0.84 
area 
Warren Field: 
Jefferson Co., Pe nebers ‘ et! out aes By 2.72 
UW ack Creek .. lk Ns Tle Or .10 
TUSCAIOOSATCONe eS! oo... sek 1.59) 38.33 5aeO4 eee Oe ao ede 
Cahaba Field, (Helena Vein. 2.00) 32.90 53.08 |11.34 | .68 
Bibb Commer { Coke Vein.... 1.78} 30.60 66.58 | 1.09 .04 


* Analyses.of Pocahontas Coal by John Pattinson, F.C.S., 1889: 
OMe), 0. N. 8.) Ashs Waren Coke.qpuea 

Lumps... 86.51 4.44 4.95 0.66 0.61 154 e208 18.8 sppeliae 
Small ... 83.13 4.29 5.383 0.66 0.56 4.63 ool. 40) — 79.8.0-442052 

+ These coals are coked in beehive ovens, and yield from 63% to 64% of coke. 

t This field covers about 120 square miles in Virginia, and about 30 square 
miles in Kentucky. 

$8 The principal use of the cannel coals is for enriching illuminating-gas. 

| Volatile matter including moisture, 

q Single analyses from Morgan, Rhea, Anderson, and Roane counties fall 
within this range. . i" 


ANALYSES OF COALS. 629 

















Moisture.|Vo! Mat.| Fixed C. | Ash. oie 
TEXAS 
THA TSUINVLITIC) aiate Gee ete ckatele aes 2 ae 8.54 30.84 50.69 14.08 arses 
SabinasPield, Velma ee s.s. 1.91 20.04 62.7 Iiseo laces 
: “e hl a cokes Mae eo 16.42 68.18 13502 eee 
4 xe SADLES fc Ac 0.84 29.35 50.18 19363 eee 
+ ye Bee) Vesa mveters raisers 0.45 21.6 45.7 29.1 | °3.15 
INDIANA. 
Caking Coals. 
ParkeiWos..)..- eS See ee i 4.50 45.50 45.50 4050) See 
Sullivan CO.COal M. cacceeas «cence 2.35 45.25 51.60 0:80) eae 
@lay COM <4'o. he Ine aah ol 7.00 BAU! a UE YG 6:00 
Spencer Co. coal L.......ees.0e. 3.50 45.00 46.00 DED sie wae 
Block Coals.* 
Glave Goris seeps ieee oe cs ety els os 8.50 31.00 57.50 3500 |Semere 
IVtEDIIY GO Seat. s.clesinats wo) wry SS of oicc 2.50 44.7 51.25 Lc bOlaeee 
Daviess Co..... Bre ale bie.os 258 shee Posto. 5.50 386.00 53.50 OO ae 
ILLINOIs.t 
Bureau Con” Ladd .....)i.cccce. 12.0 Sone 42.5 13 Fo leashes 
Seatonville......... 10.0 33.8 40.9 1526 Ales 
Christian Cow Pana. os sccessece fine 86.4 46.9 brs bal nes 
Clinton Co.: Trenton............ fons 30.4 52.0 4.3 | 0.9 
Eniton Gos (Oubass. «:.oee: ee 4.2 36.4 48.6 10..82\Raee 
Grundy Co. MOrrist. 2:02. 0. fied 3221 49.7 PTL een 
Jackson Co.: Big Muddy....... 6.4 30.6 54.6 tome) falas 
La Salle Co.: Streator........... 12.0 35.3 48.8 3.9. 12.4 
Logan Co.: Lincoln...... Tee: 8.4 35.0 44.5 Meher ce 
INMaeEOunC On ENIGDUIG oc cnes © see nes 18) 36.3 47.4 poea te supa he, 
Macoupin Co.: Gillespie..... Bite 12.6 30.6 45.3 lion lice, 
Mt. Olive....... 10.4 36.7 46.1 6.8 | 3.5 
Staunton .... 0+ 6.3 57.1 26.3 AKO) her Pee : 
Madison Co.: Collinsville........ 9.3 29.9 40.8 AG Lulworg 
Marion Co.: Centralia .......... 8.3 34.0 45.5 SOR eee 
McLean Co.: Pottstown......... 4.6 35.5 45.5 14 Fare oe 
eeriy Ose QUOI) yas ata 14.3 30.3 49.9 8.5 | 0.9 
Sanvamon Co.: Barclay......... 10.8 om. 44.8 Wale pesca ace 
SevClair Co.2 St. Bernardsex .2) 14.4 30.9 48.4 6.4 | 1.4 
Vermilion Co.: Danville..... ... 11.0 32.6 bys}, {0) BAO ees cee 
Will Co.: Wilmington............ 15.0 32.8 39.9 Bieta cpa 5 





* Indiana Block Coal (J. S. Alexander, Trans. A. I. M. E., iv. 100).—The 
typical block coal of the Brazil (Indiana) district differs in chemical com- 
position but little from the coking coals of Western Pennsylvania. The 
physical difference, however, is quite marked; the latter has a cuboid struc- 
ture made up of bituminous particles lying against each other, so that under 
the aciion of heat fusion throughout the mass readily takes place, while 
block coal is formed of alternate layers of rich bituminous matter anda 
charcoal-like substance, which is not only very slow of combustion, but so 
retards the transmission of heat that agglutination is prevented, and the 
coal burns away layer by layer, retaining its form until consumed. 

An ultimate analysis of block coal from Sand Creek by E. T. Cox gave: 
C, 72.94; H, 4.50; O, 11.77; N, 1.79; ash, 4.50; moisture, 4.50, 

+ The Illinois coals are generally high in moisture, volatile matter, sul- 
phur and ash, and are consequently low in heating value. The range of 
quality is a wide one. The Big Muddy coal of Jackson Co., which has a 
high reputation as a steam coal, has, according to the analysis given above, 
about 36% of volatile matter in the total combustible, corresponding to the 
coals of Western Pennsylvania and Ohio, while the Staunton coal has 682, 
ranking it among the poorer varieties of lignite. A boiler-test with this coal 
(see p. 636, also Trans. A. S. M. E., v. 266) gave only 6.19 lbs. water evapo- 
rated from and at 212° per lb. combustible. The Staunton coal is remarkable 
for the high percentage of volatile matter, but it is excelled in this respect by 


630 FURL. 























. . T . Sul- 
Moisture.} Vol. Mat.| Fixed C, | Ash. phur. 
Iowa.* 
Pitemaity elu. tees coats beteeels 4.99 35.27 ase CW SE eid 2 A5 3 
Keb eae tans 2. RUA 8. 9.81 37.49 44.7 CCE ee rer 
PULA BIOVS Rae hitcx coterie) oro cielstetee ds era: 9.84 40.16 6. Od tale.) 1x5 encore 
Chisholm... 2 Wis wenelee et ctee si 9.18 40.42 39.58 OSGeo eieiee 
MiIssouri.* . 
Brookfield’ oy. sen cosdste renal 4.34 40.27 50.60 4792 ce 
WECTIC OU coe tits Semamieie seticune ce’ Merete 9.03 37.48 46.24 (er 3) VD 
HamiltOmucs ures caiceceds peices OE 5.06 84.24 47.69 IB201|" eee 
PDO pees sec tele ieee de ate e Risers 80 38.29 47 24 7.14 Fis 
NEBRASKA.* 
TASTINGS UUs Ltaercs pethets omen ee hicis 0.21 27.82 60.88 | 11.09 Hd 
WYOMING.* 
Cambria .. SOcad 4.2 40.6 41.5 as ware 
es ae ickare aimietate brsla lave aupioshete ar yaa) 37.4 37.9 22 2 os 
Goose Creeks cst ote eds ces eae: 9.7 40.2 46.3 3.8 ar 
$s SOE Fees the tine ake aie etree eee oie 13.92 36.78 42.03 Teo Oheonere 
Deek*Greeky Peters oe eee as 12.8 35.0 Zeer 30 Pesce ae 
UOC SLORR NRE rg) (Mee WANy ecto apelin ee 6.04 42.37 SS SWAPO (had US Hee Dd BS F 
CoLorabDo.} 
Sunshine, Colo, average......... 2.8 36.3 37.1 23.8 f 
Neweastle, ‘‘ Ue AUR Se Re de 37.95 48.6 1.6 3 
El Moro, $6 aM ect ceva ate 1.32 88.23 55.86 3 05 ese 
Crested Buttes, s CASE Fs: ee 1.10 23.20 72.60 Sa LOiaaeete : 
UTAH (Southern). 
Castiledallie: 22.: Stee cee ac cle etiesie 8.43 42.81 47. B1t-)- 9.73 ae 
Cedanm Citys ..5: Sterna ee saseeee ue 8.50 43.66 43.i1t |} 5.95 
OREGON 
Coos) Baye f.ia.-.: mse cha Be fogs 15.45 41.55 84.95 8.05] 2.53 
RED esta Ros ANA ELE 44.15 82.40 6.18] 1.37 
NGG LONDEN Sth Alpes HABA Bona eda ince 13.03 46.20 32.60 7.10) 1.07 
JOHN DAY, Rivers, .s<csess ese ce 4.55 40.00 48.19 7.26) .60. 
ey ee Shy CORE Spree Sena 6.54 84.45 52.41 5.951 65 


VANCOUVER ISLAND. 
WORIO 34 COALS. o coca cies 17 27.17 68.27 2.86 


the Boghead coal of Linlithgowshire, Scotland, an analvsis of which by Dr. 
Penny is as follows: Proximate—moisture 0.84; vol. 67.95; fixed C, 9.54, ash, 
21.4; Ultimate—C,63.94; H, 8.86; O, 4.70; N, 0.96; which is remarkable for the 
high percentage of H. 

* The analyses of Iowa, Missouri, Nebraska, and Wyoming coals are 
selected from a paper on The Heating Value of Western Coals, by Wm, 
Forsyth, Mech. Engr. of the C., B. & O. R. R., Hnug’g News, Jan. 17, 1895. 

+ Includes sulphur, which is very high. Coke from Cedar City analyzed : 
Water and volatile matter, 1.42; fixed carbon, 76.70; ash, 16.61; sulphur, 5.27, 


+ Colorado Coals.—The Colorado coals are of extremely variable com- 
position, ranging all the way from lignite to anthracite. G.C. Hewitt 
(Trans. A. I. M. H., xvii. 377) says: The coal seams, where unchanged 
by heat and flexure, carry a lignite containing from 5% to 20% of water. In 
the south-eastern corner of the field the same have been metamorphosed so 
that in four miles the same seams are an anthracite, coking, and dry coal. 
In the basin of Coal Creek the coals are extremely fat, and produce a hard, 
bright, sonorous coke. North of coal basin half a mile of development 
shows a gradual change from a good coking coal with patches of dry coal to 
a dry coal that will barely agglutinate in a beehive oven. In another half 
mile the same seam is dry. In this transition area, a small cross-fault 
makes the coal fat for twenty or more feet on either side. The dry seams 
also present wide chemical and physical changes in short distances. A soft 
and loosely bedded coal has in a hundred feet become compact and hard 
without the intervention of a fault. A couple of hundred feet has reduced 
the water of combination from 12% to 52. 

Western Arkansas and Indian Territory. (H.M. Chance, 
Trans. A. I. M. E. 1890.)—The Choctaw coal-field is a direct westward exten- 


ANALYSES OF COALS. 631 


sion of the Arkansas coal-field, but its coals are not like Arkansas coals, ex- 
cept in the country immediately adjoining the Arkansas line. 

The western Arkansas coals are dry semi-bituminous or semi-anthracitic 
coals, mostly non-coking, or with quite feeble coking properties, ranging 
from 14% to 16% in volatile matter, the highest percentage yet found, aecord- 
ing to Mr. Winslow’s Arkansas report, being 17.655. 

In the Mitchell basin, about 10 miles west from the Arkansas line, coal 
recently opened shows 19% volatile matter; the Mayberry coal, about 8 miles 
farther west, contains 23% volatile matter; and the Bryan Mine coal, about 
the same distance west, shows 26% volatile matter. About 30 miles farther 
west, the coal shows from 38% to 4144% volatile matter, which is also about 
the percentage in coals of the McAlester and Lehigh districts, 


Western Lignites. (R. W. Raymond, Trans. A. I. M. E., vol. ii. 1873.) 








+.| <q | Calorific 

CS. pS RN FOR FS: Mois 4 Power, 

calories. 
Monte Diabolo..............- 59.72/5.08)1.01} 15.69/8.92) 8.94/5.64 5757 
Weber Cafion, Utah......... 64.84/4.34)1.29) 15.52)1.60) 9 41/3.00 5912 
Echo Cafion, Utah........... 69.84/3.90)1.93) 10.99'0.77| 9.1713.40 6400 
Carbon Station, Wyo.. ..... 64.99/38.76]1.74) 15.20)1.07] 11.56]1.68 5738 
s I AA irae 69.14/4.36]1.25) 9.54/1.03) 8.06/6.62 6578 
Coos Bay, Oregon............ 56.24/8.38]0.42) 21.82)0.81] 138.28]4.05 4565 
Atlaskiarn RMT TA OSES 8 55.79/3.26/0.61) 19.01]0.638} 16.52/4.18 4610 
SEES EE SIAR EE Ps RET 67.67/4.66]1.58) 12.80)/0.92) 3.08/9.28 6428 
Canon City Colo:.... 2)... 67.5817.42|....] 138.42/0.68] 5.1815.77 7330 
Bakexro2 rOreh 22h 8. 20 60.72/4.30). ..] 14.42/2.08] 14.68/3.80 5602 








The calorific power is calculated by Dulong’s formula, 
8080C + 34462( - ae 


deducting the heat required to vaporize the moisture and combined water, 
tha’ is, 587 calories for each unit of water. 1 calorie = 1,8 British thermal 
anits. 
Analyses of Foreign Coals. (Selected from D. L. Barnes’s paper 
on American Locomotive Practice, A. S. C. E., 1893. 


Volatile | Fixed | 
Matter. | Carbon.| 455: | 














Great Britain: 


South Wales....... .. 8.5 88.3 3.2 
#6 SF dal, BOONE oe lates 6.2 92.3 1.5 
Lancashire, Eng.. .... 17.2 80.1 r.¢ 
Derbyshire, -** Vee... 17.7 79.9 2.4 eer 
Durham, Me Bon nh 15 05 86.8 1.1 |Semi-bit. coking coal. 
ScCobland see oe. os tercienter. 17a 63.1 19.8 |Boghead cannel gas coal. 
ele os Ae 17.5 80.1 2.4 |Semi-bit. steam-coal. 
Staffordshire, Eng....} 20.4 78.6 1.0 
South America: 
Chili, Conception Bay} 21.93 70.55 7.52 
See Chiroguinecr scien 24.11 38.98 | 36.91 
Pataszonia. »...,... 6... 24.35 62.25 | 13.4 
Brazil fase evel ecihe cee we 4060 57.9 1.6 
Canada: 
Nova Scotia. .....- 06. 26.8 60.7 12.5 
Cape Breton........... 26.9 67.6 5.5 
Australia eae .s dion ee 
Australian lignite......] 15.8 64.3 10.0 
Sydney, South Wales..} 14.98 82.39 2.04 
Borneo: ews oy Sea 26.5 70.3 14.2 
Van Diemen’s Land..... 6.16 63.4 80.45 


An analysis of Pictou, N. S., coal, in Trans. A. I. M. E., xiv. 560, is: Vol., 
29.63; carbon, 56.98; ash, 13.89; and one of Syduey, Cape Breton, coal is: 
vol., 34.07; carbon, 61.43; ash, 4.50. 


632 FUEL. 


Nixon’s Navigation Welsh Coal is remarkably pure, and con- 
tains not more than 3 to 4 per cent of ashes, giving 88 per cent of hard and 
lustrous coke. The quantity of fixed carbon it contains would classify it 
among the dry coals, but on account of its coke and its intensity of com- 
bustion it belongs to the class of fat, or long-flaming coals. 

Chemical analysis gave the following results: Carbon, 90.27; hydrogen, 
4.39; sulphur, .69; nitrogen, .49; oxygen (difference), 4.16. 

The analysis showed the following composition of the volatile parts: Car- 
bon, 22.53; hydrogen, 34.96 ; O + N +S, 42.51. 

The heat of combustion was found to be, as a result of several experi- 
ments, 8864 calories for the unit of weight. Calculated according to its 
composition, the heat of combustion would be 8805 calories = 15,849 British 
thermal units per pound. 

This coal is generally used in trial-trips of steam-vessels in Great Britain. 

Sampling Ceal for Analysis.—J. P. Kimball, Trans. A. I. M. E., 
xii. 317, says: The unsuitable sampling of acoal-seam, or the improper 
preparation of the sample in the laboratory, often gives rise to errors in de 
terminations of the ash so wide in range as to vitiate the analysis for all 
practical purposes ; every other single determination, excepting moisture, 
showing its relative part of the error. The determination of sulphur and 
aah are especially liable to error, as they are intimately associated in the 
slates. 

Wm. Forsyth, in his paper on The Heating Value of Western Coals (Eng’g 
News, Jan. 17, 1895), says: This trouble in getting a fairly average sample of 
anthracite coal has compelled the Reading R. R. Co., in getting their samples, 
to take as much as 300 lbs. for one sample, drawn di:vect from the chutes, as 
it stands ready for shipment. 

The directions for collecting samples of coal for analysis at the C., B. & Q. 
laboratory are as follows: 

Two samples should be taken, one marked “ average,’’ the other ‘‘ select.” 
Each sample should contain about 10 lbs., made up of lumps about the size 
of an orange taken from different parts of the dump or car, and so selected. 
that they shall represent as nearly as possible, first, the average lot; second, 
the best coal. 

An example of the difference between an ‘‘average’’ and a ‘‘select’* 
sample, taken from Mr. Forsyth’s paper, is the following of an Illinois coals 

Moisture. Vol. Mat. Fixed Carbon. Ash. 
Average...... oh sg nksoO 27.69 35.41 35.54 
Selecty sis... sear 1.90 34.70 48.23 15.17 

The theoretical evaporative power of the former was 9.13 lbs. of water 
from and at 212° per lb. of coal, and that of the latter 11.44 lbs. 

Relative Value of Wine Sizes of Anthracite.—For buruing 
ona grate coal-dust is commercially valueless, the finest commercial an- 
thracites being sold at the following rates per ton at the mines, according 
to an address by Mr, Eckley B. Coxe (1893): 


Size. Range of Size. Price at Mines. 
Chestnut..... csc ccaitene Hecesieh oe COMey Cl $2.75 
Pea uk..2.. sdacdesetib erste atarae 9/16 1.25 
Buckwheat.....cccccocseseee 9/16 to 34 0.75 
ERIC Ortetststcicls civic slevsilelele es cleninre ce 34 to 3/16 0.25 
ISALIOV a rss sinie se te mols s Me sia tete 3/16 to 2/32 0.10 


But when coal is reduced to an impalpable dust, a method of burning it 
becomes possible to which even/the finest of these sizes is wholly unae 
dapted; the coal may be blown in as dust, mixed with its proper proportion 
of air, and no grate at all is then required. 

Pressed Fuel. (EH. F. Loiseau, Trans. A. I. M. E., viii. 314.)—Pressed 
fuel has been made from anthracite dust by mixing the dust with ten per 
cent of its bulk of dry pitch, which is prepared by separating from tar at@ 
temperature of 572° F. the volatile matter it contains, The mixture is kept 
heated by steam to 212°, at which temperature the pitch acquires its ce- 
menting properties, and is passed between two rollers, on the periphery of 
which are milled out a series of semi-oval cavities. The lumps of the mix- 
ture. about the size of an egg, drop out under the rollers on an endless belt 
which carries them to a screen in eight minutes, which time is sufficient to 
cool the lumps, and they are then ready for delivery. 

The enterprise of making the pressed fuel above described was not com- 
mercially successful, on account of the low price of other coal. In France, 
however, ‘‘ briquettes” are regularly made of coal-dust (bituminous and 
semi-bituminous), 


RELATIVE VALUE OF STEAM COALS. 633 


RELATIVE VALUE OF STEAM COALS. 


The heating value of a coal may be determined, with more or less approxs 
imation to accuracy, by three different methods. 

1st, by chemical analysis ; 2d. by combustion in a coal calorimeter ; 3d, 
by actual trial in a steam-boiler. The first two methods give what may be 
called the theoretical heating value, the third gives the practical value. 

The accuracy of the first two methods depends on the precision of the 
method of analysis or calorimetry adopted, and upon the care and skill of 
the operator. The results of the third method are subject to numerous 
sources of variation and error, and may be taken as approximately true 
only for the particular conditions under which the test is made. Analysis 
and calorimetry give with considerable accuracy the heating value which 
may be obtained under the conditions of perfect combustion and complete 
absorption of the heat produced. A boiler test gives the actual result under 
conditions of more or less imperfect combustion, and of numerous and va- 
riable wastes. It may give the highest practical heating value, if the condi- 
tions of grate-bars, draft, extent of heating surface, method of firing, etc., 
are the best possible for the particular coal tested. and it may give results 
far pte the highest if these conditions are adverse or uusuitable to the 
coal, ; 

The results of boiler tests being so extremely variable, their use for the 
purpose of determining the relative steaming values of different coals has 
frequently led to false conclusions. A notable instance is found in the 
record of Prof. Johnson's tests, made in 1844, the only extensive series of 
tests of American coals ever made. He reported the steaming value of the 
Lehigh Coal & Navigation Co.’s coal to be far the lowest of all the anthra- 
cites, a result which is easily explained by an examination of the conditions 
under which he made the test, which were entirely unsuited to that coal. 
He also reported a result for Pittsburgh coal which is far beneath that now 
obtainable in every-day practice, his low result being chiefly due to the use 
of an improper furnace. 

In a paper entitled Proposed Apparatus for Determining the Heating 
Power of Different Coals (Trans. A. I. M. E., xiv. 727) the author described 
and illustrated an apparatus designed to test fuel on a large scale, avoiding 
the errors of a steam-boiler test. It consists of a fire-brick furnace enclosed 
in a water- casing, and two cylindrical shells containing a great number of 
tubes, which are surrounded by cooling water and through which the gases 
of combustion pass while being cooled. No steam is generated in the ap- 
paratus, but water is passed through it and allowed to escape at a tempera- 
ture below 200° F. The product of the weight of the water passed through 
the apparatus by its increase in temperature is the measure of the heating 
value of the fuel. 

There has been much difference of opinion concerning the value of chemi- 
cal analysis as a means of approximating the heating power of coal. It 
was found by Scheurer-Kestner and Meunier-Dollfus, in their extensive series 
of tests, made in Europe in 1868, that the heating power as determined by 
calorimetric tests was greater than that given to chemical analysis accord- 
ing to Dulong’s law. 

Recent tests made in Paris by M. Mahler, however. show a much closer 
agreement of analysis and calorimetric tests. A brief description of these 
tests, translated from the French, may be found in an article by the author 
in The Mineral Industry, vol. i. page 97. 

Dulong’s law may be expressed by the formula, 


Heating Power in British Thermal Units = 14,5000 + 62,500 (H — 2)" 


in which C, H, and O are respectively the percentage of carbon, hydrogen, 
and oxygen, each divided by 100. A study of M. Mahler’s calorimetric tests 
shows that the maximum difference between the results of these tests and 
the calculated heating power by Dulong’s law in any single case is only a 
little over 3%, and the results of 31 tests show that Dulong’s formula gives an 
average of only 47 thermal units less than the calorimetric tests, the 
average total heating value being over 14,000 thermal units, a difference of 
less than 4/10 of 1%. 





* Mahler gives Dulong’s formula with"Berthelot’s figure for the heating 
yalue of carbon, in British thermal units, 
(Oe 1’) 


Heating Power = 14,6500 +- 62,025 ( H - 8 


634 FUEL. 


Mahler’s calorimetric apparatus consists or a strong steel vesse) or 
* bosib?’ immersed in water, proper precaution being taken to prevent radi- 
ation. One gram of the coal to be tested is placed in a platinum boat within 
this bomb, oxygen gas is introduced under a pressure of 20 to 25 atmospheres, 
and the coal ignited explosively by an electric spark. Combustion is com- 
plete and instantaneous, the heat is radiated into the surrounding water, 
weighing 2200 grams, and its quantity is determined by the rise in tempera- 
ture of this water, due corrections being made for the heat capacity of the 
apparatus itself. The accuracy of the apparatus is remarkable, duplicate 
tests giving results varying only about 2 parts in 1000. 

The close agreement of the results of calorimetric tests when properly 
eonducted, and of the heating power calculated from cheynical analysis, ins 
dicates that either the chemical or the calorimetric method may be ac- 
cepted as correct enough for all practical purposes for determining the total 
heating power of coal. The results obtained by either method may be 
takeh asa standard by which the results of a boiler test are to be eom- 
pared, and the difference between the total heating power, and the result of 
the boiler test is a measure of the inefficiency of the boiler under the con- 
ditions of any particular test. 

In practice with good anthracite coal, ina steam-boiler properly propor- 
tioned. aiid with all conditions favorable, it is possible to obtain in the 
stéam 80% of the total heat of combustion of the coal. This result was nearly 
obtained in the tests at the Centennial Exhibition in 1876, in five different 
boilers. An efficiency of 70% to 75% may easily be obtained in regular prac- 
tice. With bituminous coals it is difficult to obtain as close an approach to 
the theoretical maximum of economy, for the reason that some of the vola- 
tile combustible portion of the coal escapes unburned, the difficulty increas: 
ing rapidly as the content of volatile matter increases beyond 20%. With 
most coals of the Western States it is with difficulty that as much as 60% or 
pee of the theoretical efficiency can be obtained without the use of gas-pro- 

ucers. 

The chemical analysis heretofore referred to is the ultimate analysis, or 
the percentage of carbon, hydrogen, and oxygen of thedry coal. Itis found, 
however, from a study of Mahler’s tests that the proximate analysis, which 
pives fixed carbon, volatile matter, moisture, and ash, may be relied on ag 
giving a measure of the heating value with a limit of error of only. about 3%. 
After deducting the moisture and ash, and calculating the fixed carbon as a 
vercentage of the coal dry.and free from ash, the author has constructed the 
following table : 


APPROXIMATE HEATING VALUE oF COALS. 





Percentage| Heating |Equiv. WaterjPercentage| Heating |Equiv. Water 
F. C. in Value Evap. from @ F. C. in Value Evap. from. 
Coal Dry B.T.U. and at 212° # Coal Dry B.T.U. and at 212° 
and Free per lb. per lb. and Free per lb, per lb: 
from Ash. | Comb’le. |Combustible.§ from Ash. | Comb’le. |Combustible. 








100 14500 15.00 68 15480 16.03 
97 14760 15.28 63 15120 15.65 
94 15120 15.65 60 14580 15.09 
90 15480 16.03 57 14040 14.53 
87 15660 16.21 . 54 13320 13.79 
80 15840 16.40 51 12600 13.04 
72 15660 16.21 50 12240 12.67 





Below 50% the law of decrease of heating-power shown in the table appar- 
ently does not hold, as some cannel coals and lignites show much higher 
heating-power than would be predicted from their chemical constitution. 

The use of this table may be shown as follows: 

Given a coal containing moisture 2%, ash 8%, fixed carbon 61%, and volatile 
matter 29%, what is its probable heating value? Deducting moisture and 
ash we find the fixed carbon is 61/90 or 68% of the total of fixed earbon and 
volatile matter. One pound of the coal dry and free from ash would, by the 
table, have a heating value of 15,480 thermal units, but as the ash and moist- 
ure, having no heating value, are 10% of the total weight of the coal, the 
eoal would have 90% of the table value, or 13,932 thermal units. This divided 
by 966, the latent heat of steam at 212° gives an equivalent evaporation per 
lb. of coal of 14.42 lbs. 





ct 


RELATIVE VALUE OF STEAM COALS. 65 


The heating value that can be obtained in practice from this coal would 
depend upon the efficiency of the boiler, and this largely upon the difficulty 
of thoroughly burning its volatile combustible matter in the boiler furnace. 
If a boiler efficiency of 65% could be obtained, then the evaporation per |b. of 
coal from and at 212° would be 14.42 & .65 = 9.37 Ibs. 

With the best anthracite coal, in which the combustible portion is, say, 97% 
fixed carbon and 3% volatile matter, the highest result that can be expected 
in a boiler-test with all conditions favorable is 12.2 lbs. of water evaporated 
from and at 212° per Ib. of combustible, which is 80% of 15.28 lbs. the theo- 
retical heating-power. With the best semi-bituminous coals, such as Cum- 
berland and Pocahontas, in which the fixed carbon is 80% of the total com- 
bustible, 12 5 lbs., or 76% of the theoretical 16.4 lbs., may be obtained. For 
Pittsburgh coal, with a fixed carbon ratio of 68%, 11 lbs., or 69% of the theo- 
retical 16.03 Ibs., is about the best practically obtainable with the best boilers 
With some good Ohio coals, with a fixed carbon ratio of 60%, 10 lbs., or 66% 
of the theoretical 15.09 Ibs., has been obtained, under favorable conditions, 
with a fire-brick arch over the furnace. With coals mined west of Ohio, 
with lower carbon ratios, the boiler efficiency is not apt to be as high as 60%. 

From these figures a table of probable maximum boiler-test results from 
coals of different fixed carbon ratios may be constructed as follows: 

Fixed carbon ratio..........2... 97 80 68 60 54 50 
Evap. from and at 212° per lb. combustible, maxinium in boiler-tests: 
12.2 1225 11 10 8.3 


7.0 
Boiler efficiency, per cent....... 80 76 69 66 60 55 
Loss, chimney, radiation, imperfect combustion, ete : 
2 24 31 34 40 45 


20 

The difference between the loss of 20% with anthracite and the greater 
losses with the other coals is chiefly due to imperfect combustion of the 
bituminous coals, the more highly volatile coals sending up the cl.imney the 
greater quantity of smoke and unburned hydrocarbon gases. It is a mBasure 
of the inefficiency of the boiler furnace and of the inefficiency of heating- 
surface caused by the deposition of soot, the latter being primarily caused 
by the imperfection of the ordinary furnace and its unsuitability to the 
proper burning of bituminous coal. Ifin a boiler-test with an ordinary fur- 
nace lower results are obtained than those in the above table, it is an indica- 
tion of unfavorable conditions, such as bad firing, wrong proportions of 
boiler, defective draft, and the like, which are remediable. Higher results 
can be expected only with gas-producers, or other styles of furnace espe- 
cially designed for Smokeless combustion. 

Kind of Furnace Adapted for Different Coals. (From the 
author’s paper on “The Evaporative Power of Bituminous Coals,’’ Trans. 


A.S. M. E., iv, 257.)—Almost any kind of a furnace will be found well 


adapted to burning anthracite coals and semi-bituminous coals containing 
less than 20% of volatile matter. Probably the best furnace for burning 
those coals which contain between 20% and 40% volatile matter, ineluding the 
Scotch, English, Welsh, Nova Scotia, and the Pittsburgh and Monongahela 
river coals, is a plain grate-bar furnace with a fire-brick arch thrown over 
it, for the purpose of keeping the combustion-chamber thoroughly hot. The 
best furnace for coals containing over 40% volatile matter will be a furnace 
surrounded by fire-brick with a large combustion-chamber, and some spe- 
cial appliance for introducing very hot air to the gases distilled from the 
coal. or, preferably, a separate gas-producer and combustion-chamber, with 
facilities for heating both air and gas before they unite in the combustion- 
chamber. The character of furnace to be especially avoid: d in burning all 
bituminous coals containing over 20% of volatile matter is the ordinary fur- 
nace, in which the boiler is set directly above the grate bars, and in which the 
heating-surfaces of the boiler are directly exposed to radiation from the 
coal on the grate. The question of admitting air above the grate is still un- 
settled. The London Hngineer recently said: ‘* All our experience, extending 
Over many years, goes to show that when the production of smoke is pre- 
vented by special devices for admitting air, either there isan increase in the 
consumption of fuel or a diminution in the production of steam. * * * The 
best smoke-preventer yet devised is a good fireman.”’ 

Downward-draught Furnaces.—Recent experiments show that 
with bituminous coal considerable saving may be made by causing the 
draught to go downwards from the freshly-fired coal through the hot coal 
on the grate. Similar good results are also obtained by the upward draught 
by Pale the fresh coal under the bed of hot coal instead of ontop. (See 
Boilers, 


636 FUEL. 


Calorimetric Tests of American Coals.—From a number of 
tests of American and foreign coals, made with an oxygen calorimeter, by 
Geo. H. Barrus (Trans. A. S. M. E., vol. xiv. 816), the following are selected, 


showing the range of variation: 





Percentage 
of Ash. 

Semi-bituminous. 6.1 

George’s Cr’k, Cumberl’d, Md.,10 tests { 86 

Pocahontas, Va., 5 tests...... mn Waere tere ; 6 

New River, Va., 6 tests........0...006- : jo 

Elk Garden, Va., 1 test.. eke aeaRen 7.8 

Welsh, 1 feab och os sak. Mion eNO 0.7 
Bituminous. 

Youghiogheny, Pa., mane re adhe 5.9 

BlACK A ariccerttete seis 10.2 

Frontenac, Kansas ..............6- ahtet 17.7 

Cape Breton, GRIP > Sheen 'ae 8.7 

Lancashire, Eng . ELeKbO cue mooeL 6.8 

MAnthrccilenll tests aectnge- asc cieiaicds) cic ste } We 


of Com- 
bustion. 
Boalewue 


14,217 
12,874 
14.603 
13,608 
13,922 
13,858 
13,180 
13,581 


12,941 
11,664 
10,506 
12.420 
12,122 
11,521 
13,189 


Evaporative Power of Bituminous Coals. 
(Tests with Babcock & Wilcox Boilers, Trans. A. 8S. M. E., iv. 267.) 











Se 
: } 
Ss 
. % Gey 
o/s | 3 |e 
a asi o 2 
Dura- : 9 a @ vf 
Name of Coal. tion, of] 19.) Sp oul a 
Test. | €] 5 | 29 |De 
ee ep) iw |/3s 2 
oP eg (eae el 
oD) 5 
2 = ao 
2) wadleain 
£18) 5 183 
Oo; ]a |O 
Me Welslt.: cere e'.. oe 144% hrs/40 {1679} 7.5) 6.3 
2. Anthracite scr’s 1/5 
Powelton, Pa., 1044 hj60 {3126} 8.8:17.6 
Semi-bit. 4/5, 
3. Pittsbg’h fine slack| 4 hrs .|33.7/1679/12.3)/21.9 
‘¢ 3d Poollump| 10 ‘* /43.5/2760] 4.8/27.5 
4, Castle Shannon, nr 
Pittsb’gh, 3g nut, 4214 h\69.114784|10.5,27.9 


5g lump, 


5. lll. ‘run of mine’’| 6days.}....}1196]....].... 


‘Ind. block, “ very Rata .. {1196}. 





good 9 . eee 
§. Jackson, O,nut..| 8 hrs./48 [3358 9.6 32.4 
“ Staunton, Ill.,nut..} 8S ‘ |60 |3358]17.7/25.1 
7. Renton screenings. | 5 h 50 m/21.2/1564/13.8/31.5 
*- Wellington scrgs.. 6h 80 m}21.2)1564/18.3)/27 
“ Black Dian). ser’gs|5 h 58 m]21.2/1564/19.3/36.4 
‘* Seattle sereenings. |6 h 24 m}21.2!1564]13.4/31.3 
“ Wellington ta: 6 h 19 m)/21.2/1564/13.8 28.2 
a * Cardiff lump.. .|6h 47 m)21.2/1564]11.7/26.7 
Pibecees''> 7 h 23 m/21.2}1564/19.1/25.6 
** South Paine lump. : 4 835 n}21.2/15641138.9 28.9 
** Seattle lump ..... 5m /21.2)15641 9.5 34.1 





q. 


ft. of Heating Surface 


Water evaporated pers 
per hour, pounds. 





Water per pound Coal 





OVOr $5 SS OTe 


Coo CI CD CD WC 
209 OL 


from and at 212°, lbs. 





Water per pound Combus- 
tible from and at 212°. 





Total Heat|Total Heat 
reduced to 

Fuel free 
from Ash. 


15,141 
14.085 
15,086 
14,507 
14.427 
14.696 
14.295 
14,714 


13,752 
12,988 
12,765 
13,602 
13,006 
12,873 
14,509 


Horse-power developed. 


Rated Horse-power. 


‘ 
—— |—— 


COKE. 637 


Place of Test: 1. London, England; 2. Peacedale, R.1.; 3. Cincinnati, O.; 
4, ESD IER: Pa.; 5. Chicago, Ill.; 6. Springfield, O.; 7%. San Francisco, 
a 


Cal. 

In all the above tests the furnace was supplied with a fire-brick arch for 
preventing the radiation of heat from the coal directly to the boiler. 

Weathering of Coal. (I. P. Kimball, Trans. A. I. M. E., viii. 204.)— 
The practical eftect of the weathering of coal. while sometimes increasing 
its absolute weight, is to diminish the quantity of carbon and disposable 
hydrogen and to increase the quantity of oxygen and of indisposable hy- 
drogen. Hence a reduction in the calorific value. 

An excess of pyrites in coal tends to produce rapid oxidation and mechan- 
ical disintegration of the mass, with development of heat, loss of coking 
power, and spontaneous ignition. h 

The only appreciable results of the weathering of:anthracite within the 
ordinary limits of exposure of stocked coal are conxined to the oxidation of 
ifs accessory pyrites. In coking coals, however, weathering reduces and 
finally destroys the coking power, while the pyrites are converted from the 
state of bisulphide into comparatively innocuous sulphates. 

Richters found ‘that at a temperature of 158° to 180° Fahr., three coals lost 
in fourteen days an average of 3.6% of calorific power. (See also paper by 
R. P. Rothwell, Trans. A. I. M. E., iv. 55.) 


COKE. 


Coke is the solid material left after evaporating the volatile ingredients of 
coal, either by means of partial combustion in furnaces called coke ovens, 
or by distillation in the retorts of gas-works. 

Coke made in ovens is preferred to gas coke as fuel. It is of a dark-gray 
color, with slightly metallic lustre, porous, brittle, and hard. 

The proportion of coke yielded by a given weight of coal is very different 
for different kinds of coal, ranging from 0.9 to 0.35. 

Being of a porous texture. it readily attracts and retains water from the 
atmosphere, and sometimes, if it is kept without proper shelter, from 0.15 ta 

_ 0.20 of its gross weight consists of moisture. 


Analyses of Coke. 
(From report of John R. Procter, Kentucky Geological Survey.) 











Fixed Sul- 

Where Made. Carbon| 45h. phur. 
Connellsville, Pa. (Average of 8samples)........ 88.96 let 0.810 
Chattanooga, Tenn. ca “4 Oe agate A rod yehb gay 16.34 | 1.595 
Birmingham, Ala. “ Heal bd ial ite wale 87.29 | 10.54] 1.195 
Pocahontas, Va. ss ane oe EAR 92.53 5.74 | 0.597 
New River, W. Va. rhe beets) oe outers saath 92.38 (ool) Ovo 
Big Stone Gap, Ky. ee rat cee ee te) 93.23 5.69 | 0.749 


Experiments in Coking. CONNELLSVILLE REGION. 
(John Fulton, Amer. Mfr., Feb. 10, 1893.) 








® | o : 
gaa ae 3s| © |S. lel Per cent of Yield. 2 
SA = o Ss oo | Oo tlie 
BH | of | sgw| Ss loulus | oe . (| as Ow 
oo Sie b loened 8 a} — ae) oo | &2!] eo a) 
is) F6/08 res eae Eg S28 a = ES ee ei ear 
6 |e o| ale ol} 5 4 |BS | ao 5 | a 


: 
| 
| 
| 
| 
| 
| 
| 
| 
: 
| 
| 


1 |67 00)12,420; 99 885 | 7,518 | 7,903 | 00.80} 3 10 | 60.53} 63.63) 385.57 
2 |68 00/11,090) 90 359 | 6,580 | 6,939 | 00.81| 3.24 | 59.33] 62.57] 36.62 
8 |45 00; 9,120) 7 272 | 5,418 | 5,690 | 00.84) 2.98 | 59.41] 62.34) 36 77 
4 {45 00} 9,020) 7 349 | 5,334 | 5,683 | 00.82) 3.87 | 59.13] 63.00] 36.18 


41,650] 340 | 1365 |24,850] 26,215] 00.82| 3.28 | 59.66] 62.94] 36.24 





























These results show, in a general average, that Connellsville coal carefully 
eoked in a modern beehive oven will yield 66.17% of marketable coke, 2.30% 
of small coke or braize, and 0.82% of ash. 


638 FURL 


The total average loss in volatile matter expelled from the coal in coking 
amounts to 30.71%. 

The modern beehive coke oven is 12 feet in diameter and 7 feet high at 
crown of dome. It is used in making 48 and 72 hour coke. 

In making these tests the coal was weighed as it was charged into the 
oven; the resultant marketable coke, small coke or braize and ashes 
weighed dry as they were drawn from the oven. 

Coal Washing.—In making coke from coals that are high in ash and 
sulphur, it is advisable to crush and wash the coal before coking it. A coal- 
washing plant at Brookwood, Ala., has a capacity of 50 tons per hour. The 
average percentage of ash in the coal during ten days’ run varied from 14% to 
21%, in the washed coal from 4.8% to 8.1%, and in the coke from 6.1% to 10.5%. 
During three months the average reduction of ash was 60.9%. (Hng. and 
Mining Jour., March 25, 1893.) 

Recovery of By-products in Coke Manufacture.—In Ger- 
many considerable progress has been made in the recovery of by-products, 
The Hoffman-Otto oven has been most largely used, its principal feature 
being that it is connected with regenerators. In 1884 40 ovens on this 
system were running, and in 1892 the number had increased to 1209. 

A Hoffman-Otto oven in Westphalia takes a charge of 644 tons of dry coal 
and converts it into coke in 48 hours. The product of an oven annually is 
1025 tons in the Ruhr district, 1170 tons in Silesia, and 960 tons in the Saar dis- 
trict. The yield from dry coal is 75% to 77% of coke, 2.5% to 3% of tar, and 1.1% 
to 1.2% of sulphate of ammonia in the Ruhr district; 65% to 70% of coke, 4% to 
4.5% of tar, and 1% to 1.25% of sulphate of ammonia in the Upper Silesia region 
and 68% to 72% of coke, 4% to 4.3% 0f tar and 1.8% to 1.9% of sulphate of ammonia 
in the Saar district. A group of 60 Hoffman ovens, therefore, yields annually 
the following: 


Parc Coke Tar Sulphate 

District. Manas fons. AMMONIA, 
BRO Pee wok CNS dante aivesistpyeterem LDL avE 1860 780 
Upper Silesia........ RAGA aU Ut 48,000 8000 840 
AION: oe sc. Saree. aoscmret eto ee Rant op 40,500 2400 492 


An oven which has been introduced lately into Germany in connection 
with the recovery of by-products is the Semet-Solvay, which works hotter 
than the Hoffman-Otto, and for this reason 73% to 77% of gas coal can be 
mixed with 23% to 27% of coal low in volatile matter, and yet yield a good 
eoke. Mixtures of this kind yield a larger percentage of coke, but, on the 
other hand, the amount of gas is lessened, and therefore the yield of tar and 
ammonia is not so great. 

The yield of coke by the beehive and the retort ovens respectively is 
given as follows in a pamphlet of the Solvay Process Co.: Connellsville 
coal : beehive, €6%, retort, 73%; Pocahontas: beehive, 62%. retort, 83%; Ala- 
aoe beehive, 60%, retort, 74%. (See article in Mineral Industry, vol. viii., 

References: F. W. Luerman, Verein Deutscher Eisenhuettenleute 1891 
Iron Age, March 31, 1892; Amer. Mfr., April 28, 1893. An excellent series 
of articles on the manufacture of coke, by Jolin Fulton, of Johnstown, Pa. 
is published in the Colliery Engineer, beginning in January, 1893. ‘ : 

Making Hard Coke.—J. J. Fronheiser and ©. 8 Price, of the Cam- 
bria Iron Co., Johnstown, Pa., have made an improvement in coke manu- 
facture by which coke of any degree of hardness may be turned out. It is 
accomplished by first. grinding the coal to a coarse powder and mixing it. 
with a hydrate of lime (air or water slacked caustic lime) before it is 
charged into the coke-ovens. The caustic lime or other fluxing material 
used is mechanically combined with the coke, filling up its cell-walls. It has 
been found that about 5% by weight of caustic lime mixed with the fine coal 
gives the best results. However, a larger quantity of lime can be added to 
coals containing more than 5% to 7% of ash. (Amer. Mfr.) 

Generation of Steam from the Waste Heatand Gases of 
Coke-ovens, (Erskine Ramsey, Amer. M/r., Feb. 16, 1894.)—ihe gases 
from a number of adjoining ovens of the beehive type are led into a long 
OBA flue, and thence io! 8 combos enc han aaa under a battery of 

oilers. Two plants are in satisfactory operation at Tracy Ci ‘ND. § 
two at Pratt Mines, Ala. Sow x PN eee 
_ A Bushel of Coal,—The weight of a bushel of coal in Indiana is 70 Ibs., 
in Penna. “6 lbs,; in Ala., Colo., Ga., Ill., Ohio, Tenn., and W. Va. it is 80 lbs. 

A Bushel of Coke is almost uniformly 40 lbs., but in exceptional 





WOOD AS FUEL. 639 


eases, when the coke is very light, 38, 36, and 33 lbs. are regarded as a bushel. 
In others, from 42 to 50 Ibs. are given as the weight of a bushel ; in this case 
the coke would be quite heavy. 

Products of the Distillation of Coal.—S. P. Sadler’s Handbook 
of Industrial Organie Chemistry gives a diagram showing over 50 chemical 
products that are derived from distillation of coal. The first derivatives are 
coal-gas, gas-liquor, coal-tar, and coke. From the gas-liquor are derived 
ammonia and sulphate, chloride and carbonate of ammonia. The coal-tar 
is split up into oils lighter than water or crude naphtha, oils heavier than 
water—otherwise dead oil or tar, commonly called creosote,—and pitch. 
From the two former are derived a variety of chemical products. 

From the coal-tar there comes an almost endless chain of known combina- 
tions. The greatest industry based upon their use is the manufacture of 
dyes, and the enormous extent to which this has grown can be judged from 
the fact that there are over 600 different coal-tar colors in use, and many more 
which as yet are too expensive for this purpose. Many medicinal prepara- 
tions come from the series, pitch for paving purposes, and chemicals for 
the photographer, the rubber manufacturers and tanners, as well as for 
preserving timber and cloths. 

The composition of the hydrocarbons in a soft coal is uncertain and quite 
complex; but the ultimate analysis of the average coal shows that it ap- 
proaches quite nearly to the composition of CH, (marsh-gas). (W. H. 
Blauvelt, Trans. A. I, M. E., xx. 625.) 


Woon AS FUEL. 


Wood, when newly felled, contains a proportion of moisture which varies 
very much ip different kinds and in different specimens, ranging between 
30% and 50%, and being on an average about 40%. After 8 or 12 months’ ordi- 
nary drying in the air the proportion of moisture is from 20 to 25%. This 
degree of dryness, or almost perfect dryness if required, can be produced 
by a few days’ drying in an oven supplied with air at about 240° F, When 
coal or coke is used as the fuel for that oven, 1 lb. of fuel suffices to expel 
about 3 lbs. of moisture from the wood. This is the result of experiments 
on a large scale by Mr. J. R. Napier. If air-dried wood were used as 
fuel for the oven, from 2 to 2144 lbs. of wood would probably be required to 
produce the same effect. 

The specific gravity of different kinds of wood ranges from 0.3 to 1.2. 

Perfectly dry wood contains about 50% of carbon, the remainder consisting 
almost entirely of oxygen and hydrogen in the proportions which form 
water. The coniferous family contain a small quantity of turpentine, which 
is a hydrocarbon. Ihe proportion of ash in wood is from 1% to 5%. The 
total heat of combustion of all kinds of wood, when dry, is almost ex- 
actly the same, and is that due to the 50% of carbon. ¢ 

The above is from Rankine; but according to the table by 8S. P. Sharpless 
in Jour. C. 1. W., iv. 36, the ash varies from 0.03% to 1.20% in American woods, 
and the fuel value, instead of being the same for all woods, ranges from 
3667 (for white oak) to 5546 calories (for long-leaf pine) = 6600 to 9883 British 
thermal units for dry wood, the fuel value of 0.50 lbs. carbon being 7272 
Ba. we 

Heating Value of Wood.—The following table is given in several 
books of reference. authority and quality of coal referred to not stated. 

The weight of one cord of different woods (thoroughly air-dried) is about 
as follows: 


Hickory or hard maple.... 4500 lbs. equal to 1800 lbs. coal. (Others give 2000.) 
8850 bb ob 1540 66 oe ( 66 1 


White oak........-25-..-6- 715.) 
Beech, red and black oak.. 3250 ‘ SmwISvO yt: 4" <¢ 6 1450.) 
Poplar, chestnut, and elm.. 2850 ‘ saiaperd (ices O88 5. ¢ “ 1050.) 
The average pine.......... 2000 “ Sie BOOSIE! ESE) | ‘ 925.) 


Referring to the figures in the last column, it is said : 

From the above it is safe to assume that 214 Ibs. of dry wood are equal to 
1 lb. average quality of soft coal and that the full value of the same weight 
of different woods is very nearly the same—that is, a pound of hickory is 
worth no more for fuel than a pound of pine, assuming both to be dry. It 
is important that the wood be dry, as each 10% of water or moisture in wood 
will detract about 12% from its value as fuel. 

Taking an average wood of the analysis C 51%, H_ 6.5%, O 42.0%, ash 0.52, 
perfectly dry, its fuel value per pound, according to Dulong’s formula, V = 


640 | FUEL. 


[ 14,500 C + 62,000 (H _ )], is 8170 British thermal units. If the wood, as 


ordinarily dried in air, contains 25% of moisture, then the heating value of a 
pound of such wood is three quarters of 8170 = 6127 heat-units, less the 
heat required to heat and evaporate the 14 lb. of water from the atmospheric 
temperature, and to heat the steam made from this water to the tempera- 
ture of the chimney gases, say 150 heat-units per pound to heat the wate> to 
212°, 966 units to evaporate it at that temperature, and 100 heat-units to 
raise the temperature of the steam to 420° F., or 1216 in all = 204 for 44 lb., 
which subtracted from the 6127, leaves 5824 heat-units as the net fuel value 
of the wood per pound, or about 0.4 that of a pound of carbon, 


Composition of Wood. 
(Analysis of Woods, by M. Eugene Chevandier.) 



































Composition. 
Woods ES AEW ECT EN ait SCRE ASANO SA ear 

Carbon. | Hydrogen.| Oxygen. | Nitrogen. Ash. 

Beech ..-:....... 49.36% 6.01% 42.69% 0.91% 1.06% 
OAK eles so, creeioa srs 49.64 5.92 41.16 1.29 1.97 
Birch). oe cme. sec 50.20 6.20 41.62 1.15 0.81 
Poplar is. esciaeis 49.37 6.21 41.60 0.96 1.86 
Willow .........% 49.96 5.96 39.56 0.96 3.37 

Average ....... 49.70% 6.06% 41.30% 1.05% 1.80% 





The following table, prepared by M. Violette, shows the proportion of 
water expelled from wood at gradually increasing temperatures: 





Water Expelled from 100 Parts of Wood. 


























Temperature. EET We WT pe TE Oa TE US i ee 
Oak. Ash. Elm, Walnut, 
EFF 13 ME ELINIC Morere ces oie of steoreerereis Ts 15.26 14.78 1ooe 15.55 
BOSS MANLY e Caceics eee clone save 17.93 16.19 |. 17.02 Tis43 
ACME IIT Uecatera oc atu latietaciecoretens 32.13 21.22 36.94? 21.00 
Bi Wah eyS Ag GRE sustirecste:a (cites 35.80 27.51 33.38 41.77? 


BoP AINE et cn clesisaleitelaeleies 44.31 33.38 40.56 86.56 


The wood operated upon had been kept in store during two years. When 
wood which has been strongly dried by means of artificial heat is left ex- 
posed to the atmosphere, it reabsorbs about as much water as it contains 
in its air-dried state. 

A cord of wooed = 4% 4X8 = 128 cu. ft. About 56% solid wood and 44% 
interstitial spaces. (Marcus Bull, Phila.. 1829. J.C. I. W., vol. i. p. 293.) 

B. E. Fernow gives the per cent of solid wood in a cord as determined offi 
cially in Prussia (J. C. I. W., vol. iii. p. 20): 

Timber cords, 74.07% = 80 cu. ft. per cord; 

Firewood cords (over 6’ diam.), 69.44% = 75 cu. ft. per cord; 
** Billet’’ cords (over 3” diam.), 55.55% = 60 cu. ft. per cord; 
** Brush’ woods less than 3’’ diam., 18.52%; Roots, 37.00%. 


CHARCOAL. 


Charcoal is made by evaporating the volatile constituents of woud aud 
peat, either by a partial combustion of a conical heap of the material to be 
charred, covered with a layer of earth, or by the combustion of a separate 
portion of fuel in a furnace, in which are placed retorts containing the mia- 
terial to be charged. 

According to Peclet, 100 parts by weight of wood when charred in a heap 
yield from 17 to 22 parts by weight of charcoal, and when charred in a 
retort from 28 to 30 parts. 

This has reference to the ordinary condition of the wood used in charcoal- 
making, in which 25 parts in 100 consist of moisture. Of the remaining 75 
parts the carbon amounts to one half, or 3714% of the gross weight of the 
wood, Hence it appears that on an average nearly half of the carbon in the 


CHARCOAL i 6at 


wood is lost during the partial combustion in a heap, and about one quarter 
during the distillation in a retort. 

To char 100 parts by weight of wood in a retort, 12144 parts of wood must 
be burned in the furnace. Hence in this process the whole expenditure of 
wood to produce from 28 to 30 parts of charcoal is 112% parts; so that if the 
weight of charcoal obtained is compared with the whole weight of wood 
expended, its amount is from 25% to 27%; and tLe proportion lost is on an 
average 1144 + 3714 = 0.8, nearly. 

According to Peclet, good wood charcoal contains about 0.07 of its weight 
of ash. The proportion of ash in peat charcoal is very variable, and is es- 
timated on an average at about 0.18. (Rankine.) 

Much information concerning charcoal may be found in the Journal of the 
Charcoal-iron Workers’ Assn., vols. i. to vi. From this source the following 
notes have been taken: 

Wield of Charcoal from a Cord of Wood.—From 45 to 50 
bushels to the cord in the kiln, and from 30 to 35 in the meiler, Prof. Egles- 
ton in Trans, A. I. M. E., viii. 395, says the yield from kilns in the Lake 
Champlain region is often from 50 to 60 bushels for hard wood and 50 for 
soft wood; the average is about 50 bushels. 

The apparent yield per cord depends largely upon whether the cord is a 
full cord of 128 cu. ft. or not. 

Tn a four months’ test of a kiln at Goodrich, Tenn., Dr. H. M. Pierce found 
results as follows: Dimensions of kiln—inside diameter of base, 28 ft. 8 in.; 
diam, at spring of arch, 26 ft. 8in.; height of walls, 8 ft.; rise of arch, 5 ft.; 
capacity, 80 cords. Highest yield of charcoal per cord of wood (measured) 
59.27 bushels, lowest 50.14 bushels, average 53.65 bushels. 

No.of charges 12, length of each turn or period from one charging to 
another 11 days. (J.C. I. W., vol. vi. p. 26.) 


Results trom Different Methods of Charcoal-making. 


Yield eelec 

Olea, 

gelEsiogelaus 

Coaling Methods. Character of Wood used.|= 3 Bola SS lug 8 

ane: o @i o— a 

SEE S|GSEIMES 

ae BL SOOlL 20 

ees > ee a a re ee ery 77 fet ea 10 Secale 

Odeistjerna’s experiments'/Birch dried at 230 F.......].... BB: Ol etyeccocsl wareretats 

ER Ds a a Air dry, av. good igs | 77.0|28.3] 63.4 | 15.7 
ee arn te pat Sr eee ow pine weighing 

enens ay: fuel in abt. 28 lbs. per cu. ft. ) |65.8)24.2) 54.2 | 15.7 


Swedish ovens, av. results i maa ye fir and Be 81.0|27.7| 66.7 | 13.3 


Swedish ovens, av. resuits eis wood, mixed fir! |; ojos gl 62.0 | 13.3 


and pine 
Swedish meilers excep-|(Fir and |. white-pine ) |72.2/24 7) 59.5 | 13.3 
RiOnal’s AS a See ee ee 1 wood, mixed. Ay. 25 
Swedish meilers, av. results lbs. per cu. ft. ( 52.5/18 3) 43.9 | 13.3 





American kilns, av. results| ( Av. good yellow pine ) |54.7/22.0) 45.0 | 17 5 
American meilers, av. re- weighing abt, 25 lbs. 


SIGS Aah eee ae per cu. ft. 42.917.1| 35 0 | 17.5 


Consumption of Charcoal in Blast-furnaces per Ton of 
Pig Irom average consumption according to census of 1880, 1.14 tons 
eharcoal per ton of pig. The consumption at the best furnaces is much 
below this average. As low as 0 853 ton, is recorded of the Morgan furnace; 
Bav furnace, 0.858; Elk Rapids, 0,884. (1892.) : 

Absorption of Water and of Gases by Charcoal, —Svedlius, 
jn his hand-book for charcoal-burners, prepared for the Swedish Govern- 
ment, says: Fresh charcoal, also reheated charcoal, contains scarcely 
any water but when cooled it absorbs it very rapidly, so that after 
twenty-four hours, it may contain 4% to 8% of water. After the lapse of a 
few weeks the moisture of charcoal may not increase perceptibly, and may 
be estimated at 10% to 15%, oran average of 12%. A thoroughly charred 
piece of charcoal ought, then, to contain about 84 parts carbon, 12 parts 
water, 3 parts ash, and 1 part hydrogen. 


642 Te FUEL. 


M. Saussure, operating with blocks of fine boxwood charcoal, freshly 
burnt, found that by simply placing such blocks in contact with certain 
gases they absorbe” ther in the following proportion: 


# Volumes. Volumes. 
AMMONIA! A eee Hele eae soot cle 90.00 Carbonic Oxide......ccevesesso+. 9.42 
Hydrochloric-acid gas......... 85:00". ‘Oxyrent.. ts... Svebeetieeet es ceugred 
Sulphurous acid........... oie. OS, 0010 re NITRO PEM 2 Vat ematecle cocccoe 6.50 
Sulphuretted hydrogen ...... 55.00 Carburetted hydrogen......... 5.00 
Nitrous oxide (laughing-gas).. 40.00 Hydrogen....... See hate evipecleld SonEEO 
Garbonic acids, Welt... eee 30.00 


It is this enormous absorptive power that renders of so much value a 
comparatively slight sprinkling of charcoal over dead animal matter, as a 
preventive of the escape of odors arising from decomposition. 

In a box or case containing one cubic foot of charcoal may be stored 
without mechanical compression a little over nine cubic feet of oxygen, 
representing a mechanical pressure of one hundred and twenty-six pounds 
to the square inch. From the store thus preserved the oxygen can be 
drawn by a small hand-pump. 


Composition of Charcoal Produced at Various Tempera: 
tures. (By M. Violette.) 





Composition of the Solid Product. 





Temperature of Car- 


bonization. Hydro- Nitrogen 
gen. Ash. 


Oxygen. and Loss. 


Carbon. 








Cent. Fahr. Per cent.}Per cent./Per cent.|Per cent.}Per cent. 
.12 46.29 0.08 47.51 


1 150° 802° 47.51 6.12 

2 200 392 51.82 3.99 43.98 0.23 39.88 

3 250 482 65.59 4.81 28.97 0.63 82.98 

4 3800 592 73.24 4.25 21.96 0.57 24.61 

5 350 662 76.64 4.14 18.44 0.61 22.42 - 
6 432 810 81.64 4.65 15.24 1.61 15.40 

G 1023 1873 81.97 2.30 14.15 1.60 15.30 


The wood experimented on was that of black alder, or alder buckthorn, 
which furnishes a charcoal suitable for gunpowder. It was previously 
dried at 150 deg. C. = 302 deg. F. 


MISCELLANEOUS SOLID FUELS. 


Dust Fuel—Dust Expiosions,.—Dust when mixed in air burns with 
such extreme rapidity as in some cases to cause explosions. _Explosions of 
flour-mills have been attributed to ignition of the dust in confined passages. 
Experiments in England in 1876 on the effect of coal-dust in carrying flame in 
mines showed that in a dusty passage the flame from a blown-out shot may 
travel 50 yards. Prof. F. A. Abel (Trans. A. I. M. E, xiii. 260) says that coal- 
dust in mines much promotes and extends explosions, and that it may read- 
ily be brought into operation as a fiercely burning agent which will carry 
flame rapidly as far as its mixture with air extends, and will operate as an 
explosive agent though the medium of a very small proportion of fire-damp 
in the air of the mine. The explosive violence of the combustion of dust is 
largely due to the instantaneous heating and consequent expansion of the 
air. (See also paper on ‘‘ Coal Dust as an Explosive Agent,” by Dr. R. W. 
Raymond, Trans. A. I. M. E, 1894.) Experiments made in Germany in 1893, 
show that pulverized fuel may be burned without smoke, and with high 
economy. The fuel, instead of being introduced into the fire-box in the 
ordinary manner, is first reduced to a powder by pulverizers of any con- © 
struction. In the place of the ordinary boiler fire-box there is a combustion 
chamber in the form of a closed furnace lined with fire-brick and provided 
with an air-injector. The nozzle throws a constant stream of fuel into the 
chamber, scattering it throughout the whole space of the fire-box. When 
this powder is once ignited, and it is very readily done by first raising the 


MISCELLANEOUS SOLID FUELS, 643 


lining to « high temperature by an open fire, the combustion continues in 
an intense and regular manner under the action of the current of air which 
carries itin. (Mfrs. Record, April, 1893.) 

Records of tests with the Wegener powdered-coal apparatus, which is 
now (1900) in use in Germany, are given in Hng. News. Sept. 16, 1897. Coal- 
dust fuel is now extensively used in the United States in rotary kilns for 
burning Portland cement. 

Powdered tuel was used in the Crompton rotary puddling-furnace at 
Woolwich Arsenal, England, in 1873. (Jour. I. & S. L., i. 1878, p.91.) 

Peat or Turf, as usually dried in the air, contains from 25% to 30% of 
water, which must be allowed for in estimating its heat of combustion. This 
water having been evaporated, the analysis of M. Regnault gives, in 100 
parts of perfectly dry peat of the best quality: C 58%, H 6%, O 31%, Ash 5%. 

In some examples of peat the quantity of ash is greater, amounting to 7% 
and sometimes to 112. 

The specific gravity of peat in its ordinary state is about 0.4 or 0.5. It can 
be compressed by machinery to a much greater density. (Rankine.) 

Clark (Steam-engine, i. 61) gives as the average composition of dried Irish 
peat: C 59%, H 6%, O 302, N 1.25%, Ash 4%. SF. 

Applying Dulong’s formula to this analysis, we obtain for the heating value 
of perfectly dry peat 10,260 heat-units per pound, and for air-dried peat con- 
taining 25% of moisture, after making allowance for evaporating the water, 
7391 heat-units per pound. 

Sawdust as Fuel.—The heating power of sawdust is naturally the 
saine per pound as that of the wood from which it is derived, but if allowed 
.to get wet it is more like spent tan (which see below). The conditions neces- 
sary for burning sawdust are that plenty of room should be given it in the 
furnace, and sufficient air supplied on the surface of the mass. The same 
applies to shdvings, refuse lumber, etc. Sawdust is frequently burned in 
saw-mills, etc., by being blown into the furnace by a fan-blast. 

Wet Tan Bark as Fuel,—Tan, or oak bark, after having been used 
jn the processes of tanning, is burned as fuel. The spent tan consists of the 
fibrous portion of the bark. According to M. Peclet, five parts of oak bark 
produce four parts of dry tan; and the heating power of perfectly dry tan, 
containing 15% of ash, is 6100 English units; whilst that of tan in an ordinary 
state of dryness, containing 20% of water, is only 4284 English units. The 
weight of water evaporated from and at 212° by one pound of tan, equiva- 
lent to these heating powers, is, for perfectly dry tan, 5.46 lbs., for tan with 
30% moisture, 3.84 Ibs. Experiments by Prof. R. H. Thurston (Jour. Frank. 
Inst., 1874) gave with the Crockett furnace, the wet tan containing 59% of 
water, an evaporation from and at 212° F. of 4.24 Ibs. of water per pound 
of the wet tan, and with the Thompson furnace an evaporation of 3.19 Ibs. 
per pound of wet tan containing 55% of water. The Thompson furnace con- 
sisted of six fire-brick ovens, each 9 feet x 4 feet 4 inches, containing 234 
square feet of grate in all, for three boilers with a total heating surface of 
2000 square feet, a ratio of heating to grate surface of 9to1. The tan was 
fed through holesin the top. The Crockett furnace was an ordinary fire- 
brick furnace, 6 X 4 feet, built in front of the boiler, instead of under it, the 
ratio of heating surface to grate being 14.6 to1. According to Prof. Thurs- 
ton the conditions of success in burning wet fuel are the surrounding of the 
mass so completely with heated surfaces and with burning fuel] that it may 
be rapidly dried, and then so arranging the apparatus that thorough com- 
bustion may be secured, and that the rapidity of combustion be precisel 
equal to and never exceed the rapidity of desiccation. Where this rapidity 
of combustion is exceeded the dry portion is consumed completely, leaving 
an uncovered mass of fuel which refuses to take fire. 

Straw as Fuel, (E£ng’g Mechanics, Feb., 1893, p. 55. Experiments in 
Russia showed that winter-wheat straw, dried at 230° F., had the following 
composition: C, 46.1; H, 5.6; N, 0.42: O, 43.7; Ash, 4.1. Heating value in 
British thermal units: dry straw, 6290; with 6% water, 5770; with 10% water, 
5448. With straws of other grains the heating value of dry straw ranged 
from 5590 for buckwheat to 6750 for flax. . 

Clark (S. E., vol. 1, p. 62) gives the mean composition of wheat and barley 
straw as C, 36; H. 5; O, 38; O, 0.50; Ash, 4.75; water, 15.75, the two straws 
varying less than 1%. The heating value of straw of this composition, accord- 
ing to Dulong’s formula, and deducting the heat lost in evaporating the 
water, is 5155 heat units. Clark erroneously gives it as 8144 heat units, —~ 

Bagasse as Fuel in Sugar Manufacture.--Bagasse is the name 
given to refuse sugar-cane, after the juice has been extracted. Prof. L. A, 


644 FUEL. 


Becuel, in a paper read before the Louisiana Sugar Chemists’ Association, in 
1892, says: ‘‘ With tropical cane containing 12.5% woody fibre, a juice contain- 
ing 16.13% solids, and 83.87% water, bagasse of, say, 66% and 72% mill extrac- 
tion would have the following percentage composition: 


Woody Combustible 
Fibre. alts. Water. 

GES: DACASSCs rece cde cessetecienececLmnot 10 53 

72% DAZASSE....e.200- sill ste sibs crete RMEGO 9 46 


“Assuming that the woody fibre contains 51% carbon, the sugar and other 
combustible matters an average of 42.1%, and that 12,906 units of heat are 
generated for every ponnd of carbon consumed, the 66% bagasse is capable 
of generating 297,834 heat units per 190 Ibs. as against 345,200, or a difference 
of 47,366 units in favor of the 72% bagasse. 

““Assuming the temperature of the waste gases to be 450° F., that of the 
surrounding atmosphere and water in the bagasse at 86° F’., and the quan- 
tity of air necessary for the combustion of one pound of carbon at 24 lbs., 
the lost heat will be as follows: In the waste gases, heating air from 86° to 
450° F., and in vaporizing the moisture, etc., the 66% bagasse will require 
112,546 heat units, and 116,150 for the 72% bagasse. 

‘Subtracting these quantities from the above, we find that the 66% bagasse 
will produce 185,288 available heat units per 100 Ibs., or nearly 24% less than 
the 72% bagasse, which gives 229,050 units. Accordingly, one ton of cane of 
2000 lbs. at 66% mill extraction will produce 680 lbs. bagasse, equal to 1,259,958, 
available heat units, while the same cane at 72% extraction will produce 560 
lbs. bagasse, equal to 1,282,680 units. 

‘* A similar calculation for the case of Louisiana cane containing 10% woody 
fibre, and 16% total solids in the juice, assuming 75% mill extraction, shows 
that bagasse from one ton of cane contains 1,573,956 heat units, from which 
561,465 have to be deducted. 

‘““This would make such bagasse worth on an average nearly 92 lbs. coal 
per ton of cane ground. Under fairly good conditions, 1 lb. coal will evap- 
orate 714 lbs. water, while the best boiler plants evaporate 10 lbs. Therefore, 
the bagasse from 1 ton of cane at 75% mill extraction should evaporate from 
689 Ibg. to 919 lbs. of water. The juice extracted from such cane would un- 
der these conditions contain 1260 lbs. of water. If we assume that the 
water added during the process of manufacture is 10% (by weight) of the 
juice made, the total water handled is 1410 lbs. From the juice represented 
in this case, the commercial massecuite would be about 15% of the weight of 
the original mill juice, or say 225 lbs. Said mill juice 1500 lbs., plus 10%, 
equals 1650 lbs. liquor handled; and 1650 lbs.. minus 225 Ibs., equals 1425 lbs., 
the quantity of water to be evaporated during the process of manufacture, 
To effect a 714-lb. evaporation requires 190 ibs. of coal, and 14214 lbs. for a 10+ 
lb. evaporation. 

“To reduce 1650 Ibs. of Juice to syrup of, say, 27° Baumé. requires the evap» 
oration of 1170 lbs. of water, leaving 480 lbs. of syrup. If this work be ac- 
complished in the open air, it will require about 156 lbs. of coal at 71% lbs. 
boiler evaporation, and 117 at 10 lbs. evaporation. 

‘‘ With a double effect the fuel required would be from 59 to 78 lbs., and 
with a triple effect, from 36 to 52 lbs. 

‘*To reduce the above 480 lbs. of syrup to the consistency of commercial 
massecuite means the further evaporation of 255 lbs. of water, requiring 
the expenditure of 34 lbs. coal at 714 lbs. boiler evaporation, and 2514 lbs. 
with a 10-lb. evaporation. Hence, to manufacture one ton of cane into sugar 
and molasses, it will take from 145 to 190 lbs. additional coal to do the work 
by the open evaporator process; from 85 to 112 lbs. with a double effect, and 
only 714 lbs. evaporation in the boilers, while with 10 lbs. boiler evaporation 
the bagasse alone is capable of furnishing 8% more heat than is actually re- 
quired to do the work. With triple-effect evaporation depending on the ex- 
cellence of the boiler plant, the 1425 lbs. of water to be evaporated from the 
juice will require between 62 and 86 lbs. of coal. These values show that 
from 6 to 30 lbs. of coal can‘be spared from the value of the bagasse to run 
engines, grind cane, etc. 

“Tt accordingly appears,’’ says Prof. Becuel, ‘‘ that with the best boiler 
plants, those taking up all the available heat generated, by using this heat 
economically the bagasse can be made to supply all the fuel required by ous 
sugar-houses.”’ 


PETROLEUM. 645 


PETROLEUM, 


Products of the Distillation of Crude Petroleum. 


Crude American petroleum of sp. gr. 0.800 may be split up by fractional 
distillation as follows (Robinson’s Gas and Petroleum Engines): 








Temp. of | ‘ : Flashing 
Distillation Distillate. may cent- Specific oint. 
Pahy: ges. Gravity. Deg. F 
113° Rhigolene. ’ ' 
113 to 140° |Chymogene. t Rahs alain, sfayeig sisi alate traces. |.590 to .625|........ 4: 
140 to 158° |Gasolene (petroleum spirit)... 1.5 s080/LO .O0 ta lmee steerer 
158 to 248° |Benzine, naphtha C, benzolene.| 10. .680 to .700 14 
248° Benzine, naphtha B......... 2.5 wad CO. (18) Reece 
to $F ‘ AT ee 2. £725 to .737 382 
347° POlISHINOUSIe ere oe scle | es assis see | siciee scisiee) oa aceite 
° 
ad Kerosene (lamp-oil),........... 50. .802 to .820 |100 to 12 
482° Lubricating oil....... ocr 15. .850 to .915 SOU 
esse ek Paratiine -waxieressdcdsvecascse Poel Caalld Me te bees PH eee er SPE 
Sa se Residue and Loss.............. 16 


ce 





Lima Petroleum, produced at Lima, Ohio, is of a dark green color, 
very fluid, and marks 48° Baumé at 15° C. (sp. gr., 0.792). 

The distillation in fifty parts, each part representing 2% by volume, gave 
the following results : 


Pere opsaecer .ops) ber | (Sp.o8 Pers) Sp.) Per Sp. Per Sp. 
cent. Gr. cent. Gr. cent. Gr. cent. Gr. cent. Gr. cent. Gr. 
0.680 18 0.720 384 0.764 50 0.802 68 0.820 88 0.815 


2 
4 F 
ig E 
8 .690 24 .%735 40 .778 58 73.830 92 5 
10 694.96. .740. ) 42... 782 60. ..800) 76 »..810 to = 
12 698 28  .742 44 .788 62. .804 78 . 820... 100 = 
14 TOO a a) 22d 1 4B a get ORs Gti SOSuny Beet LOLS © 
16 2706. 6. 32. net 00... 4 49 02800 ip Sue .S12,0>- 865.1, 816 a 
RETURNS, 
16 per cent naphtha, 70° Baumé. 6 per cent paraffine oil. 
68 $$ burning oil. 10 ss residuum. 


The distillation started at 28° C., this being due to the large amount of 
naphtha present, and when 60% was reached, at a temperature of 310° C., 
the hydrocarbons remaining in the retort were dissociated, then gases 
escaped, lighter distillates were obtained, and, as usual in such cases, the 
temperature decreased from 310° C. down gradually to 200° C., until 75% of 
oil was obtained, and from this point the temperature remained constant 
until the end of the distillation. Therefore these hydrocarbons in statu 
moriendi absorbed much heat. (Jour. Am. Chem. Soc.) 

Value of Petroleum as Fuel.—Thos. Urquhart, of Russia (Proc. 
Inst. M. E., Jan. 1889), gives the following table of the theoretical evapora- 
tive power of petroleum in comparison with that of coal, as determined by 
Messrs. Favre & Silbermann: 


Specific Theoret. 











Gravity| Chem. Comp. Heating- Evap., lbs. 

power, . 

Fuel at Sa | British Water per 

32° F’., Thermal lb. Fuel. 
Water |. C. H. Os Uh tis from and 
= 1.000. LS: et Sean 
S.G |} pic. | p.¢. | p.c. | Units. Ibs. 
Penna. heavy crude oil,...| 0.886 | 84.9 | 13.7 | 1.4 20,736 21.48 
Caucasian light crude oil..} 0.884 | 86.8 | 13.6 | 0.1 22,027 22.79 
$8 heavy ‘** “.,.; 0.938 | 86.6 | 12.3 | 1.1 20,188 | 20.85 
Petroleum refuse.......... O28 SF 1D. 71.2 19,832 20.53 
Good English Coal, Mean 

of 98 Saimples........... 1.380 | 80.0] 6.0} 8.0 14,112 14.61 


646 FUEL, 


In experiments on Russian railways with petroleum as fuel Mr. Urquhart 
obtained an actual efficiency equal to 82% of the theoretical heating-value. 
The petroleum is fed to the furnace by means of a spray-injector driven by 
steam, An induced current of air is cariied in around the injector-nozzle, 
and additional air is supplied at the bottom of the furnace. 

Oil vs. Coal as Fuel. (lron Age, Nov. 2, 1893.)\—Test by the Twin 
City Rapid Transit Company of Minneapolis and St, Paul. This test showed 
that with the ordinary Lima oil weighing 6 6/10 pounds per gallon, and 
costing 214 cents per gallon, and coal that gave an evaporation of 7% lbs. of 
water per pound of coal, the two fuels were equally economical when the 
price of coal was $3.85 per ton of 2000 lbs. With the same coal at $2.00 per 
ton, the coal was 37% more economical, and with the coal at $4.85 per ton, 
the coal was 20% more expensive than the oil. These results include the 
flifference in the cost of handling the coal, ashes, and oil. 

In 1892 there were reported to the Engineers’ Club of Philadelphia some 
comparative figures, from tests undertaken to ascertain the relative value 
of coal, petroleum, and gas. 

Lbs. Water, from 


and at 212° F. 
9.70 


1 lb. anthracite coal evaporated.......csccceccesccesss: 

1 lb. bituminous cCoal........... sisle co esaacded cetera cthietatn 10.14 
1 lb. fuel oil, 36° gravity............ sec 0 06 eel He ols emscelt 16.48 
Idubic! fout gas}.20 CuP.ss cc cece coddeetidsidsiee bem Lace 


The gas used was that obtained in the destillation of petroleum, having 
about the same fuel-value as natural or coal-gas of equal candle-power. 

Taking the efficiency of bituminous coal as a basis, the calorific energy of 
petroleum is more than ¢u% greater than that of coal ; whereas, theoretically, 
petroleum exceeds coal only about 45%—the one containing 14,500 heat-units, 
and the other 21,000, 

Crude Petroleum vs. Indiana Block Coal for Steam=« 
raising at the South Chicago Steel Works, (E. C. Potter, 
Trans. A. I. M. E., xvii, 07.)—With coal, 14 tubular boilers 16 ft. x 5ft. re- 
quired 25 men to Operate them ; with fuel oil, 6 men were required, a saving 
of 19 men at $2 per day, or $83 per day. 

For one week’s work 2731 barrels of oil were used, against 848 tons of coal 
require for the same work, showing 3.22 barrels of oil to be equivalent to 1 
ton of coal. With oil at 60 cents per barrel and coal at $2.15 per ton, the rel- 
ative cost of oil to coal is as $1.93 to $2.15. No evaporation tests were 
made. 

Petroleum as a Metallurgical Fuel.—C. E. Felton (Trans. A. I. 
M. t., Xvii, 809) reports a series of trials with oil as fuel in steel-heating and 
open-hearth steel-furnaces, and in raising steam, with results as follows: 1. 
In a run of six weeks the consumption of oil, partly refined (the paraffine 
and some of the naphtha being removed), in heating 14-inch ingots in Siemens 
furnaces was about 6% gallons per ton of blooms. 2. In melting in a 30-ton 
open-hearth furnace 48 gallons of oil were used per ton of ingots. 3. Ina 
six weeks’ trial with Lima oil from 47 to 54 gallons of oil were required per 
ton of ingots. 4. In a six months’ trial with Siemens heating-furnaces the 
consumption of Lima oil was 6 gallons per ton of ingots. Under the most 
favorable circumstances, charging hot ingots and running full capacity, 444 
to 5 gallons per ton were required. 5. In raising steam in two 100-H.P. 
tubular boilers, the feed-water being supplied at 160° F., the average evap- 
oration was about 12 pounds of water per pound of oil, the best 12 hours’ 
work being 16 pounds, 

In all of the trials the oil was vaporized in the Archer producer, an apparat: 
us for mixing the oil and superheated steam, and heating the mixture toa 
high temperature. From 0.5 lb. to 0.75 lb. of pea-coal was used per gal'on 
of oil in the vroducer itself. 


FUEL GAS. 


The following notes are extracted from a paper by W. J. Taylor on ‘' The 
Energy of Fuel” (Trans. A. I. M. E., xviii. 205): 

Carbon Gas,.—In the old Siemens producer, practically, ali the heat of 

rimary combustion—that is, the burning of solid carbon to carbon monox- 
ide, or about 30% of the total carbon energy—was lost, as little or no steam 
was used in the producer, and nearly all the sensible heat of the gas was 
dissipated in its passage from the producer to the furnace, which was usu- 
ally placed at a considerable distance. 

Modern practice has improved on this plan, by introducing steam with the 


FUEL GAS. 647 


air blown into th. producer, and by utilizing the sensible heat of the gas in 
the combustion-furnace. It ought to be possible to oxidize one out of every 
four lbs. of carbon with oxygen derived from water-vapor. The thermic 
reactions in this operation are as follows: 

Heat-units. 
4lbs. C burned to CO (3 Ibs. gasified with air and 1 1b. with water) 


GOVOLOD: 5. ec. scien oat etek puoi acl coinca ke cane sire aries 17,600 
1.5 lbs. of water (which furnish 1.33 lbs. of oxygen to combine with 1 
lb; Ofscarbon) absorbyby. dissociationes. . 2.6... ccc. occsamescen see es 10,333 
The gas, consisting of 9.333 ibs. CO, 0.167 lb. H, and 13.39 lbs. N, heated . 
GOOLE ADSOLDS cae acne fet RU cutee cin deg ebicte sales wile l meme cticie A ey aes 3,748 
heaving for radiation ANG1OSS 7 ce. ose sulle Ville or wibep ns ops buclere na Male csisie sen cOLG 
17,600 


The steam which is blown into a producer with the air is almost all con- 
densed into finely-divided water before entering the fuel, and consequently 
is considered as water in these calculations. 

The 1.5 lbs. of water liberates .167 lb. of hydrogen, which is delivered to 
the gas, and yields in combustion the same heat that it absorbs in the pro- 
ducer by dissociation. According to this calculation. therefore, 60% of the 
heat of primary combustion is theoretically recovered by the dissociation of 
steam, and, even if all the sensible heat of the gas be counted, with radia- 
tion and other minor items, as loss, yet the gas must carry 4 x 14,500 — 
(3748 + 3519) = 80,733 heat-units, or 87% of the calorific energy of the carbon. 
This estimate shows a loss in conversion of 13%, without crediting the gas 
with its sensible heat, or charging it with the heat required for generating 
the necessary steam, or taking into account the loss due to oxidizing some 
of the carbon to COg. In good producer-practice the proportion of CO, in 
the gas represents from 4% to 7% of the C burned to COg, but the extra heat 
of this combustion should be largely recovered in the dissociation of more 
water-vapor, and therefore does not represent as much loss as it would indi- 
cate. Asa conveyer of energy, this gas has the advantage of carrying 4.46 
lbs. less nitrogen than would be present if the fourth pound of coal had 
been gasified with air; and in practical working the use of steam reduces 
the amount of clinkering in the producer. 

Anthracite Gas.—In anthracite coal there is a volatile combustible 
varying in quantity from 1.5% to over7%. The amount of energy derived 
from the coal is shown in the following theoretical gasification made with 
coal of assumed composition: Carbon, 85%; vol. HC, 5%; ash, 10%; 80 Ibs. car- 
bon assumed to be burned to CO; 5 lbs. carbon burned to CO,; three fourths 
of the necessary oxygen derived from air, and one fourtb from water. 


————-—-Products,_—_—__—_ 





Process. ounds. Cubic Feet. Anal. by Vol. 
80 lbs. C burned to..... eee eee OUT) 180700 2529 .24 oon 
5 Ibs:-C burned tO. seit... k eo: CO, = 18.33 157.64 2 
5 los, vol. HC’ (distilled): tis 2. 5.00 116.60 1.6 
120 lbs. oxygen are required, of which 
30 lbs. from H,O liberate......... Hea 35, 712.50 9.4 
90 lbs. from air are associatied with N 301.05 4064.17 53.6 
514.79 7580 15 100.0 
Energy in the above gas obtained from 100 lbs. anthracite: 
186.66 Ibs. CO.... ...... 807,304 heat-units. 
5.00 ee CH ce cee 117,500 - 
3.75 =“ Hrted 88 232,500 “ 
1,157,304 ff 
Total energy in gas perlb...... « 2,248 se 
as % * 100 lbs. of coal. .1,349,500 :: 
Efficiency of the conversion ............. 86%. 


The sum of CO and H exceeds the results obtained in practice. The sen- 
sible heat of the gas will probably account for this discrepancy, and, there- 
fore, it is safe to assume the possibility of delivering at least 82% of the 
energy of the anthracite. 

Bituminous Gas.—A theoretical gasification of 100 lbs. of coal, con- 
taining 55% of carbon and 32% of volatile combustible (which is above the 
average of Pittsburgh coal), is made in the following table. It is assumed 
that 50 lbs. of C are burned to CO and 5 lbs. to CO,; one fourth of the O is 


648 FUEL. 


derived from steam and three fourths from air; the heat value of the 
volatile combustible is taken at 20,000 heat-units to the pound. In comput- 
ing volumetric proportions all the volatile hydrocarbons, fixed as well as 
condensing, are classed as marsh-gas, since it is only by some such tenta- 
tive assumption that even an approximate idea of the volumetric composi- 
tion can be formed. The energy, however, is calculated from weight: 


———— —— Products. _—__——_,, 
Process. Pounds, Cubic Feet. Anal. by Vol. 
SOM bss CO Durned tote face cen tes oe CO 116.66 1580.7 27.8 
DalbsaC burneditonne as secre cates ee CO, 18.33 157.6 eats 
22 lbs. vol. HC (distilled)............... 32.00 746.2 13.2 
80 lbs. O are required, of which 20 lbs., 
derived from H,O, liberate....... H 2.5 475.0 8.3 
60 lbs. O, derived from air, are asso- 
clatedewith®s tens Salk le ae N 200.70 2709.4 7.8 
370.19 5668.9 99.8 
Energy in 116.66 lbs. CO.. .... 504,554 heat-units, 
cs *¢ 32.00 lbs. vol. HC.... 640,000 * 
es Sc) mies OO IDSA ats oie oe 155,000 $ 
1,299,554 se 
Energy; intcoaleeg iis te eases 1,437,500 vy 
Per cent of energy delivered in gas.......... -. 90.0 
Heat-units int lbs of Sass serie. eae le es 8,484 


Water-=gas.—Water-gas is made in an intermittent process, by blowing 
up the fuel-bed of the producer to a high state of incandescence (and in 
some cases utilizing the resulting gas, which is a lean producer-gas), then 
shutting off the air and forcing steam through the fuel, which dissociates 
the water into its elements of oxygen and hydrogen, the former combining 
with the carbon of the coal, and the latter being liberated. 

This gas can never play a very important part in the industrial field, owing 
to the large loss of energy entailed in its production, yet there are places 
and special purposes where it is desirable, even at a great excess in cost per 
unit of heat over producer-gas; for instance, in small high-temperature fur- 
naces, where much regeneration is impracticable, or where the ‘‘ blow-up”’ 
gas can be used for other purposes instead of being wasted. 

The reactions and energy required in the production of 1000 feet of water- 
gas, composed, theoretically, of equal volumes of CO and H, are as follows: 


500 cubic feet of H weigh.......... stills aay sate tn Meee eee 2.635 Ibs. 
500 cubic feet of CO weigh.......... ae via ames hee eee 36.89 ‘ 
Total weight of 1000 cubic feet........ .......6...0.- 39.525 Ibs. 


Now, as CO is composed of 12 parts C to 16 of O, the weight of C in 36.89 
Ibs. is 15.81 lbs. and of O 21.08 lbs. When this oxygen is derived from water 
it liberates, as above, 2.635 lbs. of hydrogen. The heat developed and ab- 
sorbed in these reactions (roughly, as we will not take into account the en- 
ergy required to elevate the coal from the temperature of the atmosphere 
to say 1800°) is as follows: 


Heat-units. 
2.635 lbs. H absorb in dissociation from water 2.625 < 62,000.. = 163,370 
15.81 lbs. C burned to CO develops 15.81 * 4400,..............- = 69,564 
Excess of heat-absorption over heat-development ........ = 93,806 


If this excess could be made up from C burnt to CO, without loss by radi- 
ation, we would only have to burn an additional 4.83 lbs. C to supply this 
heat, and we could then make 1000 feet of water-gas from 20.64 lbs. of car- 
bon (equal 24 lbs. of 85% coal). This would be the perfection of gas-making, 
as the gas would contain really the same energy as the coal; but instead, we 
require in practice more than double this amount of coal, and do not deliver 
more than 50% of the energy of the fuel in the gas, because the supporting 
heat is obtained in an indirect way and with imperfect combustion. Besides 
this, it is not often that the sum of the CO and H exceed 90%, the balance be- 
ing CO, ant N. But water-gas should be made with much less loss of en- 
ergy by burning the ‘‘ blow-up” (producer) gas in brick regenerators, the 
stored-up heat of which can be returned to the producer by the air used in 
blowing-up. 

The following table shows what may he considered average volumetric 


FUEL GAS. 649 


analyses, and the weight and energy of 1000 cubic feet, of the four types of 
gases used for heating and illuminating purposes: 





Natural| Coal- ‘Water- 
Gas. gas. gas. 


— S| | 


Producer-gas. 


COs Seas eter Aeicitaiwne sheets «6 0.50 6.0 45.0 27.0 27.0 
TG og MOR ian bos oh oe eatales spicaice ay ate 2.18 46.0 45.0 12.0 12.0 
OH a airess: Aer, DEP CODSED CORT OCeOCe 92.6 40.0 2.0 12 aD 
ag eeiie stews savace RPE oles ayorc oils 0.31 4.0 stexceg et lteqeraateess 0.4 
COg.. Suice P 0.26 0.5 4.0 2.0 2.5 
Se he clo sica’ ces clesiste PEER. one Al, sOcOL 1.5 2.0 57.0 56.2 
Qraseietdse s cierce oa «5 Uae [erarem aoa wraps s 0.34 0.5 0.5 0.3 0.3 
IVDO Se Grc ce oa is lular! uskces chains’ occas caters. 0s 1.5 Det 5) 1) Pabedan ey 
Pounds in 1000 cubic feet.......... SAS OM aa Ja) 45.6 65.6 65.9 
deat units in 1000 cubic feet...... 1,100,000} 785,000 | 322,000 | 137,455 | 156.917 


Natural Gas in Ohio and Indiana. 
(Eng. and M. J., April 21, 1894.) 











Ohio. Indiana. 

Description. Fos St Ander- | Koko- | Mar- 
toria Findlay Mary’s. Muncie. son. mo. ion, 

Hydrogen.......... 1.89 1.64 1.94 2.35 1.86 1.42 | 1.20 
Marsh-gas......... 92.84 | 98.85 | 98.85 | 92.67 | 98.07 | 94.16 193.57 
Olefiant gas........ 20 30 .20 .25 47 30 Jibs: 
Carbon monoxide.. 259 41 44 .45 3 .55 60 
Carbon dioxide.... 20 ays) .23 225 26 .29 .30 
LOXV POR REe wie 85 .39 80 30 42 380 55 
NitrOgettcc. ccc) .< 3.82 3.41 2.98 3.53 3.02 2.80 | 3.42 
Hydrogen sulphide 15 .20 21 15 15 18 .20 


Approximately 30,000 cubic feet of gas have the heating power of one 
ton of coal. 
Producer-gas from One Ton of Coal, 
(W. H. Blauvelt, Trans. A. 1. M. E., xviii. 614.) 











Analysis by Vol. Pine Cubic Feet.| Lbs. Equal to— 
CO PRE Ee. ee eh 25.3 38,213.84) 2451.20] 1050.51 lbs. -C + 1400.7 Ibs. O. 
jE Uae) See Renee 9.2 12,077.76] 63.56] 63.56 ‘** H. 
CLE eoipepinenar 3.1 4,069.68) 174.66] 174.66 ‘* CHy,. 
(CAV eo orean ao 0.8 1,050.24) 77.7 iets. ath Cg ll 4. 
OO; Malas 3.4 4,468.52] 519.02} 141.54 ‘** C-+ 377.44 lbs. O. 
‘N (by difference.} 58.2 76,404.96) 5659.63} 7350.17 ‘* Air. 
100.0] 181,280.00] 8945.85 








Calculated upon this basis, the 131,280 ft. of gas from the ton of coal con- 
tained 20,311,162 B.T.U., or 155 B.T.U. per cubic ft., or 2270 B.T.U. per Ib. 

The composition of the coal from which this gas was made was as follows: 
Water. 1.26%; volatile matter, 36.22%; fixed carbon, 57.98%; sulphur, 0.70%; 
ash, 3.78%. One ton contains 1159.6 lbs. carbon and 724.4 lbs. volatile com- 
bustible, the energy of which is 31,302,200 B.T.U. Hence, in the processes of 
gasification and purification there was a loss of 35.2% of the energy of the 
coal. 

The composition of the hydrocarbons in a soft coal is uncertain and quite 
complex; but the ultimate analysis of the average coal shows that it ap- 
proaches quite nearly to the composition of CH, (marsh-gas). G 

Mr. Blauvelt emphasizes the following points as highly important in soft- 
coal producer-practice: 


650 FUEL 


First. That a iarge percentage of the energy of the-coal is lost when the 
gas is made in the ordinary low producer and cooled to the temperature of 
the air before being used. To prevent these sources of loss, the producer 
should be placed so as to lose as little as possible of the sensible heat of the 
gas, and prevent condensation of the hydrocarbon vapors. A high fuel-bed 
should be carried, keeping the producer cool on top, thereby preventing the 
breaking-down of the hydrocarbons and the deposit of soot, as well as keep- 
ing the carbonic acid low. 

Second, That a producer should be blown with as much steam mixed with 
the air as will maintain incandescence. This reduces the percentage of 
nitrogen and increases the hydrogen, thereby greatly enriching the gas. 
The temperature of the producer is kept down, diminishing the loss of heat 
by radiation through the walls, and in a Jarge measure preventing clinkers, 

The Combustion of Producer-gas, (H. H. Campbell, Trans. 
A. IL. M, E., xix, 128.)—The combustion of the components of ordinary pro- 
ducer-gas may be represented by the following formule: 

C,H, + 60 = 2CO, + 2H,O; 2H + O = H,O; 
CH, + 40 =- CO, + 2H,O; CO -- QO= COg. 
AVERAGE COMPOSITION BY VOLUME OF PRODUCER-GAS: A, MADE WITH OPEN 
GRATES, NO STEAM IN BLAST; B, OPEN GRATES, STEAM-JET IN BLastT. 10 
SAMPLES OF EACH. 


CO.. O CoH. CO iat CH,. N. 
ASTIN eevee 3.6 0.4 0.2 20.0 5.3 8.0 58.7 
A max. . 5.6 0.4 0.4 24.8 8.5 oes 64.4 
A average... 4.84 0.4 0.34 PE | 6.8 3.74 61.78 
OMIT TS SAG ; 0.4 0.2 20.8 6.9 2.2 ae 
Bamax eros. 6.0 0.8 0.4 24.0 9.8 3.4 62.0 
B average... 5.3 0.54 0.36 22.74 8.37 2.56 60.13 


The coal used contained carbon 82%, hydrogen 4.7%. 
The following are analyses of products of combustion : 


<a Pye Co. ea ee N 


Vinimum....... Tie, ot see trace. trace. trace. 80.1 
Maximum...... 1.2 1.6 2.0 0.6 2.0 83.6 
Average ........ 16.3 0.8 0.4 0.1 0.2 82.2 


Use of Steam in Producers and in Boiler-furnaces. (R. 
W. Raymond, Trans. A. I. M. K., xx. 635.)—No possible use of steam can 
eause a gain of heat. If steam be introduced into a bed of incandescent 
carbon it is decomposed into hydrogen and oxygen. 

The heat absorbed by the reduction of one pound of steam to hydrogen is 
much greater in amount than the heat generated by the union of the 
oxygen thus set free with carbon, forming either carbonic oxide or carbonic 
acid. Consequently, the effect of steam alone upon a bed of incandescent 
fuel is to chill it. In every water-gas apparatus, designed to produce by 
means of the decomposition of steam a fuel-gas relatively free from nitro-~ 
gen, the loss of heat in the producer must be compensated by some reheat- 
ing device. 

his loss may be recovered if the hydrogen of the steam is subsequently 
burned, to form steam again. Such a combustion of the hydrogen is con- 
templated, in the case of fuel-gas, as secured in the subsequent use of that 
gas. Assuming the oxidation of H to be complete, the use of steam will 
cause neither gain nor loss of heat, but a simple transference, the heat 
absorbed by steam decomposition being restored by hydrogen combustion. 
In practice, it may be doubted whether this restoration is ever complete. 
But it is certain that an exeess of steam would defeat the reaction alto- 
gether, and that there must be a certain proportion of steam, which per- 
mits the realization of important advantages, without too great a net loss in 
heat. 

The advantage to be secured (in boiler furnaces using small sizes of 
anthracite) consists principally in the transfer of heat from the lower side 
of the fire, where it is not wanted, to the upper side, where it is wanted, 
The decomposition of the steam below cools the fuel and the grate-bars, 
whereas a blast of air alone would produce, at that point, intense combus- 
tion (forming at first CO,), to the injury of the grate, the fusion of part of 
the fuel, etc. 4 

The proportion of steam most economical is not easily determined. The 
temperature of the steam itself, the nature of the fuel mixture, and the use 
or non-use of auxiliary air-supply, introduced into the gases above or 


ILLUMINATING-GAS, 651 


beyond the fire-bed, are factors affecting the problem. (See Trans, 
A. J. M. E., xx. 625 ) ; 
~ Gas Analyses by Volume and by Weight.—To convert an an- 
alysis of a mixed gas by volume into analysis by weight: Multiply the per- 
centage of each constituent gas by the density of that gas (see p. 166). Divide 
each product by the sum of the products to obtain the percentages by weight. 
Gas-fuel for Small Furnaces,—E. P. Reichhelm (An. Mach., 
Jan, 10, 1895) discusses the use of gaseous fuel for forge fires, for drop- 
forging, in annealing-ovens and furnaces for melting brass and copper, for 
case-hardening, muffie-furnaces, and kilns. Under ordinary conditions, in 
‘such furnaces he estimates that the loss by draught, radiation, and the 
heating of space not occupied by work is, with coal, 80%, with petroleum 10%, 
and with gas aboye the grade of producer-gas 25%. He gives the following 
table of comparative cost of fuels, as used in these furnaces: 











S ts eet einige 
< » 

aoe (bese | Ze (8, & 
Sa eS el Of lmwaod 
: oe e PatSal os SO: 

Kind of Gas. ae on BE beet Sines 

Ces |°eessl 53 lesaaa 

65O |ozRAg Fa |4S58a 

4 Z < 5 

Nain GAG. shad eensine nh epsns 1,000,000) 750,000 |......2-/ece..e0e S 
Coal-gas, 20 candle-power...........-.-| 675,000] 506,250 $1.25) $2.46 
Carburetted water-gas. ....... ....0.- 646,000} 484,500 1.00} 2,06 
Gasolene gas, 20 candle-power,......... 690,000} 517,500 90) 1.73 
Water-gas from GOKe. ... 0... esegee: 313,000] 234,750 40} 1.70 
Water-gas from bituminous coal.......] 377,000] 282,750 45] 1.59 
Water-gas and producer-gas mixed....| 185,000] 138,750 -20) =1.44 
Producer-gas..:. .....-+. IAS AAR 150,000] 112,500 15) 1.33 
Naphtha-gas, fuel 244 gals. per 1000 ft..{_ 306,365| 229,774 Ane .65 
Coal, $4 per ton, per 1,000,000 heat-units utilized ................-: 3 
Crude petroleum, 3 ets. per gal., per 1,000,000 heat-units. ........ 3B 


Mr. Reichhelm gives the following figures from practice in melting brass 
with coal and with naphtha converted into gas: 1800 lbs. of metal require 
1080 Ibs. of coal, at $4.65 per ton, equal to $2.51, or, say, 15 cents per 100 Ibs. 
Mr T.’s report : 2500 Ibs. of metal require 47 gals. of naphtha, at 6 cents per 
gal., equal to $2.82, or, say, 1114 cents per 100 lbs. , 


ILLUMINATING-GAS. 


Coalegas is made by distilling bituminous coal in retorts. The retort 
is usually a long horizontal semi-eylindrical or @ shaped chamber, holding 
from 160 to 300 lbs. of coal. The retorts are set in ‘‘ benches” of from 
3 to 9, heated by one fire, which is generally of coke The vapors distilled 
from the coal are converted into a fixed gas by passing through the retort, 
which is heated almost to whiteness, 

The gas passes out of the retort through an ‘‘ aseension-pipe ” into a lon 
horizontal pipe called the hydraulic main, where it deposits a portion o 
che tar it contains: thence it goes into a condenser, a series of iron’ tubes 
surrounded by cold water, where it is freed from condensable vapors, as 
“~mmonia-water, then into a washer, where it is exposed to jets of water, 
and into a scrubber, a large chamber partially filled with trays made of 
wood or iron, containing coke, fragments of brick or paving-stones, which 
are wet with a spray of water. By the washer and scrubber the gas is freed 
from the last portion of tar and ammonia and from some of the sulphur 
compounds. The gas is then finally purified from sulphur compounds by 
passing it through lime or oxide of iron. The gas is drawn from the hy- 
drauli¢ main and forced through the washer, scrubber, etc., by an exhauster 
or gas pump. 

The kind of coal used is generally caking bituminous, but as usually this 
coal is deficient in gases of high illuminating power, there is added to it a 
portion of cannel coal or other enricher. 

The following table, abridged from one in Johnson's Cyclopedia, shows 
the analysis, candle power, etc., of some gas-coals and enrichers; 


652 ILLUMINATING-GAS, 











ce, 

ef s su lt Coke per |$°* 

g a £8.;| 3 | ton of 2240/64 2 

Sal . ~ 

Gas-coals, ete. = i SS Tae iee S 5A 

= 3 i RS 5 BO a 3 

GS AI ge) & aS 

S a 4 BOF) SS lbs. |bush, Bes 
Bittsbure by Par ein. + eutes 30,(OW OLE 9ol a Ut lpemtereete Weiaie act tae ERE leencges lke acon 
Westmoreland, Pa...... 86.00} 58.00) 6.00) 10,642] 16.62] 1544 | 40 6420 
Sterling PO grays opshasevactotece 37.50] 56.90} 5.60!10,528] 18.81] 1480 36 8993 
Despard, W. V@.......e- 40.00} 53.380) 6.70}10,765| 20.41} 1540 36 2494 
Darlinetons Oo cn. seces ue 43.00} 40.00} 17.00} 9;800) 34.98} 1320 32 2806 
Petonia, W. Va . ...... | 46.00] 41.00} 18.00/13,200} 42.779} 1880 | 382 4510 

Grahamite, W. Va....... 53.50} 44.50} 2.00)15,000] 28.70} 1056 44 


The products of the distillation of 100 lbs. of average gas-coal are about as 
follows. They vary according to the quality of coal and the temperature of 
distillation. 

Coke, 64 to 65 lbs.; tar, 6.5 to 7.5 Ibs.; ammonia liquor, 10 to 12 lbs.; puri- 
fied gas, 15 to 12 lbs.; impurities and loss, 4.5% to 3.52. 

The composition of the gas by volume ranges about as follows: Hydro- 
gen, 38% to 48%; carbonic oxide, 2% to 14%; marsh-gas (Methane, CH,), 43% to 
31%; heavy hydrocarbons (CnHgn, ethylene, propylene, benzole vapor, etc.), 
4.5% to 4.5%; nitrogen, 1% to 3%. 

In the burning of the gas the nitrogen is inert; the hydrogen and carbonic 
oxide give heat but no light: The luminosity of the flame is due to the de- 
composition by heat of the heavy hydrocarbons into lighter hydrocarbons 
and carbon, the latter being separatedin a state of extreme subdivision. 
By the heat of the flame this separated carbon is heated to intense white- 
ness, and the illuminating effect of the flame is due to the light of incandes- 
cence of the particles of carbon. 

The attainment of the highest degree of luminosity of the flame depends 
upon the proper adjustment of the proportion of the heavy hydrocarbons 
(with due regard to their individual character) to the nature of the diluent 
mixed therewith. 

Investigations of Percy F. Frankland show that mixtures of ethylene and 
hydrogen cease to have any luminous effect when the proportion of ethy- 
lene does not exceed 10% of the whole. Mixtures of ethylene and carbonic 
oxide cease to have any luminous effect when the proportion of the former 
does not exceed 20%, while all mixtures of ethylene and marsh-gas have more 
or less luminous effect. The luminosity of a mixture of 10% ethylene and 904% 
marsh-gas being equal to about 18 candles, and that of one of 20% ethylene 
and 80% marsh-gas about 25 candles. The illuminating effect of marsh-gas 
alone, when burned in an argand burner, is by no means inconsiderable. 

For further description. see the Treatises on Gas by King. Richards, and 
Hnehes: also Appleton's Cyc. Mech., vol. i. p. $00. 

Water-gas.—Water-gas is obtained by passing steam through a bed of 
coal, coke, or charcoal heated to redness or beyond. The steam is decom- 
ee its hydrogen being liberated and its oxygen burning the carbon of 

e fuel, producing carbonic-oxide gas. The chemical reaction is, C + H,O 
= CO + 2H, or 2C + 2H,O = C+ CO, + 4H, followed by a splitting up of 
the CO,, making 2CO+ 4H. By weight the normal gas CO-+ 2H is com- 
posed of C + a a is = 28 parts CO and 2 parts H, or 93.33% CO and 6.67% H; 

12+ ate 
by volume it is composed of equal parts of carbonic oxide and hydrogen. 
Water-gas produced as above described has great heating-power, but no 
illuminating-power. It may, however, be used for lighting by causing it to 
heat to whiteness some solid substance, as is done in the Welsbach incan- 
descent light. 

Ap illuminating-gas is made from water-gas by adding to it hydrocarbon 
gases or vapors, which are usually obtained from petroleum or some of its 
products. <A history of the development of modern illuminating water-gas 
processes, together with a description of the most recent forms of apparatus, 
is given by Alex. C. Humphreys, in a paper on ‘‘ Water-gas in the United 
States,’ read before the Mechanical Section of the British Association fer 
Advancement of Science, in 1889. After describing many earlier patents, he 
states that success in the manufacture of water-gas may be said to date 


ANALYSES OF WATER-GAS AND COAL-GAS COMPARED, 653 


from 1874, when the process of T. S. C. Lowe was introduced. All the later 
most successful processes are the modifications of Lowe’s, the essential 
features of which were ‘‘ an apparatus consisting of a generator and super- 
heater internally fired; the superheater being heated by the secondary 
combustion from the generator, the heat so stored up in the loose brick of 
the superheater being used, in the second part of the process, in the fixing 
or rendering permanent of the hydrocarbon gases; the second part of the 
process consisting in the passing of steam through the generator fire, and 
the admission of oil or hydrocarbon at some point between the fire of the 
generator and the loose filling of the superheater.” 

The water-gas process thus has two periods: first the ‘* blow,” during 
which air is blown through the bed coal in the generator, and the partially 
burned gaseous products are completely burned in the superheater, giving 
up a great portion of their heat to the fire-brick work contained in it, and 
then pass out to a chimney; second, the ‘‘run” during which the air blast 
is stopped, the opening to the chimney closed, and steam is blown through ° 
the incandescent bed of fuel. The resulting water-gas passing into the car- 
buretting chamber in the base of the superheater is there charged with hy- 
droearbon vapors, or spray (such as naphtha and other distillates or crude 
oil) and passes through the superheater, where the hydrocarbon vapors be- 
come converted into fixed illuminating gases. From the superheater the 
combined gases are passed, as in the coal-gas process, through washers, 
scrubbers, etc., to the gas-holder. In this case, however, there is no am- 
monia to be removed. 

The specific gravity of water-gas increases with the increase of the heavy 
hydrocarbons which give itilluminating power. The following figures, taken 
from different authorities, are given by F. H. Shelton in a paper on Water- 
gas, read before the Ohio Gas Light Association, in 1894; 


Candle-power ... 19.5 20. 22.5 24, 25.4 26.3 28.3 29.6 .30to 31.9 
Sp. gr. (Air =1).. .571 .630 .589 .60to.67 .64 .602 .70 .65 .65to .71 
Analyses of Water=gas and Coalegas Compared. 


The following analyses are taken from areport of Dr. Gideon EH. Moore 
on the Granger Water-gas, 1885: 


Composition by Volume. Composition by Weight. 






















































































Water-gas. | Coal Water-gas. 
gas. 
leat ye -titolide 29 7) PANE rane 
Wor- Lake. ere: Wor- Lake 
cester. cester. . 
Nitrogen. ......... 2.64 3.85 2.15 | 0.04402 | 0.06175] 0.04559 
farbonic acid....| 0.14 0.30 3.01 | 0.00365 | 0.00753) 0.09992 
Oxygen........... 0.06 0.01 0.65 | 0.00114 | 0.00018] 0.01569 
Ethylene.......... 11.2 12.80 2.55 | 0.18759 | 0.20454] 0.05389 
Propylene ........ 0.00 0.00 Tee Lia | peter eet 8 cases: 0.03834 
Benzole vapor..../ 1.58 2 63 1.33 | 0.07077'| 0111700] 0.07825 
QGarbonic oxide...| 28.26 23.58 8.88 0.46934 | 0.37664) 0.18758 
Marsh-gas.... .-. 18.88 | 20.95 | 34.02 | 0.17928 | 0.19133] 0.41087 
Hydrogen ........ 37.20 | 35.88 | 46.20 | 0.04421 | 0.04103] 0.06987 
100.00 | 100.00 | 100.00 | 1.00000 | 1.00000} 1.00000 
Density : Theory.| 0.5825 | 0.6057 | 0.4580 eee ee 
Practice .| 0.5915 OM GOTS Me Metter cee alc scigterotsvecc «=| 0d kaka ae SH Uns eae 
B.T. U. from 1 cu. = Pie | eae 
ft.: Water liquid.| 650.1 Sg 0a TOI eS One nn RO tai rel): 
“~yapor.| 597.0 | 646.6 | 577.0 
Flame-temp.. .... 5311.2°F.| 5281.1°F.| 5202.9°F | 0222 | 2 
Av. candle-power.| 22.06 ee |. aaa eee 








The heating values (B. T. U.) of the gases are calculated from the analysig 
by weight, by using the multipliers given below (computed from results af 


654 ILLUMINATING-GAS. 


J. Thomsen), and multiplying the result by the weight of 1 cu. ft. of the gas 
at 62° F., and atmospheric pressure. 

The flame temperatures (theoretical) are calculated on the assumption of 
complete combustion of the gases in air, without excess of air. 

The candle-power was determined by photometric tests, using a pressure 
of 4-in. water-column, a candle consumption of 120 grains of spermaceti 
per hour, and a meter rate of 5 cu. ft. per hour, the result being corrected 
for a temperature of 62° F. and a barometric pressure of 30 in. It appears 
that the candle-power may be regulated at the pleasure of the person in 
charge of the apparatus, the range of candle-power being from 20 to 29 
candles, according to the manipulation employed. 


Calorific Equivalents of Constituents of Illuminating= 


gat. 
Heat-units from 1 lb. Heat-units from 1 lb, 
Water Water Water Water 
: Liquid. Vapor. Liquid. Vapor. 
Ethylene......... 21,524.4 20,184.8 Carbonic oxide.. 4,395.6 4,395.6 
Propylene........ 21, 222.0 19,834.2 Marsh-gas....... 24,021.0 21,592.8 
Benzole vapor.... 18,954.0 17,847.0 Hydrogen....... 61,524.0 51,804.0 


Efficiency of a Water-gas Plant.—The practical efficiency of an 
illuminating water-gas setting is discussed in a paper by A. G. Glasgow 
(Proc. Am. Gaslight Assn., 1890), from which the following is abridged : 

The results refer to 1000 cu. ft. of unpurified carburetted gas, reduced te 
60° F. The total anthracite charged per 1000 cu. ft. of gas was 33.4 lbs., ash 
and unconsumed coal removed 9.9 lbs., leaving total combustible consumed 
23.5 lbs., which is taken to have a fuel-value of 14500 B. T. U. per pound, or 


a total of 340,750 heat- units. 








Composi-| Weight |Composi- 






































tion by per tion by # ase: 

Volume./|100 cu. ft.| Weight. ; 

(CO, +H,S.. 3.8 .465842 | .09647 02088 

pea ines sarees Bet 14.6 1.139968 . 23607 08720 

(St. Seater 28.0 2.1868 - 45285 11226 

I. Carburettea 4 (Or aI Fe medawersese 17.0 75854 . 15710 09314 

Wiater-Pas. MES stan. c oc. 35.6 .1991464| .04124 14041 

| tS, Cte 1.0 ‘078596 | [01627 | 00397 

lL 100.0 | 4.8288924| 1.00000 | .45786 

GOs toecstnce 3.5 -429065 .1019 .02205 

| COS Eamon ole 43.4 3.389540 .8051 . 19958 

Il. Uncarburetted 4 Pests aes sterse:. 51.8 289821 0688 23424 

gas. INYG cidisste ops peneen 1.3 .102175 .0242 .00591 

100.0 | 4.210601 | 1.0000 | .46178 

OO OP ei 9 3 17.4 2.133066 2464 .05842 

Tis Blast. products | O......ccce«.- 3.2 .2856096} .0329 .00718 

escaping from? N............ 79.4 6.2405224) .7207 . 17585 
superheater. | —— ———_} ——_____|___- 2 eee E 

100.0 8.6591980| 1.0000 . 23645 

CO, ae 12-3 1. 189128 1436 03107 

TAME Generator ee ceces saves . 5 BAS 1 “Al . 41 4% 
100.0 8.277513 | 1.0000 . 240692 


The heat energy absorbed by the apparatus is 23.5 x 14,500 = 340,750 heat- 
units = A. Its disposition is as follows: 

BP, the energy of the CO produced; 

C, the energy absorbed in the decomposition of the steam; 

D, the difference between the sensible heat of the escaping illuminating: 


gases and that of the entering oil; 


E, the heat carried off by the escaping blast products; 


F, the heat lost by radiation from the shells: 


EFFICIENCY OF A WATER-GAS PLANT. 655 


G. the heat carried away from the shel!s by convection (air-currents); 

H, the heat rendered latent in the gasification of the oil; 

I, the sensible heat in the ash and unconsumed coal recovered from the 
generator. ; 

The heat equation is d= B+C+D+#H+1+F4+G6+4+4H41; A being 
known. A comparison of the CO in Tables I and II show that By or 64.5% 
of the volume of carburetted gas is pure water-gas, distributed thus: CO,, 
2.38%; CO, 28.0%; H, 33.4%; N, 0.8%; = 64.5%. 11b. of CO at 60° F. = 13531 cu. 
CO per 1000 cu. ft. of gas = 280 + 13.531 = 20.694 lbs. Energy of the CO 
= 20.694 x 4895.6 = 91,043 heat-units, = B. 1 1b. of H at 60° F. = 189.2 cu. 
ft. H per M of gas = 334 + 1892 = 1.7653 lbs. Energy of the H per lb. 
(according to Thomsen, considering the steam generated by its combustion 
to be condensed to water at 75° F.) = 61,524 B. T. U. In Mr. Glasgow’s ex- 
periments the steam entered the generator at 331° F.; the heat required to 
raise the product of combustion of 1 lb. of H, viz., 8.98 los. H,O, from water 
at 75° to steam at 331° must therefore be deducted from Thomsen’s figure, or 
61,524 — (8.98 * 1140.2) = 51,285 B. T. U. per lb. of H. Energy of the H, then, 
is 1.7653 X 51,285 = 90,533 heat-units, = C. The heat lost due to the sensible 
beat in the illuminating-gases, their temperature being 1450° F., and that of 
the entering oil 235° F., is 48.29 (weight) x .45786 sp. heat x 1215 (rise of tem: 
perature) = 26,864 heat-units = D. 

(The specific heat of the entering oil is approximately that of the issuing 
gas.) 

The heat carried off in 1000 cu. ft. of the escaping blast products is 86.592 
(weight) x .23645 (sp. heat) x 1474° (rise of temp.) = 30,180 heat-units: the 
temperature of the escaping blast gases being 1550° F., and that of the 
entering air 76° F. But the amount of the blast gases, by registra- 
tion of an anemometer, checked by a calculation from the analyses of the 
blast gases, was 2457 cubic feet for every 1000 cubic feet of carburetted gas 
made. Hence the heat carried off per M. of carburetted gas is 30,180 x 
2.457 = 74,152 heat-units = LH. 

Experiments made by a radiometer covering four square feet of the shell 
of the apparatus gave figures for the amount of heat lost by radiation 
= 12,454 heat-units = F, and by convection = 15,696 heat-units = G. 

The heat rendered latent by the gasefication of the oil was found by taking 
the difference between all the heat fed into the carburetter and super- 
heater and the total heat dissipated therefrom to be 12,841 heat-units = H. 
The sensible heat in the ash and unconsumed coal is 9.9 lbs.  1500° x .25 
(sp. ht.) = 3712 heat-units =: J. 

The sum of all the items B+ C+D4+ #4 F+ GH A+ I= 827,295 heat- 
units, which substracted from the heat energy of the combustible consumed, 
340,750 heat-units, leaves 13,455 heat-units, or 4 per cent, unaccounted for. 

Of the total heat energy of the coal consumed, or 340,750 heat-units, the 
energy wasted is thesum of items D, #, F, G,and J, amounting to 132,878 
neat-units, or 89 per cent; the remainder, or 207,872 heat-units, or 61 per 
cent, being utilized. The efficiency of the apparatus as a heat machine is 
therefore 61 per cent. 

Five gallons, or 35 lbs. of crude petroleum were fed into the carburetter 
per 1000 cu.ft. of gas made; deducting 5 lbs. of tar recovered, leaves 30 lbs. 
xX 20,000 = 600,000 heat-units as the net heating value of the petroleum used. 
Adding this to the heating value of the coal, 340,750 B. T. U., gives 940,750 
heat-units, of which there is found as heat energy in the earburetted gas, as 
in the table below, 764,050 heat units, or 81 per cent, which is the commer- 
cial efficiency of the apparatus, i.e., the ratio of the energy contained in 
the finished product to the total energy of the coal and oil consumed. 


The heating power per M. cu. ft. of } The heating power per M. of the 
the carburetted gas is uncarburetted gas is 

CO, 38.0 CO, 35.0 

C3H.,* 146.0 & .117220 & 21222.0 = 363200/CO 434.0 x .078100 « 4395.6 = 148991 
CO ~~ 280.0 x .078100 x 4895.6= 96120/H 518.0 x .005594 x 61524.0 = 178277 
CH, 170.0 x .044620 x 24021.0 = 182210|N 13.0 
H 856.0 X .005594 x 61524.0 = 122520 
N 10.0 1000.0 327268 


—___- 


1000.0 764050 


fan heating value of the illuminants CraH,, is assumed to equal that 
oO git. 


iad 
<5 











656 ILLUMINATING-GAS. 


The candle-power of the gas is 31, or 6.2 candle-power per gallon of oil 
used. The calculated specific gravity is .6355, air being 1. 

For description of the operation of a modern carburetted water-gas 
plant, see paper by J. Stelfox, Hig’g, July 20, 1894, p. 89. 

Space required for a Water-gas Plant.—Mr. Shelton, taking 
15 modern plants. of the form requiring the most floor-space, figures the 
average floor-space required per 1000 cubic feet of daily capacity as follows: 


‘Water-gas Plants of Capacity Require an Area of Floor-space for 
in 24 hours of each 1000 cu. ft. of about 
1005000, CUlbieHfe Sty Att cashiers otal tates iste sate 4 square feet. 
200,000 ‘** Va oh sn Beh Sint ost aed eel sti « 3.5- ° 4 
400,000 ‘S SACI, PAA ARS bert ea, 2.75 ss 
600,000 *‘ Le ee Semen Se SAE, A ee: Pend PR 2 to 2.5 sq. ft. 
% to 10 million cubic feet.............. biohwtctebiets 1.25 to 1.5 sq. ft. 


These figures include scrubbing and condensing rooms, but not boiler and 
engine rooms. In coal-gas plants of the most modern and compact forms one 
with 16 benches of 9 retorts each, with a capacity of 1,500,000 cubic feet per 
24 hours, will require 4.8 sq. ft. of space per 1000 cu. ft. of gas, and one of 6 
benches of 6 retorts each, with 300,000 cu. ft. capacity per 24 hours will re- 
quire 6 sq. ft. of space per 1000 cu. ft. The storage-room required for the 
gas-making materials is: for coal-gas, 1 cubic foot of room for every 232 
cubic feet of gas made; for water-gas made from coke, 1 cubic foot of room 
for every 378 cu. ft. of gas made; and for water-gas made from anthracite, 
1 cu. ft. of room for every 645 cu. ft. of gas made. 

The comparison is still more in favor of water-gas if the case is considered 
of a water-gas plant added as an auxiliary to an existing coal-gas plant; 
for, instead of requiring further space for storage of coke, part of that 
already required for storage of coke produced and not at once sold can be 
cut off, by reason of the water-gas plant creating a constant demand for 
more or less of the coke so produced. 

Mr. Shelton gives a calculation showing that a water-gas of .625 sp. gr. 
would require gas-mains eight per cent greater in diameter than the same 
quantity coal-gas of .425 sp. gr. if the same pressure is maintained at the 
holder. The same quantity may be carried in pipes of the same diameter 
if the pressure is increased in proportion to the specific gravity. With the - 
same pressure the increase of candle-power about balances the decrease of 
flow. With five feet of coal-gas, giving, say, eighteen candle-power, 1 cubic 
foot equals 3.6 candle-power; with water-gas of 23 candle-power, 1 cubic 
foot equals 4.6 candle-power, and 4 cubic feet gives 18.4 candle-power, or 
more than is given by 5 cubic feet of coal-gas. Water-gas may be made 
from oven-coke or gas-house coke as well as from anthracite coal, A water- 
gas plant may be conveniently run in connection with a coal-gas plant, the 
surplus retort coke of the latter being used as the fuel of the former, 

In coal-gas making it is impracticable to enrich the gas to over twenty 
candle-power without causing too great a tendency to smoke, but water-gas 
of as high as thirty candle-power is quite common. A mixture of coal-gas 
and water-gas of a higher C.P. than 20 can be advantageously distributed. 

Fuel-value of, iluminating=-gas.—E. G. Love (School of Mines 
Qtly, January, 1892) describes F. W. Hartley’s calorimeter for determining 
the calorific power of gases, and gives results obtained in tests of the car- 
buretted water-gas made by the municipal branch of the Consolidated Co. 
of New York. The tests were made from time to time during the past two 
years, and the figures give the heat-units per cubic foot at 60° F. and 30 
inches pressure: 715, 692, 725, 732, 691, 738, 735, 703, 734, 730, 731,727. Average, 
721 heat units. Similar tests of mixtures of coal- and water-gases made by 
other branches of the same company give 694, 715, 684, 692, 727, 665, 695, and 
686 heat-units per foot, or an average of 694.7. The average of all these 
tests was 710.5 heat-units, and this we may fairly take as representing the 
calorific power of the illuminating gas of New York. One thousand feet of 
this gas, costing $1.25, would therefore yield 710,500 heat-units, which would 
be equivalent to 568,400 heat-units for $1.00. 

Jne common coal-gas of London, with an illuminating power of 16 to 17 
candles, has a calorific power of about 668 units per foot, and costs from 60 
to 70 cents per thousand. 

The product obtained by decomposing steam by incandescent carbon, as 
SOe cE a in the Motay process, consists of about 40% of CO, and a little over 

of H. 


FLOW OF GAS IN PIPES. 657 


_This mixture would have a heating-power of about 300 units per cubic foot, 
and if sold at 50 cents per 1000 cubic feet would furnish 600,000 units for $1.00, 
as compared with 568,400 units for $1.00 from illuminating gas at $1.25 per 1000 
cubic feet. This illuminating-gas if sold at $1.15 per thousand would there- 
fore be a more economical heating agent than the fuel-gas mentioned, at 50 
cents per thousand, and be much more advantageous than the latter, in that 
one main, service, and meter could be used to furnish gas for both lighting 
and heating. 

A large number of fuel-gases tested by Mr. Love gave from 184 to 470 heat- 
units per foot, with an average of 309 units. 

Taking the cost of heat from illuminating-gas at the lowest figure given 
by Mr. Love, viz., $1.00 for 600,000 heat-units, it is a very expensive fuel, equal 
to coal at $40 per ton of 2000 Ibs., the coal having a calcrific power of only 
12,000 heat-units per pound, or about 83% of that of pure carbon: 


600,000 : (12,000 « 2000) :: $1 : $40. 


FLOW OF GAS IN PIPES, 


The rate of flow of gases of different densities, the diameter of pipes re- 
quired, etc., are given in King’s Treatise on Coal Gas, vol. ii. 374, a follows: 


8 Qisl 


If d = diameter of pipe in inches, d= ph tied ES 
Q@ = quantity of gas in cu. ft. per (13850)? 
] iD f a Q?sl 
= length of pipe in yards, h= —— 
h = pressure in inches of water, — | (1350)2dS ° 
oo. — 


ifi it i , air be- Sh 
Pie ‘s gravity of gas, air | Q = rss0at4/ SE = 1300 doh 


; ah 
Molesworth gives Q = 1000 Te 


6 
J. P. Gill, Am, Gas-light Jour. 1904, gives Q = 12914 / —-" 


s(t -+ d)’ 

This formula is said to be based on experimental data, and to make allow- 
ance for obstructions by tar, water, and other bodies tending to check the 
flow of gas through the pipe. 


A set of tables in Appleton’s Cyc. Mech. for flow of gas in 2. 6, and 12 in. 
pipes is calculated on the supposition that the quantity delivered varies 
as the square of the diameter instead of as d2 x Vd, or Vd5. 

These tables give a flow in large pipes much less than that calculated by 
the formule above given, as is shown by the following example. Length of 
pipe 100 yds., specific gravity of gas 0.42, pressure 1-in. water-column 


2-in. Pipe. 6-in. Pipe. 12-in. Pipe. 


Q 5 18504 Je eee oe | 11 18,368 103,912 
oi" | 

Q= 10004 / at rcececerceceee 873 13,606 76,972 

Fae ty Su he Li late Pwasith 16,327 98,845 
s(l + d) ; ; 

Table in App. Cyc........ Ate 1290 11,657 46,628 


An experiment made by Mr. Clegg, in london. with a 4-in. pipe, 6 miles 
long, pressure 3in. of water, specific gravity of gas .398, gave a discharge 
into the atmosphere of 852 cu. ft. per hour, after a correction of 33 cu. ft. 
was made for leakage. 


Substituting this value, 852 cu. ft., for Qin the formula Q = C V/dbh ~ sl, 
we find C, the coefficient, = 997, which corresponds nearly with the formula 
given by Molesworth, 


ILLUMINATING-GAS, 


Services for Lamps. (Molesworth.) 


Ft. from Require Ft. from Requ.ce 
Lamps. Main. _Pipe-bore. Lamps Main. _Pipe-bore. 
Qrrsivavece 40 34 in. beer or ris 130 lin. 
4i.dséisies 40 1 in. 20. 55.54.083 150 14 in 
ae pee 50 5g in EME ee en -« 180 144 in, 
lO Keser se <x 100 3% in 30. 200 134 in, 
(In cold climates no service less than 34 in. should be used.) 
Maximum Supply of Gas through Pipes in cu, ft. per 


Hour, Specific Gravity being taken at .45, calculated 
from the Formula Q = 1000 //d5h ~ sl, (Molesworth.) 


LENGTH OF PIPE = 10 YARDS. 





Pressure by the Water-gauge in Inches. 





























Diameter 
of Pipe in 
pRele sal dtaadat 8 1a [eB ty eer | DL ya Seem aOR nae 
34 13 18 22 26 29 31 34 36 88 41 
14 26 37 46 53 59 64 70 74 79 83 
34 %3 103 126 145 162 187 192 205 218 230 
1 149 211 258 298 333 365 394 422 447 71 
1% 260 868 451 521 582 638 689 737 781 823 
1144 411 581 711 821 918 | 1006 | 1082 | 1162 | 1232 | 1299 
2 848 | 1192 | 1460 } 1686 | 1886 | 2066 | 2231 | 2385 | 2530 | 2667 
LENGTH OF Pipz = 100 YARDs. 
Pressure by the Water-gauge in Inches, 
s1 | 22 Pes 4 5 is) 1.0 | 1.25 | 1.5 2 2.5 
4 Shree 14} 17 19 23 26 29 32 36 42 
A 23| 32) 42 46 51 63 73 81 89 103 115 
1 47 7} 82 94 105 129 149 167 183 211 236 
1% 82) 116) 143) 165 184 225 269 291 319 868 412 
1% 130} 184} 225; 260 290 356 411 459 503 581 649 , 
2 267| 377) 462) 5383 596 730 843 943 | 1083 | 1193 | 1333 
214 466/ 659] 807} 982 | 1042 | 1276 | 147% 1647 | 1804 } 2088 | 2329 
3 735|1039|1270] 1470 | 1643 | 2012 | 23823 | 2598 | 2846 | 3286 | 3674 
344 1080|1528)1871; 2161 | 2416 | 2958 | 8416 | 3820 | 4184 | 48381 | 5402 
4 1508/2133)2613| 3017 | 8873 | 4131 | 4770 | 5333 | 5842 | 6746 | 7542 
LENGTH oF PIPE = 1000 YaRDs. 
Pressure by the Water-gauge in Inches. 
5 afte) 1.0 Bs 2.0 2.5 3.0 
1 33 41 47 58 67 5 82 
14% 92 113 130 159 184 205 226 
2 189 231 267 827 377 422 462 
24 829 403 466 571 659 G37 807 
8 520 636 735 900 1039 1162 127 
4 1067 1306 1508 1847 2133 2885 2613 
5 1863 2282 2635 38227 3727 4167 4564 
6 2939 8600 4157 5091 5879 6573 720C 


STEAM. 659 


LENGTH OF PIPE = 5000 YARDS. 








Diameter Pressure by the Water-gauge in Inches. 
of Pipe 
in 
Inches. 1.0 1:5 2.0 2.5 3.0 
2 119 146 169 189 207 
3 329 402 465 520 569 
4 67 826 955 1067 1168 
5 1179 1443 1667 1863 2041 
6 1859 2277 2629 2939 3220 
q 2733 3347 3865 4321 47384 
8 3816 4674 53897 6034 6610 
9 5123 6274 9245 8100 887 
10 6667 8165 9428 10541 11547 
12 10516 12880 14872 16628 18215 


Mr. A. C. Humphreys says his experience goes to show that these tables 
give too small a fiow, but it is difficult to accurately check the tables, on ac- 
count of the extra friction introduced by rough pipes, bends, etc. For 
bends, one rule is to allow 1/42 of an inch pressure for each right-angle bend. 

Where there is apt to be trouble from frost if is well to use no service of 
less diameter than 34 in., no matter how short it may be. In extremely cold 
climates this is now often increased to 1 in., even for a single lamp. The best 
practice in the U. S. now condemns any service less than 34 in, 


STEAM. 


The Temperature of Steam in contact with water depends upon 
the pressure under which it is generated. At the ordinary atmospheric 
pressure (14.7 lbs. per sq. in.) its temperature is 212° F, As the pressure is 
increased, as by the steam being generated in a closed vessel, its témpera- 
ture, and that of the water in its presence, increases. 

Saturated Steam is steam of the temperature due to its pressure— 
not superheated 

Superheated Steam is steam heated to a temperature above that due 
to its pressure. 

Dry Steam is steam which contains no moisture. It may be either 
saturated or superheated. 

Wet Steam is steam containing intermingled moisture, mist, or spray. 
It has the same temperature as dry saturated steam of the same pressure. 

Water introduced into the présence of superheated steam will flash into 
vapor until the temperature of the steam is reduced to that due its pres- 
sure. Water in the presence of saturated steam has the same temperature 
as the steam. Should cold water be introduced, lowering the témperature 
of the whole mass, some of the steam will be condensed, reducing the press- 
ure and temperature of the remainder, until an equilibrium is established. 

Wemperature and Pressure of Saturated Steam,.—The re- 
lation between the temperature and the pressure of stéam. according to 
Regnault’s eet a ae is expressed by the formula (Buchanan’s, as given 


by Clark) t= 993544 — log p 


per square inch and ¢ the temperature of the steam in Fahrenheit degrees. 
It applies with accuracy between 120° F. and 446° F., corresponding to pres- 
sures of from 1.68 lbs. to 445 lbs. per square inch. (For other formule see 
Wood's and Peabody’s Thermodynamices.) 

Total Heat of Saturated Steam (above 32° F.).—According to 
Regnault’s experiments, the formula for.total heat of steam is H = 1091,7-+ 
.805(¢ — 32°), in which ¢ is température Fahr., and H the heat-units. (Ran- 
kine and many others; Clark gives 1091.16 instead of 1091.7.) 

Latent Heat of Steam .—tThe formula for latent heat of steam; as 
given by Rankine and others, is L = 1091.7 — .695(¢ — 32°). Clausius’s for- 
mula, in Fahrenheit units, as given by Clark, is L = 1092.6 — .708(¢ — 32°). 


a 


— 371.85, in which p is the pressure in pounds 


660 | STEAM. 


The total heat in steam (above 32°) includes three elements: 

1st. The heat required to raise the temperature of the water to the tem~- 
perature of the steam. 

2d. The heat required to evaporate the water at that temperature, called 
internal latent heat. 

3d. The latent heat of volume, or the external work done by the steam in 
making room for itself against the pressure of the superincumbent atmos- 
phere (or surrounding steam if inclosed in a vessel). 

The sum of the last two elements is called the latent heat of steam. In 
Buel’s tables (Weisbach, vol. ii., Dubois’s translation) the two elements are 
given separately. 

Latent Heat of Volume of Saturated Steam, (External 
Work.)—The following formulas are sufficiently accurate for occasional use 
within the given ranges of pressure (Clark, S. E.): 


From 14.7 lbs. to 50 lbs, total pressure per square inch... 55.900 -++ .0772¢. 
From 50 lbs. to 200 Ibs. total pressure per square inch.... 59.191 +- .0655é. 


Heat required to Generate 1 Ib. of Steam from water at 32° F. 
, Heat-units, 
Sensible heat, to raise the water from 32° to 212° =.... 180.9 
Latent heat, 1, of the formation of steam at 212° =.... 894.0 
2, of expansion against the atmospheric 
pressure, 2116.4 lbs. per sq. ft. 26.36 cu. ft. 
= 55,786 foot-pounds + 778 =........ eee, bide obne ft 


Total heat above 82° F......... 1146.6 


The Heat Unit, or British Thermal Unit.—The definition of 
the heat-unit used in this work is that of Rankine, accepted by most modern 
writers, viz., the quantity of heat required to raise the temperature of 1 Ib. 
of water 1° F. at or near its temperature of maximum density (39.1° F.). 
Peabody’s definition, the heat required to raise a pound of water from 62° 
to 63° iy is not generally accepted. (See Thurston, Trans. A. S. M. E,, 
xiii. 351. 

Specific Heat of Saturated Steam,.—The specific heat of satu- 
rated steam is .305, that of water being 1; or itis 1.281, if that of air be 1. 
The expression .305 for specific heat is taken in a compound sense, relating — 
to changes both of volume and of pressure which takes place in the eleva- 
tion of temperature of saturated Steam. (Clark, S. E.) 

This statement by Clark is not strictly accurate. When the temperature 
of saturated steam is elevated, water being present and the steam remain- 
ing saturated, water is evaporated. To raise the temperature of 1 Ib. of © 
water 1° F’. requires 1 thermal unit, and to evaporate it at 1° F. higher would 
require 0.695 /ess thermal unit, the latent heat of saturated steam decreas- 
ing 0.695 B.T.U. for each increase of temperature of 1° F. Hence 0.305 is 
the specific heat of water and its saturated vapor combined. 

When a unit weight of saturated steam is increased in temperature and in 
pressure, the volume decreasing so as to just keep it saturated, the specific 
heat is negative, and decreases as temperature increases. (See Wood, 
Therm., p. 147; Peabody, Therm., p. 93.) 

Density and Volume of Saturated Steam.—The density of 
steam is expressed by the weight of a given volume, say one cubic foot; and 
the volume is expressed by the number of cubic feet in one pound of steam. 

Mr. Brownlee’s p= pression for the density of saturated steam in terms of 
5058" or log D = .941 log p—2.519, in which Dis the den- 
sity, and p the pressure in pounds per square inch. In thisexpression, p*®4} — 
is the equivalent of p raised to the 16/17 power, as employed by Rankine. 

The volume v being the reciprocal of the density, 


36 
pe ae or log v = 2.519 — .941 log p. 


the pressure is D = 


Relative Volume of Steam.—tThe relative volume of saturated 
steam is expressed by the number of volumes of steam produced from cne 


STEAM. 661 


volume of water, the volume of water being measured at the temperature 
39° F. The relative volume is found by multiplying the volume in cu. ft. of 
one lb. of steam by the weight of a cu. ft. of water at 39° F., or 62.425 lbs. 

Gaseous Steam.—When saturated steam is superheated, or sur- 
charged with heat, it advances from the condition of saturation into that of 
gaseity. The gaseous state is only arrived at by considerably elevating the 
temperature, supposing the pressure remains the same. Steam thus suffi- 
ciently superheated is known as gaseous steam or steam gas. 

Total Heat of Gaseous Steam.—Regnault found that the total 
heat of gaseous steam increased, like that of saturated steam, uniformly 
with the temperature, and at the rate of .475 thermal units per pound for 
each degree of temperature, under a constant pressure. 

The general formula for the total heat of gaseous steam produced from 
1 pound of water at 32° F. is H = 1074.6 + .475t. [This formula is for vapor 
generated at 32°. It is nottrueif generated at 212°, or at any other tempera- . 
ture than 82°. (Prof. Wood.)] 

The Specific Heat of Gaseous Steam is .475, under constant 
pressure, as found by Rexuault. It is identical with the coefficient of in- 
crease of total heat for each degree of temperature. [This is at atmospheric 
pressure and 212° F. He found it not true for any Other pressure. Theory 
indicates that it would be greater at higher temperatures. (Prof. Wood.)| 

The Specific Density of Gaseous Steam is .622, that of air being 
1. That is to say, the weight of a cubic foot of gaseous steam is about five 
eighths of that of a cubic foot of air, of the same pressure and temperature. 

The density or weight of a cubic foot of gaseous steam is expressible by 
the same formula as that of air, except that the multiplier or coefficient is 
less in proportion to the less specific density. Thus, 


2.7074p X .622 _ 1.684p 

t + 461 ~ t+ 461’ 
in which D’ is the weight of a cubic foot of gaseous steam, p the total pres- 
sure per square inch, and ¢ the temperature Fahrenheit. 

Superheated Steam.—The above remarks concerning gaseous steam 
are taken from Clark’s Steam-engine. Wood gives for the total heat (above 
82°) of superheated steam H = 1091.7 + 0.48(¢ — 32°). 

The following is abridged from Peabody (Therm., p. 115, etc.). 

_ When far removed from the temperature of saturation, superheated steam 
follows the laws of perfect gases very nearly, but near the temperature of 
saturation the departure from those laws is too great to allow of calculations 
by them for engineering purposes. 

The specific heat at constant pressure, Cp, from the mean of three experi- 
ments by Regnault, is 0.4805. 

Values of the ratio of Cp to specific heat at constant volume: 


Dye 


Pressure p, pounds per square inch.. 5 50 100 200 @&§=©300 
Ratio Cp = Cv=k= 1.885 1.3882 1.380 1.324 1.316 


Zeuner takes k as a constant = 1.333. 


SpeciFIC HEAT AT CONSTANT VOLUME, SUPERHEATED STEAM. 


‘Pressure, pounds per square inch..... 5 50 100 200 300 
Specific heat Cus... cig awke 02 sens lee yiete 0.3851 .848 .346 .344 .341 


It is quite as reasonable to assume that Cv is a constant as to suppose that 
Cp is constant, as has been assumed. If we take Cv to be constant, then Cp 
will appear as a variable. 

If p = pressure in lbs. per sq. ft., vy = volume in cubic feet, and T= 


temperature in degrees Fahrenheit + 460.7, then pu = 93.5T — 971ps. 
Total heat of superheated steam, H = 0.4805(7' — 10.38p¢) + 857.2. 


“he ERationalization of Regnault’s Experiments on 
Steam. (J. McFarlane Gray, Proce. Inst. M. E., July, 1589.)--The formulas 
constructed by Regnault are strictly empirical, and were based entirely on 
his experiments. They are therefore not valid beyond the range of temper- 
atures and pressures observed. 

Mr. Gray has made a most elaborate calculation, based not on experiments 
but on fundamental principles of thermodynamics. from which he deduces 
formule for the pressure and total heat of steam, and presents tables calcu- 


662 STBAM, 


lated therefrom which show substantial agreement with Regnault’s figures, 
He gives the following examples of steam-pressures calculated for temper*+ 
tures beyond the range of Regnault’s experiments. 








Temperature. Pounds per | Temperature. Pounds per 
oF Fahr. Aq; C. Fahr a Ol 
230 446 406.9 340 644 2156.2 
240 464 488.9 860 680 2742.5 
250 482 579.9 380 716 8448.1 
260 500 691.6 400 152 4300.2 
280 536 940.0 415 vue 5017.1 
300 572 1261.8 427 800.6 5659.9 
820 608 1661.9 





These pressures are higher than those obtained by Regnault’s formula, 
which gives for 415° C. only 4067.1 lbs. per square inch. 

Table of the Properties of Saturated Steam.—In the table 
of properties of saturated steam on the following pages the figures for tem- 
perature, total heat, and latent heat are taken, up to 210 lbs. absolute pres- 
sure, from the tables in Porter’s Steam-engine Indicator, which tables have 
been widely accepted as standard by American engineers. The figures for 
total heat, given in the original as from 0° F., have been changed to heat 
above 32° F. The figures for weight per cubie foot and for cubic feet per 
pound have been taken from Dwelshauvers-Dery’s table, Trans. A.S. M. E., 
vol. xi., as being probably more accurate than those of Porter. The figures 
for relative volume are from Buel’s table, in Dubois’s translation of Weis- 
bach, vol. ii. They agree quite closely with the relative volumes calculated 
from weights as given by Dwelshauvers. From 211 to 219 Ibs. the figures 
for temperature, total heat, and latent heat are from Dwelshauvers’ table ; 
and from 220 to 1000 lbs. all the figures are from Buel’s table. The figures 
have not been carried out to as many decimal places as they are in most of the 
tables given by the different authorities ; but any figure beyond the fourth 
significant figure is unnecessary in practice, and beyond the limit of error of 
the observations and of the formule from which the figures were derived. 


Weighs of 1 Cubic Foot of Steam in Decimals of a Pound, 
Comparison of Different Authorities. 








A S| 
oo Weight of 1 cubic foot Oo. Weight of 1 cubic foot 
S : ‘ 
See according to— ssf according to— 
Ot Por- Pea- §2 = ™) Por- |, Pea. 
<A As Clark} Buel.|Dery. body. a yf ter, |Clark| Buel.|Dery. body 














1 |.0030 | .003 |.00303) .00299| .00299§ 120 |.27428} .2788) .2735) .2724) .2605 








14.7] .08797| .0380) .03793}......|.0376 140 |.31386) .3162] .3163| .3147|.3113 
20. |.0511 | .0507).0507 |.0507 | .0502 160 |.35209} .3590} .8589) .3567) .3530 
40 |.0994 | .0974/.0972 | .0972 |.0964 180 |.38895, .4009} .4012) .3983) .3945 
60 |.1457 | .1425).1424 |.1422 |.1409 200 |.42496) .4431| .4433) .4400} 4359 
80 |.19015) .1863).1866 |.1862 |.1843 § 220 ]|..... 4842) .4852) 22.1477 
100 |.28302| .23071.2803 |.2296 |.2271 240 5248! 5270 5186 








There are considerable differences between the figures of weight and vol- 
ume of steam as given by different authorities. Porter’s figures are based 
on the experiments of Fairbairn and Tate. The figures given by the other 
authorities are derived from theoretical formule which are believed to give 
more reliable results than the experiments. The figures for temperature, 
total heat, and latent heat as given by different authorities show a practical 
agreement, all being derived from Regnault’s experiments. See Peabody’s 
Tables of Saturated Steam; also Jacobus, Trans, A, §. M, E,, vol, xii., 593. 


Properties of Saturated Steam. 


STEAM. 


663 





Vacuum Gauge, 
Inches of Mer- 


Gauge 
Pressure 


2.3 


Wwte witswe wammwo wawwo wo 


£2 2939 Need eel cel ee god 


Absolute Press- 
ure, lbs. per 
square inch. 


=>) 
ie) 
Ve) 


"122 


e 
_ 
Si 
ion 


0204 


359 
-502 
692 
943 


OWIRo Mowe 


Temperature 
Fahrenheit. 








ete eee 








Total Heat 
above 82° F, 
In the | In the 
Water | Steam 
h H 
Heat- | Heat- 
units. | units. 

0 1091.7 
8. 1094.1 
18. 1097.2 
28.01 | 1100.2 
38.02 } 1103.3 
48.04 | 1106.3 
58.06 | 1109.4 
68.08 | 1112.4 
70.09 | 1113.1 
94.44 | 1120.5 
109.9 1D iso | 
121.4 1128.6 
180.7 | 1181.4 
1388.6 | 1183.8 
145.4 1135.9 
1515» 11ST 
156.9 1139.4 
161.9 | 1140.9 
166.5 1142.3 
170.7 1143.5 
174.7 1144.7 
178.4 1145.9 
180.9 | 1146.6 , 
181.9 | 1146.9 
185.3 1147.9 
188.4 1148.9 
191.4 1149 8 
194.3 1150.6 
197.0 | 1151.5 
199.7 1152.2 
202.2 1153.0 
204.7 At 
207.0 | 1154.5 
# 209.3 | 1155.1 
211.5 de®. 8 
PDB 1156.4 
OI hed bagel 
217.8 Ae 
219.7 | 1158.3 
221.6 8 
223.5 | 1159.4 
225.3 9 
227.1 1160.5 
228.8 | 1161.0 
230.5 | 1161.5 | 
232.1 1162.0 











° 2 ‘= 
HH .| 8s 
Saeee | Taso 
o-<'a | See 
aa 15 oH 
BL OBES Oe 
Sue | ee 
gum | ops 
4 iar 
1091.7 | 208080 
1086.1 | 154330 
1079.2 | 107630 
1072.2 | 76370 
1065.3 | 54660 
1058.3 | 39690 
1051.3 992990 
1044.4 21830 
1043.0 | 20623 
1026.0 10730 
1015.3 W325 
1007.2 5588 
1000.7 4530 
995.2 8816 
990.5 8302 
986.2 2912 
982.4 2607 
979.0 2361 

975.8 2159 
972.8 1990 
970.0 1846 
967.4 1721 
965.7 1646 
965.0: 1614 
962.7 1519 
960.5 1434 
958.3 1359 
956.3 1292 | 
954.4 1231 
952.6 1176 
950.8 1126 
949.1 1080 
947.4 1038 
945.8 | 998.4 
944.3 | 962.3 
942.8 | 928.8 
941.3 897.6 
939.9 | 868.5 
938.9 | 841.3 
937.2 | 815 8 
935.9 | 791.8 
9384.6 | 769.2 
933.4 | 748.0 
932.2 | 727.9 
931.0 | 708.8 
929.8 | 690.8 


Cu. ft. 
in 1 lb. of Steam. 


Volume, 


Weight of 1 cu. 
ft. Steam, lb. 


500213 
*00286 


.00299 
00577 
00848 
01112 


.01373 
.01631 
.01887 
02140 
02391 


02641 
02889 
.03136 
.03381 
03625 


03794 


.03868 
-04110 
04352 
04592 
04831 


-05070 
05308 
.05545 
-05782 
.06018 


06253 
.06487 
06721 
.06955 
07188 


.07420 
07652 
07884 
.08115 
08346 


08576 


-08806 


09035 - 


664 STEAM. 


Properties of Saturated Steam, 




















Os , Total Heat . oy. Tiss ae 
he es : above 32°F. |N. Eos a ac 
ovd C= iy beeen Ook eee Rae ees ol sy ot 
2 oF 6 Qo ED Sst | 6 OR - 
G @ ao 8 24 on _ SE : et oo 
ty # | G's {In the |In the| ty, 5 ca .° 68 
Ay 2 Tso an) I © do a ® 
2, == 5h Water | Steam/ pe | &~S 2 ier 
2”, 2.8 5 BMS | pec | ge aD 
OF om 693,| E3 h H 2,2) eon | Se coe 
S52 | 255| Ee | Heat-| Heat-| Zt | sea! se r= 
o | = units. | units. | 4 ee eae = 
23.3 88 264.0 | 283.8 }| 1162.5 | 92 @ 673.7 | 10.79 | .09264 
24.3 39 265.6 | 235.4 5 927.6 | 657.5 | 10.53 | .09493 
25.3 40 267.1 | 236.9 | 1163.4 | 926.5 | 642.0 | 10.28 } .09721 
26.3 41 268.6 | 238.5 F 925.4 | 627.3] 10.05 | .09949 
27.3 42 270.1 | 240.0 | 1164.3} 924.4 | 613.3 9.83 | .1018 
28.3 43 271.5 | 241.4 ; 923.3 | 599.9 9.61 | .1040 
29.3 44 272.9 | 242.9 | 1165.2 | 922.3 | 587.0 9.41 | .1063 
80.3 45 274.3 | 244.3 6} 921.3 | 574.7 9.21 | .1086 
31.3 46 275.7 | 245.7 | 1166.0 | 920.4 | 563.0 9.02 | .1108 
32.3 49 20. 247.0 .4 | 919.4 | -551.7 8.84 | .1131 
33.3 48 278.3 | 248.4 8 | 918.5 | 540.9 8.67 | .1153 
84.3 49 279.6 | 249.7 | 1167.2 | 917.5 | 530.5 8.50 | .117 
35.3 50 280.9 ; 251.0 .6 | 916.6 | 520.5 8.34 | .1198 
86.3 5l 282.1 252.2 | 1168.0 | 915.7 | 510.9 8.19 | .1221 
37.3 52 283.3 | 253.5 4 | 914.9) 501.7 8.04 | .1243 
38.3 53 284.5: | 254.7 | .7 | 914.0 | 492.8 7.90 | .1266 
39.3 54 285.7 | 256.0 1169.1 | 918.1 | 484.2 7.76 | .1288 
40.3 55 286.9 | 257.2 4} 912.3} 475.9 ?.63 | .1311 
41.3 56 288.1 258.3 68) | #91125 1) 46729 7,50)|olood 
42.3 57 289.1 | 259.5 | 1170.1 | 910.6 | 460.2 7.88 | .13855 
43.3 58 290.3 | 260.7 .5 | 909.8 | 452.7 47.26 1377 
44.3 59 291.4 | 261.8 -8 | 909.0] 445.5 7.14 | .1400 
45.3 60 292.5 | 262.9 | 1171.2 | 908.2 | 438.5 7.03 | .1422 
46.3 61 2938.6 | 264.0 35 | 6907.5) |) 1431/07 6.92 | .1444 
47.3 62 294.7 | 265.1 8 | 906.7 | 425.2 6.82 | .1466 
48.3 63 295.7 | 266.2 } 1172.1 905.9 | 418.8 6.72 | .1488 
49.3 64 296.8 | 267.2 -4| 905.2 | 412.6 6.62 | .1511' 
50.3 65 297.8 | 268.3 8} 904.5} 406.6 6.53 1533 
51.3 66 298.8 | 269.3 | 1173.1 | 903 7 | 400.8 6.43 | .1555 
52.3 67 299.8 | 270.4 4] 903.0 | 395.2 6.34 | .1577 
53.3 68 300.8 71.4 .¢ | 902.3 | 389.8 6.25 1599 
54.3 69 801.8 | 272.4 | 1174.0 | 901.6 | 384.5 6.17 | .1621 
55.3 70 802.7 | 2738.4 -3 | 900.9 | 379.3 6.09 | .1643 
56.3 vel 803.7 | 274.4 -6 | 900.2 | 374.3 6.01 | .1665 
57.3 92 804.6 | 275.3 -8 | 899.5 | 369.4 5.93 | .1687 
58.3 73 305.6 | 276.3 | 1175.1 898.9 | 364.6 5.85 | .1709 
59.3 74 | 806.5 | 277.2 -4 {| 898.2 | 360.0 5.78 | .1731 
60.3 %3 807.4 | 278.2 «¢ | 897.5 | 355.5 5.71 1753 
61.3 vi 808.3 | 279.1 | 1176.0 | 896.9 | 351.1 5.63 107 
62.3 G7? 809.2 | 280.0 2} 896.2 | 346.8 Ds Ov rl eekaae 
63.3 %8 810.1 280.9 -5 | 895.6 | 342.6 5.50 | .1819 
64.3 “9 810.9 | 281.8 8 | 895.0 | 338.5 5.43 | .1840 
65.3 80 $11.8 | 282.7 | 1177.0 | 894.8! 834.5 5.37 | .1862 
66.3 81 312.7 | 283.6 -3 | 893.7 | 330.6 5.81 | .1884 
67.3 82 818.5 | 284.5 -6 | 893.1 326.8 5.25 | .1906 
68.3 83 : ; 8 : ; , 
69.3 84 sil 
90.3 , 85 é 3 








STEAM, «665 


Properties of Saturated Steam, 














oa . Total Heat ‘ Os, | a3 te 
58 Zt of Sot above 32°F. | if Buck ae 52 
- ha o tas Sad »~ | = exe 

g@ [RPE | Be $25 | Se. b Oe | aie 
aS o2o | sa |Inthe|In the!) 5 | Gu& ATS os 
o™ |s a | oH | Water |Steam|/ os | SS 2.5 a 
Dh Sos see h H ats Bao ee is 
22 | 255 | Se, | Heat-|Heat-| Sud | ore] sa | SH 
io} <4 =a units. | units. | 4 faa} ae > 
71.3 86 816.8 | 287.9 | 1178.6 | 890.7 | 312.5 | 5.02 1993 
92.3 87 317.7 |} 288.7 8} 890.1 809.1 4.96 -2015 
%3.3 88 818.5 | 289.5 | 1179.1 889.5 | 305.8 | 4.91 .2036 
74.3 89 319.3 } 290.4 8 | 888.9} 302.5 | 4.86 2058 
95.38 90 320.0 | 291.2 .6 | 888.4 | 299.4 | 4.81 .2080 
76.3 91 320.8 | 292.0 8 | 887.8 | 296.38 | 4.76 -2102 
77.3 92 321.6 | 292.8 | 1180.0 | 887.2 | 293.2} 4.71 22123 
78.3 93 822.4 293.6 -3 886.7 | 290.2 | 4.66 2145 
79.3 94 3823.1 | 294.4 5 | 886.1 287.3 | 4.62 2166 
80.3 95 823.9 | 295.1 2 {| 885.6 | 284.5 | 4.57 .2188 
81.3 96 324.6 | 295.9 | 1181.0 | 885.0 | 281.7] 4.58 2210 
82.3 ¢ 825.4 | 296.7 2} 884.5] 279.0] 4.48 02231 
83.3 98 326.1 297.4 .4| 884.0 | 276.3 | 4.44 .2253 
84 3 99 826.8 | 298.2 6 | 883.4 | 273.7 | 4.40 02274 
85.3 100 327.6 | 298.9 +8] 882.9) | (27101 4.36 -2296 
86.3 101 828.3 | 299.7 { 1182.1 882.4 | 268.5 | 4.32 .2317 
87.3 102 829.0 | 300.4 3 | 881.9 | 266.0 | 4.28 2339 
88.3 103 329.7 | 301.1 5 | 881.4 | 263.6 | 4.24 2360 
89.3 104 830.4 | 301.9 3 | 880.8 | 261.2] 4.20 22002 
90.3 105 831.1 | 302.6 9 | 880.38} 258.9 | 4.16 . 2403 
91.3 106 831.8 | 303.3 | 1183.1 879.8 | 256.6 | 4.12 02425 
92.3 107 332.5 | 304.0 4} 879.3 | 254.8 | 4.09 22446 
93.3 108 333.2 | 3804.7 6; 878.8 | 252.1 4.05 | .2467 
94.3 109 833.9 | 3805.4 8 | 878.3 | 249.9] 4.02 -2489 
95.3 110 834.5 | 306.1 | 1184.0 | 877.9 | 247.8 | 3.98 . 2510 
96.3 111 335.2 | 3806.8 2 | 877.4 | 245.7 |. 3.95 .2531 
97.3 112 335.9 | 307.5 4 | 876.9 | 243 3.92 22003 
98.3 113 336.5 | 308.2 6 | 876.4 | 241.6 | 3.88 02074 
99.3 114 337.2 | 3808.8 8 | 875.9 | 239.6 | 38.85 2596 
100.3 115 337.8 | 309.5 | 1185.0 | 875.5 | 287.6 | 3.82 -2617 
101.3 116 388.5 | 310.2 .2 | 875.0) 235.7 | 8.79 . 2638 
102.3 117 339.1 | 310.8 4 74.5 | 233.8 | 3.76 -2660 
103.3 118 339.7 | 311.5 -6 | 874.1 231.9 | 3.73 -2681 
104.3 119 340.4 | 312.1 8 | 873.6 | 230.1} 8.70 22708 
105.3 120 341.0 | 312.8 9 | 873.2 | 228.3] 8.67 22024 
106.3 221 841.6 | 313.4 | 1186.1 | 872.7 | 226.5 | 3.64 22745 
197.3 122 842.2 | 314.1 4 872.3 | 224.7 | 3.62 2766 
198.3 123 342.9 | 3814.7 -5 | 871.8 | 223.0 | 3.59 22788 
109.3 124 343.5 | 315.3 ef |} 871.4 | 221.3] 3.56 2809 
110.3 125 344.1 | 3160 870.9 |} 219.6 | 3.53 . 2830 
111.3 126 344.7 | 316.6 | 1187.1 870.5 218.0 | 3.51 22851 
112.3 127 845.3 ) 317.2 870.0 | 216.4 | 3.48 -2872 
113.3 128 3845.9 | 317.8 4 | 869.6 | 214.8 | 3.46 2894 
114.3 129 346.5 | 3818.4 6 | 869.2 | 213.2 | 3.43 22915 
115.38 130 847.1 319.1 -8} 868.7 | 211.6 | 3.41 .2936 
116.3 131 347.6 | 319.7 | 1188.0 | 868.3] 210.1 3.38 -2957 
117.3 132 848.2 | 820.3 -2 | 867.9 | 208.6 | 8.36 | .2978 
118.3 133 348.8 | 320.8 8.) 867.5 | 207.1 | 3.33 - 3000 
119.3 134 349.4 | 921.5 -) | 867.0 1 205.7) 3.31 





666 STEAM. 


Properties of Saturated Steam, 

















oe dh Total Heat : £3 
pelts wot $ : above 82°F. |}, ee 
> o od Ow 4 WM =) >) 
oo |e Ss] 3 acc |. dees 3 
oe o%. | 3 | InthelIn the ms Pe 
#4 | GES) ES | neat. | neat-| 29g | Sse 
Sa om eat- eat- {| ¥ {J aCe 
&= | r= units. | units. | 9 ers 
120.3 135 850.0 | 322.1 | 118&.% | 866.6 | 204.2 
121.3 136 3850.5 | 822.6 -9 | 866.2 | 202.8 
122.3 1387 851.1 | 323.2 | 1189.0 | 865.8 | 201.4 
123.3 138 351.8 | 323.8 2} 865.4 | 200.0 
124.3 139 852.2 | 3824.4 -4{ 865.0 | 198.7 
125.3 140 852.8 | 3825.0 -5 | 864.6} 197.3 
126.3 141 353.3 | $825.5 -¢ | 864.2 196.0 
127.3 142 853.9 | 326.1 9; 863.8 194.7 
128.3 143 | 354.4 | 826.7 1190.0| 863.4] 193.4 
129.3 144 855.0 | 3827.2 | -2 863.0 | 192.2 
130.8 145 855.5 } 827.8 4; 862.6} 190.9 
131.8 146 356.0 | 328.4 2 | 862.2 1 189.7% 
132.3 147 856.6 | 828.9 -@ | 861.8 | 188.5 
133.3 148 357.1 829.5 9} 861.4 187.3 
134.3 149 357.6 | 3830.0 | 1191.0} 861.0 | 186.1 
135.3 150 858.2 | 330.6 -2| 860.6 | 184.9 
136.3 151 858.7 | 3831.1 -3 | 860.2 | 183.7 
137.3 152 359.2 } 3831.6 .5 | 859.9 182.6 
138.3 153 359.7 | 382.2 @1 859.54 181.5 
139.3 154 860.2 | 3382.7 8} 859.1 | 180.4 
140.3 155 360.7% | 333.2 | 1192.0] 858.7 79.2 
141.3 156 361.3 | 333.8 ol 858 .4 sWeeheg 
142.3 157 861.8 | 334.3 .3 | 858.0 107.0 
143.3 158 862.3 | 3834.8 4 857.6 176.0 
144.3 159 362.8 | 335.3 6) 857.2 | 174.9 
145.3 160 ; 363.3] 385.9 7 | 856.9 | 173.9 
146.3 , 161 863.8 | 336.4 9 | 856.5 | 172-9 
147.3 162 364.3 | 336.9 | 1193.0 | 856.1 171.9 
148.3 163 364.8 | 387.4 2 | 855.8 | 171.0 
149.3 164 365.3 | 3837.9 3 | 855.4 | 1270.0 
150.3 165 365.7 | 338.4 .5| 855.1 | 169.0 
151.3 166 366.2 | 338.9 6) 854.7 | 168.1 
152.3 167 366.7 | 3839.4 ~6| 854.4 | 167.1 
153.3 168 867.2 | 339.9 9 | 854.0 | 166.2 
154.3 169 367.7 | 340.4 | 1194.1 6 | 165.3 
155.3 170 368.2 | 3840.9 2 8 | 164.3 
156.3 171 368.6 | 3841.4 4] 852.9) 163.4 
157.3 172 369.1 341.9 5] 852.6; 162.5 
158.3 1%3 369.6 | 342.4 2} 852.8 | 161.6 
159.3 174 870.0 | 342.9 8} 851.9 160.7 
160.3 175 870.5 | 3843.4 9 | 851.6 | 159.8 
161.3 176 871.0 | 343.9 | 1195.1 | 851.2} 158.9 
162.3 177 871.4 | 344.3 .2 | 850.9 | 158.1 
163.3 1%8 371.9 | 344.8 -4|] 850.5 | 157.2 
164.3 179 872.4 | 345.3 5 | 850.2 | 156.4 
165.3 180 872.8 | 345.8 2 | 849.9 | 155.6 
166.3 181 873.3 | 346.3 8 | - 849.5 | 154.8 
167.3 182 873.7 | 346.7 9 | 849.2 | 154.0 
148.3 183 874.2 | 347.2 | 1196.1 | 848.9 | 153.2 


{ 
| 


ft. Steam, lb. 


| Volume. Cu. ft. 
: | Weicht of 1 cu. 


$9 09 99 69 69 


ce co C2 CO CO 


ee 


DOBSF 9822-3-2H WMOMWMD OwWMwODO SOSSCO CBHRHH PNewDW 


Sz2S2 SRRSS SSSBR SBSS28 RSISS SRARS BYFSR SBERSR SHKRAQO GS aaa 


ee 
4 


2920252 RWW WW WWW WWW PVM! Wwwjqww 31719 WIW 0.09.00 0000 


STEAM. 667 


Pruperties of Saturated Steam, 




















= ‘ Total Heat : ox 34 
Es 2S .! 9. | aboveae Rr. |H , ES “8 3 5 
ge |m.8 8% gee | oe, | 62 | oo 
ae gua ea In the |} In the m8 i oO boi! 
a =e = | Water | Steam vee fae et ors o§ 
© a See oD lem eerie lacs 2 
Bb Soa] Bz h | A | BMS | Se | ES | Se 
a4 |455| ES | Heat-| Heat-| gm | 3o8 | Sa | By 
om qr 2 units. | units. | 4 ere | po eo 

169.3 184 874.6 | 3847.7 | 1196.2 | 848.5 | 152.4 ~ 2.46 4066 
170.3 185 875.1 | 348.1 03 | 848.2 |) 15156) )) 2-45 4087 
171.3 186 875.5 | 3848.6 5 | 847.9 | 150.8] 2.48 4108 
172.3 187 875.9 | 349.1 3610 5840.06) O150 Onlmms. 42 4129 
173.3 188 376.4 | 349.5 el ESA oe 149.2] 2.41 .4150 
174.3 189 376.9 | 350.0 - 9 | 846.9] 148.5 | 2.40 .4170 
175.3 190 377.3 | 350.4 | 1197.0 | 846.6 | 147.8 | 2.39 4191 
176.3 191 377.7 | 350.9 1 | 846.3) 147.0] 2.87 sdel2 
177.3 192 878.2 | 351.3 3 | 845.9] 146.8 | 2.36 4233 
178.3 193 878.6 | 3851.8 4} 845.6 145.6 | 2.85 04254 
179.3 194 379.0 5 352.2 -5 | 845.3 | 144.9 | 2.34 4275 
180.8 195 379.5 | 3852.7 % | 845.0} 144.2] 2.83 -4296 
181.3 196 880.0 | 353.1 8} 844.7 143.5 2.32 4317 
183.3 197 380.8 | 358.6 9 | 844.4] 142.8] 2.81 4337 
183.3 198 380.7 | 354.0 | 1198.1 844.1 142.1 2.29 04358 
184.3 199 881.2 | 354.4 «2 | 843.7 | 141.4] 2.28 04379 
185.3 200 881.6 | 354.9 8 | 843.4] 140.8) 2.27 4400 
186.3 201 382.0 | 355.3 4} 843.1 140.1 2.26 4420 
187.3 202 382.4 355.8 6 | 842.8 139.5 | 2.25 4441 
188.3 203 382.8 | 356.2 -¢ | 842.5 | 138.8 | 2.24 4462 
189.3 204 383.2 | 3856.6 8 | 842.2 1 138.1 | 2.23 4482 
190.3 205 383.7 | 3857.1 | 1199.0 | 841.9 | 187.5 | 2.22 .4503 
191.3 206 384.1 357.5 1 841.6 186.9 | 2.21 «4523 
192.3 207 884.5 357.9 2] 841.3 136.3 2.20 4544 
193.3 208 384.9 | 358.3 -3 | 8410] 185.7 | 2.19 .4564 
194.3 209 885.3 | 358.8 5 | 840.7 1385.1 | 2.18 .4585 
195.3 210 Beare |. Be sOni 840245 134 Di lee a. .4605 
196.3 211 886.1 | 359.6 -7 | 840.1 133.9 | 2.16 4626 
197.3 212 886.5 | 360.0 -8 | 839.8 |* 183.3 | 2.15 4646 
198.3 213 386.9 | 860.4 9 | 8389.5 |, 182.7]. 2.14 4667 
199.3 214 887.3 | 3860.9 | 1200.1 |} 839.2; 132.1 2.18 4687 
200.3 215 387.7 | 3861.3 2} 888.9 | 131.5] 2.12 4707 
201.3 216 388.1 | 361.7 +8) |) 8386 | 130.9' | 2.12 4728 
202.3 217 388.5 362.1 4} 838.3 180.3 | 2.11 .4748 
203.3 218 388.9 | 362.5 -6 | 888.1 129.7} 2.10 .4768 
204.3 219 889.3 | 3862.9 of | 8387.8] 129.2; 2.09 4788 
205.3 220 889.7 | 362.2%) 1200.8 | 838.6*} 128.7] 2.06 .4852 
215.3 230 393.6 | 3866.2 | 1202.0 | 835.8 | 123.3] 1.98 -5061 
225.3 240 397.3 370.0 | 1208.1 833.1 118.5 1.90 -5270 
235.3 250 400.9 | 873.8 | 1204.2 | 880.5] 114.0] 1.838 5478 
245.3 260 404.4 | 377.4 | 1205.3 827.9} 109.8] 1.7 5686 
255.3 270 407.8 | 380.9 | 1206.3 | 825.4 105.9 1.70 .5894 
265.3 280 411.0 | 384.3 | 1207.3 | 823.0] 102.3] 1.64 -6101 
275.3 290 414.2 | 387.7 | 1208.3 | 820.6 99.0 | 1.585 | .6308 
R85 .3 800 417.4 | 390.9 | 1209.2 | 818.3 95.8 | 1.5385 6515 
335.3 350 432.0 | 406.3 | 1213.7 | 807.5 82.7 1.825 7545 








*The discrepancies at 205.3 lbs, gauge are ue Wo the change from 
Dwelshauvers-Dery’s to Buel’s figures, ‘ 


668 STEAM. 


Properties of Saturated Steam, 








¢ : Total Heat , o,, 3.5 4 
Bo AC We ees above 82°F. |W | | ES ek eS 
nn fed | es 8:2 1s sh- he 
os Ae | Be TSE) Sed | OF are 
hg gut | oa iin the | in the} "ny sr sey 5 o8 
cp So ao Water | Steam 253 pigs a as 293 
Ha | 888.) 2S | nee | wat | Sig | eee | ce | 2 
ao Sy eat- eat- | & Ger: > O45 
a= —22/ © | units. | units. | 9 ees | Se Gest 
385.3 | 400 | 444.9| 419.8 | 1217.7] 797.9] 72.8 | 1.167 | .9572 
435.3 450 456.6 | 432.2 | 1221.38 | 789.1] 65.1 1.042 . 9595 
485.3 500 467.4 | 448.5 | 1224.5 | 781.0} 58.8 942 1.062 
535.3 550 477.5 | 454.1 | 1227.6 | 7738.5) 58.6 -859 | 1.164 
585.3 600 486.9 | 464.2 | 1230.5 766.3} 49.8 790 | 1.266 
635.3 650 495.7 | 473.6 | 1233.2 | 759.6] 45.6 731 1.368 
685.3 700 504.1} 482.4 | 1285.7 | 753.3} 42.4 .680 | 1.470 
735.3 750 512.1 490.9 | 1238.0 | 747.2] 39.6 .636 1.572 
785.3 800 519.6 | 498.9 | 1240.3 | 741.4] 37.1 597 | 1.674 
835.3 850 526.8 | 506.7 | 1242.5 735.8 | 34.9 563 | 1.776 
885.3 900 533.7 | 514.0 | 1244.7 | 780.6 | 383.0 .5382 | 1.878 
935.3 950 540.3 | 521.8 | 1246.7 | 725.4] 381.4 .505 | 1.980 
985.3 1000 546.8 | 528.3 | 1248.7 720.3 | 30.0 .480 | 2.082 


FLOW OF STEAM. 


Flow of Steam through a Nozzle. (From Clark on the Steam- 
engine.)—The flow of steam of a greater pressure into an atmosphere of a 
less pressure increases as the difference of pressure is increased, until the 
external pressure becomes only 58% of the absolute pressure in the boiler. 
The flow of steam is neither increased nor diminished by the fall of the ex- 
ternal pressure below 58%, or about 4/7ths of the inside pressure, even to the 
extent of a perfect vacuum. In flowing through a nozzle of the best form, 
the steam expands to the external pressure, and to the volume due to this 
pressure, so long as it is not less than 58% of the internal pressure. For an 
external pressure of 58%, and for lower percentages, the ratio of expansion 
is 1 to 1.624. The following table is selected from Mr, Brownlee’s data exemn- 
plifying the rates of discharge under a constant internal pressure, into 
various external pressures: 


Outflow of Steam; from a Given Initial Pressure into 
Various Lower Pressures. 
Absolute initial pressure in boiler, 75 lbs. per sq. in. 




















Absolute | external | Ratioof | Velocit Discharge 
? ‘ y of Actual 
ee Zo Pressure |Expansion| Outflow  |Velocity of a ae hee 
couate | Per square in at Constant |_ Outflow | orifice per 
hich inch. Nozzle, Density. | Expanded.| ~jjinute 
lbs lbs. ratio. feet per sec. | feet p. sec. lbs. 
15 G4 1.012 227.5 230 16.68 
(ts) 42 1.037 886.7 401 28.35 
G5 40 1.063 490 521 35.93 
ts) 65 1.136 660 749 48 .38 
ff 61.62 1.198 736 876 53.97 
5 60 1.219 765 933 56.12 
5 50 1.434 87 1252 64 
ff 5 " 1.575 890 1401 65.24 
75 { ie oct ! 1.624 890.6 1446.5 65.3 
15 1446.5 65.3 
1446.5 


65.3 


FLOW OF STEAM. 669 


When steam of varying initial pressures is discharged into the atmos- 
phere—the atmospheric pressure being not more than 58% of the initial 
pressure—the velocity of outflow at constant density, that is, supposing the 
initial density to be maintained, is given by the formula V = 3.5953 v/h. 


V = the velocity of outflow in feet per second, as for steam of the initial 
density ; 

h = the height in feet of a column of steam of the given absolute initial 
pressure of uniform density, the weight of which is equal to the pres- 
sure on the unit of base. 


The lowest initial pressure to which the formula applies, when the steam 
is discharged into the atmosphere at 14.7 lbs. per square inch, is (14.7 x 
100/58 =) 25.37 lbs. per square inch. Examples of the application of the 
formula are given in the table below. 

From the contents of this table it appears that the velocity of outflow into 
the atmosphere, of steam above 25 lbs. per square inch absolute pressure, 
or 10 lbs. effective, increases very slowly with the pressure, obviously be- 
cause the density, and the weight to be moved, increase with the pressure, 
An average of 900 feet per second may, for approximate calculations, be 
taken for the velocity of outflow as for constant density, that is, taking the 
volume of the steam at the initial volume. 

Outflow of Steam into the Atmosphere,.—External pressure 
per square inch 14.7 lbs. absolute. Ratio of expansion in nozzle, 1.624. 





Pars a 2 a) Sg = 58 
= ° = oa % ° 
Se. (Sob) B Csg(eSot hse Jsoh) P ‘3 Ao k. 
ct) | om = CaS 3) S| om Bg Las 
Sans OUG Seg DE RIES ) SE5/00S Seg {Bow we OOS 
eS loval SES fagol/POystsSloea!] SEV [ago | POs 
FPA S82) Deg [oH Blew TPP soso! CLs lone | Fae 
SSO |p ZAl PSs [Movi SSassosol(,4zA| Peg [hoo 28) Soa gd 
£48 |5-.8| ZA acc $8 > Bade e isp Secs oS 
o¢0s a Sorin pion al = Sr Sl mn ea ag 
~ O° Sa MN HO Gels p= O° Huh foot s 
Sue [oenl Som (250(5 SeS/ 20 Fisaez| Soe 12208] SFe2 
< > <q a a <q > <q A iy 




















30 867 | 1408 | 26.84) 53.7 100 } 898} 1459 86.34 12.7 
40 874 | 1419 | 35.18} 70.4 115} 902} 1466 98.7 197.5 
50 880 | 1429 |} 44.06) 88.1 185 | 906} 1472 | 115.61 | 231.2 
60 885 | 1437 | 52.59) 105.2 155 |} 910} 1478 | 182.21 | 264.4 
7 889 | 1444 | 61.07) 122.1 165 | 912 | 1481 | 140.46 | 280.9 
75 891 1 1447 | 65.30} 130.6 215} 919 1 1493 | 181.58 | 363.2 


Napier’s Approximate BRule.—Flow in pounds per second = ab- 
solute pressure X area in square inches + 70. This rule gives results which 
closely correspond with those in the above table, as shown below. 


Abs. press., lbs. p. sq. in. 25.37 40 60 %5 100 = 185 165 215 


Discharge per min., by 
table, lbs............... 22.81 35.18 52.59 65.380 86.84 115.61 140.46 181.58 
By Napier’s rule,........ 21.74 34.29 51.43 64.29 85.71 115.71 141.43 184.29 


Prof. Peabody, in Trans. A. 8. M. E., xi, 187, reports a series of experi- 
ments on flow of steam through tubes 14 inch in diameter, and 14, 4, and 144 
inch long, with rounded entrances, in which the results agreed closely with 
Napier’s formula, the greatest difference being an excess of the experimental 
over the calculated result of 3.2%. An equation derived from the theory of 
thermodynamics is given by Prof. Peabody, but it does not agree with the 
a aaa ot results as well as Napier’s rule, the excess of the actual flow 
being 6.6%. 

Flow of Steam in Pipes,—A formula commonly used for velocity 
of flow of steam in pipes is the same as Downing’s for the flow of water in 


smooth cast-iron pipes, viz., V = 50 / - D, in which V = velocity in feet 


per second, LZ = length and D = diameter of pipe in feet, H = height in 
feet of a column of steam, of the pressure of the steam at the entrance, 


670 5 STEAM. 


which would produce a pressure equal to the difference of pressures at the 
two ends of the pipe. (For derivation of the coefficient 50, see Briggs on 
** Warming Buildings by Steam,”’ Proc. Inst. C. E. 1882.) 

If Q = quantity in cubic feet per minute, d = diameter in inches, ZL and H 
being in feet, the formula reduces to 


- Fig QL 5/ QL 
Q= aressg / Has, H= 04S E> d= sstsg/ 2% 


(These formule are applicable to air and other gases as well as steam.) 

If p; = pressure in pounds per square inch of the steam (or gas) at the en- 
trance to the pipe, pg = the pressure at the exit, then 144(p, — pe) = differ- 
ence in pressure per square foot. Let w= density or weight per cubic foot 
of steam at the pressure pj, then the height of column equivalent to the 
difference in pressures 


= H= SAP ~ Ps) and Q = 60 x .7854 x s0D*4/ hy PP 


If W = weight of steam flowing in pounds per minute = Qw, and d is 
taken in inches, Z being in feet, 


— D.)as — p.\as 
Ws= 56.054 / Pr Pak Ou 50.08 / Pi — pad 


‘:/Goripee 5 /f2,,7T, 
d= 0.1994/ EN 0109 f/e 
w(P1 — Pa) Pi- Ps 


2 


, : EI Be Breet A he (Pi — Pad 
Velocity in feet per minute = V=Q-+. (8545 n= 10392 / Bree rig > 


wh wL 
For a velocity of 6000 feet per minute, d = —————_;; =), = -—=. 
y Pp 3(p, —- Da) Pi P2 3d 
For a velocity of 6000 feet per minute, a steam-pressure of 100 lbs. gauge, 
or w =.264, and a length of 100 feet, d = ————; p, — pg = Fie That is, a 


1 
pipe 1 inch diameter, 100 feet long, carrying steam of 100 lbs. gauge-pressure 
at 6000 feet velocity per minute, would have a loss of pressure of 8.8 lbs. per 
square inch, while steam travelling at the same velocity in a pipe 8.8 inches 
diameter would lose only 1 lb. pressure. 
G. H. Babcock, in ‘‘ Steam," gives the formula 


W = ar4/ Pa = Pade, 
L(1+%) 
In earlier editions of ‘‘Steam ” the coefficient is given as 300,—evidently an 
error,—and this value has been reprinted in Clark’s Pocket-Book (1892 edi- 
tion). It is apparently derived from one of the numerous formule for flow 
of water in pipes, the multiplier of Zin the denominator being used for an 
expression of the increased resistance of small pipes, Putting this formula 


w — Pg)d® 
in the form W=c ae in which c will vary with the diameter 


of the pipe, we have, 


For diameter, inches.... 1 2 3 4 6 9 12 
Value of C...5 .icees sccas ee a0.d, 52.1 58.8 63 68.8 73.7 99.3 


mstead of the constant value 56.68,’given with the simpler formula. 
One of the most widely accepted formule for flow of water is D’Arcy’s, 
V=ec ae in which c has values ranging from 65 for a 14-inch pipe up to 


FLOW OF STEAM. _ 671 


111.5 for 24-inch. Using D’Arcy’s coefficients, and modifying his formula te 
make it apply to steam, to the form 


(jy an iS Wein eerie 
Q=04/ Patt oe Wac4/ rs = Balt 


we obtain, 


For diameter, inches.... 1% 1 2 3 4 5 6 ? 8 
Wit UGLOLIC soac cob isioictes -. 86.8 45.38 52.7 56.1 57.8 58.4 59.5 60.1 60.7 
For diameter, inches.... 9 10 12 14 16 18 208 R27 24 
WilIeOLic. cts. eee ec bees Oli cee Ol. O02.) 02.5002: GunOe. foe Ol Oo. cum Ooes 


In the absence of direct experiments these coefficients are probably as 
accurate as any that may be derived from formule for flow of water. 


2085) N72 
Loss of pressure in lbs. per sq. in. = p,; — py = oes Way 


Sad ode Moa THe 


Loss of Pressure due to Radiation as well as Friction.— 
E. A. Rudiger (Mechanics, June 30, 1888) gives the following formule and 
tables for flow of steam in pipes. He takes into consideration the losses in 
pressure due both to radiation and to friction. 








Wl 
10p2as" 





Loss of power, expressed in heat-units due to friction, Hf = 


Loss due to radiation, Hr = 0.262r1d. 


In which W is the weight in lbs. of steam delivered per hour, f the coeffi- 
cient of friction of the pipe, / the length of the pipe in feet, » the absolute 
terminal pressure, d the diameter of the pipe in inches, and 7 the coefficient 
of radiation. jf is taken as from .0165 to .0175, and r varies as follows: 


TABLE OF VALUES FOR 7. 


Absolute Pressure. 
Pipe Covering. 


40 lbs. | 65 Ibs. 90 Ibs. | 115 lbs. 


WNGOVEFCA PENCE... ae sie shersiticwie olsieisies 437 555 620 684 
2-inch cement composition......... 146 178 193 209 
OER a Pe ASOUST-OS:  pitieteny clstestejeaveceatote 157 192 202 222 
Dee rache tos tloGkre cesta cian @ ce 150 185 197 210 
2) 7S wood enjlogs | alge) eset 100 122 145 151 
2... samineral. wool... snewcasee S- 61 76 85 93 
Rae Dain felts goede ne atnsee 48 58. [ 66 73 


The appended table shows the loss due to friction and radiation in asteam- 
pipe where the quantity of steam to be delivered is 1000 Ibs. per hour, / = 
1000 feet, the pipe being so protected that loss by radiation r = 64, and the 
absolute terminal pressure being 90 lbs.: 





Diameter| Loss by Loss by Total {| Diam. | Loss by Loss by Total 


of Pipe, | Friction, pels Loss, fof Pipe,| Friction, pee Loss 

inches. Af. oe L. inches. Af. Tie L. 
1 197,531 16,768 | 214,300 3144 876 58,688 59,064 
114 64,727 20,960 85,687 4 193 67,072 | 67,265 
1% 26,012 25,152 51,164 5 63 83,840 83,903 
134 12,035 29,344 41,379 6 25 100,608 110,623 
2 6,173 33,536 39,709 f 12 117,376 117,388 
214 2,028 41,920 43,943 8 6 134,144 134,150 


3 813 50,304 51,117 


672 STEAM. 


If the pipes are carrying steam with minimum loss, then for same f, 2, 
and p, the loss of pressure LZ for pipes of different diameters varies in- 
versely as the diameters. 

The general equation for the loss of pressure for the minimal loss from 
friction and radiation is 

rie 0.0007023_drlp 
ac MGUIERS V7 ER 

The loss of pressure for pipes of 1 inch diameter for different absolute 
terminal pressures when steam is flowing with minimal loss is expressed by 


the formula L =C13/ r?, in which the coefficient C has the following values: 


For 65 lbs, abs. term. pressure.... ..e.sse-ceeseeeeeC = 0.00089387 
oe "5 ee 66 66 66 


cece e 00: cecceserce- 0.00093684 
SUE Beat tae ty sees cece ccoeceecesees 0.00099573 
ee 10¢ Se se oc ae Ceee reer eeeeres+oreoe 0.001031382 
se 115 56 se Ab se eee oees C88 CeeSOLOC®e 0.00108051 


In order to find the loss of pressure for any other diameter, divide the loss 
of pressure in a 1-inch pipe for the given terminal pressure by the given 
diameter, and the quotient will be the loss of pressure for that diameter. 

The following is a general summary of the results of Mr. Rudiger’s inves- 
tigation : 

The flow of steam in a pipe is determined in the same manner as the flow 
of water, the formula for the flow of steam being modified only by substi- 
tuting the equivalent loss of pressure, divided by the density of the steam, 
for the loss of head. 

The losses in the flow of steam are two in number—the loss due to the 
friction of flow and that due to radiation from the sides of the pipe. The 
sum of these is a minimum when the equivalent of the loss due to fric- 
tion of flow is equal to one fifth of the loss of heat by radiation. Fora 
greater or less loss of pressure—i.e., for a less or greater diameter of pipe 
—the total loss increases very eee 

For delivering a given quantity of steam at a given terminal pressure, 
with minimal] total loss, the better the non-conducting material employed, 
the larger the diameter of the steam-pipe to be used. 

The most economical loss of pressure for a pipe of given diameter is equal 
to the most economical loss of pressure in a pipe of 1 inch diameter for same 
conditions, divided by the diameter of the given pipe in inches. 

The following table gives the capacity of pipes of different diameters, to 
deliver steam at different terminal pressures through a pipe one half mile 
long for loss of pressure of 10 Ibs., and a mean value of f = 0.0175. Let W' 
denote the number of pounds of steam delivered per hour : 





Diameter Abs. Term. Pressure. Diameter Abs. Term. Pressure. 


of Pipe, GN NE OL IPOs | ila SI sev eae 
inches. inches. 
65 Ibs. | 80 Ibs. {100 Ibs. 65 lbs. | 80 Ibs, | 100 lbs, 
W Ww Ww Ww w Ww 
Taawscerte 102 118 125.8 i 4igaveeues 4,397 | 4,872] 5,390 
VA i awiave slots 179 198 219 Bi Gece s 5,721 6,339 7,013 
AEG alsin cg cteclela 282 312 846.8 6.0 .cceess 9,024 | 10,00 11,063 
Siok Satvele ihe 415 459 DOSE Nee canteens 13,268 | 14,701 | 16,265 
ASE OBA 579 641 710 F 8..cccce...) 18,526 | 20,528 | 22,711 
ee 1,011} 1,121 | 1,240] 9....... 24,870 | 27,556 | 30,488 
3 Veslevece (ee droge 1,768 195608 10 aac cer 32,364 | 35,860 | 39,675 
BUG rsetiyaiedelde 2,346 2,599 POLO Mil cewem rants 41,081 | 45,507 | 50,349 
Hie Ben, 5! te ebbrees 8,210 3.629 4042/8 19: ae ee 51,049 | 56,564 | 62,581 


Resistance to Flow by Bends, Valves, ete. (From Briggs on 
Warming Buildings by Steam.)—The resistance at the entrance to a tube 
when no special bell-mouth is given consists of two parts. The head y? + 2g 

q2 


ig expended in giving the velocity of flow; and the head 0 505 5 in over. 


¥LOW OF STEAM. 672 


coming the resistance of the mouth of the tube. Hence the whole loss of 
head at the entrance is 1.505 x . This resistance is equal to the resistance 


of a straight tube of a length equal to about 60 times its diameter. 

The loss at each sharp right-angled elbow. is the same as in flowing 
through a length of straight tube equal to about 40 times its diameter, For 
a globe steam stop-valve the resistance is taken to be 14% times that of the 
right-angled elbow. i 

Sizes of Steamepipes for Stationary Engines,—Authorities 
on the steam-engine generally agree that steam-pipes supplying engines 
should be of such size that the mean velocity of steam in them does not 
exceed 6000 feet per minute, in order that the loss of pressure due to friction 
may not be excessive. The velocity is calculated on the assumption that the 
cylinder is filled at each stroke, In very long pipes, 100 feet and upward, it 
is well to make them larger than this rule would give, and to place a large 
steam receiver on the pipe near the engine, especially when the engine cuts 
orf early in the stroke. 

An article in Power, May, 1893, on proper area of supply-pipes for engines 
gives a table showing the practice of leading builders. To facilitate com. 
parison, all the engines have been rated in horse-power at 40 pounds mean 
effective pressure. The table contains all the varieties of simple engines, 
from the slide-valve to the Corliss, and it appears that there is no general 
difference in the sizes of pipe used in the different types, 

The averages selected from this table are as follows: 


Diam. of pipe, in...... 22% 3 34 4 44% 5 6 ?%? 8 9 10 
Av. H.P.of engines.... 25 39 56 77 100 126 156 225 306 400 506 625 
Calculated,formula (1) 23 36 51 70 91 116 148 206 278 366 463 571 
xd formula (2) 24 37.5 54 73 96 121 150 216 294 384 486 600 
Formula (1) is: 1 H P. requires .1375 sq. in. of steam-pipe area. 
Formula (2) is: Horse-power = 6d?. d = diam. of pipe in inches, 


The factor .1375 in formula (1)is thus derived: Assume that the linear 
velocity of steam in the pipeshould not exceed 6000 feet per minute, then 
pipe area = cyl. area X piston-speed -- 6000 (a). Assume that the av, mean 
effective pressure is 40 lbs. per sq. in., then cyl. area X piston-speed x 40 + 
33,000 = horse-power (b). Dividing (a) by (b) and cancelling, we have pipe 
area -- H.P. = .1375 sq. in. If we use 8000 ft. per min. as the allowable 
velocity, then the factor .1375 becomes .1031; that is, pipe area + H.P. = 
.1031, or pipe area X 9.7 = horse-power. This, however, gives areas of pipe 
smaller than are used inthe most recent practice. A formula which gives 
results closely agreeing with practice, as shown in the above table is 


Horse-power = 6d?, or pipe diameter = V ae: = .408 LP, 


DIAMETERS OF CYLINDERS CORRESPONDING TO VARIOUS SIZES OF STHAM- 
PIPES BASED ON PISTON-SPEED OF ENGINE OF 600 FT. PER MINUTE, AND 
ALLOWABLE MEAN VELOCITY OF STEAM IN PIPE OF 4000, 6000, anp 8000 
FT. PER MIN. (STEAM asSUMED TO BE ADMITTED DURING FULL STROKE.) 


Diam. of pipe, mcnes......... 2 24 38 av 4 4% 5 6 


Vek 54000,)5:) \.cCEREN Ea encode Dee oe Osteiny 4:0 10.3 11.6 12.9 15.8 
penOOOO racic eeamees bee hO.Oume (som 9500011 ,1 e126 14.2) 15k8.019% 
$8) 13000, 0. ieee eden, ove e-set Oskes0;0 12.8'9 14.6 16.4° 18.38! 2109 


Horse-power, Approx.......e2 20 31 45 62 80 100 125 180 
Diam. of pipe, inches......... 8 9 10 11 12) 1S 4 


Vel .°4000 (725: sinas cor Bele ste tee ate 18.1 20.7 23.2 25.8 28.4 31.0 33.6 36.1 
ee SBGOOO! eee es cet secccccecseses 22.1 25.3 28.5 31.6 34.8 387.9 41.1 44.3 
*§ “58000 Lictetes see ssp ome eseee 20.6 29.2 32.9 36.5 40.2 48.8 47.5 51.1 
Horse-power, approx....... -- 245 320 406 500 606 718 845 981 


Area of cylinder x piston-speed 
mean velocity of steam in pipe ° 


For piston-speed of 600 ft. per min. and velocity in pipe of 4000, 6000, and 
8000 ft. per min. area of pipe = respectively .15, .10, and .075 x area of cyl-~ 
inder. Diam. of pipe = respectively .3873, .3162, and .2739 X diam. of cylin- 
der. Reciprocals of these figures are 2.582, 3.162, and 3.651. 

The first line in the above tablemay be used for proportioning exhaust 


Formula, Area of pipe = 


674 STEAM, 


pives, in which a velocity not exceeding 4000 ft. per minute is advisable, 
he last line, approx. H.P. of engine, is based on the velocity of 6000 ft. per 
min. in the pipe, using the corresponding diameter of piston, and taking 


H.P. = 14(diam. of piston in inches)* 

Sizes of Steam-pipes for Marine Engimnes,—In marine-engine 
practice the steam-pipes are generally not as large as in stationary practice 
for the same sizes of cylinder. Seaton gives the following rules: 

Main Steam-pipes should be of such size that the mean velocity of flow 
does not exceed 8000 ft. per min. ; 

In large engines, 1000 to 2000 H.P., cutting off at less than half stroke, the 
steam-pipe may be designed for a mean velocity of 9000 ft., and 10,000 ft. 
for still larger engines. 

In small engines and engines cutting later than half stroke, a velocity of 
less than 8000 ft. per minute is desirable. 

Taking 8100 ft. per min. as the mean velocity, S speed of piston in feet per 
min,, and D the diameter of the cyl, 


Diam. of main steam-pipe = J Dire 2 V8. 


8100 


Stop and Throttle Valves should have a greater area of passages than the 
area of the main steam-pipe, on account of the friction through the cir- 
cuitous passages. The shape of the passages should be designed so as to 
avoid abrupt changes of direction and of velocity of flow as far as possible. 

Area of Steam Ports and Passages = A 


Area of piston < speed of piston in ft. per min, _ (Diam.)? x speed 
6000 i 7639 . 


Opening of Port to Steam.—To avoid wire-drawing during admission the 
area of opening to steam should be such that the mean velocity of flow does 
not exceed 10,000 ft. per min. To avoid excessive clearance the width of 

ort should be as short as possible, the necessary area being obtained by 

ength (measured at right angles to the line of travel of the valve). In 
practice this length is usually 0.6 to 0.8 of the diameter of the cylinder, but 
in long-stroke engines it may equal or even exceed the diameter. 

Exhaust Passages and Pipes.—The area should be such that the mean 
velocity of the steam should not exceed 6000 ft. per min., and the area 
should be greater if the length of the exhaust-pipe is comparatively long. 
The area of passages from cylinders to receivers should be such that the 
velocity will not exceed 5000 ft. per min. 

The following table is computed on'the basis of a mean velocity of flow 
of 8000 ft. per min. for the main steam-pipe, 10,000 for opening to steam, | 
and 6000 for exhaust. A = area of piston, D its diameter. 


STEAM AND EXHAUST OPENINGS. 








Piston- Diam. of Area of | Diam.of | Area of Opening 

speed, Steam-pipe |Steam-pipe| Exhaust | Exhaust | to Steam 
ft. per min. + D. + A. + Dz. + A, + A, 
300 0.194 0.03875 0.223 0.0500 0.03 
400 0.224 0.0500 0.258 0.0667 - 0 04 
500 0.250 0.0625 0.288 0.0833 0.05 
600 0.274 0.0750 0.316 0.1000 0.06 
700 0.296 0.0875 0.341 0.1167 0.07 
800 0.316 0.1000 0.365 0.13383 0.08 
900 0.335 0.1125 0.387 0.1500 0.09 
1000 0.353 0.1250 0.400 0.1667 0.10 


STEAM PIPES. 


Bursting-tests of Copper Steam-pipes. (From Report of Chief 
Engineer Melville, U.S. N., for 1892.)—Some tests were made at the New 
York Navy Yard which show the unreliability ‘of brazed seams in cop: 

er pipes. Each pipe was 8 in. diameter inside and 38 ft. 15g in. long. 
Both ends were closed by ribbed heads and the pipe was subjected to a hot- 
water pressure, the temperature being maintained constant at 871° F, Three 


STEAM-PIPES. 675 


of the pipes were made of No. 4 sheet copper (‘Stubbs ” gauge) and the 
fourth was made of No. 3 sheet. 
- The following were the results, in Ibs. per sq. in., of bursting-pressure: 


Pipe mum Der casas meals brie ue 1 2 3 4 4/ 

Actual bursting-strength........ 835 785 950 1225 1275 
Calculated °° MS rie Gast ebeele 1836 1569 1568 1568 
DitLerencCe. .c aeitscias ss gs sicustetsterceies 501 ool 619 343 293 


The theoretical bursting-pressure of the pipes was calculated by using the. 
figures obtained inthe tests for the strength of copper sheet with a brazed 
joint at 350° F. Pipes 1and 2 are considered as having been annealed. 

The tests of specimens cut from the ruptured pipes show the injurious 
action of heat upon copper sheets; and that, while a white heat does not 
change the character of the metal, a heat of only slightly greater degree 
causes it to lose the fibrous nature that it has acquired in rolling, and a 
serious reduction in its tensile strength and ductility results. a 

All the brazing was done by expert workmen, and their failure to make a, 
pipe-joint without burning the metal at some point makes it probable that, 
with copper of this or greater thickness, it is seldom accomplished. 

That it is possible to make a joint without thus injuring the metal was 
proven in the cases of many of the specimens, both of those cut from the 

pipes and those made separately, which broke with a fibrous fracture, 
* Rule for Thickness of Copper Steam-pipes. (U. S. Super- 
vising Inspectors of Steam Vessels.)—Multiply the working steam-pressure 
in lbs. per sq. in. allowed the boiler by the diameter of the pipe in inches, ~ 
then divide the product by the constant whole number 8000, and add .0625 to. 
the quotient; the sum will give the thickness of material required. 

ExamMpLe.—Let 175 lbs. = working steam-pressure per sq. in. allowed the 
boiler, 5 in. = diameter of the pipe; then ra + .0625 = .1718 ++ inch, 
thickness required. 

Reinforcing Steamspipes. (F£ng., Aug. 11, 1893.)—In the Italian 
Navy copper pipes above 8 in. diam. are reinforced by wrapping them with 
a close spiral of copper or Delta-metal wire. Two or three independent 
spirals are used for safety in case one wire breaks. They are wound at a 
tension of about 11% tons per sq. in. 

Wire-wound Steam-=pipes.—The system instituted by the British 
Admiralty of winding all steam-pipes over 8 in. in diameter with 3/16-in. 
copper wire, thereby about doubling the bursting-pressure, has within re- 
cent years been adopted on many merchant steamers using high-pressure 
steam, says the London Hngineer. The results of some of the Admiralty 
tests showed that a wire pipe stood just about the pressure it ought to have 
stood when unwired, had the copper not been injured in the brazing. 

Kiveted Steel Steame=pipes have recently been used for high 
pressures. See paper on A Method of Manufacture of Large Steam-pipes, 
by Chas. H. Manning, Trans. A. S. M. E., vol. xv. - 

Valves in Steam-=pipes.—Should a globe-valve on a steam-pipe have 
the steam-pressure on top or underneath the valve is a disputed question. 
With the steam-pressure on top, the stuffing-box around the valve-stem can- 
~ not be repacked without shutting off steam from the whole line of pipe; on 
the other hand, if the steam-pressure is on the bottom of the valve it all hag 
to be sustained by the screw-thread on the valve-stem, and there is danger 
of stripping the thread. 

A correspondent of the American Machinist, 1892, says that it is a very 
uncommon thing in the ordinary globe-valve to have the thread give out, 
but by water-hammer and merciless screwing the seat will be crushed down 
quite frequently. Therefore with plants where only one boiler is used he 
advises placing the valve with the boiler-pressure underneath it. On plants 
where several boilers are connected to one main steam-pipe he would re- 
verse the position of the valve, then when one of the valves needs repacking 
the valve can be closed and the pressure in the boiler whose pipe it controls 
can be reduced to atmospheric by lifting the safety-valve. The repacking 
can then be done without interfering with the operation of the other boilers 
of the plant. ; 

He proposes also the following other rules for locating valves: Place 
valves with the stems horizontal to avoid the formation of a water-pocket. 
Never put the junction-valve close to the boiler if the main pipe is above 
the boiler, but put it on the highest point of the junction-pipe, If the other 


676 STEAM. 


plan {fs followed, the pfpe fills with water whenever this bofler fs stopped 
and the others are running, and breakage of the pipe may cause serious re- 
sults. Never let a junction-pipe run into the bottom of the main pipe, but 
into the side or top. Always use an angle-valve where convenient, as there 
is more room in them. Never use a gate valve under high pressure unless @ 
by-pass is used withit. Never open a blow-off valve on a boiler a little and 
then shut it; it is sure to catch the sediment and ruin the valve; throw it 
well open before closing. Never use a globe-valve on an indicator-pipe. For 
water, always use gate or angle valves or stop-cocks to obtain a clear pas- 
sage. Buy if possible valves with renewable disks. Lastly, never let a man 
g0 inside a boiler to work, especially if he is to hammer on it, unless you 
break the joint between the boiler an” the valve and put a plate of steel 
between the flanges. 


A Failure of a Brazed CUpper Steam-pipe on the British 
steamer Prodano was investigated by Prof. J.O. Arnold. He found that 
the brazing was originally sound, but that it had deteriorated by oxidation 
of the zine in the brazing alloy by electrolysis, which was due to the presence 
of fatty acids produced by decomposition of the oil used in the engines. 
A full account of the investigation is given in The Engineer, April 15, 1898. 

The **Steam Loop”? is a system of piping by which water of con- 
densation in steam-pipes is automatically returned to the boiler. In its 
simplest form it consists of three pipes, which are called the riser, the hori- 
zontal, and the drop-leg. When the steam-loop is used for returning to the 
boiler the water of condensation and entrainment from the steam-pipe 
through which the steam flows to the cylinder of an engine, the riser is gen- 
erally attached to a separator; this riser empties at a suitable height into 
the horizontal, and from thence the water of condensation is led into the 
drop-leg, which is connected to the boiler, into which the water of condensa 
tion is fed as soon as the hydrostatic pressure in drop-leg in connection with 
the steam-pressure in the pipes is sufficient to overcome the boiler-pressure. 
The action of the device depends on the following principles: Difference of 
pressure may be balanced by a water-column; vapors or liquids tend to flow 
to the point of lowest pressure; rate of flow depends on difference of pres- 
sure and mass; decrease of static pressure in a steam-pipe or chamber ig 
proportional to rate of condensation; in a steam-current water will be car- 
par swept along rapidly by friction. (Illustrated in Modern Mechanism, 
p. 807.) 

Loss from an Uncovered Steams-pipe. (Bjorling on Pumping: 
engines.)—The amount of loss by condensation in a steam-pipe carried down 
a deep mine-shaft has been ascertained by actual practice at the Clay Cross 
Colliery, near Chesterfield, where there is a pipe 7% in. internal diam., 1100 
ft. long. The loss of steam by condensation was ascertained by direct 
measurement of the water deposited in a receiver, and was found to be, 
equivalent to about 1 Ib. of coal per I.H.P. per hour for every 100 ft. of 
steam-pipe; but there is no doubt that if the pipes had been in the upcast 
shaft, and well covered witha good non-conducting material, the loss would. 
have been less. (For Steam-pipe Coverings, see p. 469, ante.) 


THE HORSE-POWER OF A STEAM-BOILER. 677 


THEK STEAM-BOILER. 


The Horse-power of a Steam-boiler.—The term horse power 
has two meanings in engineering: First, an absolute unit or measure of the 
vate of work, that is, of the work done ina certain definite period of time, 
by a source of energy, as a steam-boiler, a waterfall, a current of air or 
water, or by aprime mover, as a steam-engine, a water-wheel, or a wind- 
mill. The value of this unit, whenever it can be expressed in foot-pounds 
of energy, as in the case of steam-engines, water-wheels, and waterfalls, is 
33,000 foot-pounds per minute. In the case of boilers, where the work done, 
the conversion of water into steam, cannot be expressed in foot-pounds of 
available energy, the usual value given to the term horse-power is the evap- 
oration of 30!bs. of water of a temperature of 100° F. into steam at 70 lbs. 
pressure above the atmosphere. Both of these units are arbitrary; the first, 
33,000 foot-pounds per minute, first adopted by James Watt, being considered. 
equivalent to the power exerted by a good London draught-borse, and the 
30 lbs. of water evaporated per hour being considered to be the steam re- 
quirement per indicated horse-power of an average engine. 

The second definition of the term horse-power is an approximate measure 
of the size, capacity, value, or *‘ rating” of a boiler, engine, water-wheel, or 
other source or conveyer of energy, by which measure it may be described, 
bought and sold, advertised, etc. No definite value can be given to this 
measure, which varies largely with local custom or individual opinion of 
makers and users of machinery. Thenearest approach to uniformity which 
can be arrived at in the term ‘‘ horse-power,”’ used in this sense, is to say 
that a boiler, engine, water-wheel, or other machine, ‘‘ rated’? at a certain 
horse-power, should be capable of steadily developing that horse-power for 
a long period of time under ordinary conditions of use and practice, leaving 
to local custom, to the judgment of the buyer and seller, to written contracts 
of purchase and sale, or to legal decisions upon such contracts, the interpree 
tation of what is meant by the term ‘‘ordinary conditions of use and 
practice.”? (Trans. A. S. M. E., vol. vii. p. 226.) 

The committee of the A.S. M. E. on Trials of Steam-boilers in 1884 (Trans., 
vol. vi. p. 265) discussed the question of the horse-power of boilers as follows; 

The Committee of Judges of the Centennial Exhibition, to whom the trials 
of competing boilers at that exhibition were intrusted, met with this same 
problem, and finally agreed to solve it, at least so far as the work of that 
committee was concerned, by the adoption of the unit, 30 Ibs. of water evap- 
orated into dry steam per hour from feed-water at 100° F., and under a 
pee of 70 lbs. per square inch above the atmosphere, these conditions 

eing considered by them to represent fairly average practice. The quane 
tity of heat demanded to evaporate a pound of water under these conditions 
is 1110.2 British thermal units, or 1.1496 units of evaporation. The uxit of 
power proposed is thus equivalent to the development of 33,305 heat-units 
per hour, or 34.488 units of evaporation. ... 

Your committee, after due consideration, has determined to accept the 
Centennial Standard, the first above mentioned, and to recommend that in 
all standard trials the commercial horse-power be taken as an evaporation 
of 30 lbs. of water per hour from a feed-water temperature of 100° F. into 
steam at 70 lbs. gauge pressure, which shall be considered to be equal to 3444 
units of evaporation, that is, to 34% lbs. of water evaporated from a feed- 
water temperature of 212° F. into steam at the same temperature. This 
standard is equal to 33,305 thermal units per hour. 

It is the opinion of this committee that a boiler rated at any stated number 
of horse-powers should be capable of developing that power with easy firing, 
moderate draught, and ordinary fuel, while exhibiting good economy ; and 
further, that the boiler should be capable of developing at least one third 
more than its rated power to meet emergencies at times when maximum 
economy is not the most importart object to be attained. 

Unit of Evaporation,.—lIt is the custom to reduce results of boiler- 
tests to the common standard of weight of water evaporated by the unit 
weight of the combustible portion of the fuel, the evaporation being consid- 
ered to have taken place at mean atmospheric pressure, and at the temper- 
ature due that pressure, the feed-water being also assumed to have been 
suprlied at that temperature, This is, in technical language, said to be the 
equivalent evaporation from and at the boiling point at atmospheric pres- 
suro, or “from and at 212° F,” This unit of evaporation, or one pound of 


678 THE STEAM-BOILER. 


water evaporated from and at 212°, is equivalent to 965.7 British thermal 
units. 

Measures for Comparing the Duty of Boilers.—The meas- 
ure of the efficiency of a boiler is the number of pounds of water evaporated 
per pound of combustible, the evaporation being reduced to the standard of 
**from and at 212°;” that is, the equivalent evaporation from feed-water at a 
temperature of 212° F, into steam at the same temperature. 

The measure of the capacity of a boiler is the amount of ‘‘ boiler horse- 
power ”’ developed, a horse-power being defined as the evaporation of 80 lbs. 
of water per hour from 100° F. into steam at 70 lbs. pressure, or 3414 lbs. per 
hour from and at 212°. 

The measure of relative rapidity of steaming of boilers is the number of 
pends of water evaporated per hour per square foot of water-heating sur- 

ace. 

The measure of relative rapidity of combustion of fuel in boiler-furnaces 
is the number of poundsof coal burned per hour per square foot of grate- — 


surface. 
STEAM-BOILER PROPORTIONS, 


Proportions of Grate and Heating Surface required for 
agiven Horseepower.—The term horse-power here means capacity 
to evaporate 80 lbs. of water from 100°F., temperature of feed-water, to 
steam of 70 Ibs., gauge-pressure = 34.5 lbs. from and at 212° PF, 

Average proportions for maximum economy for land boilers fired with 
good anthracite coal: 

Heating surtace per horse-pOWer......escccssccccrcoce 11.5 Sq. ft. 
6 os ob 1/3 6 


Grate . Riois'ala wisisiaic'staversiars «sive ete 

Ratio of heating to grate surface.................06- . 45 
Water evap’d from and at 212° persq.ft.H.S. perhour 8 Ibs. 
Combustible burned per H.P. per hour................ 8 
Coal with 1/6 refuse, lbs. per H.P. per hour........ a4. ROB 
Combustible burned per sq. ft. grate per hour........ gue 


Coal with 1/6 refuse, lbs. per sq. ft. grate per hour.... 10.8 ‘ 
Water evap’d from and at 212° per lb. combustible... 11.5 * 
66 66 6 46 66 66 66 66 coal (1/6 refuse) 9.6 oe 


The rate of evaporation is most conveniently expressed in pounds evapo- 
rated from and at 212° per sq. ft. of water-heating surface per hour, and the 
rate of combustion in pounds of coal per sq. ft. of grate-surface per hour, 

Heating-surface.—For maximum economy with any kind of fuel a 
boiler should be proportioned so that at least one square foot of heating- 
surface should be given for every 3 lbs. of water to be evaporated from and 
at 212° F. per hour. Still mere liberal proportions are required if a portion 
of the heating-surface has its efficiency reduced by: 1. Tendency of the 
heated gases to short-circuit, that is, to select passages of least resistance 
and flow through them with high velocity, to the neglect of cther passages. 
2. Deposition of soot from smoky fuel. 3. Incrustation. If the heating-sur- 
faces are clean, and the heated gases pass over it uniformly, little if any 
increase in economy can be obtained by increasing the heating-surface be: 
yond the proportion of 1sq. ft. to every 3 lbs. of water to be evaporated, and 
with all conditions favorable but little decrease of economy will take place 
if the proportion is 1 sq. ft. to every 4 lbs. evaporated; but in order to pro- 
vide for driving of the boiler beyond its rated capacity, and for possible 
decrease of efficiency due to the causes above named, it is better to adopt 1 
sq. ft. to 3 lbs. evaporation per hour as the minimum standard proportion. 

Where economy may be sacrificed to capacity, as where fuel is very cheap, 
it is customary to proportion the heating-surface much less liberally. The 
following table shows approximately the relative results that may be ex- 
pected with different rates of evaporation, with anthracite coal. 

Lbs. water evapor’d from and at 212° per sq. ft. heating-surface per hour: 

2 2.5 8 8.5 4 5 6 TONY HAS 9 10 
Sq. ft. heating-surface required per horse-power: 
17.3 13.8 11.5, 9.8 8.6 6.8 5.8 4.9 4.3 3.8 8.5 

Ratio of heating to grate surface if 1/3 sq. ft. of G. S. is required per H.P.: 
52 41.4 84.5 29.4 25.8 20.4 17.4 = 13.7 129 11.4 10.5 

Probable relative economy: 

100 =©100 100 95 90 85 80 5 . 70 65 60 


Probable temperature of chimney gases, degrees F.: 
450 450 450 518 — 585 652 720 (87 855 922 6990 


STEAM-BOILER PROPORTIONS. 679 


The relative economy will vary not only with the amount of heating-sur- 
face per horse-power, but with the efficiency of that heating-surface as 
regards its capacity for transfer of heat from the heated gases to the water, 
which will depend on its freedom from soot and incrustation, and upon the 
circulation of the water and the heated gases. 

With bituminous coal the efficiency will largelydepend upon the thorough- 
ness with which the combustion is effected in. the furnace. 

The efficiency with any kind of fuel will greatly depend upon the amount. 
of air supplied to the furnace in excess of that required to support com- 
bustion. With strong draught and thin fires this excess may be very great,, 
causing a serious loss of economy. 

Measurement of Heating-surface.—Authorities are not agreed 
as to the methods of measuring the heating-surface of steam-boilers. The 
usual rule is to consider as heating-surface all the surfaces that are sur- 
rounded by water on one side and by flame or heated gases on the other, but 
there is a difference of opinion as to whether tuoular heating-surface should 
be figured from the inside or from the outside diameter. Some writers say, 
measure the heating-surface always on the smaller side—the fire side of the 
tube in a horizontal return tubular boiler and the water side in a water-tube 
boiler. Others would deduct from the heating-surface thus measured an 
allowance for portions supposed to be ineffective on account of being cov- 
ered by dust, or being out of the direct current of the gases. 

It has hitherto been the common practice of boiler-makers to consider all 
surfaces as heating-surfaces which transmit heat from the flame or gases 
to the water, making no allowance for different degrees of effectiveness; 
also, to use the external instead of the internal diameter of tubes, for 
greater convenience in calculation, the external diameter of boiler-tubes 
usually being made in even inches or half inches. This method, however, 
is inaccurate, for the true heating-surface of a tube is the side exposed to 
the hot gases, the inner surface in a fire-tube boiler and the outer surface 
in a water-tube boiler. The resistance to the passage of heat from the hot 
gases on one side of a tube or plate to the water on the other consists almost 
entirely of the resistance to the passage of the heat from the gases into the 
metal, the resistance of the metal itself and that of the wetted surface being 
practically nothing. See paper by C. W. Baker, Trans. A.S.M.E., vol. xix. 

Ruts for finding the heating-surface of vertical tubular boilers: Multiply 
the circumference of the fire-box (in inches) by its height above the grate ; 
multiply the combined circumference of all the tubes by their length, and 
to these two products add the area of the lower tube-sheet ; from this sum 
subtract the area of all the tubes, and divide by 144: the quotient is the 
number of square feet of heating-surface. 

Rute for finding the heating-surface of horizontal tubular boilers: Take 
the dimensions in inches. Multiply two thirds of the circumference of the 
shell by its length; multiply the sum of the circumferences of all the tubes 
by their common length; to the sum of these products add two thirds of the 
area of both tube-sheets; from this sum subtract twice the combined area of 
all the tubes; divide the remainder by 144 to obtain the result in square feet. 

Rutz for finding the square feet of heating-surface in tubes: PAultiply the 
Se ad ae ple by the diameter of a tube in inches, by its length in feet, 
and by . . 

Horse-power, Builder's Rating. Heating-surface per 
Worse-power.—It is a general practice among builders to furnish about 
12 square feet of heating-surface per horse-power, but as the practice is not 
uniform, bids and contracts should always specify the amount of heating- 
surface to be furnished. Not less than one third square foot of grate-surface 
should be.furnished per horse-power. 

Engineering News, July 5, 1894, gives the following rough-and-ready rule 
for finding approximately the commercial horse-power of tubular or water- 
tube boilers: Number of tubes X their length in feet x their nominal 
diameter in inches + 50 = nLd +50. The number of square feet of surface 


: aL 
in the tubes is‘ a, wes and the horse-power at 12 square feet of surface 


of tubes per horse-power, not counting the shell, = nZd + 45.8. If 15 square 
feet of surface of tubes be taken, it is nZd +- 57.3. Making allowance for 
the heating-surface in the shell will reduce the divisor to about 50. 

Horse-power of Marine and Locomotive Boilers.—The 
term horse-power is not generally used in connection with boilers in marine 
practice, or with locomotives. The boilers are designed to suit the engines, 
and are rated by extent of grate and heating-surface only. 


680 THE STEAM-BOILER. 


Grate-surface.—The amount of grate-surface required per horse 
power, and the proper ratio of heating-surface to grate-surface are ex- 
tremely variable, depending chiefly upon the character of the coal and upon 
the rate of draught. With good coal, low in ash, approximately equal results 
may be obtained with large grate-surface and light draught and with small 
grate-surface and strong draught, the total] amount of coal burned per hour 
being the same in both cases. With good bituminous coal, like Pittsburgh, 
low in ash, the best results apparently are obtained with strong draught 
and high rates of combustion, provided the grate-surfaces are cut down so 
that the total coal burned per hour is not too great for the capacity of the 
heating-surface to absorb the heat produced. 

With coals high in’ ash, especialiy if the ash is easily fusible, tending to 
choke the grates, large grate-surface and a slow rate of combustion are 
required, unless means, such as shaking grates, are provided to get rid of 
the ash as fast as it is made. 

The amount of grate-surface required per horse-power under various con- 
ditions may be estimated from the following table; 





— — 








fay 

23 7 3n35 Pounds of Coal burned per square foot 

Ea a Ste = of Grate per hour. 

wONES ao > ST TT 

RESO) SER | g | 10] 12| 15 | 20 | 25 | 30 | 35 | 40 
Sq. Ft. Grate per H. P. 

Good coal 10 3.45 .43] .85] .28] .23] .17) .14] .11] .10) .09 
and boiler, 9 3.83 48 38 32] 25) 19) 15] 13) <3] 10 
' , '50| .40| .33] .26] .20| .16} 113] 12] 210 

ea Gen onl) 8 4.31 "54| .43| 136) 29] 129] Laz] cia} 113] l11 

’ uss 4.93 "62| .49| .41| .33) .24| 201 Laz} a4] 112 

6. ( "63| .50| .42| .34| .25] .20] 117] 15] 218 

Tuan, |} 6 5.5 72] 158] 148} 138] .29] 223] .191 17] l44 
aD 5 6.9 86} .69] 58} .46) .35] .28] .23] .22) .17 
CS chsiek t 3.45 10. 1.2511.00] .83] .67] .50! .40| .33] .29| .25 


In designing a boiler for a given set of conditions, the grate-surface should 
be made as liberal as possible, say sufficient for a rate of combustion of 10 
lbs. per square foot of grate for anthracite, and 15 lbs. per square foot for 
bituminous coal, aud in practice a portion of the grate-surface may be 
bricked over if it is found that the draught, fuel, or other conditions render, 
it advisable. 

Proportions of Areas of Flues and other Gas-passages,. 
—Rules are usually given making the area of gas-passages bear a certain 
ratio to the area of the grate-surface; thus a common rule for horizontal 
tubular boilers is to make the area over the bridge wall 1/7 of the grate- 
surface, the flue area 1/8, and the chimney area 1/9. 

For average conditions with anthracite coal and moderate draught, say a 
tate of combustion of 12 lbs. coal per square foot of grate per hour, and a ratio 
of heating to grate surface of 30 to 1, this rule is as good as any, but it is evi- 
dent that if the draught were increased so as to cause a rate of combustion 
of 24 lbs., requiring the grate-surface to be cut down to a ratio of 60 to 1, the 
areas of gas-passages should not be reduced in proportion. The amount 
of coal burned per hour being the same under the changed conditions, and 
there being no reason why the gases should travel at a higher velocity, the 
actual areas of the passages should remain as before, but the ratio of the 
area to the grate-surface would in that case be doubled. 

Mr. Barrus states that the highest efficiency with anthracite coal is 
obtained when the tube area is 1/9 to 1/10 of the grate-surface, and with 
bituminous coal when it is 1/6 to 1/7, for the conditions of medium rates of 
couibustion, such as 10 to 12 lbs. per square foot of grate per hour, and 12 
square feet of heating-surface allowed to the horse-power. 

The tube area should be made large enough not to choke the draught, and 
so lessen the capacity of the boiler; if made too large the gases are apt to 
select the passages of least resistance and escape from them at a high 
velocity and high temperature. 

This condition is very commonly found in horizontal tubular boilers where 


PERFORMANCE OF BOILERS. 681 


the gases go chiefly through the upper rows of tubes; sometimes also in 
vertical tubular boilers, where the gases are apt to pass most rapidly 
through the tubes nearest to the centre. eit: i 

Air=-passages through Grate-bars.—tThe usual practice is, air- 
opening = 30% to 50% of area of the grate; the larger the better, to avoid 
stoppage of the air-supply by clinker; but with coal free from clinker much 
smaller air-space may be used without detriment. See paper by F. A. 
Scheffler, Trans. A. S. M. E., vol. xv. p. 503. 


PERFORMANCE OF BOILERS. 


The performance of a steam-boiler comprises both its capacity for gener- 
ating steam and its economy of fuel. Capacity depends upon size, both of 
grate-surface and of heating-surface, upon the kind of coal burned, upon 
the draft, and also upon the economy. Econemy of fuel depends upon the 
completeness with which the coal is burned in the furnace, on the proper 
regulation of the air-supply to the amount of coal burned, and upon the 
thoroughness with which the boiler absorbs the heat generated in the 
furnace. The absorption of heat depends on the extent of beating-sur- 
face in relation to the amount of coal burned or of water evaporated, upon 
the arrangement of the gas-passages, and upon the cleanness of the sur- 
faces. The capacity of a boiler may increase with increase of economy 
when this is due to more thorough combustion of the coal or to better regu- 
lation of the air-supply, or it may increase at the expense of economy 
when the increased capacity is due to overdriving,-causing an increased 
loss of heat in the chimney gases. The relation of capacity to economy 
is therefore a complex one, depending on many variable conditions. 

Many attempts have been made to construct a formula expressing the rela- 
tion between capacity, rate of driving, or evaporation per square foot of 
heating-surface, to the economy, or evaporation per pound of combustible, 
but none of them can be considered satisfactory, since they make the 
economy depend only on the rate of driving (a few so-called ‘‘ constants,” 
however, being introduced in some of them for different classes of boilers, 
kinds of fuel, or kind of draft), and fail to take into consideration the nu- 
merous other conditions upon which economy depends. Such formule are 
Rankine’s, Clark’s, Emery’s. Isherwood’s, Carpenter’s, and Hale’s. A dis- 
cussion of them allmay be found in Mr. R. 8S. Hale’s paper on “ Efficiency 
of Boiler Heating Surface,” in Trans. A.S. M. E., vol. xviii. p. 328. Mr. 
Hale’s formula takes into account the effect of radiation, which reduces the 
economy considerably when the rate of driving is less than 3 lbs. per square 
foot of heating-surface per hour. 

Selecting the highest results obtained at different rates of driving obtained 
with anthracite coal in the Centennial tests (see p. 685), and the highest 
result. with anthracite reported by Mr. Barrus in his book on Boiler Tests, 
the au_,or has plotted two curves showing the maximum results which 
may be expected with anthracite coal, the first under exceptional conditions 
such as obtained in the Centennial tests, and the second under the best 
conditions of ordinary practice. (Trans. A.S. M. E., xviii. 854), From these 
curves the following figures are obtained. 

Lbs. water evaporated from and at 212° per sq. ft. heating-surface per hour: 


16°. Le 26 8 35 4 45 5 6 vite) 


Lbs. water evaporated from and at 212° per Jb. combustible: 
Centennial. 11.8 11.9 12.0 12.1 12.05 12 11.85 11.7% 11.5 1085 9.8 8.5 
Barrus..... 11.4) 11, RaT550 1.66 EG t.b: 21102") 10:9" °10.6" 9.9) |. 9.2158.5 
Avg. Cent’l .... «0. 12.0 11.6 11.2 10.8 10.4 10.0 96 88 80 72 


The figures in the last line are taken from a straight line drawn as nearly 
as possible through the average of the plotting of all the Centennial tests, 
The poorest results are far below these figures. It is evident that no formula 
can be constructed that will express the relation of economy to rate of 
driving as well as do the three lines of figures given above. 

For semi-bituminous and bituminous coals the relation of economy to the 
rate of driving no doubt follows the same general law that it does with 
anthracite, i.e., that beyond a rate of evaporation of 3 or 4 Ibs. per sq. ft. of 
heating-surface per hour there is a decrease of economy, but the figures 
obtained in different tests will show a wider range between maximum and 
average results on account of the fact that it is more difficult with bituminous 
than with anthracite coal to secure complete combustion in the furnace. 


682 » THE STEAM-BOILER, 


The amount of the decrease in economy due to driving at rates exceeding 
4 Ibs. of water evaporated per square foot of heating-surface per hour 
differs greatly with different boilers, and with the same boiler it may differ 
with different settings and with different coal. The arrangement and size 
of the gas-passages seem to have an important effect upon the relation of 
economy to rate of driving. There is a large field for future research to 
determine the causes which influence this relation. 

General Conditions which secure Economy of Steam-« 
boilers.—In general, the highest results are produced where the tempera- 
ture of the escaping gases is the least. An examination of this question is 
made by Mr. G. H. Barrus in his book on ‘ Boiler Tests,” by selecting those 
tests made by him, six in number, in which the temperature exceeds the 
average, that is, 375° F., and comparing with five tests in which tne temper- 
ature is less than 375° The boilers are all of the common horizontal type, 
and all use anthracite coal of either egg or broken size. The average flue 
temperatures in the two series was 444° and 343° respectively, and the dif- 
ference was 101°. The average evaporations are 10.40 lbs. and 11.02 lbs. ree 
spectively, and the lowest result corresponds to the case of the highest flue 
temperature. In these tests it appears, therefore, that a reduction of 101° 
in the temperature of the waste gases secured an increase in the evaporation 
of 6%. This result corresponds quite closely to the effect of lowering the 
temperature of the gases by means of a flue-heater where a reduction of 
107° was attended by an increase of 7% in the evaporation per pound of coal. 

A similar comparison was made on horizontal tubular boilers using Cum- 
beriand coal. The average flue temperature in four tests is 450° and the 
average evaporation is 11.34 lbs. Six boilers have temperatures below 415°, 
the average of which is 383°, and these give an average evaporation of 11.75 
Ibs. With 67° less temperature of the escaping gases the evaporation is 
higher by about 42. 

The wasteful effect of a high flue temperature is exhibited by other boilers 
than those of the horizontal tubular class. This source of waste was shown 
to be the main cause of the low economy produced in those vertical boilers 
which are deficient in heating-surface. 

Relation between the Heating-surface and Grate-surface to obtain the 
Highest Hfficitency.—A comparison of three tests of horizontal tubular 
boilers with anthracite coal, the ratio of heating-surface to grate-surface 
being 36.4 to1, with three other tests of similar boilers, in which the ratio 
was 48 to 1, showed practically no difference in the results. The evidence | 
shows that a ratio of 36 to 1 provides a sufficient quantity of heating-surface 
to secure the full efficiency of anthracite coal wherethe rate of combustion 
is not more than 12 lbs. per sq. ft. of grate per hour. 

In tests with bituminous coal an increase in the ratio from 36.8 to 4° .8 se- 
cured a small improvement in the evaporation per pound of coal, ane a high 
temperature of the escaping gases indicated that a still further increase 
would be beneficial. Among the high results produced on common horizon- 
tal tubular boilers using bituminous coal, the highest occurs where the ratio 
is53.1 to 1. This boiler gave an evaporation of 12.47 Ibs. A double-deck 
boiler furnishes another example of high performance, an evaporation of 
12.42 lbs. having been obtained with bituminous coal, and in this case the 
ratio is 65 to 1. These examples indicate that a much larger amount of 
heating-surface is required for obtaining the full efficiency of bituminous 
coal than for boilers using anthracite coal. The temperature of the escap- 
ing gases in the same boiler is invariably higher when bituminous coal is 
used than when anthracite coal is used. The deposit of soot on the surfaces 
when bituminous coal is used interferes with the full efficiency of the sur- 
face, and an increased area is demanded as an offset to the loss which this 
deposit occasions. It would seem, then, that if a ratio of 36 to 1 is sufficient 
for anthracite coal, from 45 to 50 should be provided when bituminous coal 
is burned, especially in cases where the rate of combustion is above 10 or 12 
Ibs. per sq. ft. of grate per hour. 

The number of tubes controls the ratio between the area of grate-surface 
and area of tube-opening. A certain minimum amount of tube-opening is 
required for efficient work. 

The best results obtained with anthracite coal in the common horizontal 
boiler are in cases where the ratio of area of grate-surface to area of tube- 
opening is larger than 9to1. The conclusion is drawn that the highest effi- 
ciency with anthracite coal is obtained when the tube-opening is from 1/9 to 
1/10 of the grate-surface. 


PERFORMANCE OF BOILERS. 683 


When bituminous coal is burned the requirements appear to be different. 
The effect of a large tube-opening does not seem to make the extra tubes 
inefficient when bituminous coal is used. The highest result on any boiler of 
the horizontal tubular class, fired with bituminous coal, was obtained where 
the tube-opening was the largest. This gave an evaporation of 12.47 lbs., the 
ratio of grate-surface to tube-opening being 5.4 to 1. The next highest re- 
sult was 12.42 lbs., the ratio being 5.2 to1. Three high results, averaging 
12.01 lbs., were obtained when the average ratio was 7.1 to 1. Without going 
to extremes, the ratio to be desired when bituminous coal is used is that 
which gives a tube-opening having an area of from 1/6 to 1/? of the grate- 
surface. This applies to medium rates of combustion of, say, 10 to 12 lbs. per 
sq. ft. of grate per hour, 12 sq. ft. of water-heating surface being allowed per 
horse-power. 

A comparison of results obtained from different types of boilers leads to 
the general conclusion that the economy with which different types of 
boilers operate depends much more upon their proportions and the condi- 
tions under which they work, than upon their type ; and, moreover, that 
when these proportions are suitably carried out, and when the conditions 
are favorable, the various types of boilers give substantially the same eco- 
nomic result. 

Efficiency of a Steame-boiler.—tThe efficiency of a boiler is the 
percentage of the total heat generated by the combustion of the fuel 
which is utilized in heating the water and in raisingsteam. With anthracite 
coal the heating-value of the combustible portion is very nearly 14,500 
B. T. U. per lb., equal to an evaporation from and at 212° of 14,500 + 966 
= 15 lbs. of water. A boiler which when tested with anthracite coal shows 
an evaporation of 12 lbs. of water per lb. of combustible, has an efficiency of 
12 -- 15 = 80%, a figure which is approximated, but scarcely ever quite 
reached, in the best practice. With bituminous coal it is necessary to have 
a determination of its heating-power made by a coal calorimeter before the 
efficiency of the boiler using it can be determined, but a close estimate may 
be made from the chemical analysis of the coal. (See Coal.) 

The difference between the efficiency obtained by test and 100% is the sum 
of the numerous wastes of heat. the chief of which is the necessary loss due 
to the temperature of the chimney-gases. If we have an analysis anda 
calorimetric determination of the heating-power of the coal (properly sam- 
pled), and an average analysis of the chimney-gases, the amounts of the 
several losses may be determined with approximate accuracy by the method 
described below. 

Data given: 





1. ANALYSIS OF THE COAL. 2. ANALYSIS OF THE Dry CHIMNEY- 
Cumberland Semi-bituminous. GASES, BY WEIGHT, 
Carbon........ wie ate lero we tioe 80.55 Cc: O. N. 
FL VAROSEH terse tee cle clloistesias cle 4.50 CO, = 13.6 = 3.71 9.89 eoce 
ORY WEUis. ceedccclacdsesdsetedacie (0 COM = 7.2309 Vile Oi ae 
Nitrogen ........ ed oheeeesedeset 61.08 O She eseee | LL eOi teat 
Moisture. .....ecccece eeeces e@ecoe 2.92 N = 75.0 = esece 95.00 
Ash.... COC SSS HECTOR FSOOHRESLEe Ses 8.25 a, —— Saw, beat 
—_—-— 100.0 8.80 21.20 %5.00 


Heating-value of the coal by Dulong’s formula, 14,243 heat-units, 

Ene. gases being collected over water, the moisture in them is net deter- 
mined. 

3. Ash and refuse as determined by boiler-test, 10.25, or 2% more than that 
found by analysis, the difference representing carbon in the ashes obtained 
in the boiler-test. 

4. Temperature of external atmosphere, 60° F. 

5. Relative humidity of air, 60%, corresponding (see air tables) to .007 lb. of 
vapor in each lb. of air. 

6. Temperature of chimney-gases, 560° F. 

Calculated results ; 

The carbon in the chimney-gases being 3.8% of their weight, the total 
weight of dry gases per lb. of carbon burned is 100 -+ 3.8 = 26.32 lbs. Since 
the carbon burned is 80.55 — 2 = 78.55% of the weight of the coal, the weight 
of the dry gases per lb. of coal is 26.32 < 78.55 + 100 = 20.67 lbs. 

Each pound of coal furnishes to the dry chimney-gases .7855 Ib, C, .0108N, 


and (2 G0 = *) +> 100 = .0214 Ib. O; a total of .817%, say .82]b. This sub- 


Got THE STEAM-BOILER, 


tracted from 20.67 Ibs. leaves 19.85 Ibs. as the quantity of dry air (not includ 
ing moisture) which enters the furnace per pound of coal, not counting the 
air required to burn the available hydrogen, that is, the hydrogen minus one 
eighth of the oxygen chemically combined in the coal. Each lb. of coal 
burned contained .045 lb. H, which requires .045 x 8 = .36 lb. O for its com- 
bustion, Of this, .027 lb. is furnished by the coal itself, leaving .333 lb. to 
come from the air. The quantity of air needed to supply this oxygen (air 
containing 28% by weight of oxygen) is .332 + .23 = 1.45 lb., which added to 
the 19.85 Ibs. already found gives 21.30 lbs. as the quantity of dry air sup- 
plied to the furnace per lb. of coal burned. 

The air carried in as vapor is .0071 lb. for each Ib. of dry air, or 21.3  .0071 
= 0.15 lb. for each lb. of coal. Each lb. of coal contained .029 lb. of mois- 
ture, which was evaporated and carried into the chimney-gases. The .045 Ib. 
of H per Ib. of coal when burned formed .045 x 9 = .405 lb. of H,O. 

From the analysis of the chimney-gas it appears that .09 -- 3.80 = 2.37% of 
the carbon in the coal was burned to CO instead of to COg. 

We now have the data for calculating the various losses of heat, as follows, 
for each pound of coal burned: 

Per cent of 
gieet Heat-value 
* of the Coal, 


20.67 lbs. dry gas x (560° — 60°) x sp. heat 0 24 = 2480.4 17.41 
.15 1b. vapor in air x (560° — 60°) x sp. heat .48 = 86.0 0.25 
-029 lb. moisture in coal heated from 60° to 212° = 4.4 0.03 

uy evaporated from and at 212°; .029 x 966 = 28.0 0.20 

“ ~—s steam (heated from 212° to 560°) x 348 x .48 = 4.8 0,03 
.405 lb. H,O from H in coal & (152 + 966 + 348 x .48)= 520.4 8.65 
-0237 Ib. C burned to CO; loss by incomplete com- 

bustion, .0237 « (14544 — 4451) 239.2 


.02 lb. coal lost in ashes; .02 « 14544 
Radiation and unaccounted for, by difference 


Woulel 
ca) 
le} 
So 
Vo) 
Xs) 
S 
reg 





4228.1 29.68 
10,014.9 70.32 


—enee 


14,243.0 100.00 


The heat lost by radiation from the boiler and furnace is not easily deter- 
mined directly, especially if the boiler is enclosed in brickwork, or is pro- 
tected by non-conducting covering. It is customary to estimate the heat 
lost by radiation by difference, that is, to charge radiation with all the heat 
lost which is not otherwise accounted for. 

One method of determining the loss by radiatiun is to block off a portion 
of the grate-surface and build a small fire on the remainder, and drive this 
fire with just enough draught to keep up the steam-pressure and supply the 
heat lost by radiation without allowing any steam. to be discharged, weigh- 
ing the coal consumed for this purpose during a test of several hours’ dura- 
tion. 

Estimates of radiation by difference are apt to be greatly in error, as in 
this difference are accumulated all the errors of the analyses of the coal 
and of the gases. An average value of the heat lost by radiation from a 
boiler set in brickwork is about 4 percent. When several boilers are in a 
battery and enclosed in a boiler-house the loss by radiation may be very 
much less, since much of the heat radiated from the boiler is returned to it 
in the air supplied to the furnace, which is taken from the boiler-room. 

An important source of error in making a ‘‘heat balance’’ such as the 
one above given, especially when highly bituminous coal is used, may be 
due to the non-combustion of part of the hydrocarbon gases distilled trom 
the coal immediately after firing, when the temperature of the furnace may 
be reduced below the point of ignition of the gases. Each pound of hydro- 
gen which escapes burning is equivalent to a loss of heat in the furnace of 
62,500 heat-units. 

In analyzing the chimney gases by the usual method the percentages of 
the constituent gases are obtained by volume instead of by weight. To 
reduce percentages by volume to percentages by weight, multiply the per- 
centage by volume of each gas by its specific gravity as compared with air, 
and divide each product by the sum of the products. 


Utilized in making steam, equivalent evaporation 
10.37 lbs. from and at 212° per Ib. of coal 





TESTS OF STEAM-BOILERS. 685 


ff O, CO, CO,, and_N represent the per cents by volume of oxygen, car- 
pene oxide, carbonic acid, and nitrogen, respectively, in the gases of com- 
ustion; 





Lbs. of air required to burn ) _ 3.082. N 
one pound of carbon SCOR aaCO, 
Ratio of total air to the theoretical requirement = No 3.720" 
Z e — 0.10% 
Lbs. of air per pound) _ } Lbs. of air per pound j Per cent of carbon 
of coal a of carbon x ( in coal. 
11CO, + 80 + 7(CO + N) 
Lbs. dry gas produced per pound of carbon = a = 
BRAY od % 3(CO, + CO) 


‘TESTS OF STEAM-BOILERS., 


Boiler-tests at the Centennial Exhibition, Philadel- 
phia, 18'76.—(See Reports and Awards Group XX, Internationa] Exhibi- 
tion, Phila., 1876; also, Clark on the Steam-engine, vol. i, page 253.) 

Competitive tests were made of fourteen boilers, using good anthracite 
coal, one boiler, the Galloway, being tested with both anthracite and semi- 
bituminous coal. Two tests were made with each boiler: one called the 
capacity trial, to determine the economy and capacity at a rapid rate of 
driving; and the other called the economy trial, to determine the economy 
when driven at a rate supposed to be near that of maximum economy and 
rated capacity. The following table gives the principal results obtained in 
the economy trial, together with the capacity and economy figures of the 
capacity trial for comparison. 










Economy Tests. Capacity 











Tests, 
eel. | |Seles 7 3 
Hels | 3 latlso3 | A ee 
we) |B ISo|aak!| S ® ao) 
cI es ei era er i eae g? 
Name efi, 8] oc En = iom Pre | a 3.9 
of 2O/2S) 8 EME en] F] Slo EA 
Boiler. TBlom We eon Rem! ete ert) marca a 
mis | ot loan Obs =] o |a2 
S5/85| 3 Sole°e] B]s/2] 8 7 & 188, 
Soffa SIS eS Ssl a] 5 3 5 5 > 12 
PSlsol g [eco “S| 5] & 2 S, 2 |*h2 
offal 8 [s4/5FO  a/ S18} 2 o [BRAG 
Satake] Cesleeanpe | 2 Suki b 2 |Sag 
GN Oe OU ote aa O | bis oS oe ie ace 
me iO Je Sees aelelal a qq if 
lbs.|p.ct| lbs.] Ibs. |deg| % jdeg| H.P.@ H.P. | Ibs. 
ROOGRe re wecisteccne -/384.6} 9.1]10.4]2.25]12.094] 393 41.4] 119.8 .6/10.441 
Firmenich......... 64.3)12.0 10.4/1.68 11.988} 415 .]82.6] 57.8 .4)11.064 
EEO W Gira sie teres fe ale tele 30.6] 6.8 11.31.87 11.923] 38338]....] 9.4] 47.0 .3/11.163 
Srmittits. see 45.8}13.1/11.1/2.42]11.906] 411] 1.3 «| 99.8 0111. 925 
Babcock & Wilcox!37.7/10.0|11.0/2.43/11.822] 296) 2.7 135.6 .6|10.330 
Galloway.......... 23.7| 9.6]11.1/3.63)11 583) 303)....] 1.4] 103.3) .8/11.216 
Do. semi-bit. coal|23.7| 7.9) 8.8 3.20/12.125] 325 90.9 .1/11.609 
Andrews.... ..-... 15.6} 8.0)10.3 2.32/11.039] 420 1.7) 42.6 0) 9.745 
EEEEPISOM sitc'sls pcre tale 27.3)12.4] 8.5 2.75]10.930] 517 82.4 .4| 9.889 
Wiegand.........../30.7/12.3) 9.5 3.30)10.834) 524 20.5) 147.5 .8) 9.145 
Anderson... ..... |17.5] 9.7] 9.3 2.64/10.618} 417 15.7] 98.0 2.8) 9.568 
GLY a aorets slwia taralevatars 20.9]10.8] 9.0 3.82)10.3812]....] 5.6 81.0 -9| 8.397 
Exeter..........-.+{/33.0| 9.3}/11.4 1.38]10.041| 430} 4.2 Geom .0} 9.97 
PicrCe Re occics, cote < 14.0) 8.0)11.0 4.44]10.021] 374) 5.2 Sy hal .8] 9.865 
Rogers & Black ...|19.0} 8.6] 9.9 3.48) 9.613) 572) 2.1 45.7 .2| 9.429 








—— | | | | | | 


Averares@e.....|-.2 sles teers ES ee ee a 85.09 110.8110. 251 


The comparison of the economy and capacity trials shows that an average 
increase in capacity of 30 per cent was attended by a decrease in economy 
of 8 per cent, but the relation of economy to rate of driving varied greatly 
in the different boilers. In the Kelly boiler an increase in capacity of 22 per 
cent was attended by a decrease in economy of over 18 per cent, while the 
Smith boiler with an increase of 25 per cent in capacity showed a slight 
increase in economy, 





686 THE STEAM-BOILER. 


One of the most important lessons gained from the above tests is that 
there is no necessary relation between the type of a boiler and economy. 
the five boilers that gave the best results, the total range of variation be- 
tween the highest and lowest of the five being only 2.3%, three were water- 
tube boilers, one was a horizontal tubular boiler, and the fifth was a com- 
bination of the two types. The next boiler on the list, the Galloway, was an 
internally fired boiler, all of the others being externally fired. The following 
og ri brief description of the principal constructive features of the fourteen 
oilers: 
4-in. water-tubes, inclined 20° to horizontal; reversed 
Root eeeveeeeece ece draug ht. 
Firmenich .....0.0-.02. 3-in. water euhee nearly vertical; reversed draught, 
Lowe.....ccecccccesees Cylindrical shell, multitubular flue. 
Smith. Bit ii eth cite shell, multitubular flue=-water-tubes in 
@ereeeeeeeeeees maui ee < : : ine : ‘ ' 
6-in, water-tubes, incline o horizontal; re- 
Babcock & Wilcox.... { versed draught. 
Cylindrical shell, furnace-tubes and water-tubes. 
Square fire-box and double return multitubular flues, 
ne 8 slabs of cast-iron spheres, 8 in. in diameter; re- 
versed draught, 
Wiegand.....s.secesee a Seana pe tubes, vertical, with internal circulating 
Anderson.............. 3-in. flue-tubes, nearly horizontal; return circulation. 
Kell i 8-in. water-tubes, slightly inclined; each divided by 
Y ccesect pines see te internal diaphragm to promote circulation. 


Galloway...... ssese- 
ANGFOWSi.ice coreclaches 


Harrison........ 


Ub oi) eg 27 hollow rectangular cast-iron slabs. 
PICTCe aj. ob o's o's .see- Rotating horizontal cylinder, with flue-tubes. 
Rogers & Black....... Vertical cylindrical boiler, with external water-tubes. 


Tests of Tubulous Boilers.—tThe following tables are given by S. 
H. Leonard, Asst. Engr. U.S. N., in Jour. Am. Soc. Naval Engrs. 1890. The 
tests were made at different times by boards of U.S. Naval Engineers, ex- 
cept the test of the locomotive-torpedo boiler, which was made in England. 




















2 Evaporation c=] 

e from and at Weights, lbs. 2 2 | 

ot 212° F. 4 etd reat 

5 : & an oe 

as aa A ° iat, | vate tee led 

2 | Si ; or m | ed] £9] a /5 

s| Type. Bo] Slosle./28 |a les] ss] ga] 2 l4 

Fe | §1#sls8/ 28. jg (esl ES] Ze] Gig 

Se | Ol] sl 5e/e8el/G lou] 59/2 | 3/3 

2s s\ 2s]. 2 eae | t (es) 8a) hie: 

ao | Fl pal oP]. o | 5 15m) eS) 2 | sig 

ESR Paps (ld Peat Pacsssomeed Finda i css pe Pel 

1 [Belleville ..] 12.8 /10.42] 5.2] 6.4 |B 49:0") 004 |53.2110.1 [Nat'L| 111/B. 

9.3 |10.23| 3.1] 9.1 |B 21945] 96 4.8 | Jet. | 120/A, 

2 |Herreshoff { 25.8 | 5.68} 8 | 28:8 |S, 3.050) 33 14.8 18 wets | 125) 

4.3 |13.412.7| 1 1,380/172 "1 [Nat’l.| 148/4. 

Bi Townes. ; 24.5 | 6-77| 8.2 | 30.4 |S 15640) 56 |*2-8) 9:6 | 1.14] 15214" 

7.9 |10.77] 1.7] 5.8 | 4 ggolt54 7.7 |Nat’l| Ola. 

4 Ward......12 15:5 (10.011 312 | 11 o yos0| 82 [18.2] 4.07] Jet. | 17/4. 

on 3.98 "3 6 rie E 18,900 bo 47 Yaris 7 re 

"3 | 9.93] 8.6 | 11 hea: 08] 77/A, 

5 |Scotch.. i} 38 | 9.06/12.8 | 16.3 |S 30,000] 80 |42-*, 3:1 | 4.01] lA: 

6 Locomtivs 98.3 |..... 17.1 | 80.5 (6 94 opp? lay at 1-81. 8.13) Jen Bh 

torpedo, | {120.8 |..-.-/20.05] 36.2 een (83.38[/°° °° | 1.2 | 4.95] 123/B, 

q |Ward......|_ 55.04] 8.44] 9.47] 32.1 {© 26.533) 96 |10.3 1.8] @ | 160/B, 

mete S 30.474 

Ol rots, (U.l | gemaiiarL | +... H 20.160 (#31 110.8).....| 8 | 245/B, 

S.S.Cush- , 
ing.) 





* Appr oximate, 
Per cent tiolatute in steam: Belleville, 6.31; Herreshoff (first test), 3.5 
weoleh, Ist, 3.44; 2d. 4.29; Ward, 11.6; others not given, 


TESTS OF STEAM-BOILERS. 


DIMENSIONS OF THE BOILERS, 





No. 1 2 3 4 ad ne ” 8 


Length, ft. and in.. 4/9” 








8’ 6” 4’ g”/ a 6// 3/ or 9g/ 0” 16/ 8 10’ 3//* 10’ 03 

WEE ope Oe Pars eS Ge i NaGe 0 ie 6d ARG 5T ORO 
Heicnteus Site Orr sdeO 8 Sr to | aaa 7 6 11 8 8 Ot 
Space, cu. ft....... 645.5) 69.6 |20 8 | 42.7 | 572.5) 630.3 729.3 560t 
Grate-area, sq. ft..| 34.17} 9 | 4.25 | 3.68 | 31.16} 28 66.5 38.3 
Heating-surface, 

SQuLOM ee bee 804°) 205 | %5 146°) 727 = 1116 2490 2375 
Ratio H.S. + G....} 23.5 |. 22 | 17.6 | 89.5 | 23.38 | 39.8 37.4 62 


* Diameter. +t Diam. of drum. t+ Approximate. 


The weight per I.H.P. is estimated ona basis of 20 lbs. of water per hour 
for all cases excepting the Scotch boiler, where 25 lbs. have been used, as this 
boiler was limited to 80 lbs. pressure of steam. 

The following approximation is made from the large table, on the assump- 
tion that the evaporation varies directly as the combustion, and 25 lbs. of 
coal per square foot of grate per hour used as the unit. 


r ; Weight 

beh com fERaPora'| Weight | West | per tb, 

Type of Boiler. bustion. | cu. ft. of UP Heating- heen 
Space. tie uae *RSULLACe: rar Bee 

Bellevillocin csscseses ses 0.50 0.50 2.02 2.10 2.50 
Herreshoff....... setae 1.00 0.95 0.72 0.60 0.90 
IRONS as54q54 Soatiquone 1.00 1.20 1.12 0.87 1.30 
DC OUCMenteetacecterta ste « tcls 1.00 0.44 2.40 1.64 2.30 
UQCOMOLVE }.-Bescc ences 3.90 0.31 3.70 1.25 3.50 
SWEATY 6a5 ben: BAASE a enee 2.20 0.58 1.27 0.50 1.53 


The Belleville boiler has no practical advantage over the Scotch either in 
space occupied or weight. All the other tubulous boilers given greatly 
exceed the Scotch in these advantages of weight and space. 


Some High Rates of Evaporation.—ng’g, May 9, 1884, p. 415. 


Locomotive. Torpedo-boat, 

Water evap. per sq. ft. H.S. per hour. ... 12.57 13.73 12.54 20.74 
& so ‘s Ib. fuel from and at 212°. 8.22 8.94 8.37 7 04 
Thermal units transf’d per sq. ft. of H.S, 12,142 13,263 12,113 20,034 
HMciency:s.-.....5-6- oc aae feet tas ae oe 586 637 .542 .468 


A 
It is doubtful if these figures were corrected for priming. 


Economy Effected by Heating the Air Supplied to 
Boiler-furnaces,. (Clark, §. E.)—Meunier and Scheurer-Kestner ob- 
tained about 7% greater evaporative efficiency in summer than in winter, 
from the same boilers under like conditions,—an excess which had been ex- 
plained by the difference of loss by radiation and conduction. But Mr, 
Poupardin, surmising that the gain might be due in some degree also to the 
greater temperature of the air in summer, made comparative trials with 
two groups of three boilers, each working one week with the heated air, 
and the next week with cold air. The following were the several efficien- 
cies: 

First Triats: THREE Borers; RoNcHAMP COAL. 
Water per Jb. of Water per lb. of 


Coal. Combustible. 
With heated air (128° F.) ............ @.77 lbs. 8.95 lbs. 
Wiaithicold .airi(693. Sie e vee, V.80 °° fees) PY 
Difference in favor of heated air .... 0.44 ‘‘ (yes Bp 
Sreconp Trias: SAME CoaL; THREE OTHER BoiLERs. 
With heated air (120°.4 F.)..........-. 8.70 Ibs. 10.08 Ibs, 
Witte Cold ait (75°. 2) see cece O09 5 9.34 * 
Difference in favor of heated air..... 0.61 “* A 


688 THE STEAM-BOILER. 


These results show economies in favor of heating the aii of 6% and 716%. 
Mr. Poupardin believes that the gain in efficiency is due chiefly to the 
_ better combustion of the gases with heated air. It was observed that with 
heated air the flames were much shorter and whiter, and that there was 
notably less smoke from the chimney. 

An extensive series of experiments was made by J. C. Hoadley (Trans. 
A.S. M.E., vol. vi., 676) on a ‘‘Warm-blast Apparatus,” for utilizing the 
heat of the waste gases in heating the air supplied to the furnace. The ap- 
paratus, as applied to an ordinary horizontal] tu: ular boiler 60 in. diameter, 
21 feet long, with 65 314-inch tubes, consisted of 240 2-inch tubes, 18 feet long, 
through which the hot gases passed while the air circulated around them. 
The net saving of fuel effected by the warm blast was from 10.7% to 15.5% of 
the fuel used with cold blast. The comparative temperatures averaged as 
follows, in degrees F.: 


Cold-blast Warm-blast 


Boiler. Boiler, Difference. 

In heat of fire........ SORE eee (24938 2793 300 
At bridge wall................... 1340 1600 260 
In smoke box!) os. 062. ob. eee aloe 375 2 
Air admitted to furnace......... 32 332 300 
Steam and water in boiler....... 300 300 

Gases escaping to chimney... .. 37 162 211 
POXCOLUAUAIL eve toda hee oes 32 82 0 


With anthracite coal the evaporation from and at 212° per lb. combustible 
was, for the cold-blast boiler, days 10.85 lbs., days and nights 10.51; and for 
the warm-blast boiler, days 11.83, days and nights 11.03. 


Results of Tests of Heine Water-tube Boilers with 
_ Different Coals. 


(Communicated by E. D. Meier, C.E., 1894.) 


























Number........ SORE pes 1 2 3 4 5 6 vg 8 
ve a la la als 
42 | 24 Pool, | |e} s |] os | e. 
Kind of Coal. giz | Youghiogh-| | 2s | 25 | Be | oS 
ea i. cay. aa | se | 20/25) 
Sw 5 a ¢ |eAIsS 
6) H e) se ro) a 
Per cent ash............. 5h al ea OO de eee 11.6 | 16.1 | 11.5 | 21.8 | 12.8 
Heating-surface, sq. ft..| 2900 | 2040 | 2040 | 2300 | 1260 | 38780 | 1168 | 277 
Grate-surface, sq. ft.....| 54 | 44.8 | 44.8 | 50 21°’ | 73:8 | 27.9.1 50 
Ratio H.S. toG.S........ 58094 acon 45. eo 60 | 50.9 | 41.9 | 55.4 


Coal per sq. ft. G.per hr.| 24.7 | 23.5 | 22.7 | 385 | 83.7 | 26.2 | 27.7 ] 86 
Water per sq. ft. H.S.per 

hr. from and at 212°....) 5.03 | 5.14 | 5.24 | 5.56 | 4.26 | 4.28 | 4.86 | 5.08 
Water evap. from and at 

212° per lb. coal....... -| 10.91 | 9.94 | 10:51 | 7.31 | 7.59 | 8.83 | 7.386 | 7.81 
Per lb. combustible...... 11.50 | 10.48 |... 8.27 | 9.05 | 9.41 | 9.41 | 8.96 
Temp. of chimney gases} 530° |..... 2007), D000! bv see 609 | 707 
Oalorific value of fuel. ..|13,800)12, 936 12, 936/10, 48711, 785/11, 616] $,739 |10,359 
Efficiency of boiler perce.! 77.0 | 74.3 1738.5 | 67.2 | 62.5 | 69.3 | 73.0 | 72.6 





Tests Nos. 7 and 8 were made with the Hawley Down-draught Furnace, 
the others with ordinary furnaces. 

These tests confirm the statement already made as to the difficulty of 
obtaining, with ordinary grate-furnaces, as high a percentage of the calo- 
rific value of the fuel with the Western as with the Eastern coals. 

Test No 3, 78.5% efficiency, is remarkably good for Pittsburgh (Youghiogh- 
eny) coal. If the Washington coal had given equal efficiency, the saving of 


— 62.3 
fuel would be a = 20.2%. The results of tests Nos. 7 and 8 indicate 


eae the downward-draught furnace is well adapted for burning Illinois 
coals. 





BOILERS USING WASTE GASES, 689 


Maximum Boiler Efficiency with Cumberland Coal.,-- 
About 12.5 lbs. of water per lb. combustible from and at 212° is about the 
highest evaporation that can be obtained from the best steam fuels in the 
United States, such as Cumberland, Pocahontas, and Clearfield. In excep- 
tional cases 13 lbs. has been reached, and one test is on record (F. W. Dean, 
Eng’g News, Feb. 1, 1894) giving 13.23 lbs. The boiler was internally fired, 
of the Belpaire type, 82 inches diameter, 31 feet long, with 160 3-inch tubes 
12% feetlong. Heating-surface,1998 square feet; grate-surface,45 square feet, 
reduced during the test to 30144 square feet. Double furnace, with fire-brick 
arches and a long combustion-chamber. Feed-water heater in smoke-box. 
The following are the principal results ; 


1st Test. 2d Test, 
8.85 6.06 


Dry coal burned per sq. ft. of grate per hour, lbs....... 8. 1 
Water evap. per sq. ft. of heating-surface per hour, lbs 1.63 3.00 
Water evap. from and at 212° per lb. combustible, in- 

cluding feed-water heater. ........... 2... cece cece seeew ould 13.23 
Water evaporated, excluding feed-water heater......... 12.88 12,90 
Temperature of gases after leaving heater, F........... 360° 469° 


BOILERS USING WASTE GASES, 


Proportioning Boilers for Blast-Furnaces,.—(F. W. Gordon, 
Trans, A. I. M. E., vol. xii., 1883.) 


Mr. Gordon’s recommendation for proportioning boilers when properly set 
for burning blast-furnace gas is, for coke practice, 30 sq. ft. of heating-sur- 
face per ton of iron per 24 hours, which the furnace is expected to make, 
calculating the heating-surface thus: For double-flued boilers, all shell- 
surface exposed to the gases, and half the flue-surface; for the French type, 
all the exposed surface of the upper boiler and half the lower boiler- 
ec ape for cylindrical boilers, not more than 60 ft. long, all the heating- 
surface. 

To the above must be added a battery for relay in case of cleaning, repairs, 
etc., and more than one battery extra in large plants, when the water carries 
much lime. 

For anthracite practice add 50% to above calculations. For charcoal prac. 
tice deduct 20%. 

In a letter to the author in May, 1894, Mr. Gordon says that the blast- 
furnace practice at the time when his article (from which the above extract 
is taken) was written was very different from that existing at the present 
time; besides, more economical engines are being introduced, so that less 
than 30 sq. ft. of boiler-surface per ton of iron made in 24 hours may now be 
adopted. He says further: Blast-furnace gases are seldom used for otner 
than furnace requirements, which of course is throwing away good fuel. In 
this case a furnace in an ordinary good condition, and a condition where it 
can take its maximum of blast, which is in the neighborhood of 200 to 225 
eubic ft., atmospheric measurement, per sq. ft. of sectional area of hearth, 
will generate the necessary H.P. with very small heating-surface, owing to 
the high heat of the escaping gases from the boilers, which frequently is 
1000 degrees. 

A furnace making 200 tons of iron a day will consume about 900 H.P. in 
blowing the engine. About a pound of fuel is required in the furnace per 
pound of pig metal. 

In practice it requires 70 cu ft. of air-piston displacement per Ib. of fuet 
consumed, or 22,400 cu. ft. pei minute for 200 tons of metal in 1400 working 
minutes per day, at, say, 10 lbs. discharge-pressure. This is equal to 94 lbs. 
M.E.P. on the steam-piston of equal area to the blast-piston, or 9001.H.P. To 
this add 20% for hoisting, pumping and other purposes for which steam is em- 
ployed around blast-furnaces, and we have 1100 H.P., or say 544 H.P. per 
ton of iron per day. Dividing this into 30 gives approximately 54 sq. ft. of 
heating-surface of boiler per H.P. 

Water-tube Boilers using Blast-furnace Gases.—D. S. 
Jacobus (Trans. A. I. M. E., xvii. 50) reports a test of a water-tube boiler using 
blast-furnace gas as fuel. The heating-surface was 2535 sq. ft. It developed 
328 H.P. (Centennial standard), or 5.01 lbs. of water from and at 212° per 
sq. ft. of heating-surface per hour. Some of the principal data obtained 
were as follows: Calorific value of 1 lb. of the gas, 1413 B T.U., including 
the effect of its initia] temperature, which was 650° F. Amount of air used 
to burn 1 lb. of the gas = 0.91b. Chimney draught, 114 in. of water. Area of 
gas inlet, 300 sq. in.; of air inlet, 100 sq. in. Temperature of the chimney 


690 THE STEAM-BOILER. 


gases, 775° F. Efficiency of the boiler calculated from the temperatures 
and analyses of the gases at exit and entrance, 61%. The average analyses 
were as follows, hydrocarbons being included in the nitrogen: 


By Weight. | By Volume. 
At Entrance.| At Exit. |At Entrance.) At Exit. 
CO cuikls tis wate s ela sek avis 10.69 26.37 7.08 18.64 
wesleisvsisen Bistecis elesisieitereets aul 3.05 10 2.96 
COne ees ASOrne 26.71 Ate) 27.80 1.98 
INTIT OR CM iiss eisiow cece cies « 62.48 68.80 65.02 %6.42 
CARO g 5, occ peene vine nr: 2.92 7.19 
INVOO Sears te cee s ce amcst 11.45 a 
Mote WCar ce. ass avis 14.37 7.95 





Steam-boilers Fired with Waste Gases from Puddling 
and Heating Furnaces,—the Iron Age, April 6, 1893, contains a report 
of a number of tests of steam-boilers utilizing the waste heat from pud 
dling and heating furnaces in rolling-mills. The following principal data are 
selected: In Nos. 1, 2, and 4 the boiler is a Babcock & Wilcox water-tube 
boiler, and in No. 3 it is a plain cylinder boiler, 42 in. diam. and 26 ft. long. 
No. 4 boiler was connected with a heating-furnace, the others with puddling 
furnaces. 

No.1. No.2. No.3. No.4. 


Heating-surface, sq. ft......c0-csccersccece 1026 1196 143 1380 


Grate-surface, sq. ft............ Scieisiete.s AOC 19.9 13 6 13.6 16.7 

RatiopAiSntouG. Shmu Meas as careers 2 S36¢ 2 87.2 10.5 82.8 

Water evap. per hour, Ibs.................. 3358 2159 1812 3055 
re ae per sq. ft. H.S. per hr., lbs... 3.3 1.8 12.7 2.2 
“8 per Ib. coal from and at 212°. 5.9 6.24 38.76 6.34 
ih ho ee ee COMED SS als ence re ip 7.20 864.381 8.34 


In No. 2, 1.38 lbs. of iron were puddled per Ib. of coal. 

In No. 3, 1.14 lbs. of iron were puddled per Ib. of coal. 

No, 3 shows that an insufficient amount of heating-surface was provided 
for the amount of waste heat available, 


RULES FOR CONDUCTING BOILER-TESTS. 


Code of 1899. 
(Reported by the Committee on Boiler Trials, Am. Soc. M. E.*) 


I. Determine at the outset the specific object of the proposed trial, 
whether it be to ascertain the capacity of the boiler, its efficiency as a 
steam-generator, its efficiency and its defects under usual working condi- 
tions, the economy of some particular kind of fuei, or the effect of changes 
of design, proportion, or operation; and prepare for the trial accordingly. 

Il. Examine the boiler, both outside and inside; ascertain the dimensions 
of grates, heating surfaces, and all important parts ; and make a full rec- 
ord, describing the same, and illustrating special features by sketches. 

Ill. Notice the general condition of the boiler and its equipment, and 
record such facts in relation thereto as bear upon the objects in view. 

If the object of the trial is to ascertain the maximum economy or capa- 
city of the boiler as a steam-generator, the boiler and all its appurtenances 
should be put in first-class condition. Clean the heating surface inside and 
outside, remove clinkers from the grates and from the sides of the furnace. 
Remove all dust, soot, and ashes from the chambers, smoke-connections, 
and flues. Close air-leaks in the masonry and poorly fitted cleaning-doors. 
See that the damper will open wide and close tight. Test for air-leaks by 
firing a few shovels of smoky fuel and immediately closing the damper, ob- 
serving the escape of smoke through the crevices, or by passing the flame 
of a candle over cracks in the brickwork. 


* The code is here slightly abridged. The complete report of the Com- 
mittee may be obtained in pamphlet form from the Secretary of the Ameri- 
can Society of Mechanical Engineers, 12 West 31st St., New York, 


RULES FOR CONDUCTING BOILER-TESTS. 691 


IV. Determine the character of the coal to be used. For tests of the effi- 
ciency or capacity of the boiler for comparisen with other boilers the coal 
should, if possible, be of some kind which is commercially regarded as a 
standard. For New England and that portion of the country east of the 
Allegheny Mountains, good anthracite egg coal, containing not over 10 per 
cent. of ash, and semi-bituminous Clearfield (Pa.), Cumberland (Md.), and 
Pocahontas (Va.) coals are thus regarded. West of the Allegheny Moun- 
tains, Pocahontas (Va.) and New River (W. Va.) semi-bituminous, and 
Youghiogheny or Pittsburg bituminous coals are recognized as standards.* 

For tests made to determine the performance of a boiler with a partic- 
ular kind of coal, such as may be specified in a contract for the ‘sale of a 
boiler, the coal used should not be higher in ash and in moisture than that 
specified, since increase in ash and moisture above a stated amount is apt to 
eause a falling off of both capacity and economy in greater proportion than 
the proportion of such increase. 

V. Establish the correctness of all apparatus used in the test for weighing 
and measuring. These are: 

i. Scales for weighing coal, ashes, and water. 

2. Tanks or water-meters for measuring water. Water-meters, as a rule, 
should only be used as a check on other measurements. For accurate work 
the water should be weighed or measured in a tank. 

3. Thermometers and pyrometers for taking temperatures of air, steam, 
feed-water, waste gases, etc. 

4. Pressure-gauges, draught-gauges, etc. 

VI. See that the boiler is thoroughly heated before the trial to its usual 
working temperature. If the boiler is new and of a form provided with a 
brick setting, it should be in regular use at least a week before the trial, so 
as to dry and heat the walls. If it has been laid off and become cold, it 
should be worked before the trial until the walls are well heated. 

VIL. The boiler and connections should be proved to be free from leaks 
before beginning a test, and all water connections, including blow and 
extra feed-pipes, should be disconnected, stopped with blank flanges, or 
bied through special openings beyond the valves, except the particular pipe 
through which water is to be fed to the boiler during the trial. During the 
test the blow-off and feed pipes should remain exposed to view. 

If an injector is used, it should receive steam directly through a felted 
pipe from the boiler being tested.t 

If the water is metered after it passes the injector, its temperature should 
be taken at the point where it leaves the injector. If the quantity is deter- 
mined before it goes to the injector, the temperature should be determined 
on the suction side of the injector, and if no change of temperature occurs 
other than that due to the injector, the temperature thus determined is 
properly that of the feed-water. When the temperature changes between 
the injector and the boiler, as by the use of a heater or by radiation, the 
temperature at which the water enters and leaves the injector and that at 
which it enters the boiler should all be taken. In that case the weight to be 
used is that of the water leaving the injector, computed from the heat units 
if not directly measured; and the temperature, that of the water entering 
the boiler. 


Let w = weight of water entering the injector; 
x = oe 66 steam 66 6s “6 ‘ 

h, = heat-units per pound of water entering injector; 

h Es 46 «0% 4c 66 79 steam ee 66 5 

Y ee _ 4 

Ihe ay) eee eS amaberion ying ras bahes 





* These coals are selected because they are about the only coals which 
possess the essentials of excellence of quality, adaptability to various 
kinds of furnaces, grates, boilers, and methods of firing, and wide distribu- 
tion and general accessibility in the markets. 

+In feeding a boiler undergoing test with an injector taking steam from 
another boiler, or from the main steam-pipe from several boilers, the evap- 
orative results may be modified by a difference in the quality of the steam 
from such source compared with that supplied by the boiler being tested, 
and in some eases the connection to the injector may act as a drip for the 
main steam-pipe. If it is known that the steam from the main pipe is of 
the same pressure and quality as that furnished by the boiler undergoing 
the test, the steam may be taken from such main pipe, 


692 THE STEAM-BOILER, 


Then w+ a= weight of water leaving injector, 
UE eg | 
= od Le hg 

See that the steam-main is so arranged that water of condensation cannot 
run back into the boiler. 

VILL. Duration of the Test.—For tests made to ascertain either the max- 
imum economy or the maximum capacity of a boiler, irrespective of the 
particular class of service for which it is regularly used, the duration should 
be at least ten hours of continuous running. If the rate of combustion ex- 
ceeds 25 pounds of coal per square foot of grate-surface per hour, it may be 
stopped when a total of 250 pounds of coal has been burned per square foot 
of grate. 

IX. Starting and Stopping a Test.—The conditions of the boiler and fur- 
nace in all respects should be, as nearly as possible, the same at the end as 
at the beginning of the test. The steam-pressure should be the same ; the 
water-level the same ; the fire upon the grates should be the same in quan- 
tity and condition; and the walls, flues, etc., should be of the same tempera- 
ture. Two methods of obtaining the desired equality of conditions of the 
fire may be used, viz., those which were called in the Code of 1885 ‘‘ the 
standard method ” and ‘‘the alternate method,” the latter being employed 
where it is inconvenient to make use of the standard method.* 

X. Standard Method of Starting and Stopping a Test.—Steam being 
raised to the working pressure, remove rapidly all the fire from the grate, 
close the damper, clean the ash-pit, and as quickly as possible start a new 
fire with weighed wood and coal, noting the time and the water-level + while 
the water is in a quiescent state, just before lighting the fire. 

At the end of the test remove the whole fire, which has been burned low, 
clean the grates and ash-pit, and note the water-level when the water is in 
a quiescent state, and record the time of hauling the fire. The water-level 
should be as nearly as possible the same as at the beginning of thetest. If 
it is not the same, a correction should be made by computation, and not by 
operating the pump after the test is completed. 

XI. Alternate Method of Starling and Stopping a Test.—The boiler being 
thoroughly heated by a preliminary run, the fires are to be burned low and 
well cleaned. Note the amount of coal left on the grate as nearly as it can 
be estimated; note the pressure of steam and the water-level. Note the 
time. and record it as the starting-time. Fresh coal which has been weighed 
should now be fired. The ash-pits should be thoroughly cleaned at once | 
after starting. Before the end of the test the fires should be burned low, 
just as before the start, and the fires cleaned in such a manner as to leave a 
bed of coal on the grates of the same depth, and in the same condition, as 
at the start. When this stage is reached, note the time and record it as the 
stopping-time. The water-level.and steam-pressures should previously ba 
brought as nearly as possible to the same point as at thestart. If the water- 
level is not the same as at the start, a correction should be made by com- 
putation, and not by operating the pump after the test is completed. 

XII. Uniformity of Conditions.—In all trials made to ascertain maximum 
economy or capacity the conditions should be maintained uniformly con- 
stant. Arrangements should be made to dispose of the steam so that the 
rate of evaporation may be kept the same from beginning to end. 

XIII. Keeping the Records.—Take note of every event connected with the 
progress of the trial, however unimportant it may appear. Record the 
time of every occurrence and the time of taking every weight and every 
observation. 

The coal should be weighed and delivered to the fireman in equal propor- 
tions, each sufficient for not more than one hour’s run, and a fresh portion 





*The Committee concludes that it is best to retain the designations 
“standard” and ‘‘ alternate,” since they have become widely known and 
established in the minds of engineers and in the reprints in the Code of 
1885. Many engineers prefer the ‘‘ alternate” to the ‘‘standard ’’ method 
on account of its being less liable to error due to cooling of the boiler at the 
beginning and end of a test. 

+The gauge-glass should not be blown out within an hour before the 
water-level is taken at the beginning and end of a test, otherwise an error 
in the reading of the water-level may be caused by a change in the tempera- 
ture and density to the water in the pipe leading from the bottom of the 
glass into the boiler, at 


RULES FOR CONDUCTING BOILER-TESTS. 693 


should not be delivered until the previous one has all been fired. The time 
required to consume each portion should be noted, the time being recorded 
at the instant of firing the last of each portion. It is desirable that at the 
same time the amount of water fed into the boiler should be accurately 
noted and recorded, including the height of the water in the boiler, and the 
average pressure of steam and temperature of feed during the time. By 
thus recording the amount of water evaporated by successive portions of 
coal, the test may be divided into several periods if desired, and the degree 
of uniformity of combustion, evaporation, and economy analyzed for each 
period. In addition to these records of the coal and the feed-water, half- 
hourly observations should be made of the temperature of the feed-water, 
of the flue-gases, of the external air in the boiler-room, of the temperature 
of the furnace when a furnace-pyrometer is used, also of the pressure of 
steam, and of the readings of the instruments for determining the moisture 
in the steam. A tog should be kept on properly prepared blanks containing 
columns for record of the various observations. 

XIV. Quality of Steam.—The percentage of moisture in the steam should 
be determined by the use of either a throttling or a separating steam-calo- 
rimeter. The sampling-nozzle should be placed in the vertical steam-pipe 
rising from the boiler. It should be made of 3-inch pipe, and should extend 
across the diameter of the steam-pipe to within half an inch of the opposite 
side, being closed at the end and perforated with not less than twenty 4-inch 
holes equally distributed along and around its cylindrical surface, but none 
of these holes should be nearer than 4 inch to the inner side of the steam- 
pipe. The calorimeter and the pipe leading to it should be well covered 
with felting. Whenever the indications of the throttling or separating 
calorimeter show that the percentage of moisture is irregular, or occasion- 
ally in excess of three per cent., the results should be checked by a steam; 
separator placed in the steam-pipe as close to the boiler as convenient, with 
a calorimeter in the steam-pipe just beyond the outlet from the separator. 
The drip from the separator should be caught and weighed, and the per- 
centage of moisture computed therefrom added to that shown by the calo- 
rimeter. 

Superheating should be determined by means of a thermometer placed in 
a mercury-well inserted in the steam-pipe. The degree of superheating 
should be taken as the difference between the reading of the thermometer 
for superheated steam and the readings of the same thermometer for satu- 
rated steam at the same pressure as determined |by a special experiment, 
and not by reference to steam-tables. 

XV. Sampling the Coal and Determining its Moisture.—As each barrow- 
load or fresh portion of coal is taken from the coal-pile, a represen- 
tative shovelful is selected from it and placed in a barrel or box in a cool 
place and kept until the end of the trial. The samples are then mixed and 
broken into pieces not exceeding one inch in diameter, and reduced by the 
process of repeated quartering and crushing until a final sample weighing 
about five pounds is obtained, and the size of the larger pieces is such that 
they will pass through a sieve with j-inch meshes. From this sample two 
one-quart, air-tight glass preserving-jars, or other air-tight vessels which 
will prevent the escape of moisture from the sample, are to be promptly 
filled, and these samples are to be kept for subsequent determinations of 
moisture and of heating value and for chemical analyses. During the pro- 
cess of quartering, when the sample has been reduced to about 100 pounds, 
a quarter to a half of it may be taken for an approximate determination of 
moisture. This may be made by placing it in a shallow iron pan, not over 
three inches deep, carefully weighing it, and setting the pan in the hottest 
place that can be found on the brickwork of the boiler-setting or flues, 
keeping it there for at least 12 hours, and then weighing it. The determina- 
tion of moisture thus made is believed to be approximately accurate for 
anthracite and semi-bituminous coals, and also for Pittsburg or Youghio- 
gheny coal; but it cannot be relied upon for coals mined west of Pittsburg, 
or for other coals containing inherent moisture. For these latter coals it is 
important that a more accurate method be adopted. The method recom- 
mended by the Committee for all accurate tests, whatever the character of 
the coal, is described as follows: : 

Take one of the samples contained in the glass jars, and subject it toa 
thorough air-drying, by spreading it in a thin layer and exposing it for 
several hours to the atmosphere of a warm room, weighing it before and 
after, thereby determining the quantity of surface moisture it contains, 


694 THE STEAM-BOILER, 


Then crush the whole of it by running it through an ordinary coffee-mill 
adjusted so as to produce somewhat coarse grains (less than 7, inch), thor- 
oughly mix the crushed sample, select from it a portion of from 10 to 50 
grams, weigh it in a balance which will easily show a variation as small as 
1 part in 1000, and dry it in an air- or sand-bath at a temperature between 
240 and 280 degrees Fahr. for one hour. Weigh it and record the loss, then 
heat and weigh it again repeatedly, at intervals of an hour or less, until the 
minimum weight has been reached and the weight begins to increase by 
oxidation of a portion of the coal. The difference between the original and 
the minimum weight is taken as the moisture in the air-dried coal. This 
moisture test should preferably be made on duplicate samples, and the 
results should agree withix 0.3 to 0.4 of one per cent., the mean of the two 
determinations being taken as the correct result. The sum of the percent- 
age of moisture thus found and the percentage of surface moisture previ- 
ously determined is the total moisture, 

XVI. Treatment of Ashes and Refuse.—The ashes and refuse are to be 
weighed in a dry state. If it is found desirable to show the principal char- 
acteristics of the ash, a sample should be subjected to a proximate analysis 
and the actual amount of incombustible material determined. For elabo- 
rate trials a complete analysis of the ash and refuse should be made. 

XVII. Calorific Tests and Analysis of Coal.—The quality of the fuel 
should be determined either by heat test or by analysis, or by both. 

The rational method of determining the total heat of combustion is to 
burn the sample of coal in an atmosphere of oxygen gas, the coal to be 
sampled as directed in Article XV of this code. 

The chemical analysis of the coal should be made only by an expert 
chemist. The total heat of combustion computed from the results of the 
ultimate analysis may be obtained by the use of Dulong’s formula (with 
constants modified by recent deterniinations), viz., 


14,600 C + 62,000( — +) -++ 4000 8, 


in which OC, H, O, and § refer to the proportions of carbon, hydrogen, oxy- 
gen, and sulphur respectively, as determined by the ultimate analysis.* 

It is.desirable that a proximate analysis should be made, thereby deter- 
mining the relative proportions of volatile matter and fixed carbon. These 
proportions furnish an indication of the leading characteristics of the fuel, 
and serve to fix the class to which it belongs. 

XVIII. Analysis of Flue-gases.—The analysis of the flue-gases is an 
especially valuable method of determining the relative value of different 
methods. of firing or of different kinds of furnaces. In making these 
analyses great care should be taken to procure average samples, since the 
composition is apt <~o vary at different points of the flue. The composition 
is also apt to vary from minute to minute, and for this reason the drawings 
of gas should last a considerable period of tine. Where complete deter- 
minations are desired, the analyses should be intrusted to an expert 
chemist. For approximate determinations the Orsat or the Hempel appa- 
ratus may be used by the engineer. 

For the continuous indication of the amount of carbonic acid present in 
the flue-gases an instrument may be employed which shows the weight of 
CO, in the sample of gas passing through it. 

XIX. Smoke Observations.—It is desirable to have a uniform system of 
determining and recording the quantity of smoke produced where bitumin- 
ous coal is used. The system commonly employed is to express the degree 
of smokiness by means of percentages dependent upon the judgment of the 
observer. The actual measurement of a sample of soot and smoke by some 
form of meter is to be preferred. 

XX. Miscellaneous.—In tests for purposes of scientific research, in which 
the determination of all the variables entering into the test is desired, 
certain observations should be made which are in general unnecessary for 
ordinary tests. As these determinations are rarely undertaken, it is not 
deemed advisable to give directions for making them. 

XXI. Calculations of Effictency.—Two methods of defining and caleulat- 
ing the efficiency of a boiler are recommended. They are: 





* Favre and Silbermann give 14,544 B.T.U. per pound carbon; Berthelot, 
14,647 B.T.U. Favreand Silbermann give 62,032 B.T.U. per pound hydrogen; 
Thomsen, 61,816 B.T.U. 


RULES FOR CONDUCTING BOILER-TESTS. 695 


Heat absorbed per Ib. combustible 
Calorific value of 1 lb. combustible ° 


: 2 __ Heat absorbed per lb. coal 
2. Efficiency of the boiler and grate = Galgiie taindur ie eecks 


The first of these is sometimes called the efficiency based on combustible, 
and the second the efficiency based on coal. The first is recommended as a 
standard of comparison for all tests, and this is the one which is under- 
stood to be referred to when the word ‘“‘ efficiency ’’ alone is used without 
qualification. The second, however, should be included ina report of a 
test, together with the first, whenever the object of the test is to determine 
the efficiency of the boiler and furnace together with the grate (or mechan- 
ical stoker), or to compare different furnaces, grates, fuels, or methods of 
firing. 

The heat absorbed per pound of combustible (or per pound coal) is to be 
calculated by multiplying the equivalent evaporation from and at 212 degrees 
per pound combustible (or coal) by 965.7. 

XXII. The Heat Balance.—An approximate ‘‘ heat balance,’? may be in- 
cluded in the report of a test when analyses of the fuel and of the chimney- 
gases have been made. It should be reported in the following form: 


HEAT BALANCE, OR DISTRIBUTION OF THE HEATING VALUE OF THE CoM- 
BUSTIBLE. 


Total Heat Value of 1 1b. of Combustible............ Bet; Us 





1. Efficiency of the boiler = 


Per 
B.T.U. Cent. 


1. Heat absorbed by the boiler = evaporation from and at 
212 degrees per pound of combustible x 965.7 ........ 
2. Loss due to moisture in coal = per cent of moisture re- 
ferred to combustible ~ 100 x [(212 — tf) + 966 + 
0.48(7' — 212)|(f = temperature of air in the boiler- 
room, 7’ = that of the flue-gases)...........-.sss00.-- 
3. Loss due to moisture formed by the burning of hydro- 
gen = per cent of hydrogen to combustible + 100 x 9 
1212, — t) + 966 4) 0.480 TIS) in eieincs a-tecee coe. 
4.* Loss due to heat carried away in the dry chimney-gases 
= ts of gas per pound of combustible x 0.24 x 


( : 
5.t Loss due to incomplete combustion of carbon 
CO per cent. C in combustible 
= 60, +00 BK 100 POO ALO o lg 
6. Loss due to unconsumed hydrogen and hydrocarbons, 
to heating the moisture in the air, to radiation, and 


unaccounted for. (Some of these losses may be sep- 
arately itemized if data are obtained from which 





they may be calculated)...... RAPED. epiGAe eects Acree 
Totals %asttiw-weases Sow his hie tee Bese ele Marine 100.00 





* The weight of gas per pound of carbon burned may be calculated from 


the gas analyses as follows: ee » be 
Dry gas per pound carbon = CO ae “r oe a ) in which COg, CO, 
2 


O, and N are the percentages by volume of the several gases. As the samp- 
ling and analyses of the gases in the present state of the art are liable to 
considerable errors, the result of this calculation is usually only an approxi- 
mate one. The heat balance itself is also only approximate for this reason, 
as well as for the fact that it is not possible to determine accurately the per- 
centage of unburned hydrogen or hydrocarbons in the fine-gases. 

The weight of dry gas per pound of combustible is found by multiplying 
the dry gas per pound of carbon by the percentage of carbon in the combus- 
tible, and dividing by 100. : 

+ CO, and CO are respectively the percentage by volume of carbonic acid 
and carbonic oxide in the flue-gases. The quantity 10,150 = number of heat- 
units generated by burning to carbonic acid one pound of carbon contained 
in carbonic oxide. 





2 


695a THE STEAM-BOILER, 


XXIII. Report of the Trial.—The data and results should be reported in 
_ the manner given in either one of the two following tables [only the “ Shoiu 
Forni” of table is given here], omitting lines where the tests have not been 
made as elaborately as provided for in such tables. Additional lines may be 
added for data relating to the specific object of the test. The Short Form of 
Report, Table No. 2, is reeommended for commercial tests and as a conven- 
ient form of abridging the longer form for publication when saving of space 
is desirable. For elaborate trials it is recommended that the full log of the 
trial be shown graphically, by means of a chart. 


TABLE NO. 2. 
DaTA AND RESULTS OF EVAPORATIVE TST, 


Arranged in accordance with the Short Form advised by the Boiler Test 
Committee of the American Society of Mechanical Engineers. 
Code of 1899. 





PACES DY ceca as epee ts ate eee oh ON Pee sos ase cee boiler,*at ess Poe ee eee te 
GELOTIIING ces alec elas tel gai o's cp ae gs eisiciels so ele eitlsise ele/cre winte re: cle erat s Mee ete Seat 
WGN OTOL LUC hase caste ccciss © tecie sereis cit eee ee ere terns eanre eens Searle seine faye 
KIN GOL LUYNACE So's ewicwsice oo eee abeinc's ocho arc ore occas hecelersa eee aT ie anne 
Method of starting and stopping the test (‘‘stand- 
ard” or “ alternate,”’ Arts. X and XI, Code)...... 
Grate surface ti certnres- wins enielasnieern teat cenia earner sq. ft. 
Weater-heating surfaced: ick .iSite sists cheicteclo cllechiaats ake * 
Superheating surface........ OCR ie cee S 
TOTAL QUANTITIES. 
1. Date ofitrial di... senses wiaie'otosa Rais sie aie: sferctole et: 
OMDurationvOLjoriall ye yest ee seis els Pispaes isles wd al? (oi 8 hours 
dow eight of ‘coal as firedstiee out aside fssnes Ss\e ig Ibs. 
4, Percentage of moisture in coalt . ............. per cent. 
5. Total weight of dry coal consumed........:..... lbs. 
Ge Totawmashvan d TEluses..ap.<pits hate oe rok eels ack oh 
7. Percentage of ash and refuse in dry coal....... per cent. 
8. Total weight of water fed to the boiler} ........ Ibs. 
9. Water actually evaporated, corrected for moist- 
ure or superheatin Steam. 2 cts was ciew sccm vhs ¥ 
9a~ Kactor of evaporation $e)... .e5 sosnest oya0 ee bee 
10; Equivalent water evaporated into dry steam 
from and at 212 degrees.| (Item 9 x Item 9a.) ss 
HOURLY QUANTITIES. 
11. Dry coal consumed per hour... .........00. 065. we 
12. Dry coal per square foot of grate surface per ’ 
WOME’ 2.).'- ss. Ger ee etteteists Pana sie reieersoepesis ieee : 
13. Water evaporated per hour corrected for qual- 
ALY OL SCCAIMG «2 ceca) + era sicwelalsiole ated areicetere Poel ticie ents we 
14. Equivalent evaporation per hour from and at 
MIRE TEOS UL) sais cece coe ree tls oa seer aie ent Tere ake ° 


15. Equivalent evaporation per hour from and at 212 
degrees per square foot of water-heating sur- 
FEDICIE ILS Ghady Gait e BREEORIBee trteee aes to cn oc nanan 


* Including equivalent of wood used in lighting the fire, not including un- 
burnt coal withdrawn from furnace at times of cleaning and at end of test. 
One pound of wood is taken to be equal to 0.4 pound of coal, or, in case 
greater accuracy is desired, as having a heat value equivalent to the evap- 
oration of 6 pounds of water from and at 212 degrees per pound. 
(6 X 965.7 = 5794 B.T.U.) The term ‘‘as fired ” means in its actual con- 
dition, including moisture. ; 

+ This is the total moisture in the coal as found by drying it artificially, as 
described in Art. XV of Code. : 

+ Corrected for inequality of water-level and of steam-pressure at be- 
ginning and end of test. 


§ Factor of evaporation = —., in which H and h are respectively the 


total heat in steam of the average observed pressure, and in water of the 
average observed temperature of the feed. . 
| The symbol “U.E,” meaning ‘‘ units of evaporation,’’ may be cone 





RULES FOR CONDUCTING BOILER-TESTS. 6956 








AVERAGE PRESSURES, TEMPERATURES, ETC. 





16. Steam pressure by gauge... ........ ....... »se-| LOS, per sq. in. 
17. Temperature of feed-water entering boilev...... deg. 
18. Temperature of escaping gases from boiler..... ‘ 
19. Force of draft between damper and boiler......| ins. of water 
20. Percentage of moisture in steam, or number of 
degrees of superheating............ idieites cs per cent.or deg. 
HORSE-POWER. 
21. Horse-power developed. (Item 14 + 3414.)4..... H.P. 
22. Builders’ rated horse-power..... itdates 24 AES AOHe: i 
23. Percentage of builders’ rated horse-power de- 
veloped’ jc). -saec.. she bie oie. shotsns o's dotnet Hele» aise per cent. 


ECONOMIC RESULTS. 


26. Equivalent evaporation frcm and at 212 degrees 
per pound of dry coal || (Item 10 + Item. 5.)..| 
27. Equivalent evaporation from and at 212 degrees/ 
per Tee) combustible. [Item 10 + (Item 
— em eifakeN@bey Mele Shae ove. felarelh is 0’ elefasstolstiel cl eie\'a:e 16) (e" 
(f Items 25, 26, and 27 are not corrected for 
quality of steam, the fact should be stated.) 


66 


EFFICIENCY. 
28. Calorific value of the dry coal per pound... ... BeESU, 
29. Calorific value of the combustible per pound.... 2" 
80. Efficiency of boiler (based on combustible)**... per cent. 
31. Efficiency of boiler, including grate (based on 
adrylcoaleen.. Si95.3 alelcs tS ss, « Thee a Cee: a: 
COST OF EVAPORATION. 
32. Cost of coal per ton of —— lbs. delivered in 
boiler-room ai.5) 55. 6eaoek Leer oes Mclnche 3 £3 ni 
33. Cost of coal required for evaporating 1000 pounds 
of water from and at 212 degrees. ...... ..... $ 





veniently substituted for the expression ‘*‘ Equivalent water evaporated into 
dry steam from and at.212 degrees,” its definition being given in a foot-note. 
‘| Held to be the equivalent of 30 lbs. of water evaporated from 100 degrees 
Fahr. into dry steam at 70 lbs. gauge-pressure. E 
** In all cases where the word ‘‘combustible”’ is used, it means the coal 
without moisture and ash, but including all other constituents. It is the 
same as what is called in Europe ‘‘ coal-dry and free from ash.” 


Factors of Evaporation.—tThe table on the following pages was 
originally published by the author in Trans. A. S, M. E., vol. vi., 1884, under 
the title, Tables for Facilitating Calculations of Boiler-tests. The table 
gives the factors for every 3° of temperature of feed-water from 32° to 212¢ 
F., and for every two pounds pressure of steam within the limits of ordinary 
working steam-pressures. 

The difference in the factor corresponding to a difference of 3° tempera. 
ture of feed is always either .0031 or .0032. For interpolation to find a factor 
for a feed-water temperature between 32° and 212°, not given in the table, 
take the factor for the nearest temperature and add or subtract, as the case 
may be, .0010 if the difference is .0031, and .0011 if the difference is .0032, As 
in nearly all cases a factor of evaporation to three decimal places is accu- 
rate enough, any error which may be made in the fourth decimal place by 
interpolation is of no practical importance. 

_ The tables used in calculating these factors of evaporation are those given 
in Charles T, Porter’s Treatise on the Richards’ Steameengine Indicator, 


= H a : : 
The formula is Factor = 905.77 12 which H is the total heat of steam at the 


observed pressure, and h the total heat of feed-water of the observed 
temperature. Tomine ett aS rey 


696 


THE STEAM-BOILER 



























































Lbs. 
Gauge-pressures....0 +] 10 +] 20+] 30+] 40+ | 45+ | 50+ | 52 + | 54 +4 | 56 + 
Absolute pressures be 25 35 45 55 60 65 | 67 69 | val 
Feed-water | Factors or EVAPORATION. 
Temperature. 
212° FF. 1.0003, 1.0088|1.0149|1.0197)|1.02387|1.0254)1.0271)1.0277|1.0283)\1.0290 
209 35/ 1.0120 80/1.0228 68 86/1 .0302)1.03809|1.0315)1.0321 
206 66 51}1.0212 60 99/1.0817 34 40 46 52 
203 98 83 43 91)1.0331 49 65 W% "8 84 
200 1.0129)1.0214 75/1.0323 62 80 97/1.0403)1.0409)1.0415 
197 60 46|1.0306 54 94!1.0412)1.0428 34 41 47 
194 92 et 38 85]1.0425 43 60 66 72 78 
191 1.0223/1.0308 69}1.0417 57 74 91 97)1.0503/1.0510 
188 55 40}1.0400 48 88)1.0506)1 .0522)1.0528 85 41 
185 86 | 382 80}1.0519 37 54 60 66 72 
182 1.0317/1.0403 63/1.0511 51 68 85 91 98} 1.0604 
179 49 34 95 42 82/1.0600/1.0616/1.0623/1.0629 35 
176 80 6511.0526 74|1.0613 81 48 54 60 66 
173 1.0411 97 711.0605 45 68 79 85 92 98 
170 43]1.0528 89 36 6 94)1.0710)1.0717)1.0723)1.0729 
167 74 59/1.0620 68}1.0707}1 .0725 42 48 54 60 
164 1.0505 91 51 99 39 56 fi) 80 86 92 
161 37/1.0622 82)1.0730 70 88]1.0804/1.0811/1.0817) 1.0823 
158 68 53]1.0714 62]1.0801]1.0819 386 42 48 54 
155 99 84 45 93 83 50 67 [3 80 86 
152 1.0631)1.0716 %6)1.0824 64. 82 98)1.0905}1.0911) 1.0917 
149 62 47|1.0808 55 95)1.0913)1.0930 36 42 ce 
146 93 %8 5 87}1.0926 44 61 67 73 
143 1.0724/1.0810 70\1.0918 58 5 92 98)1.1005}1. 044 
140 56 41)1.0901 49 89}1.1007)1.1023)1.1030 36 42 
137 87 Yfe3 83 80/1.1020 = 55 61 67 "3 
134 1.0818]1.0903 64/1.1012 51 86 92 98/}1.1104 
131 49 34 95 43 83) 1. to 1.1117/)1.1123)1.1130 36 
128 81 66]1.1026 94)1.1114 82 48 55 61 67 
125 1.0912 97 57|1.1105 45 63 79 86 92 98 
122 43)1.1028 89 36 76 94/1.1211/1.1217/1. oH 1.1229 
119 %4 59/1.1120 68}1.1207/1.1225 42 48 a 
116 1.1005 90 bI 99 39 56 3 79 eB 
113 B6)1.112%| | 82/1.1230) | 70) 88/1.1904/1.1810/1.131714, 188 
110 68 53}1.1213 61}1.1801]1.1819 3D 48 
107 99 84 45 92 382 50 66 Be "9 or 
104 1.1130)1.1215 76)1.1823 63 81 98)1.1404/1.1410}1. 1416 
101 61 46) 1.1807 55 94)1.1412/1.1429 385 41 47 
98 92 vue 38 86)1.1426 43 60 66 3 79 
95 1.1223/1.1309 69)1.1417 57 75 9] 97/1.1504!1.1510 
ra 55 40}1.1400 48 88) 1.1506/1.1522)1.1529 85 4} 
89 86 G1 3i 79\1.1519 37 53 60 66 72 
86 1.13817/1.1402 63/1.1510 50 68 84 91 971.1603 
83 48 33 94 41 81 99]1.1616)1.1622)1.1628 34 
80 "9 64)1.1525 73) 1.1612}1.1630 i 53 59 65 
U7 1.1410 95 56|1.1604 44 61 vi 84 90 96 
74. 41}1.1526 87 35 95 92/1.1709}1.1715)1.1722/1.1728 
71 92 58]1.1618 66/1.1706]1.1723 40 46 53 59 
68 1.1504 89 49 97 37 55 71 78 84 90 
65 35|1.1620 80}1.1728 68 86}1.1802)1.1809}1.1815}1.1821 
62 66 51 aie 59 99)1.1817 33 40 46 52 
59 97 82 901.1880 48 64 71 UT 83 
56 1.1628}1.17138 a 1.1821 61 "9 96/1.1902]1.1908'1 1914 
53 59 44)1.1805 BR 92)1.1910}1. 1927 33 39 45 
50 90) [5 36 84]1.1923 41 58 64 70 %6 
47 1.1721/1.1806 67/1.1915 54 2 89 95}1.2001/1 . 2007 
44 52 3f 98 46 86] 1.2003)1. 2020) 1.2026 82 39 
41 83) 68} 1.1929 77|2.2017 34 51 aye 64 vi 
388 1.1814]1.1900 60}1.2008 48 65 82 88 95)1.2101 
35 45} 31 -91,_— 89] 79} =~ 96/1.2118/1.2119]1.2126} 2 
32 76} _ eat. 90221 44} 51] 57] 63 












70}1 2110)1.2128 





FACTORS OF EVAPORATION. 697 


Gauge-press., lbs. 58 -+ } 60 62 64 66 68 70 12 716 
Atiaalsta Pressures. af 1: | # G7 3 | 9 B | 2 | § 5 | 3 a‘ 87 i mle 7 
Feed-water | 


Temp. FACTORS OF EVAPORATION. 





212° F. | 1.0295 }1.0301}1.0307/1. ey 1. ett Melhe 0329}1. ‘ial 0339/1 .0344 
1.0327 33 38 60 

















209 65 70 75 
206 58 64 70 75 81 86 91 97{1.0402/1. 0407 
203 90 96}1.0401/1.0407)1. ae 1. “gt il. es 1.0428 33 38 
200 1.0421 {1.0427 83 38 59 65 69 
197 53 58 64 70 is a 86 91 96]1.0501 
194 84 90 96}1.0501|1.0507)1.0512/1. ae 1.052211 .0527 32 
191 1.0515 |1.0521/1.0527 83 38 43 54 59 be, 
188 47 53 58 64 69 75 30 85 90 
185 %8 84 90 95) 1.0601) 1.0606/1.0611}1.0616)1.0622)1. 0626 
182 1.0610 }1. nee 1.0621}1.0627 32 37 43 os 53 58 
179 41 52 58 63 69 74 84 89 
176 72 73 84 89 95/1 .0700}1 .0705}1. ori 1.0716]1.0721 
173 1.0704 }1. lhe iy hte 072111 0726 32 37 42 47 52 
170 35 52 57 63 68 %3 %8 83 
167 66 = 83 89 94 99]1.0805 1. ot 1.0815 
164 98 {1.0803 nee ae Bs ents aie 1.0831 36, 46 
161 1.0829 35 _ 67 72 W7 
158 60 66 22 a &3 88 98 1.0904) 1.0908 
155 92 97 |1.0903/1.0909/1.0914)1.0919 1.0988 1.0930 35 40 
152 1.0923 |1.0929 34 e. 45 51 56 61 66 71 
149 54 60 66 ine 82 87 92) 97/1.1002 
146 85 91 97/1. 1002)1. 1008/1. ot 1.1018|1. pee ee 34 
143 1.1017 |1.1022/1.1028 34 39 50 5 60 65 
140 48 54 59 65 70 76 81 86 91 96 
137 79 85 91 96)1.1102)1.1107)1.1112]1.1117/1.1122)1.1127 
134 1.1110 {1.1116 aa 1.1127 33 38 43 49 54 59 
131 42 47 59 64 69 75 80 85 90 
128 73 79 84 90 95)1.1201/1.1206)1.1211/1.1216)1. 1221 
125 1.1204 1.1210) 1.1215) 1.1221/1.1226 82 37 42 47 52 
122 35 41 47 52 58 63 68 73 78 83 
119 66 72 78 83 89 94 99}1.13805)1.1810)1.1315 
116 98 |1.1303)1.1809)1.1315/1. 1320/1. 1325) 1.1331 36 41 46 
113 1.1329 34 40 46 51 57 62 67 72 ri 
110 60 66 71 G7 82 88 93 98/1.1403)1.1408 
107 91 97|1.1403)1.1408}1.1414]1.1419/1.1424/4.1429 34 39 
104 1.1422 }1.1428 34 39 45 50 55 60 65 70 
101 53 59 65 70 76 81 86 92 7|1.1502 
98 85 90 96/1.1502 1.1507 1.1512}1.1518]1,1523)1.1528 33 
95 1.1516 |1.1521/1.1527 33 38 43 49 54 59 64 
92 47 53 58 64 69 %5 80 85 90 95 
89 78 84 89 95)1. carl 1606) 1.1611]1.1616)1.1621/1.1626 
86 1.1609 }1.1615)1. aot 1.1626 37 42 47 52 57 
83 40 46 57 83 68 73 78 83 §8 
80 71 (7 83 88 94 99/1.1704)1.1710)1.1715)1.1720 
(7 1.1702 |1 1708)1.1714'1.1719)1.1725)1.17380 35 41 46 51 
G4 34 39 45 51 56 61 67 72 os 82 
vel 65 70 76 82 87 92 98) 1.1803)1.1808/1.1813 
68 96 |1 Bee 1807|1.1813)1.1818}1.1824/1.1829 34 39 44 
65 1.1827 ss 41 49 55 60 65 70 (i) 
62 58 y %5 80 86 Ail 96|1.1901|1.1906 
59 89 95/1. 1901 1,1906)1.1912}1.1917/1.1922)1.1927 32 37 
56 1.1920 {1.1926 37 43 48 53 58 63 68 
53 51 57 83 68 74 ao 84 89 94 99 
50 82 88 94 99}1.2005) 1.2010} 1.2015) 1.2021)1.2026/1.2031 
47 1.2013 |1.2019 1 1.2030 36 41 46 52 57 62 
44 a4 50 61 67 @2 78 83 88] 93 
41 76 81 a7 93 98]1.2103)1.2109}1. Per 1.2119 ee 
38 1.2107 |1.2112/1. eth: 2124/1 £2129 34 40 50 
35 38 43 55 60 65 71 76 81 36 
32 69 75 80 86 91 9711220211 220711. 221211. aa 





698 THE STEAM-BOILER. 


Ga cab ety fe 


80 + | so 4 84 + | 864 88 + | 90 + | 92 + 




















Ibs., 94+ | 96+ | OBE 
Absolute 
Pressures, 93! 95 97 99 101 103 105 107 109 111 113 
Sree | FACTORS OF EVAPORATION. 


212 (1.0349) 1.0353/1.0358/1.0363/1 . 0367/1 0372/1 .0376/1.0381)1.0385 1.0389]1.0393 
209 80 85 90 94 99/1 .0403/1.0408]1.041211.0416]1.9421!1 .0425 
206 |1.0411 e046): 0421|1.0426] 1.0430 35 39 £8 48 52 56 
203 43 52 57 62 66 71 79|' 83 88 
200 "4 "0 84 89 93 98] 1.050211. 0508|1. 0511]1.0515}1.0519 
197 11.0506/1.0511|1.0515]1.0520/1.0525}1.0529 33 38 42 46 50 
194 37 = 47 51 56 60 65 69 "3 78 82 


—s 








191 69 78 83 87 92 96}1.0601)1. vee 1.0609}1.0613 
188 |J.0600 1.0608 Te 0610 1.0614]1.0619) 1.0623) 1.0628 82 40 45 
185 31 36 41 Rs 50 55 59 63 88 72 76 
182 63 68 72 81 86 90 95 99] 1.0703} 1.0707 


179 94} 99/1.0704/1. orbs 1.0713]1.0717|1.0722|1.0726/1.0730] 35] 39 
.0730/ 35/40) «44, «a9]Ssi53]sS7]Ss«Q}Sséi@]_—Ss 70 
173 svi 62}—S sé] Stl =} = 80], =~ 84] ~— 89) S98] Sz} .0801 
170 88 93 —-98/1.0802]1.0807|1.0811]1.0816|1.0820/1.0824]1.0829] 33 
.0s24'1.0829 34] 38] 43! 47] 51| 56] 60l 64 
164 51]. 56) 60; 65} 69] 74) ‘78| $3] 87) 911 95 
161 82} 87} 92! —96/1.0801]1.0905]1.0910 1.0914 1.0918|1.0923| 1.0927 
.0918/1.0923/1.0927/ 32] 37] 41 50] =«Bd| —Ssi58 
155 45} 49} 54 59] 63! 68} 72 oe 81} 85] 89 
152 76} 81} 85} 901 95} 99]1.1004 1.1008 1.1012|1.1016]1.1021 
149 |1.1007/1.1012]1.1017/1.1021|1.1026|1.1030 35 43 48 52 
146 38} 43; 48! 53| 57) 6 20 

143 70| 74/79] = 84] 88] ~—s 98 o7|t. 1102|1. 1106|1. 1110 1.1114 
140 |1.1101]1.1106/1.1110]1.1115]1.1120/1.1124]1.1129] 33] a7| 41| 46 
137 32} 37] 42i 46] 51] 55] Gol 64| 6s} | 7 
134 6s} 68; 3]. 78] «82 7} 91! —-95/1.1200]1.120411.1208 
131 95} — 99/1.1204]1.1209]1.1213 1.1222/1.1227} 31| 35{ 39 
198 |1.1226/1.1231| 35] 40]. —s 45]~Ss«o49]—SsB]StCiw SSC} SCS 
125 57} -62|—=Ss«S|_ = T1] S76] =~ 80}, ~S 85} ~—s 89} ~— 93] ~—Ss«8|1. 1802 
122 88} 93} ~~ 9811.1802]1.1307]1.1311/1.1316|1.1320)1,1325]1.1329] 33 
119 |1.1820/1.1324/1.1329}  34/ 38] 43) 47] 511 56; 60] 64 
116 1] BBL Bob eres]! ear a zat ire) ee gaht eter) tort Bans 
113 82} 87; 91}, ~—« 961.1401 1.1405] 1. 1409/1. 1414]1.1418]1.1422|1.1426 
110 |1.1418/1.1418/1.1422]/1.1427} 32] 36) = 41] — ss 45} Ss a9] S53] S58 


107 44 49 54 58 63 67 72 7 80 85 89 

104 75 80 85 89 94 99]1.1503)1.1507/1.1512)1.1516/1.1520 . 

101 |1.1506)1.1511}1.1516)1.1521/1.1525 34 38 fc 47 51 
42 47 52 56 


10 74 78 

95 69 74 78 83 87 92 96)1.1601/1.1605]1.1609]1.1613 
92 }1.1600)1.1605]1.1609]1.1614/1.1619]1.1623)1.1628 82 36 40 45 
89 31 36 41 45 50 54 59 63 67 72 q 
86 62 67 72 76 81 85 90 94 98)1.1703/1.1707 
83 93 98)1.1703/1.1707/1.1712)1.1717)1.1721]1.1725|1.1730 84 38 
1.1724)1.1729 34 39 43 48 52 56 61 65 63 

56 60 65 70 74 79 83 88 92 96}1.1800 

87 91 96)1.1801]1.1805)1.1810)1.1814/1.1819)1.1823)1.1827 31 
1.1818)1.1823)1.1827 32 36 41 45 50 54 58 62 
49 54 58 63 68 2 G7 81 85 89 94 
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62 |1.1911|1.1916)1.1921)1.1925)/1 1930 34 39 43 47 52 56 
59 42 av 52 56 61 65 70 G4 78 83 87 
56 73 8 83 87 92 96]1.2001)1.2005)1.2010)1.2014/1.2018 
53 |1.2004/1 2009/1.2014/1. 2018) 1.2023/1.2028 32 36 41 45 49 


50 35 40 45 50 54 59 63 67 72 7 80 
47 66 71 76 81 85 90 94 98) 1.2103) 1.2107/1.2111 
44 98) 1.2102)1.2107]1.2112) 1.2116) 1.2121] 1.2125)1 .2130 34 38 42 
41 }1.2129 33 38 43 47 52 56 61 65 69 it 


60 64 69 74 78 83 87 92 96 
91 96]1.2200)1.2205)1 .2209) 1.2214] 1.2218]1.2223)1.2227 
1.2227 31 36] 41 45 49 54 58 


1.2200}1 
31 
62 















































































































FACTORS OF EVAPORATION, 699 
Gauge “CaS | | | | | | 
Ibs. 100 + [105 + | 110 +] 115 +} 120 + | 125 + | 130 + }135 + |] 140 + | 145 +] 150 + 
Absolute Presa, 
lbs, 115. | 120 125 130 135 140 145 150 155 160 165 
lens. | FACTORS OF EVAPORATION. 
™ 212°) 1 .0397)1.0407|1.0417)1.0427)1.0436/1.0445 1.0470/1.0478 1.0486 
209 |1.0429| 39) 49} 58] 67) %6 85 0311. 0501}1.0509/1.0517 
206 60 70 80 89 99}1.0508/1.0516/1.0525 33 41 48 
203 92/1. 0502/1.0511/1.0521/1.0530 39 48 56 64 " 80 
200 11.0523 33 43 52 62 70 79 87 96 1.0604|1.0611 
197 55 65 74 84 93} 1.0602! 1.0610)1.0619| 1.0627 35 43 
194 86 96] 1.0606]1.0615}1.0624 33 4 50 58 66 % 
191 |1.0617/1.0627 37 47 56 65 7 82 90 98/1 .0706 
188 49 59 69 78 87 96/1.0705]1.0713]1.0721]1.0729 37 
185 80 90/1.0700/1.0709]1.0719]1.0727 36 44 53 61 68 
182 {1.0712/1,0722 31 41 50 59 67 Vi 84 9211 .0800 
179 43 53 63 72 81 90 99} 1.0807/1.0815]1 0823 31 
176 774 84 94/1. og08it. bere beg 1.0830 39 47 55 62 
173 |1.0806/1.0816]1.0825 61 70 78 86 94 
170 37 47 57 eh 25 ad 93]1.0901/1.0909]1.091711.0925 
167 68 “h 88 97/1 .090711.0915}1.0924 82 41 49 56 
164 11.0900 1.0910]. opigi2. 0929 38 47 5d 64 72 80 88 
161 31 41 60 69 78 87 95}1.1003}1.1011/1.1019 
158 62 72 4 91|1.1000]1.1009/1.1018]1.1026 35 43 50 
155 93}1.1003]1.1013]1.1023 32 41 49 58 66 74 82 
152 11.1025 35 44 54 63 72 81 89 9711 .1105/1.1118 
149 56 66 76 85 94|1.1103/1.1112}1,1120]1.1128 36 44 
146 87 97|1.1107}1.1116.1.1126 34 43 51 60 68 TE 
143 |1.1118]1.1129 388 48 57 66 74 83 91 99}1.1207 
140 50. 60 70 79 88 97/1. 1206]1.1214]1.122211 1230 38 
137 81 91}1.1201/1.1210]1.1219]1.1228 37 45 53 61 69 
134 |1.1212/1.1222 32 at 51 59 68 "6 85 93/1.1300 
131 43 53 63 73 82 91 99}1.1 1308/1. 1316] 1.1324 32 
128 "5 85 94/1 .1304/1.1313]1.1322]1.1331 39 47 AB 63 
125 |1.1806/1.1316]1.1326 35 44 53 62 70 78 86 94 
122 v 47 57 66 v5) 84 93\1.1401|1. shel 1.1417]1.1425 
119 68 78 88 97|1.1407]1.1415]1.1424 49 56 
116 99|1.1409]1.1419)1.1429 38 47 55 80 88 
113 [1.1431 41 50 60 69 78 86 Hf 1.150314. 1584 1.1519 
110 2 72 82 91/1. 1500]1.1509/1.1518]1. 1526 34 42 50 
107 93]1.1503/1. 1518/1. 1522 31 40 49|° BY 65 7 81 
104 }1.1524 34 53 62 71 80 88 97/1.1605/1.1612 
101 55 65 3 84 94/1.1602/1.1611]1.1620/1.1628 36 43 
98 86 96|1.1606]1. 1616/1. 1625 34 42 51 59 67 ves) 
95 |1 1618]1.1628 37 47 56 65 73 82 90 98|1.1706 
92 49 59 68 78 87 96/1.1%05]1.1713/1.1721/1.1729 37 
89 80 90)1.1700/1.1709/1.1718/1.1727 36 44 52 60 68 
86 |1.1711/1.1721 31 40 49 58 67 "5 83 91 99 
83 42 52 62 71 80 89 98/1. 1806/1.1815/1.1823/1.1830 
80 "3 83 93|1.1802/1.1812/1.1820)1.1829 37 46 54 61 
7? 11.1804]1.1814/1.1824 34 43 52 60 69 7 85 93 
i 35 45 55 65 %4 83 91]/1.1900/1. ls 1.1916]1.1924 
7 67 ih 86 96/1.1905/1.1914/1. 1922 31 47 55 
68 98/1. 1908) 1.1917/1.1927 36 45 54 62 70 78 86 
65 11.1929 39 49 58 67 76 85 93]1.2001|1.2009]1 .2017 
62 60 70 80 89 98/1.2007]1.2016]1.2024 3 40 48 
59 91]1.2001/1.2011]1.2020 1.2029 38 47 55 63 va | 79 
56 (1.2022] 32 42 51 60 69 %8 86 94/1.2102]1.2110 
53 53 63 73 82 91}1.2100]1.2109]1.2117)1.2126 34 41 
50 84 94/1.2104/1.2113/1 2128 31 40 48 57 65 72 
47 }1.2115]1.2125 35 44 54 63 71 80 88 96}1 .22038 
44 46 56 66 %6 85 94} 1.2202] 1.2211/1-2219] 1.2227 35 
41 77 87 97/1. 2207) 1.2216/1 2225 33 42 50 58 66 
88 |i.2208]1.2219/1. ae 38 47 56 64 73 81 89 U7 
35 40 50 69 78 87 95/1. 2304/1.281211 ‘ 
32 71 81 bolt. 2300 1.2309/1 2318/1 2326 35 | 




















700 THE STEAM-BOILER, 


STRENGTH OF STEAM-BOILERS. VARIOUS RULES 
FOR CONSTRUCTION. 


There is a great lack of uniformity in the rules prescribed by differ- 
ent writers and by legislation governing the construction of steam-boilers 
In the United States, boilers for merchant vessels must be constructed ac- 
cording to the rules and regulations prescribed by the Board of Supervising 
Inspectors of Steam Vessels; in the U. S. Navy, according to rules of the 

Navy Department, and in some cases according to special acts of Congress. 
On land, in some places, as in Philadelphia, the construction of boilers is 
governed by local laws; but generally there are no laws upon the subject, 
and boilers are constructed according to the idea of individual engineers and 
boiler-makers. In Europe the construction is generally regulated by strin- 
gent inspection laws. The rules of the U. S. Supervising Inspectors of 
Steam-vessels, the British Lloyd’s and Board of Trade, the French Bureau 
Veritas, and the German Lloyd’s are ably reviewed in a paper by Nelson 
Foley, M. Inst. Naval Architects, etc., read at the Chicago Engineering Con- 
gress, Division of Marine and Naval Engineering. From this paper the fol- 
lowing notes are taken, chiefly with reference to the U.S. and British rules; 

(Abbreviations.—T. S., for tensile strength; El., elongation; Contr., con- 
traction of area.) 

Wydraulie Tests.—Board of Trade, Lloyd’s, and Bureau Veritas.— 
Twice the working pressure. 

United States Statutes.—One and a half times the working pressure. 

Mr. Foley proposes that the proof pressure should be 114 times the work- 
ing pressure + one atmosphere. 

Established Nominal Factors of Safety.—Board of Trade.— 
4.5 a4 a boiler of moderate length and of the best construction and work- 
manship. 

Lloyd’s.—Not very apparent, but appears to lie between 4 and 5. 

United States Statutes.—Indefinite, because the strength of the joint is 
not Semen except by the broad distinction between single and double 
riveting. 

Bureau Veritas: 4.4. 

German Lloyd’s: 5 to 4.65, according to the thickness of the plates. 

Material for Riveting.—Board of Trade.—Tensile strength of 
rivet bars between 26 and 30 tons, el. in 10’’ not less than 25%, and contr. of 
area not less than 50%, 

Lloyd’s.—T. S., 26 to 80 tons; el. not less than 20% in 8’. The material 
must stand bending to a curve, the inner radius of which is not greater than 
114 times the thickness of the plate, after having been uniformly heated to 
a low cherry-red, and quenched in water at 82° F. 

United States Statutes.—No special provision. 

Rules Connected with Riveting.—Board of Trade.—The shear- 
ing resistance of the rivet steel to be taken at 23 tons per square inch, 5 to 
be used for the factor of safety indepenjently of any addition to this factor 
for the plating. Rivets in double shear to have only 1.75 times the single 
section taken in the calculation instead of 2. The diameter must not be less 
than the thickness of the plate and the pitch never greater than 814’. The 
thickness of double butt-straps (each) not to be less than 5 the thickness of 
the plate; single butt-straps not less than 9/8. 

Distance from centre of rivet to edge of hole = diameter of rivet X 114. 

Distance between rows of rivets 


= 2 X diam. of rivet or = ((diam. x 4) + 1] + 2, if chain, and 


(pitch X 11) + (diam. x 4)] X (pitch + diam. X 4) if zigzag. 


ee ee 


10 


Diagonal pitch = (pitch x 6+ diam. x 4) + 10. 

Lloyd’s.—Rivets in double shear to have only 1.75 times the single section 
taken in the calculation instead of 2. Theshearing strength of rivet steel to 
be taken at 85% of the T. S. of the material of shell plates. In any case 
where the strength of the longitudinal joint is satisfactorily shown by ex- 
peewee to be greater than given by the formula, the actual strength may 

e taken in the calculation. 

United States Statutes.—No rules. 

Material for Cyindrical Shells Subject to Internal Pres- 
sure.—Board of Trade.—T. 8. between 27 and 32 tons. In the normal con- 
dition, el. not less than 18% in 10’’, but should be about 25% ; if annealed, not 

@ ’ 


STRENGTH OF STEAM-BOILERS. 701 


less than 20%. Strips 2/7 wide should stand bending until the sides are 
parallel at a distance from each other of not more than three times the 
plate’s thickness. 

Lloyd’s.—T. S. between the limits of 26 and 30 tons per squareinch. El. 
not less than 20%in 8’. Test strips heated to a low cherry-red and plunged 
into water at 82° F. must stand bending to a curve, the inner radius of 
which is not greater than 11% times the plate’s thickness. 

U. 8S. Statutes.—Plates of 44” thick and under shall show a contr. of not 
less than 50%; when over 44” and up to 34’, not less than 45%; when over 
34/’, not less than 40%. 

Mr. Foley’s comments : The Board of Trade rules seem to indicate a steel 
of too high T. S. when a lower and more ductile one can be got: the lower 
tensile limit should be reduced, and the bending test might with advantage 
be made after tempering, and made to a smaller radius. Lloyd’s rule for 
quality seems more Satisfactory, but the temper testis not severe. The 
United States Statutes are not sufficiently stringent to insure an entirely 
satisfactory material. 

Mr. Foley suggests a material which would meet the following: 25 tons 
lower limit in tension ; 25% in 8’’ minimum elongation ; radius for bending 
test after tempering = the plate’s thickness. 


Shell-plate Formulz.— Board of Trade; P= 


D = diameter of boiler in inches ; 
P = working-pressure in lbs. per square inch ; 
t = thickness in inches ; 
B= percentage of strength of joint compared to solid plate ; 
T = tensile strength allowed for the material in lbs. per square inch ; 
#' =a factor of safety, being 4.5, with certain additions depending on 
method of construction. 


Tigo ee) BY 


t = thickness of plate in sixteenths ; B and Das before; C = a constant 
depending on the kind of joint. 

When longitudinal seams have double butt-straps, C = 20. When longi- 
tudinal seams have double butt-straps of unequal width, only covering on 
one side the reduced section of plate at the outer line of rivets, C = 19.5. 

When the longitudinal seams are lap-jointed, C = 18.5. 

U. S. Statutes.—Using same notation as for Board of Trade, 

jo eX tor single-riveting ; add 20% for double-riveting 3 
where T is the lowest T. S. stamped on any plate. 

Mr. Foley criticises the rule of the United States Statutes as follows: The 
rule ignores the riveting, except that it distinguishes between single and 
double, giving the latter 20% advantage ; the circumferential riveting or 
class of seam is altogether ignored. The rule takes no account of workman- 
ship or method adopted of constructing the joints. The factor, one sixth, 
simply covers the actual nominal factor of safety as well as the loss of 
strength at the joint, no matter what its percentage ; we may therefore 
dismiss it as unsatisfactory. 

C(é + 1)2 


Rules for Flat Plates.—Board of Trade; P= “gle ° 
P = working-pressure in lbs. per square inch; 
S = surface supported in square inches; 
t = thickness in sixteenths of an inch; 
C = aconstant as per following table: 


C = 125 for plates not exposed to heat or flame, the stays fitted with nuts 
and washers, the latter at least three times the diameter of the stay 
and % the thickness of the plate; : : 

C = 187.5 for the same condition, but the washers 24 the pitch of stays in 
diameter, and thickness not less than plate; 

C = 200 for the same condition, but doubling plates in place of washers, the 
width of which is 34 the pitch and thickness the same as the plate; 

C = 112.5 for the same condition, but the stays with nuts only; ; 

C = 75 when exposed to impact of heat or flame and steam in contact with 
the plates, and the stays fitted with nuts and washers three times the 
diameter of the stay and % the plate’s thickness; 


Nib al © a St 7 
Derek had 


702 THE STEAM-BOILER. 


C = 67.5 for the same condition, but stays fitted with nuts only; 

C = 100 when exposed to heat or fiame, and water in contact with the plates, 
and stays screwed into the plates and fitted with nuts; 

C = 66 for the same condition, but stays with riveted heads. : 

Cx 


U. S. Statutes.—Using same notation as for Board of Trade. P= sagt 





where p = greatest pitch in inches, P and t as above; 


C = 112 for plates 7/16’ thick and under, fitted with screw stay-bolts 
riveted over, screw stay-bolts and nuts, or plain bolt fitted 
with single nut and socket, or riveted head and socket; 

C = 120 for plates above 7/16’, under the same conditions; 

C = 140 for fiat surfaces where the stays are fitted with nuts inside 

and outside; 

C = 200 for flat surfaces under the same condition, but with the addi- 

tion of a washer riveted to the plate at least 14 plate’s thick- 
ness, and of a diameter equal ‘to?gof the pitch of the stay-bolts, 


N.B.—Plates fitted with double angle-irons and riveted to plate, with leaf 
at least 24 the thickness of plate and depth at least 44 of pitch, would be 
allowed the same pressure as determined by formula for plate with washer 
riveted on. 

N.B.—No brace or stay-bolt used in marine boilers to have a greater pitch 
than 1014” on fire-boxes and back connections. 

Certain experiments were carried out by the Board of Trade which showed 
that the resistance to bulging does not vary as the square of the plate’s 
thickness. There seems also good reason to believe that it is not inversely 
as the square of the greatest pitch. Bearing in mind, says Mr. Foley, that 
mathematicians have signally failed to give us true theoretical foundations 
for calculating the resistance of bodies subject to the simplest forms of 
stresses, we therefore cannot expect much from their assistance in the 
matter of flat plates. 

The Board of Trade rules for flat surfaces, being based on actual experi- 
ment, are especially worthy of respect; sound judgment appears also to 
have been used in framing them. 

Furnace Formulz.—Boarp or Trape.—Long Furnaces.— 

Y 2 : 
= Paar but not where L is shorter than (11.5¢— 1), at which length 
the rule for short furnaces comes into play. 

P = working-pressure in pounds per square inch; ¢ = thickness in inches; 
D = outside diameter in inches; L = length of furnace in feet up to 10 ft.; 
C = a constant, as per following table, for drilled holes: 

C = 99,000 fon welded or butt-jointed with single straps, double- 
riveted; 

C = 88,000 for butts with single straps, single-riveted ; 

C = 99,000 for butts with double straps, single-riveted. 


Provided always that the pressure so found does not exceed that given by 
the following formule, which apply also to short furnaces ; 


Cxt 
Sure D 





for all the patent furnaces named; 


Cxt LX 12 : : 
3x D\° ~ 675 x ;) when with Adamson rings. 


C= 8,800 for plain furnaces; 

C = 14,000 for Fox; minimum thickness 5/16”, greatest 54’; plain part 
not to exceed 6” in length; 

C = 18,500 for Morison: minimum thickness 5/16’, greatest 5¢’’; plain 
part not to exceed 6” in length; 

C = 14,000 for Purves-Brown; limits of thickness 7/16’ and 5¢’’; plain 
part 9” in length; 

C= 8,800 for Adamson rings; radius of fiange next fire 114”. 


U.S. Statutes.—Long Furnaces.—Same notation. 


89,600 x ¢ 
P= aah, clea but Z not to exceed 8 ft. 


N.B.—If rings of wrought iron are fitted and riveted on properly around 
and to the flue in such a manner that the tensile stress on the rivets shall 





STRENGTH OF STBRAM-BOILERS, 703 


not exceed 6000 Ibs. per sq. in., the distance between the rings shall be taken 
as the length of the flue in the formule. 
Short Furnaces, Plain and Patent.—P, as before, when not 8 ft. 


ine 89.690 x vg 
1 ey S98, 
De oe Lx when 
C = 14,000 for Fox corrugations where D = mean diameter; 


C 2 14,000 for Purves-Brown where D = diameter of flue; 
C = 5677 for plain flues over 16’’ diameter and less than 40’’, when 
not over 3 ft. lengths. 


Mr. Foley comments on the rules for long furnac:s as follows: The Board 
of Trade general formula, where the Jength is a factor, has a very limited 
range indeed, viz., 19 ft. as the extreme length, and at thicknesses — 12/’, 


as the short limit. The original formula, P = en is that of Sir W. 


Fairbairn, and was, I believe, never intended by him to apply to short fur- 
naces. On the very face of it, it is apparent, on the other hand, that if it is 
true for moderately long furnaces, it cannot be so for very long ones. We 
are therefore driven to the conclusion that any formuia which includes 
simple Z as a factor must be founded on a wrong basis. 

With Mr. Traill’s form of the formula, namely, substituting (Z + 1) for LZ, 
the results appear sufficiently satisfactory for practical purposes, and in- 
deed, as far as can be judged, tally with the results obtained from experi- 
ment as nearly as could be expected. The experiments to which I refer 
were six in number, and of great variety of length to diameter; the actual 
factors of safety ranged from 4.4 to 6.2, the mean being 4.78, or practically 
5. It seems tome, therefore, that, within the limits prescribed, the Board of 
Trade formula may be accepted as suitable for our requirements. 

The United States Statutes give Fairbairn’s rule pure and simple, except 
that the extreme limit of length to which it applies is fixed at 8 feet. As 
far as can be seen,no limit for the shortest length is prescribed, but the 
‘rules to me are by no means clear, flues and furnaces being mixed or not 
well distinguished. 

; peeeeripl for Stays.—The qualities of material prescribed are as 
ollows: 

Board of Trade.—The tensile strength to lie between the limits of 27 and 
32 tons per square inch, and to have an elongation of not less than 20% in 
ee Bie stays which have been welded or worked in the fire should not 

e used, 

Lloyd’s.—26 to 30 ton steel, with elongation not less than 20% in 8’. 

U. S. Statutes.—The only condition is that the reduction of area must not 
be less than 40% if the test bar is over 34’’ diameter. 

Loads allowed on Stays.— Board of Trade.—9000 Ibs. per square 
inch is allowed on the net section, provided the tensile strength ranges from 
27 to 32 tons. Steel stays are not to be welded or worked in the fire. 

Lloyd’s.—For screwed and other stays, not exceeding 114” diameter effec- 
tive, 8000 lbs. per square inch is allowed; for stays above 114’’, 9000 lbs. No 
stays are to be welded. 

U.S, Statutes.— Braces and stays shall not be subjected toa greater stress 
than 6000 lbs. per square inch. 

(Rankine, S. E., p. 459, says: ‘* The iron of the stays ought not to be ex- 
posed to a greater working tension than 3000 Ibs. on the square inch, in 
order to provide against their being weakened by corrosion. This amounts 
to making the factor of safety for the working pressure about 20.”’ It is 
evident, however, that an allowance in the factor of safety for corrosion may 
reasonably be decreased with increase of diameter. W. K.]| 


A Cx da?xt 2 

{ Girders.—Board of Trade. P= (a npx L P= working pres- 
sure in lbs. per sq.in.; W = width of flaine-box in inches; DZ = length of 
girder in inches; p = pitch of bolts in inches; D = distance between girders 
from centre to centre in inches; d = depth of girder in inches; ¢ = thick- 
ness of sum of same in inches; C = a constant = 6600 for 1 bolt, 9900 for 2 
or 3 bolts, and 11,220 for 4 bolts. 

Lloyd’s.—The same formula and constants, except that C = 11,000 for 4 or 
5 bolts, 11,550 for 6 or 7, and 11,880.for 8 or more. 

U. S. Statutes.—The matter appears to be left to the designers, 


"04 THE STHAM-BOILER. 


Tube-Flatess{ Board of Trades oP o> 2 Oa Meas 


horizontal distance between centres of tubes in inches; d = inside diameter 
of ordinary tubes; ¢ = thickness of tube-plate in inches; W = extreme 
width of combustion-box in inches from front tube-plate to back of fire- 
box, or distance between combustion-box tube-plates when the boiler is 
double-ended and the box common to both ends. 

The crushing stress on.tube-plates caused by the pressure on the flame- 
box top is to be limited to 10,000 lbs. per square inch. J 

Material for Tubes.—Mr. Foley proposes the following: If iron, the 
quality to be such as to give at least 22 tons per square inch as the minimum 
tensile strength, with an elongation of not less than 15% in 8’. If steel, the 
elongation to be not less than 26% in 8’’ for the material before being rolled 
into strips; and after tempering, the test bar to stand completely closing 
together. Provided the steel welds well, there does not seem to be any ob- 
ject in providing tensile limits. 

The ends should be annealed after manufacture, and stay-tube ends should — 
be annealed before screwing. 

Holding-power of Boiler-tubes.—Experiments made in Wash- 
ington Navy Yard show that with 214 in. brass tubes in no case was the holding- 
power less, roughly speaking, than 6000 Ibs., while the average was upwards 
of 20,000 lbs. It was further shown that with these tubes nuts were super- 
fluous, quite as good results being obtained with tubes simply expanded into 
the tube-plate and fitted with a ferrule. When nuts were fitted it was shown 
that they drew off without injuring the threads. 

In Messrs. Yarrow’s experiments on iron and steel tubes of 2” to 214” 
diameter the first 5 tubes gave way on an average of 23,740 lbs., which would 
appear to be about % the ultimate strength of the tubes themselves. Im all 
these cases the hole through the tube-plate was parallel with a sharp edge 
to it, and a ferrule was driven into the tube. 

Tests of the next 5 tubes were made under the same conditions as the first 
5, with the exception that in this ease the ferrule was omitted, the tubes be- 
ing simply expanded into the plates. The mean pull required was 15,270 Ibs., 
or considerably less than half the ultimate strength of the tubes. 

Effect of beading the tubes, the holes through the plate being parallel and 
ferrules omitted. The mean of the first 3, which are tubes of the same 
kind, gives 26,876 lbs. as their holding-power, under these conditions, as com- 
pared with 23,740 lbs. for the tubes fitted with ferrules only. This high 
figure is, however, mainly due to an exceptional case where the holding- 
power is greater than the average strength of the tubes themselves. 

It is disadvantageous to cone the hole through the tube-plate unless its 
sharp edge is removed, as the results are much worse than those obtained 
with parallel holes, the mean pull being but 16,031 Ibs,, the experiments be- 
ing made with tubes expanded and ferruled but not beaded over, 

In experiments on tubes expanded into tapered holes, beaded over and 
fitted with ferrules, the net result is that the holding-power is, for the size 
experimented on, about 34 of the tensile strength of the tube, the mean pull 
being 28,797 lbs. 

With tubes expanded into tapered holes and simply beaded over, better 
results were obtained than with ferrules; in these cases, however, the sharp 
edge.of the hole was rounded off, which appears in general to have a good 
effect. 

In one particular the experiments are incomplete, as it is impossible to 
reproduce on a machine the racking the tubes get by the expansion of a 
boiler as it is heated up and cooled down again, and it is quite possible, 
therefore, that the fastening giving the best results on the testing-machine 
may not prove so efficient in practice. 

N B.—It should be noted that the experiments were all made under the 
cold condition, so that reference should be made with caution. the circum- 
stances in practice being very different, especially when there is scale on 
Kes tube-plates, or when the tube-plates are thick and subject to intense 

eat. 

fron versus Steel Boiler-tubes. (Foley.)— Mr. Blechynden 
prefers iron tubes to those of steel, but how far he would go in attributing 
the leaky-tube defect to the use of steel tubes we are not aware. It appears, 
however, that the results of his experiments would warrant him in going a 
considerable distance in this direction. The test consisted of heating and 
cooling two tubes, one of wrought iron and the other of steel. Both tubes 
were 234 in. in diameter and .16 in. thickness of metal. The tubes were 


STRENGTH OF STEAM-BOILERS. 705 


ut in the same furnace, made red-hot, and then dipped in water. The 
engih was gauged at a temperature of 46° F 
dN 


. 


nis operation was twice repeated. with results as follows: 


Steel. Iron. 

Orvizimalilene tise erence cece oscces seeees 55.495 in, 55,495 in, 
Heated to 186° F.; increase...........5.ec0000 052 ** 048 ** 
Coefficient of expansion per degree F'........ .0000067 .0000062 
Heated red-hot and dipped in water; decrease .007 in. .003 in. 
Second heating and cooling, decrease........ -031 in, .004 in, 
Third heating and cooling, decrease.... ..... .017 in, .006 in, 

Total contraction 2.) 5.05.02. se Abeta nay .055 in, .013 in. 


Mr. A. C. Kirk writes : That overheating of tube ends is the cause of the 
leakage of the tubes in boilers is proved by the fact that the ferrules at 
present used by the Admiralty prevent it. These act by shielding the tube 
ends from the action of the flame, and consequently reducing evaporation, 
and so allowing free access of the water to keep them cool. 

Although many causes contribute; there seems no doubt that thick tube- 
plates must bear a share of causing the mischief. 


Rules for Construction of Boilers in Merchant Vessels 
im the United States. 
(Extracts from General Rules and Regulations of the Board of Supervising 
Inspectors of Steam-vessels (as amended 1898).) 


Wensile Strength of Plate. (Section 3.)—To ascertain the tensile 
strength and other qualities of iron plate there shall be taken from each 
i sheet to be used in shell or other 
parts of boiler which are subject ta 
tensile strain a test piece prepared 
in form according to the following 
diagram, viz.: 10 inches in length, 2 
inches in width, cut out in the 
centre in the manner indicated. 

_ To ascertain the tensile strength 
and other qualities of steel plate, there shall be taken from each sheet to be 
used in shell or other parts of boiler which are subject to tensile strain a test- 
piece prepared in form according to the following diagram: 

The straight part in centre shall 
be 9 inches in length and 1 inch in 
width, marked with light prick- & 
punch marks at distances 1 inch §§ 
apart, as shown, spaced so as to 
give 8 inches in length. 8 to 6 inches 8 to 6 inches 

The sample must show when 
tested an elongation of at least 25% in a length of 2 in. for thickness up to 
14 in., inclusive; in a length of 4 in. for over 14 to 7/16, inclusive; in a 
length of 6 in., for all plates over 7/16 in. and under 134 in, thickness. 

The reduction of area shall be the same as called for by the rules of the 
Board. No plate shall contain more than .06% of phosphorus and .04% of 
sulphur. 

The samples shall also be capable of being bent to a curve, of which the 
inner radius is not greater than 1144 times the thickness of the plates after 
tee eter heated uniformly to a low cherry-red and quenched in water 
of 82° F. 

[Prior to 1894 the shape of test-piece for steel was the same as that for fron, 
viz., the grooved shape. This shape has been condemned by authorities on 
strength of materials for over twenty years, It always gives results which 
are too high, the error sometimes amounting to 25 per cent. See pages 242, 
243, ante; also, Strength of Materials, W. Kent, Van N. Science Series No. 41, 
and Beardslee on Wrought-iron and Chain Cables. ]} 

Duetility. (Section 6.)—To ascertain the ductility and other lawful 
qualities, iron of 45,000 lbs. tensile strength shall show a contraction of area 
of 15 per cent, and each additional 1000 lbs, tensile strength shall show 1 
per cent additional contraction of area, up to and including 55,000 tensile 
strength. Iron of 55,000 tensile strength and upwards, showing 25 per cent 
reduction of area, shall be deemed to have the lawful duetility, All steel 

late of 4 inch thickness and under shall show a contraction of area of not 

ess than 50 per cent, Steel plate over 1 inch in thickness, up to 3 inch in 








706 THE STEAM-BOILER. 


thickness, shall show a reduction of. not less than 45 per cent. All steel plate 
over 34 inch thickness shall show a reduction of not less than 40 per cent. 

Bumped Heads of Boilers. (Section 17 as amended 1894.) — 
Pressure Allowed on Bumped Heads.—Multiply the thickness of the plate 
by one sixth of the tensile strength, and divide by six tenths of the radius to 
which head is bumped, which will give the pressure per square inch of 
steam allowed. 

Pressure Allowable for Concaved Heads of Boilers.—Multiply the pressure 
per square inch allowable for bumped heads attached to boilers or drums 
convexly, by the constant .6, and the product will give the pressure per 
square inch allowable in conecaved heads. 

The pressure on unstayed flat-heads on steam-drums or shells 
of boilers, when flanged and made of wrought iron or steel or of cast steel, 
shall be determined by the following rule: 

The thickness of plate in inches multiplied by one sixth of its tensile 
strength in pounds, which product divided by the area of the head in square 
inches multiplied by 0.9 will give pressure per square inch allowed. The 
material used in the construction of flat-heads when tensile strength has 
mee nee officially determined shall be deemed to have a tensile strength of 
45,000 Ibs. 


Table of Pressures allowable on Steam-boilers made of 
Riveted Iron or Steel Plates. 


(Abstract from a table published in Rules and Regulations of the U.S. 
Board of Supervising Inspectors of Steam-vessels.) 


Plates 144 inch thick. For other thicknesses, multiply by the ratio of ths 
thickness to 44 inch. 


50,000 Tensile | 55,000 Tensile | 60,000 Tensile | 65,000 Tensile |70,000 Tensile 








S a Strength. Strength. Strength. Strength. Strength. 
wo 5 4 Sie ° ih i Me LAA) US ae, ° ° : . 
el as cS ® = ® a © rs © ia 
~~ o ba 8 u 3 ran 4 oO fa 3 pa to} 
Sie des ih) Boles el| eh eel oouimeiimeS 
aa; 2 ghee n mes 2 3 2 <-5 nH mie 
Ate ea > wis e ee © wis 2 De] 
Lon! Len! 
lat scalar} Tes a | & a | & am | & a | & 




















36 115.74) 188.88 |127.31| 152.77 |138.88] 166.65 |150.46) 180.55 |162.03]} 194.43 
38 |109.64) 131.56 /120.61] 144.73 |131.57) 157.88 |142.54) 171.04 |153.5 | 184.20 
40 |104.16! 124.99 j114.58] 137.49 125 150 135.41] 162.49 |145.83) 174.99 
42 | 99.2 | 119.04 |109.12| 180.94 |119.04} 142 81 |128.96] 154.75 |138.88) 166.65 
44 | 94.69) 113.62 |104.16) 124.99 |113.63] 1386.35 /123.1 | 147.72 |1382.56) 159.07 
46 | 90.57] 108.68 | 99.63} 119.55 |108.69] 130.42 |117.75) 141.3 |126.8 | 152.16 | 
48 | 86.8 | 104.16 | 95.48) 114.57 |104.16) 124.99 |112.84] 185.4 121.52] 145.82 
54 | 77.16} 92.59 | 84.87) 101.84 | 92.59) 111.10 |100.3 | 120.36 |108.02] 129.62 
60 | 69.44) 83.32 | 76.38) 91.65 | 83.33) 99.99 | 90.27] 108.32 | 97.22] 116.66 
66 | 63.13} 75.75 | 69.44) 83.32 | 75.75) 90.90 | 82.07} 98.48 | 88.37] 106.04 
72 | 57.87] 69.44 | 63.65) 76.38 | 69.44; 83.32 | 75.22} 90.26 | 81.01] 97.21 
78 | 538.41] 64.09 | 58.76) 70.5 | 64.4] 76.92 | 69.44| 83.32 | 74.78] 89.73 
84 | 49.6 | 59.52 | 54.56) 65.47 | 59.52) 71.42 | 64.48) 77.37 | 69.44) 83.32 
90 | 46.29) 55.44 | 50.92; 61.1 | 55.55) 66.66 | 60.18] 72.21 | 64.81] 77.77 
96 | 43.4! 52.08 | 47.74) 57.28 | 52.08] 62.49 | 56.42] 67.67 | 60.76] 72.91 


The figures under the columns headed “ pressure” are for single-riveted 
boilers. Those under the columns headed ‘‘ 20% Additional” are for double- 
riveted. 














U. S. RuLE For ALLOWABLE PRESSURES. 


The pressure of any dimension of boilers not found in the table annexed 
to these rules must be ascertained by the following rule: 

Multiply one sixth of the lowest tensile strength found stamped on any 
plate in the cylindrical shell by the thickness (expressed in inches or parts 
of an inch) of the thinnest plate in the same cylindricaj shell, and divide by 
the radius or half diameter (also expressed in inches), the quotient will be 
the pressure allowable per square inch of surface for single-riveting, ta 
which add twenty per centum for double-riveting when all the rivet-holes 
in the shell of such boiler have been ‘fairly drilled’? and no part of sucn 
hole has been punched. 

The author desires to express his condemnation of the above rule, and of 

the tables derived from it, as giving too lowa factor of safety. (See also 
criticism by Mr. Foley, page 101, ante.) 


STRENGTH OF STEAM-BOILERS. 107 


If Po = bursting-pressure, ¢t = thickness, 7’= tensile strength, c = coef 
ficient of strength of riveted joint, that is, ratio of strength of the joint to 


that of the solid plate, d = diameter, Pp = es or if c be taken for double- 
riveting at 0.7, then Pb = a. 
By the U.S. rule the allowable pressure Pa = aa S 1.20 = ee whence 


Pb = 3.5Pa; that is, the factor of safety is only 3.5, provided the ‘‘ tensile 
strength found stamped in the plate” is the real tensile strength of the 
material. But in the case of iron plates, since the stamped T:S. is obtained 
from a grooved specimen, it may be greatly in excess of the real T.S., which 
would make the factor of safety still lower. According to the table, a boiler 
40 in. diam., 14 in. thick, made of iron stamped 60,000 T.S., would be licensed 
to carry 150 lbs. pressure if double-riveted. If thereal T.S. is only 50,000 lbs. 
the calculated bursting-strength would be 


P= — a 2x ee! = 437.51bs., 


and the factor of safety only 437.5 + 150 = 2.91) 
The author's formula for safe working-pressure of externally-fired boilers 


P=gauge- 





with longitudinal seams double-riveted, is P= ‘i ON 74000" 
pressure in lbs. per sq. in.; ¢ = thickness and d = diam. in inches. 
This is derived from the formula P = , taking c at 0.7 and f = 5 for 


steel of 50,000 lbs. T.S., or 6 for 60,000 lbs. T.S.; the factor of safety being 
increased in the ratio of the T.S., since with the higher T.S. there is greater 
danger of cracking at the rivet-holes from the effect of punching and rivet- 
ing and of expansion and contraction caused by variations of temperature. 
For external shells of internally-fired boilers, these shells not being exposed 
to the fire, with rivet-holes drilled or reamed after punching, a lower factor 
of safety and steel of a higher T.S. may be allowable. 


If the T.S. is 60,000, a working pressure P = Mev would give a factor of 


ad 
safety of 5,25. 
The following table gives safe working pressures for different diameters 
of shell and thicknesses of plate calculated from the author’s formula, 


Safe Working Pressures in Cylindrical Shells of Boilers, 
Tanks, Pipes, etc., in Pounds per Square Inch. 


Longitudinal seains double-riveted. 
(Calculated from formula P= 14,000 x thickness + diameter.) 




















BO 

as! Diameter in Inches. 

BS a 

oor 

228| 24 | 80 | 36 | 88 |} 40 | 42 | 44 | 46 | 48 | 50 | 82 
1 | 36.5) 29.2) 24.3) 23.0] 21.9] 20.8} 19.9] 19.0) 18.2) 17.5) 16.8 
2 | 72.9] 58.3] 48.6] 46.1] 43.8] 41.7] 39.8} 38.0} 36.5) 35.0] 33.7 
3 | 109.4} 87.5} 72.9] 69.1| 65.6] 62.5) 59.7] 57.1) 54.7] 52.5) 50.5 
4 | 145.8] 116.7| 97.2) 92.1] 87.5) 83.3] 79.5] 76.1) 72.9) 70.0] 67.3 
5 | 182.3! 145.8] 121.5) 115.1] 109.4] 104.2] 99.4] 95.1] 91.1] 87.5) 84.1 
6 | 218.7| 175.0} 145.8) 138.2) 181.3] 125.0) 119.3] 114.1] 109.4) 105.0) 101.0 
7 | 255.2! 204.1] 170.1] 161.2) 158.1] 145.9] 139.2) 133.2) 127.6] 122.5) 117.8 
8 | 291.7} 283.3) 194.4] 184.2) 175.0] 166.7] 159.1] 152.2] 145.8) 140.0) 134.6 
9 | 328.1] 262.5} 218.8} 207.2] 196.9] 187.5] 179.0] 171.2] 164.1) 157.5) 151.4 


182.3) 175.0) 168.3 
200.5} 192.5} 185.1 
218.7) 210.0} 201.9 
337.0} 227.5} 218.8 


10 | 864.6) 291.7) 248.1) 230.3] 218.8] 208.3) 198.9] 190. 
11 | 401.0) 320.8) 267.4) 253.3) 240.6] 229.2) 218.7) 209. 
12 | 487.5) 350.0) 291.7) 276.3) 262.5) 250.0} 238.6] 228. 
13 | 473.9) 379.2] 3816.0] 299.3) 284.4) 270.9) 258.5) 247. 
14 | 410.4) 408.3) 340.3) 322.4] 306.3) 291.7) 278.4) 266.3) 255.2) 245.0) 235.6 
15 | 546.9) 437.5) 364.6} 845.4) 328.1) 312.5) 298 3) 285.3) 273.4) 266.5) 252.4 
16 | 583.3) 466.7) 388.9! 368.4] 350.0] 333.3) 318.2] 304.4) 291.7] 280.0) 269.2 


COWS WNWWNWWWHH 





708 THE STEAM-BOILER, 











oe 



























Me 
mM ° 
22d Diameter in Inches. 
a3 6 
Beg 54 60 66 2 %8 84 90 96 | 102 | 108 | 114 
1 16:2) AL4.6]-9 1858), a12.2)" 112211024) 927 9.1) 8.6) “eel 
2 32.4, 29.2] 26.5} 24.38) 22.4) 20.8) 19.4) 18.2) 17.2) 16.2 15 4 
3 48.6} 438.7) 39.8) 386.5) 383.7] 31.3) 29.2] 27.3) 25.7| 24.3) 23.0 
4 64.8] 58.3] 53.0) 48.6) 44.9] 41.7) 38.9] 36.5] 34.3] 32.4) 30.7 
5 81.0] 72.9] 66.3} 60.8) 56.1] 52.1) 48.6) 45.6] 42.9] 40.5) 38.4 
6 97.2] 87.5) 79.5) 72.9) 67.3) 62.5) 58.3) 54.7) 51.5) 48.6) 46.1 
q 113.4] 102.1] 92.8] 85.1) 8.5) 72.9) 68.1] 68.8] 60.0] 56.7) 53.7 
8 129.6] 116.7] 106.1} 97.2) 89.7) 83.3) 77.8) 72.9] 68.6] 64.8) 61.4 
9 145.8] 1381.2] 119.8) 109.4) 101.0) 98.8) 87.5] 82.0] 77.2) 72.9] 69.1 
10 162.0] 145.8] 182.6) 121.5) 112.9)104.2) 97.2) 91.1] 85.8] 81.0] 76.8 
: 145.8) 183.7; 128.4]114.6/106.9/100.3] 94.4] 89.1] &4.4 
145.8) 134.6/125.0/116.7/109.4)102.9} 97.2) 92.1 
358.0) 145.8]135.4/126.4/118.5}111.5)105.38) 99.8 
170.1) 157.1)145.8/136.1/127.6)120.1/118.4/107.5 102. 1 
182.3) 168.3/156.3)145.8/1386.7)128.7/121.5/115.1 109. 4 
194.4) 179.5|166.7 145.8}137. 














Rules governing Inspection of Boilers in Philadelphia, 


In estimating the strength of the longitudinal seams in the cylindrical 
shells of boilers the inspector shall apply two formule, A and B: 


~~ 


A { Pitch of rivets — diameter of holes punched to receive the rivets 
. pitch of rivets 
percentage of strength of the sheet at the seam. 
Area of hole filled by rivet x No. of rows of rivets in seam X shear- 
B ing strength of rivet i 
: pitch of rivets < thickness of sheet X tensile strength of sheet ~— 
percentage of strength of the rivets in the seam, 
Take the lowest of the percentages as found by formule A and B and — 


apply that percentage as the ‘‘strength of the seam”’ in the following 
formula C, which determines the strength of the longitudinal seams: 


Thickness of sheet in parts of inch X strength of seam as obtained 
C by formula A or B X ultimate strength of iron stamped on plates 
? 


internal radius of boiler in inches X 5 as a factor of safety f 
safe working pressure. 


TABLE OF PROPORTIONS AND SAFE WORKING PRESSURES WITH FoORMULa A 
D CO, @ 50,000 Las., T.S. 


Diameter of rivet. ....... 5g” 11/16 34 13/16 % 
Diameter of rivet-hole...}| 11/16” 34 13/16 % 15/16 
Pitch of rivetsS........... ae 2 1/16 246 2 3/16 214 
Strength of seam, %.. ... 656 .636 .62 -60 .58 
Thickness of plate. .... ye 5/16 3% 7/16 % 


A age Working Pressure with Longitudinal Seams, 
Single-riveted. 


24 137 165 193 220 242 


Diameter cf boiler, in. 





30 109 132 154 176 194 
32 102 124 144 165 182 
34 96 117 136 155 171 
86 91 110 129 147 161 
38 86 104 122 189 153 
40 82 99 116 132 145 
44 74 91 105 120 132 
48 68 83 96 110 121 
54 60 73 86 98 107 
60 55 66 7 88 97 


i 


STRENGTH OF STEAM-BOILERS. 70% 





Diameter of rivet........ 5!’ 11/16 34 18/16 % 
Diameter of rivet-hole...| 11/16’ 34 13/16 X% 15/16 
Pitehof rivets. ..02% Ave 3! 31g 314 336 314 
Strength of seam, %..... AKA 76 avin 74 ai 
Thickness of plate.. .... 14" 5/16 34 7/16 % 


Diameter of boiler, in...|52fe Working Pressure with Longitudinal Seams, 
; Double-riveted. 


24 160 198 235 269 305 
30 127 158 188 215 243 
32 119 148 176 202 228 
34 112 140 166 190 215 
36 106 132 156 179 208 
38 101 125 148 70 192 
40 96 119 141 161 183 
44 87 108 128 147 166 
48 9 99 118 135 152 
54 70 88 104 120 135 
60 64 79 94 108 122 





Flues and Tubes for Steam-boilers.—(From Rules of U. S. 
Supervising Inspectors. Steam-pressures per square inch allowable on 
riveted and lap-welded flues made in sections. Extract from table in Rules 
of U. 8. Supervising Inspectors.) 

T = least thickness of material allowable, D= greatest diameter in inches, 
P= allowable pressure. For thickness greater than 7’ with same diameter 
P is increased in the ratio of the thickness. 


Deine oon 10;e lly ote uslou site Om elo Os opm clue eom on 
T= Aneel Oe eel, eligsee “soe, seo ete eel Bs CON alg 42o Boo 80 ol oe cade 
P=lbs. 189 184179174 172 158 152 147 1438 1389 136 134 181 129 126 125 122 


JO veer hay 24 25 26 27 28 29 30 31 382 33 34 35 36 37 388 39 40 
iain, .34 .85 .86 .37 .88 .89 .40 .41 .42 .43 .44 .45 .46 .47 .48 .49 .50 
P=lbs. 121 120 119 117 116 115 115 114 112 112 110 110 109 109 108 108 107 


For diameters not over 10 inches the greatest length of section allowable 
is 5 feet; for diameters 10 to 23 inches, 3 feet; for diameters 23 to 40 inches, 30 
inches. If lengths of sections are greater than these lengths, the allowable 
pressure is reduced proportionately. 

The U.S. rule for corrugated flues, as amended in 1894, is as follows: Rule 
II, Section 14. The strength of all corrugated flues, when used for furnaces 
or steam chimneys (corrugation not less than 1144 inches deep and not exceed- 
ing 8 inches from centres of corrugation), and provided that the plain parts 
at the ends do not exceed 6 inches in length, and the plates are not less than 
5/16 inch thick, when new, corrugated, and practically true circles, to be 
calculated from the following formula: 


14,000 


D x T = pressure, 


T = thickness, in inches; D = mean diameter in inches, 


Ribbed Fiuwes.—The same formula is given for ribbed flues, with rib 
projections not less than 13g inches deep and not more than 9 inches 
apart. 

Flat Stayed Surfaces in Steam-boilers.—Rulc II., Section 6, of 
the rules of the U. S. Supervising Inspectors provides as follows: 

No braces or stays hereafter employed in the construction of boilers 
shall be allowed a greater strain than 6000 lbs. per square inch of 
section. 

Clark, in his treatise on the Steam-engine, also in his Pocket-book, gives 
the following formula: p = 407ts + d, in which p is the internal pressure in 
pounds per square inch that will strain the plates to their elastic limit, ¢ is 


_ the thickness of the plate in inches, d is the distance between two rows of 


stay-bolts in the clear, and s is the tensile stress in the plate in tons of 
2240 lbs. per square inch, at the elastic limit. Substituting values of s 
for iron, steel, and copper, 12, 14, and 8 tons respectively, we have the 
following: 


710 THE STEAM-BOILER. 


ForRMULH FOR ULTIMATE ELASTIC STKENGTH OF FLAT STAYED SURFACES. 














Iron. Steel. Copper. 
é rsa t 
Pressure........ Sais wets ais cal Ma TD gee 50007, ‘pis 57006 p = 3300- 
, _pxd 2D Moet _pxd 
Thickness of/ptate.... Js... Gis 5000” t= 5700 i 3300 
00 70 3300t 
Pitch, of Doltsiac..s sdaee adi sae d= ei 4 == 
PEE TALS BOL DP Pp Pp 





For Diameter of the Stay-bolts, Clark gives d’ = ooa1g/ ——t, 


in which d’ = diameter of screwed bolt at bottom of thread, P = longitudi- 
nal and P’ transverse pitch of stay-bolts between centres, p = internal 
pressure in lbs. per sq. in. that will strain the plate to its elastic limit, s = 
elastic strength of the stay-bolts in lbs. per sq. in. Taking s = 12, 14, and 8 
tons, respectively for iron, steel, and copper, we have 


For iron, d’ = .00069 / PP’p,’or if P = P’, d’ = .00069P VD; 
For steel, d/ = .000644/PP’p, “ ¢  d! = .00064P Vp; 
For copper, d’ = .00084 7 PP’p, ‘“ ¢ d’ = .00084P Vp. 

In using these formule a large factor of safety should be taken to allow 
for reduction of size by corrosion. Thurston’s Manual of Steam-boilers, p. 
144, recommends that the factor be as large as 15 or 20. The Hartford 
Steam Boiler Insp. & Ins. Co. reeommends not less than 10. 

Strength of Stays.—A. F. Yarrow (£ng7., March 20, 1891) gives the 


following results of experiments to ascertain the strength of water-space 
stays: 





| 





Length : Y Ulti- 

Description. between D Sta ame ee mate 
Plates. 4 Stress. 
lbs. © 


Hollow stays screwed into {| 4.75in. |1in.(hole 7/16 in. and 5/16 in.) 25,457 
plates and hole expanded }| 4.64in. |1lin.(hole 9/16 in. and‘%/16 in.| 20,992 
Solid stays screwed into}| 4.80in. % in, 22,008 
plates and riveted over. (| 4.80 in. ¥ in. 22,070 


The above are taken as a fair average of numerous tests. 


Stay-bolts in Curved Surfaces, as in Water-legs of Verti- 
eal Boilers.—The rules of the U. S. Supervising Inspectors provide as 
follows: All vertical boiler-furnaces constructed of wrought iron or steel 
plates, and having a diameter of over 42 in. or a height of over 40 in. shall be 
stayed with bolts as provided by §6 of Rule II, for flat surfaces; and the 
thickness of material required for the shells of such furnaces shall be de- 
termined by the distance between the centres of the stay-bolts in the fur- 
nace and not in the shell of the boiler; and the steam-pressure allowable 
shall be determined by the distance from centre of stay-bolts in the furnace 
and the diameter of such stay-bolts at the bottom of the thread. 

The Hartford Steam-boiler Insp. & Ins. Co. approves the above rule (The 
Locomotive, March, 1892) as far as it states that curved surfaces are to be 
computed the same as flat ones, but prefers Clark’s formule for flat 
stayed surfaces to the rules of the U. S. Supervising Inspectors. 

Fusible-plugs.—Fusible-plugs should be put in that portion of the 
heating-surface which first becomes exposed from lack of water. The rules 
of the U.S. Supervising Inspectors specify Banca tin for the purpose. Its 
melting-point is about 445° F. The rule says: All steamers shall have 
inserted in their boilers plugs of Banca tin, at least 14 in. in diameter at the 
smallest end of the internal opening, in the following manner, to wit: 
Cylinder- boilers with flues shall have one plug inserted in one flue of each 
boiler; and also one plug inserted in the shell of each boiler from the inside, 
immediately before the fire line and not less than 4ft. from the forward 
end of the boiler. All fire-box boilers shall have one plug inserted in the 
crown of the back connection, or in the highest fire-surface of the boiler. 


IMPROVED METHODS OF FREDING COAL. V11 


All upright tubular boilers used for marine purposes shail have a fusible 
plug inserted in one of the tubes at a point at least 2 in. below the lower 
gauge-cock, and said plug may be placed in the upper head sheet when 
deemed advisable by theflocal inspectors. 

Steam=-domes,—Steam domes or drums were formerly almost univer- 
sally used on horizontal boilers, but their use is now generally discontinued, 
as they are considered a useless appendage to a steam-boiler, and unless 
properly designed and constructed are an element of weakness. 

Heicht of Furnace.—Recent practice in the United States makes 
the height of furnace much greater than it was formerly. With large sizes 
of anthracite there is no serious objection to having the furnace as low as 12 
to 18 in., measured from the surface of the grate to the nearest portion of 
the heating surface of the boiler, but with coal containing much volatile 
matter and moisture a much greater distance is desirable. With very vola- 
tile coals the distance may be as great as 4 or 5 ft. Rankine (S. E., p. 457) 
says: The clear height of the ‘‘ crown ” or roof of the furnace above the grate- 
bars is seldom less than about 18in., and often considerably more. In the 
fire-boxes of locomotives it is on an average about 4 ft. The height of 18 in. 
is Suitable where the crown of the furnace isa brick arch. Where the crown 
of the furnace, on the other hand, forms part of the heating-surface of the 
boiler, a greater height is desirable in every case in which it can be 
obtained; for the temperature of the boiler-plates, keing much lower than 
that of the flame, tends to check the combustion of the inflammable gases 
which rise from the fuel. Asa general principle a high furnace is favorable 
to complete combustion. 


IMPROVED METHODS OF FEEDING COAL, 


Mechanical Stokers. (William R. Roney, Trans. A. S. M. E., vol. 
xii.)—Mechanical stokers have been used in England to a limited extent 
since 1785. In that year one was patented by James Watt. It wasa simple 
device to push the coal, after it was coked at the front end of the grate, 
back towards the bridge. It was worked intermittently by levers, and was 
designed primarily to prevent smoke from bituminous coal. (See D. K. 
Clark’s Treatise on the Steam-engine.) 

After the year 1840 many styles of mechanical stokers were patented in 
England, but nearly all were variations and modifications of the two forms 
of stokers patented by John Jukes in 1841, and by E. Henderson in 1843. 

The Jukes stoker consisted of longitudinal fire-bars, connected by links, 
so as to form an endless chain, similar to the familiar treadmill horse-power. 
The small coal was delivered from a hopper on the front of the boiler, on to 
the grate, which slowly moving from front to rear, gradually advanced the 
fuel into the furnace and discharged the ash and clinker at the back. 

The Henderson stoker consists primarily of two horizontal fans revolving 
on vertical spindles, which scatter the coal over the fire. 

Numerous faults in mechanical construction and in operation have limited 
the use of these and other mechanical stokers. The first American stoker 
was the Murphy stoker, brought out in 1878. It consists of two coal maga- 
zines placed in the side walls of the boiler furnace, and extending back from 
the boiler front 6 or 7 feet. In the bottom of these magazines are rectangu- 
lar iron boxes, which are moved from side to side by means of a rack and 
pinion, and serve to push the coal upon the grates, which incline at an angle 
of about 35° from the inner edge of the coal magazines, forming a V-shaped 
receptacle for the burning coal. The grates are composed of narrow parallel 
bars, so arranged that each alternate bar lifts about an inch at the lower 
end, while at the bottom of the V, and filling the space between the ends of 
the grate-bars, is placed a cast-iron toothed bar, arranged to be turned by a 
crank. The purpose of this bar is to grind the clinker coming in contact 
with it. Over this V-shaped recepvacle is sprung a fire-brick arch. 

In the Roney mechanical stoker the fuel to be burned is dumped into a 
hopper on the boiler front. Set in the lower part of the hopper isa ‘‘ pusher”’ 
to which is attached the ‘ feed-plate’’ forming the bottom of the hopper. 
The “ pusher,” by a vibratory motion, carrying with it the ‘‘ feed-plate,” 
gradually forces the fuel over the ‘“‘ dead-plate’’ and on the grate. The 
grate-bars, in their normal condition form a series of steps, to the top step 
of which coal is fed from the “ dead-plate.” Each bar rests in a concave 
seat in the bearer, and is capable of a rocking motion through an adjustable 
angle. All the grate-bars are coupled together by a ‘‘rocker-bar.” .A vari- 
able back-and-forth motion being given to the ‘“‘ rocker-bar,” through a con- 


712 THE STEAM-BOILER. 


necting-rod, the grate-bars rock in unison, now forming a series of steps, 
and now approximating to an inclined plane, with the grates partly over- 
lapping, like shingles on a roof. When the grate-bars rock forward the fire 
will tend to work down ina body. But before the coal can move too far 
the bars rock back to the stepped position, checking the downward motion, 
breaking up the cake over the whole surface, and admitting a free volume 
of air through the fire. The rocking motion is slow, being from 7 to 10 
strokes per minute, according to the kind of coal. This alternate starting 
and checking motion is continuous, and finally lands the cinder and ash on 
the dumping-grate below, 

Mr. Roney gives the following record of six tests to determine the com- 
parative economy of the Roney mechanical stoker and hand-firing on return 
tubular boilers, 60 inches x 20 feet, burning Cumberland coal with natural 
draught. Rating of boiler at 12.5 square feet, 105 H. P. 


‘ “eG Three tests, hand-firing. Three tests, Stoker. 
vaporation per pound, dry 

reporabion Der pound 3 t 10.86 10.44 11.00 11.89 1225 12.64 
H.P. developed above rating, % Brot ales 68 54.6 66.7 84.3 


Results of comparative tests like the above should be used with caution 
in drawing generalizations. It by no means follows from these results that 
a stoker will always show such comparative excellence, for in this case the 
results of hand-firing are much below what may be obtained unier favor- 
able circumstances from hand-firing with good Cumberland coal. 

The Hawiey Down-draught Furnace.—A foot or more above 
the ordinary grate there is carried a second grate composed of a series of 
water-tubes, opening at both ends into steel drums or headers, through which 
water is circulated. The coal is fed on this upper grate, and as it is par- 
tially consumed falls through it upon the lower grate, where the combustion 
is completed in the ordinary manner. The draught through the coal on the 
upper grate is downward through the coal and tke grate. The volatile gases 
are therefore carried down through the bed of coal, where they are thor- 
oughly heated, and are burned in the space beneath, where they meet the 
excess of hot air drawn through the fire on the lower grate. In tests in 
Chicago, from 30 to 45 lbs. of coal were burned per square foot of grate upon 
this system, with good economical results. (See catalogue of the Hawley 
Down Draught Furnace Co., Chicago.) 

Under-feed Stokers,—Results similar to those that may be obtained 
with downward draught are obtained by feeding the coal at the bottom of 
the bed, pushing upward the coal already on the bed which has had its 
volatile matter distilled from it. The volatile matter of the freshly fired 
coal then has to pass through a body of ignited coke, where it meets a sup- 
ply of hot air. (See circular of The American Stoker Co., New York, 1898.) 


SMOKE PREVENTION. 


A committee of experts was appointed in St. Louis in 1891 to report on the 
smoke problem. A summary of its report is given in the Iron Age of April 
7, 1892. It describes the different means that have been tried to prevent 
smoke, such as gas-fuel, steam-jets, fire-brick arches and checker-work, 
hollow walls for preheating air, coking arches or chambers, double combus- 
tion furnaces, and automatic stokers, All of these means have been more or 
fess effective in diminishing smoke, their effectiveness depending largely 
upon the skill with which they are operated ; but none is entirely satisfac- 
tory. Fuel-gas is objectionable chiefly on account of its expense. The 
average quality of fuel-gas made from a trial run of several car-loads of 
Illinois coal, in a well-designed fuel-gas plant, showed a calorific value of 
243,391 heat-units per 1000 cubic feet. This is equivalent to 5052.8 heat-units 
per lb. of coal, whereas by direct calorimeter test an average sample of the 
coal gave 11,172 heat-units. One lb, of the coal showed a theoretical evap- 
oration of 11.56 lbs. water, while the gas from 1 Ib. showed a theoretical 
evaporation of 5.28 lbs, 48.17 lbs. of coal were required to furnish 1000 cubic 
feet of the gas, In 39 tests the smoke-preventing furnaces showed only 74% 
of the capacity of the common furnaces, reduced the work of the boilers 
28%, and required about 2% more fuel to do the same work. In one case with 
steam-jets the fuel consumption was increased 12% for the same work. 

Prof. O. H. Landreth, in a report to the State Board of Health of Tennes- 
see (Engineering News, June 8, 1892), writes as follows on the subject of 
smoké prevention: 


SMOKE PREVENTION. 713 


As pertains to steam-boilers, the object must be attained by one or more 
of the following agencies : 

1. Proper design and setting of the boiler-plant. This implies proper grate 
area, sufficient draught, the necessary air-space between grate-bars and 
through furnace, and ample combustion-room under boilers. 

2. That system of firing that is best adapted to each particular furnace to 
secure the perfect combustion of bituminous coal. This may be either: (a) 
‘*coke-firing,’’ or charging all coal into the front of the furnace until par- 
tially coked, then pushing back and spreading; or (6b) ‘alternate side-fir- 
ing’’; or (c) ‘‘spreading,’’ by which the coal is spread over the whole grate 
area in thin, uniform layers at each charging. 

8. The admission of air through the furnace-door, bridge-wall, or side walis. 

4, Steam-jets and other artificial means for thoroughly mixingjthe air and 
combustible gases. 

5. Preventing the cooling of the furnace and boilers by the inrush of cold 
air when the furnace-doors are opened for charging coal and handling the 


re. 

6. Establishing a gradation of the several steps of combustion so that the 
coal may be charged, dried, and warmed at the coolest part of the furnace, 
and then moved by successive steps to the hottest place, where the final 
combustion of the coked coal is completed, and compelling the distilled 
combustible gases to pass through this hottest part of the fire. 

7%. Preventing the cooling by radiation of the unburned combustible gases 
until perfect mixing and combustion have been accomplished. 

8. Varying the supply of air to suit the periodic variation in demand. 

9. The substitution of a continuous uniform feeding of coal instead of 
intermittent charging. 

10. Down-draught burning or causing the air to enter above the grate and 
pass down through the coal, carrying the distilled products down to the high 
temperature plane at the bcttom of the fire. 

The number of smoke-prevention devices which have been invented is 
legion. A brief classification is: 

(a) Mechanical stokers. They effect a material saving in the labor of 
firing, and are efficient smoke-preventers when not pushed above their 
capacity, and when the coal does not cake badly. They are rarely suscepti- 
ble to the sudden changes in the rate of firing frequently demanded in 
service. 

(b) Air-flues in side walls, bridge-wall, and grate-bars, through which air 
when passing is heated. The results are always beneficial, but the flues are 
difficult to keep clean and in order. 

(c) Coking arches, or spaces in front of the furnace arched over, in which 
the fresh coal is coked, both to prevent cooling of the distilled gases, and te 
force them to pass through the hottest part of the furnace just beyond the 
arch. The results are good for normal conditions, but ineffective when the 
fires are forced. The arches also are easily burned out and injured by 
working the fire. : 

(d) Dead-plates, or a portion of the grate next the furnace-doors, reserved 
for warming and coking the coal before it is spread over the grate. These 
give good results when the furnace is not forced above its normal capacity. 
This embodies the method of ‘* coke-firing’’ mentioned before. 

(e) Down-draught furnaces, or furnaces in which the air is supplied to the 
coal above the grate, and the products of combustion are taken away from 
beneath the grate, thus causing a downward draught through the coal, carry- 
ing the distilled gases down to the highly heated incandescent coal at the 
bottom of the layer of coal on the grate. This is the most perfect manner 
of producing combustion, and is absolutely smokeless. 

(f) Steam-jets to draw air in or inject air into the furnace above the grate, 
and also to mix the air and the combustible gases together. A very efficient 
SURG: DE SNPSPRR, but one liable to be wasteful of fuel by inducing too rapid 
a draught. 

(g) Baffle-plates placed in the furnace above the fire to aid in mixing the 
combustible gases with the air. ; 

(h) Double furnaces, of which there are two different styles; the first of 
which places the second grate below the first grate; the coal is coked on the 
first grate, during which process the distilled gases are made to pass over 
the second grate, where they are ignited and burned; the coke from the first. 
grate is dropped onto the second grate: a very efficient and economical 
smoke-preyenter, but rather complicated to construct and maintain. In the 
second form the products of combustion from the first furnace pass through 


714 THE STEAM-BOILER. 


the grate anu rire of the second, each furnace being charged with fresh fuel 
when needed, the latter generally with a smokeless coal or coke: an irra. 
tional and unpromising method. 

Mr. C. F. White, Consulting Engineer to the Chicago Society for the Pre- 
vention of Smoke, writes under date of May 4, 1893: 

The experience had in Chicago has shown plainly that it is perfectly easy 
to equip steam-boilers with furnaces which shall burn ordinary soft coal in 
such a manner that the making of smoke dense enough to obstruct the vision 
shall be confined to one or two intervals of perhaps a couple of minutes’ 
duration in the ordinary day of 10 hours. 

Gas-=fired Steam=boilers.—Converting coal into gas in a separate 
producer, before burning it under the steam-boiler, is an ideal method of 
smoke-prevention, but its expense has hitherto prevented its general intro- 
duction. A series of articles on the subject, iliustrating a great number of 
devices, by F. J. Rowan, is published in the Colliery Engineer, 1889-90. See 
also Clark on the Steam-engine. 


FORCED COMBUSTION IN STEAM-BOILERS. 


For the purpose of increasing the amount of steam that can be generated 
by a boiler of a given size, forced draught is of great importance. It is 
universally used in the locomotive, the draught being obtained by a steam- 
jet in the smoke-stack. It is now largely used in ocean steamers, especially 
in ships of war, and to a small extent in stationary boilers. Economy of fuel 
is generally not attained by its use, its advantages being confined to the 
securing of increased capacity from a’ boiler of a given bulk, weight, or cost. 
The subject of forced draught is well treated ina paper by James Howden, 
entitled, ‘‘ Forced Combustion in Steam-boilers’’? (Section G, Engineering 
Congress at Chicago, in 1893), from which we abstract the following: 

Edwin A, Stevens at Bordentown, N. J., in 1827, in the steamer ‘‘ North 
America,”’ fitted the boilers with closed ash-pits, into which the air of com- 
bustion was forced by afan, In 1828 Ericsson fitted in a similar manner the 
steamer ‘‘ Victory,’’ commanded by Sir John Ross. 

Messrs. E. A. and R. L. Stevens continued the use of forced draught for 
a considerable period, during which they tried three different modes of using 
the fan for promoting combustion: 1, blowing direct into a closed ash-pit; 
2, exhausting the base of the funnel by the suction of the fan; 3, forciug air 
into an air-tight boiler-room or stoke-hold. Each of these three methods 
was attended with serious difficulties. 

In the use of the closed ash-pit the blast-pressure would frequently force 
the gases of combustion, in the shape of a serrated flame, from the joint 
around the furnace doors in so great a quantity as to affect both the effi- 
ciency and health of the firemen. 

The chief defect of the second plan was the great size of the fan required 
to produce the necessary exhaustion. The size of fan required grows in a 
rapidly increasing ratio as the combustion increases, both on account of the 
greater air-supply and the higher exit temperature enlarging the volume of 
the waste gases. 

The third method, that of forcing cold air by the fan into an air-tight 
boiler-room—the present closed stoke-hold system—though it overcame the 
difficulties in working belonging to the two forms first tried, has serious 
defects of its own, as it cannot be worked, even with modern high-class 
boiler-construction, much, if at all, above the power of a good chimney 
draught, in most boilers, without damaging them. 

In 1875 John I. Thornycroft & Co., of London, began the construction of 
torpedo-boats with boilers of the locomotive type, in which a high rate of 
combustion was attained by means of the air-tight boiler-room, into which 
air was forced by means of a fan. 

§n 1882 H.B.M. ships ‘‘Satellite”’ and ‘‘Conqueror’’ were fitted with this 
system, the former being a small ship of 1500 I.H.P., and the latter an iron- 
clad of 4500 1.H.P. On the trials with forced draught, which lasted from two 
to three hours each, the highest rates of combustion gave 16.9 I.H.P. per 
square foot of fire-grate in the ‘‘ Satellite,’ and 13.41 I.H.P. in the ‘‘ Con- 

ueror. 

:- None of tne short trials at these rates of combustion were made without 
injury to the seams and tubes of the boilers, but the system was adopted, 
and it has been continued in the British Navy to this day (1898). 

In Mr. Howden’s opinion no advantage arising from increased combustion 
over natural-draught rates is derived from using forced draught in a closed 
ash-pit sufficient to compensate the disadvantages arising from difficulties 


FUEL ECONOMIZERS, W15 


ir working, there being either excessive smoke from bituminous coal! or 
reduced evaporative economy. , 

In 1880 Mr. Howden designed an arrangement intended to overcome the 
defects of both the closed ash-pit and closed stoke-hold systems. 

An air-tight reservoir or chamber is placed on the front end of the boiler 
and surrounding the furnaces. This reservoir, which projects from 8 to 10 
inches from the end of the boiler, receives the air under pressure, which is 
passed by the valves into the ash-pits and over the fires in proportions 
suited to the kind of fuel used and the rate of combustion required. The 
air nsed above the fires is admitted to a space between the outer and inner 
furnace-doors, the inner having perforations and an air-distributing box 
through which the air passes under pressure. 

By means of the balance of air-pressure above and below the fires all 
tendency for the fire to blow out at the furnace-door is removed. 

By regulating the admission of the air by the valves above and below the 
fires, the highest rate of combustion possible by the air-pressure us€d can 
be effected, and in same manner the rate of combustion can be reduced to 
far below that of natural draught, while complete and economical combus- 
tion at all rates is secured. ; 

A feature of the system is the combination of the heating of the air of 
combustion by the waste gases with the controlled and regulated admission 
of air to the furnaces. This arrangement is effected most conveniently by 
passing the hot fire-gases after they leave the boiler through stacks of 
vertical tubes enclosed in the uptake, their lower ends being immediately 
above the smoke-box doors. 

Installations on Howden’s system have hitherto been arranged for a rate 
of combustion to give at full sea-power an average of from 18 to 22 I.H.P. 
per square foot of fire-grate with fire-bars from 5’ 0” to 5’ 6” in length. 

It is believed that with suitable arrangement of proportions even 50 
1,H.P. per square foot can be obtained. 

For an account of recent uses of exhaust-fans for increasing draught, see 
paper by W. R. Roney, Trans. A. S. M. E., vol. xv. 


FUEL ECONOMIZERS,. 


Green’s Fuel Economizer,.—Clark gives the following average re- 
sults of comparative trials of three boilers at Wigan used with and without 


economizers : 
Without With 
Eeonomizers. Economizers, 
Coal per square foot of grate per hour...... 21.6 21.4 
Water at 100° evaporated per hour.......... 73.55 79 .32 
Water at 212° per pound of coal ... ...... 9.60 10.56 


Showing that in burning equal quantities of coal per hour the rapidity of 
evaporation is increased 9.3% and the efficiency of evaporation 10% by the 
addition of the economizer. 

The average temperatures of the gases and of the feed-water before and 
after passing the economizer were as follows: 


With 6-f6. grate. With 4-ft. grate. 


Before. After, Before. After. 
Average temperature of gases....... 649 340 501 312 
Average temperature of feed-water. 47 157 41 137 


Taking averages of the two grates, to raise the temperature of the feed- 
water 100° the gases were cooled down 250°. 

Performance of a Green Economizer with a Smoky Coal, 
—The action of Green’s Economizer was tested by M. W. Grosseteste for a 
period of three weeks. The apparatus consists of four ranges of vertical 
pipes, 644 feet high, 334 inches in diameter outside, nine pipes in each range, 
connected at top'and bottom by horizontal pipes. The water enters all the 
tubes from below, and leaves them from above. The system of pipes is en- 
veloped in a brick casing, into which the gaseous products of combustion 
are introduced from above, and which they leave from below. The pipes 
are cleared of soot externally by automatic scrapers. The capacity for 
water is 24 cubic feet, and the total external heating-surface is 290 square 
feet. The apparatus is placed in connection with a boiler having 355 square 
feet of surface. 

This apparatus had been at work for seven weeks continuously without 
having been cleaned, and had accumulated a 4-inch coating of soot and 


716 THE STEAM-BOILER 


ash, when its performance, in the same condition, was observed for one 
week. During the second week it was cleaned twice every day; but during 
the third week, after having been cleaned on Monday morning, it was 
worked continuously without further cleaning. A smoke-making coal was 
used. The consumption was maintained sensibly constant from day to day. 


GREEN’s ECONOMIZER.—RESULTS OF EXPERIMENTS ON ITS EFFICIENCY AS 
AFFECTED BY THE STATE OF THE SURFACE. (W, Grosseteste.) 





Temperature of Feed- | Temperature of Gas- 
water. eous Products. 


TIME 
‘ Enter- | Leav- Enter- | Leav- 
(February and March). ing ing | Differ- ing ing | Differ- 
Feed- | Feed- | ence. | Feed- | Feed- | ence. 
heater.} heater. heater.| heater. 


SS | | Ss | | | | 





deb Weaelketl. 4c 1ecvilbsd. bakes 73.5° | 161.5° | 88.0° | 849° | 261° | 588° 





2d: WOK is. ia wids ds dees hike 77.0 | 230.0 | 153.0 882 297 585 
38d Week—Monday ....... 3.4) 1 19620.))).122.6 831 284 547 
Tuesday........ 73.4 | 181.4 | 108.0 71 309 562 
Wednesday..... 79.0, | 178.0 99.0 —— sa 
Thursday.....-.} 80.6 | 170.6 90.0 952 329 623 
iti ayrjerat-ayntis 80.6 | 169.0 88.4 889 338 551 
Saturday........ 79.0 1.17%2.4 93.4 901 351 550 
ist Week. 2d Week. 3d Week. 
Coal consumed per hour.............:..66 2141lbs. 216lbs. 218 1bs, 
Water evaporated from 32° F. per hour.. 1424 1525 1428 
Water per pound of coal.... .. ..... skews, 6.65 7.06 6.70 


it is apparent that there is a great advantage in cleaning the pipes dailv 
—thke elevation of temperature having been increased by it from 88° to 153°. 
In the third week, without cleaning, the elevation of temperature relapsed 
in three days to the level of the first week; even on the first day it was 
quickly reduced by as much as half the extent of relapse. By cleaning the 
pipes daily an increased elevation of temperature of 65° F., was obtained, 
whilst a gain of 6% was effected in the evaporative efficiency. 


INCRUSTATION AND CORROSION, 


Encrustation and Scale.—Incrustation (as distinguished from . 
mere sediments due to dirty water, which are easily blown out, or gathered 
up, by means of sediment-collectors) is due to the presence of salts in the 
feed-water (carbonates and sulphates of lime and magnesia for the most 
part), which are precipitated when the water is heated, and form hard de- 
posits upon the boiler-plates. (See Impurities in Water, p. 551, ante.) 

Where the quantity of these salts is not very large (12 grains per gallon, 
say) scale preventives may be found effective. The chemical preventives 
either form with the salts other salts soluble in hot water; or precipitate 
them in the form of soft mud, which does not adhere to the plates, and can 
be washed out from time to time. The selection of the chemicai must de- 
pend upon the composition of the water, and it should be introduced regu- 
larly with the feed. 

EXAMPLES.—Sulphate-of-lime scale prevented by carbonate of soda: The 
sulphate of soda produced is soluble in water; and the carbonate of lime 
falls down in grains, does not adhere to the plates, and may therefore be 
blown out or gathered into sediment-collectors. The chemical reaction is: 


Sulphate of lime+-Carbonate of soda = Sulphate of soda+ Carbonate of lime 
CaSO, a,gCOs NagSO, CaCO, 
Sodium phosphate will decompose the sulphates of lime and magnesia: 
Sulphate of lime -+ Sodium phosphate = Calcium phos. -++ Sulphate of soda. 
Ca 4 agHPO, a 4 Na,SO, 

Sul. of magnesia+ Sodium phosphate = Phosphate of magnesia-+-Sul. of soda, 

MgSO, NagHPO, MgHPO, Na,SO, 


INCRUSTATION AND CORROSION. ey 2 hig 


Where the quantity of salts is large, scale preventives are not of much 
use. Some other source of supply must be sought, or the bad water purified 
before it is allowed to enter the boilers. The damage done to boilers by un- 
suitable water is enormous. 

Pure water may be obtained by collecting rain, or condensing steam by 
means Of surface condensers. The water thus obtained should be mixed 
with a little bad water, or treated with a little alkali, as undiluted, pure 
water corrodes iron; or, after each periodic cleaning, the bad may be used 
for a day or two to put a skin upon the plates. 

Carbonate of lime and magnesia may be precipitated either by heating the 
water or by mixing milk of lime (Porter Clark process) with it, the water 
being then filtered. 

Corrosion may be produced by the use of pure water, or by the presence 
of acids in the water, caused perhaps in the engine-cylinder by the action of 
high-pressure steam upon the grease, resulting in the production of fatty 
acids. Acid water may be neutralized by the addition of lime. 

Amount of Sediment which may collect in a 100-H.P. steam-boiler, 
evaporating 3000 lbs. of water per hour, the water containing different 
amounts of impurity in solution, provided that no water is blown off: 


Grains of solid impurities per U. S. gallon: 
5 10 20 30 40 50 60 %0 80 90 100 


Equivalent parts per 100,000: 
8.57 17.14 34.28 51.42 68.56 85.71 102.85 120 187.1 154.3 171.4 


Sediment deposited in 1 hour, pounds: 
ay ere Ss RD eileen | DEO pb yo eG Neb teria) 4.11 4.68 5.14 


In one day of 10 hours, pounds: 

2.57 5.14 10.28 15.42 20.56 25.71 30.85 386.0 41.1 46.3 51.4 
In one week of 6 days, pounds: 

15.43 80.85 61.7% 92.55 123.4 154.8 185.1 216.0 246.8 277.6 308.5 


If a 100-H.P. boiler has 1200 sq. ft. heating-surface, one week’s running 
without blowing off, with water containing 100 grains of solid matter per 
gallon in solution, would make a scale nearly .02 in. thick, if evenly depos- 
ited all over the heating-surface, assuming the scale to have a sp. gr. of 
2.5 = 156 lbs. per cu. ft.; .02 X 1200 x 156 X 1/12 = 312 Ibs. 

Boiler-scale Compounds.—The Bavarian Steam-boiler Inspection 
Assn. in 1885. reported as follows: 

Generally the unusual substances in water can be retained in soluble form 
or precipitated as mud by adding caustic soda or lime. This is especially 
desirable when the boilers have small interior spaces. 

It is necessary to have a chemical analysis of the water in order to fully 
determine the kind and quantity of the preparation to be used for the 
above purpose. 

All secret compounds for removing boiler-scale should be avoided. (A list 
of 27 such compounds manufactured and sold by German firms is then given 
which have been analyzed by the association.) 

Such seeret preparations are either nonsensical or fraudulent, or contaia 
either one of the two substances recommended by the association for re- 
moving scale, generally soda, which is colored to conceal its presence, and 
sometimes adulterated with useless or even injurious matter. 

These additions as well as giving the compound some strange, fanciful 
name, are meant simply to deceive the boiler owner and conceal from him 
the fact that he is buying colored soda or similar substances, for which he is 
paying an exorbitant price. 

The Chicago, Milwaukee & St. P. R. R. uses for the prevention of scale in 
locomotive-boilers an alkaline compound consisting of 3750 gals. of water, 
2600 Ibs. of 70% caustic soda, and 1600 lbs. of 58% soda-ash (Hing. News, Dec. 5, 
1891). 

Me H. E. Smith, chemist of the Ry. Co., writes May, 1902, that this com- 
pound was abandoned several years ago and commercial soda-ash, known 
as ‘'58° soda,’’ containing about 97% pure carbonate of soda, substituted in 
the water in the locomotive tender tanks, where it dissolves and passes to — 
the boiler. Its action is to precipitate a portion of the scale forming solids 
in a flocculent form so that they are kept loose and free from the metal un- 
til they can be blown or washed out. 

The amounts used vary according to the character of the water and are 
based on the following rules: For calcium and magnesium sulphates and 


718 THE STEAM BOILER , 


chlorides, use soda-ash equal to the chemical] equivalent of those cotne 
pounds present. For calcium and magnesium carbonates, the amount of 
soda-ash to be used varies from nothing when sulphates or chlorides ar 
high, up to about one fifth the equivalent of the carbonates, when sulphate 
and chlorides are low or absent. A few waters contain carbonate of soda 
originally, and for these less soda-ash or none at all is necessary. It may 
also be necessary to make some reduction in the dose of soda-ash when 
large amounts of other alkali salts are present. In any case it is not desir- 
able to use more than 2 lbs. of soda-ash per 1000 gallons of.water, or more 

_ than 10 lbs. per 100 miles of locomotive run, on account of the foaming pro- 
duced. The above rule assumes that the boilers are fairly clean and are 
kept fairly free from sludge by blowing and washing out, ntheC.,M. & 
St. P. Ry. boilers are usually washed once in 500 to 2000 miles run, accord- 
ing to the character of the waters used. ‘ 

In the upper Mississippi valley the majority of the waters are below 20 or 
25 grains of incrusting solids per gallon, and the greater portion of this is 
carbonates. For these the above treatment is very successful. From 25 to 
50 grains, increasing difficulty is encountered on account of foaming pro- 
duced by the large amounts of sludge and alkali, and above 50 grains, soda- 
ash alone fails to keep the boilers clean in practical service. 

Kerosene and other Petroleum Oils; Foaming.—Kerosene 
has recently been highly recommended as a scale preventive. See paper by 
L. F. Lyne(Trans. A. 8. M.E., ix. 247). The Am. Mach., May 22, 1890, says: Kcr- 
osene used in moderate quantities will not make the boiler foam; itis recom- 
mended and used for loosening the scale and for preventing the formation of 
scale. The presence of oil in combination with other impurities increases the 
tendency of many boilers to foam, as the oil with the impurities impedes the 
free escape of steam from the watersurface. The use of common oil not only 
tends to cause foaming, but is dangerous otherwise, The grease appears to 
combine with the impurities of the water, and when the boiler is at rest this 
compound sinks to the plates and clings to them ina loose, spongy mass, pre- 
venting the water from coming in contact with the plates, and thereby pro- 
ducing overheating, which may lead to an explosion. Foaming may also 
be caused by forcing the fire, or by taking the steam ‘from a point over the 
furnace or where the ebullition is violent; the greasy and dirty state of new 
boilers is another good cause for foaming. Kerosene should be used at first 
in small quantities, the effect carefully noted, and the quantity increased if 
necessary for obtaining the desired results. 

R. C. Carpenter (Trans. A. S. M. E., vol. xi.) says: The boilers of the State 
Agricultural College at Lansing, Mich., were badly incrusted with a hard 
scale, It was fully three eighths of an inch thick in many places. The first 
application of the oil was made while the boilers were being but little used, 
by inserting a gallon of oil, filling with water, heating to the boiling-point. 
and allowing the water to stand in the boiler two or three weeks before 
removal. By this method fully one half the scale was removed during the 
warm season and before the boilers were needed for heavy firing. The oil 
was then added in small quantities when the boiler was in actual use. For 
boilers 4 ft. in diam. and 12 ft. long the best results were obtained by the 
use of 2 qts. for each boiler per week, and for each boiler 5 ft. in diam. 3 qts. 
per week, The water used in the boilers has the following analysis: CaCOg, 
206 parts ina million; MgCOg, 78 parts; FegCOs, 22 parts; traces of sulphates 
and chlorides of potash and soda. Total solids, 325 parts in 1,000,000, 

Tannate of Soda Compound.—T. T. Parker writes to Am. Mach.: 
Should you find kerosene not doing any good, try this recipe: 50 lbs. sal-soda, 
35 Ibs. japonica; Pa the ingredients in a 50-gal. barrel, fill half full of water, 
and run a steam hose into it until it dissolves and boils. Remove the hose, 
fill up with water, and allow to settle. Use one quart per day of ten hours 
for a 40-H.P. boiler, and, if possible, introduce it as you do cylinder-oil to 
your engine. Barr recommends tannate of soda asa remedy for scale com- 
posed of sulphate and carbonate of lime. As the japonica yields the tannic 
acid, I think the resultant equivalent to the tannate of soda. 

Petroieum Oiis heavier than kerosene have been used with good re- 
sults. Crude oil should never be used. The more volatile oils it contains 
make explosive gases, and its tarry constituents are apt to form a spongy 
incrustation, 

Removal of Hard Seale.—When boilers are coated with a hard 
scale difficult to remove the addition of 14 lb. caustic soda per horse-power, 
and steaming for some hours, according to the thickness of the scale, just 
before cleaning, will greatly facilitate that operation, rendering the scale 


INCRUSTATION AND CORROSION. 719 


soft and loose. This should be done, if possible, when the boilers are not 
otherwise in use. (Steam.) 

Corrosion in Marine Boilers. (Proc. Inst. M. E., Aug. 1884).—The 
investigations of the Committee on Boilers served to show that the internal 
corrosion of boilers is greatly due to the combined action of air and sea- 
water when under steam, and when not under steam to the combined action 
of air and moisture upon the unprotected surfaces of the metal. There are 
other deleterious influences at work, such as the corrosive action of fatty 
acids, the galvanic action of copper and brass, and the inequalities of tem- 
perature; these latter, however, are considered to be of minor importance. 

Of the several methods recommended for protecting the internal surfaces 
of boilers, the three found most effectual are: First, the formation of a 
thin layer of hard scale, deposited by working the boiler with sea-water; 
second, the coating of the surfaces with a thin wash of Portland cement, 

particularly wherever there are signs of decay; third, the use of zinc slabs 
suspended in the water and steam spaces. 

As to general treatment for the preservation of boilers in store or when 
laid up in the reserve, either of the two following methods is adopted, as 
may be found most suitable in particular cases. First, the boilers are 
dried as much as possible by airing-stoves, after which 2 to 3 cwt. of quick- 
lime, according to the size of the boiler, is placed on suitable trays at the 
bottom of the boiler and on the tubes. The boiler is then closed and made 
as air-tight as possible. Periodical inspection is made every six months, 
when if the lime be found slacked it is renewed. Second, the other 
method is to fill the boilers up with sea or fresh water, having added soda 
to it in the proportion of 1 lb. of soda to every 100 or 120 lbs. of water. The 
sufficiency of the saturation can be tested by introducing a piece of clean 
new iron and leaving it in the boiler for ten or twelve hours; if it shows 
signs of rusting, more soda should be added. It is essential that the boilers 
be entirely filled, to the complete exclusion of air. 

Great care is taken to prevent sudden changes of temperature in boilers. 
Directions are given that steam shall not be raised rapidly, and that care 
shall be taken to prevent arush of cold air through the tubes by too sud- 
denly opening the smoke-box doors. The practice of emptying boilers by 
blowing out is also prohibited, except in cases of extreme urgency. As a 
rule the water is allowed to remain until it becomes cool before the boilers 
are emptied. 

Mineral oil has for many years been exclusively used for internal lubrica- 
tion of engines, with the view of avoiding the effects of fatty acid, as this oil 
does not readily decompose and possesses no acid properties. 

Of all the preservative methods adopted in the British service, the use of 
zine properly distributed and fixed has been found the most effectual in 
saving the iron and steel surfaces from corrosion, and also in neutralizing 
by its own deterioration the hurtful influences met with in water as ordina- 
rily supplied to boilers. The zine slabs now used in the navy boilers are 12 
in. long, 6 in. wide, and 4% inch thick; this size being found convenient for 
general application. The amount of zinc used in new boilers at present is 
one slab of the above size for every 20 1.H.P., or about one square foot of 
zinc surface to two square feet of grate surface. Rolled zine is found the 
most suitable for the purpose. To make the zine properly efficient as a 
protector especial care must be taken to insure perfect metallic contact 
between the slabs and the stays or plates to which they are attached. The 
slabs should be placed in such positions that all the surfaces in the boiler 
shall be protected. Each slab should be periodically examined to see that 
its connection remains perfect, and to renew any that may have decayed; 
this examination is usually made at intervals not exceeding three months, 

- Under ordinary circumstances of working these zinc slabs may be expected. 
to last in fit condition from sixty to ninety days, immersed in hot sea-water; 
but in new boilers they at first decay more rapidly. The slabs are generally 
secured by means of iron straps 2 in. wide and 3 inch thick, and long 
enough to reach the nearest stay, to which the strap is firmly attached by 
screw-bolts. 

Yo promote the proper care of boilers when not in use the following order 
has been issued to the French Navy by the Government: On board all ships 
in the reserve, as well as those which are laid up, the boilers will be com- 
pletely filled with fresh water. In the case of large boilers with large tubes 
there will be added to the water a certain amounts of milk of lime, or a 
solution of soda may be used instead. In the case of tubulous boilers with 
small tubes milk of lime or soda may be added, but the solution will not be 


720 THE STEAM-BOILER. 


WE 


so strong asin the case of the larger tube, so as to avoid any danger of 
contracting the effective area by deposit from the solution; but the strength 
of the solution wili be just sufficient to neutralize any acidity of the water. 
(Iron Age, Nov. 2, 1893.) : 

Use of Zime.—Zinc is often used in boilers to prevent the corrosive 
action of water on the metal. The action appears to be an electrical one, 
the iron being one pole of the battery and the zine being the other. The 
hydrogen goes to the iron shell and escapes as a gas into the steam. The 
oxygen goes to the zine. 

On account of this action it is generally believed that zine will always 
prevent corrosion, and that it cannot be harmful to the boiler or tank. 
Some experiences go to disprove this belief, and in numerous cases zine has 
not only been of no use, but has even been harmful. In one case a tubular 
boiler had been troubled with a deposit of scale consisting chiefly of.or- 
ganic matter and lime, and zinc was tried as a preventive. The beneficial 
action of the zinc was so obvious that its continued use was advised, with 
frequent opening of the boiler and cleaning out of detached scale until all 
the old scale should be removed and the boiler become clean. Eight or ten 
months later the water-supply was changed, it being now obtained from 
another stream supposed to be free from lime and to contain only organic 
matter. Two or three months after its introduction the tubes and shell 
were found to be coated with an obstinate adhesive scale, and composed of 
zinc oxide and the organic matter or sediment of the water used. The 
deposit had become so heavy in places as to cause overheating and bulging 
of the plates over the fire. (The Locomotive.) 

Effect of Deposit on Flues. (Rankine.)—An external crust of a 
carbonaceous kind is often deposited from the flame and smoke of the fur- 
naces in the flues and tubes, and if allowed to accumulate seriously impairs 
the economy of fuel. It is removed from time to time by means of scrapers 
and wire brushes. The accumulation of this crust is the probable cause of 
the fact that in some steamships the consumption of coal per indicated 
horse-power per hour goes on gradually increasing until it reaches one and 
a half times its original amount, and sometimes more. 

Dangerous Steame-boilers discovered by Inspection.— 
The Hartford Steam-boiler Inspection and Insurance Co. reports that its 
inspectors during 1893 examined 163,328 boilers, inspected 66,698 boilers, 
both internally and externally, subjected 7861 to hydrostatic pressure, and 
found 597 unsafe for further use. The whole number of defects reported 
was 122,898, of which 12,390 were considered dangerous. A summary is _ 
given below. (The Loconotive, Feb. 1894.) 


SUMMARY, BY DEFECTS, FOR THE YEAR 1893. 


; Whole Dan- ; Whole Dan- 

Nature of Defects. No... gerous, Nature of Defects. No. gerous. 
Deposit of sediment..... 9,77 548i Leakage around tubes...21,211 2,909 
Incrustation and scale...18,369 865fLeakage at seams.. .. . 5,424 482 
Internal grooving........ 1,249 1488Water-gauges defective. 3,670 660 
Internal corrosion....... 6,252 397# Blow-outs defective...... 1,620 425 
External corrosion....... 8,600  586§Deficiency of water ..... 204 107 
Def’tive braces and stays 1,966 485§#Safety-valves overloaded 723 203 
Settings defective........ 3,094 852¢Safety-valves defective.. 942 300 
Furnaces out of shape... 4,575  254§Pressure-gauges def’tive 5,953 552 
fractured plates......... 3,532 6408 Boilers without pressure- 

Burned plates............ 2,162 . P8258 Iranees is. 6 ake Uaneeee 5 115 
Blistered plates.......... 3,381 1648 Unclassified defects...... 75% 4 
Defective rivets..... .... 17,415 1,569 — - 
Defective heads, ........ 1,357.) S509 Dotalise scart sso 122,893 12,3890 


The above-named company publishes annually a classified list of boiler- 
explosions, compiled chiefly from newspaper reports, showing that from 
200 to 300 explosions take place in the United States every year, killing from 
200 to 800 persons, and injuring from 300 to 450. The lists are not pretended 
to be complete, and may include only a fraction of the actual number of 
explosions. 

Steam-boilers as Magazines of Explosive Energy.—Prof. 
R. H. Thurston (Trans. A. 8S. M. E., vol. vi.), in a paper with the above 
title, presents calculations showing the stored energy in the hot water and 
steam of various boilers. Concerning the plain tubular boiler of the 
form and dimensions adopted as a standard by the Hartford Steam-boiler 


SAFETY-VALYES, 21 


Insurance Co., he says: It is 60 inches in diameter, conta:ning 66 3-inch 
tubes, and is 15 feet long. It has 850 feet of heating and 30 feet of grate 
surface; is rated at 60 horse-power, but isoftener driven up to %5; weighs 
9500 pounds, and contains nearly its own weight of water, but only 21 
pounds of steam when under a pressure of 75 pounds per square inch, 
which is below its safe allowance. It stores 52,000,000 foot-pounds of en- 
ergy, of which but 4 per cent is in the steam, and this is enough to drive 
the boiler just about one mile into the air, with an initial velocity of nearly 
600 feet per second. 


SAFETY-VALVES. 
Calculation of Weight, etc., for Lever Safety-valves, 


Let W = weight of ball at end of lever, in pounds; 

w = weight of lever itself, in pounds; 

V = weight of valve and spindle, in pounds; 
I. = distance between fulcrum and centre of ball, in inches; 

ee § “ “ e ** valve, in inches; 
st ss wv eo - “6 gravity of lever, in in.; 

area of valve, in square inches; 
pressure of steam, in lbs. per sq. in., at which valve will open. 


Then PAXIL=WXL+wxXg9g4+VX]; 
WL+wg-+ Vi 


Hat Wl 


1 
g 
A 
ies 


whence P= ai ® 
PAl —wg — Vl 

72 aT 

_ PAl~wg— Vl 

L= WwW es 


Exampie.—Diameter of valve, 4’’; distance from fulcrum to centre of ball, 
86’; to centre of valve, 4’’; to centre of gravity of lever, 1514’; weight of 
valve and spindle, 3 lbs.; weight of lever, 7 lbs.; required the weight of ball 
to make the blowing-off pressure 80 lbs. per sq. in.; area of 4’” valve = 12.566 
sq.in. Then 


PAl-—wg— Vl _ 80 12.566 X4—7X 154-3 x4 
L " 36 


The following rules governing the proportions of lever-valves are given by 
the U.S. Supervisors. The distance from the fulerum to the valve-stem 
must in no case be less than the diameter of the valve-opening; the length 
of the lever must not be more than ten times the distance from the fulcrum 
to the valve-stem; the width of the bearings of the fulcrum must not be 
less than three quarters of an inch; the length of the fulerum-link must not 
be less than four inches; the lever and fulcrum-link must be made of 
wrought iron or steel, and the knife-edged fulcrum points and the bearings 
for these points must be made of steel and hardened; the valve must be 
guided by its spindle, both above and below the ground seat and above the 
Jever, through supports either made of composition (gun-metal) or bushed 
with it; and the spindle must fit loosely in the bearings or supports. 


BRules for Area of Safety-valves. 
(Rule of U. S. Supervising Inspectors of Steam-vessels (as amended 1894).) 


Lever safety-valves to be attached to marine boilers shall have an area of 
not less than 1 sq. in. to 2 sq. ft. of the grate surface in the boiler, and the 
seats of all such safety-valves shall have an angle of inclination of 45° to the 
ceutre line of their axes. 

Spring-loaded safety-valves shall be required to have an area of not less 
than 1 sq. in. to 3 sq. ft. of grate surface of the boiler, except as hereinafter 
otherwise provided for water-tube or coil and sectional boilers, and each 
spring-loaded valve shall be supplied with a lever that will raise the valve 
from its seat a distance of not less than that equal to one eighth the diam- 
eter of the valve-opening, and the seats of all such safety-valves shall have 
an angle of inclination to the centre line of their axes of 45°. All spring- 
loaded safety-valves for water-tube or coil and sectional boilers required to 


We = 108.4 Ibs. 


{ 


Ton THE STEAM-BOILER. 


carry a steam-pressure exceeding 175 Ibs. per square inch shail be required 
to have an area of not less than 1 sq. in. to 6 sq. ft. of the grate surface of 
the boiler. Nothing herein shall be construed so as to prohibit the use of 
two safety-valves on one water-tube or coil and sectional boiler, provided 
the bates area of such valves is equal to that required by rule for one 
such valve. : 

Rule in Philadelphia Ordinances: Bureau of Steam-= 
engine and Boiler Inspection.—Every boiler when fired sepa- 
rately, and every set or series of boilers when placed over one fire, shall 
have attached thereto, without the interposition of any other valve, two or 
more safety-valves, the aggregate area of which shall have such relations to 
the area of the grate and the pressure within the boiler as is expressed in 
schedule A. 

SCHEDULE A,—Least aggregate area of safety-valve (being the least sec- 
tional area for the discharge of steam) to be placed upon all stationary boil- 
ers with natural or chimney draught [see note a]. 

22.54 
aan P + 8.62’ 
in which A is area of combined safety-valves in inches; G is area of grate in 
square feet; Pis pressure of steam in pounds per square inch to be carried 
in the boiler above the atmosphere. 

The following table gives the results of the formula for one square foot of 
grate, as applied to boilers used at different pressures: 

Pressures per square inch: 


TO ge 00.) 30). 40) a0 ee OOln rn ( OL EGOmman OU 100 ns 110 R20 
Area corresponding to one square foot of grate: 
1.21 0.79 0.58 0.46 0.38 0.383 0.29 0.25 0.23 0.21 0.19 0.17 


[Note a.] Where boilers have a forced or artificial draught, the inspector 
must estimate the area of grate at the rate of one square foot of grate-sur- 
face for each 16 lbs. of fuel burned on the average per hour. 

Comparison of Various Rules for Area of Lever Safety= 
valves. (From an article by the author in American Machinist, May ~1, 
1894, with some alterations and additions.)—Assume the case of a boiler 
rated at 100 horse-power; 40 sq. ft. grate; 1200 +q. ft. heating-surface; using 
400 lbs, of coal per hour, or 10 lbs. per sq. ft. of grate per hour, and evapora- 
ting 3600 lbs. of water, or 3 Ibs. per sq. ft. of heating-surface per hour; 
steam-pressure by gauge, 100 lbs. What size of safety-valve, of the lever 
_ type, should be required ? 

A compilation of various rules for finding the area of the safety-valve disk, 
from The Locomotive of July, 1892, is given in abridged form below, to- 
gether with the area calculated by each rule for the above example. 

Disk Area in sq. bes 
4 


Or ees ce nme eee cere sees es 


U.S. Supervisors, heating-surface in sq. ft. -- 25* 


English Board of Trade, grate-surface in sq. ft. + 2...............0.00- 20 

Molesworth, four fifths of grate-surface in sq.ft..... 0.2.0.2... 0.02.05 32 

Thurston, 4 times coal burned per hour X (gauge pressure + 10)....... 14.5 
1 (5 X heating-surface) 

AN SOLES (Ob AS aapeenemenercroee reer 41 ee siged dus Sip 'aad sid aholiets ns ioe aiseseg else 
2 gauge pressure + 10 

Rankine, .006 x water evaporated per hour,............ceceoscseecvecree « 21.6 

Committee of U. S. Supervisors, .005 x water evaporated per hour..... 18 


Suppose that, other data remaining the same, the draught were increased 
so as to burn 134 lbs. coal per square foot of grate per hour, and the grate- 
surface cut down to 30 sq. ft. to correspond, making the coal burned per 
hour 400 Ibs.. and the water evaporated 3600 lbs., the same as before; then 
the English Board of Trade rule and Molesworth’s rule would give an area 
of disk of only 15 and 24 sq. in., respectively, showing the absurdity of mak- 
ing the area of grate the basis of the calculation of disk area. 

Another rule by Prof, Thurston is given in American Machinist, Dec. 1877, 

WZes 

16 max. wt. of water evap. per hour 
gauge pressure + 10 

This gives for the example considered 16.4 sq. in. 


Disk area = 





* The edition of 1893 of the Rules of the Supervisors does not contain this 
rule, byt gives the rule grate-surface + 2. 94 it i 


SAFETY-VALVES. 9193 


One rule by Rankine is 1/150 to 1/180 of the number of pounds of water 
evaporated per hour, equals for the above case 27 to 20 sq. in. A communi- 
tion in Power, July, 1890, gives two other rules: 

Ist. 1 sq. in. disk area for 3 sq. ft. grate, which would give 13.3 sq. in. 

2d. 34 sq. in. disk area for 1 sq. ft. grate, which would give 30 sq. in.; but 
if the grate-surface were reduced to 30 sq. ft. on account of increased 
draught, these rules would make the disk area only 10. and 22.5 sq. in., 
respectively. : 

The Philadelphia rule for 100 lbs. gauge pressure gives a disk area of 0.21 
sq. in. for each sq. ft. of grate area, which would give an area of 8.4 sq. in. 
for 40 sq. ft. grate, and only 6.3 sq. in. if the grate is reduced to 30 sq. ft. 

According to the rule this aggregate area would have to be divided between 
two valves. But if the boiler was driven by forced draught, then the in- 
spector ‘‘ must estimate the area of grate at 1 sq. ft. for each 16 Ibs. of fuel 
burned per hour.”’ 

Under this condition the actual grate-surface might be cut down to 400 + 
16 = 25 sq. ft., and by the rule the combined area of the two safety-vaives 
would be only 25 X 0.21 = 5.25 sq. in. 

Nystrom’s Pocket-book, edition of 1891,.gives 34 sq. in. for 1 sq. ft. grate: 
also quoting from Weisbach, vol. ii, 1/3000 of the heating-surface, This iu 
the case considered is 1200/3000 = .4 sq. ft. or 57.6 sq. in. 

We thus have rules which give for the area of safety-valve of the same 100. 
horse-power boiler results ranging all the way from 5.25 to 57.6 sq. in. 

All of the rules above quoted give the area of the disk of the valve as the 
thing to be ascertained, and it is this area which is supposed to bear some 
direct ratio to the grate-surface, to the heating-surface, to the water evap- 
orated, ete. It is difficult to see why this area has been considered even 
approximately proportional to these quantities, for with small lifts the area 
of actual opening bears a direct ratio, not to the area of disk, but to the 
circumference. 

Thus for various diameters of valve: 


DiameLerger tes cs tek tics sc 1 2 a PY” 5 6 " 
ET ORM eae nitt codlenics ABSA OD io Lea Ol eee 1, 19.64 28.27 38.48 
Cireumference............ 8.14 G28 O42 ee le. DG 15.71 18.85 21.99 
Gireum: >< liftiof 0.lin.... 31 .63 .94 1.26 aledaifg 1.89 2.20 
MP RATIOLCOCATCU Heep sctens cs ce 4 ae ris, “ih .08 .067 .057 


The apertures, therefore, are therefore directly proportional to the diam- 
eter or to the circumference, but their relation to the area is a varying one. 

If the lift = 14 diameter, then the opening would be equal to the area of 
the disk, for circumference < 14 diameter = area, but such a lift is far 
beyond the actual lift of an ordinary safety-valve. 

A correct rule for size of safetv-valves should make the product of the 
diameter and the lift proportional to the weight of steam to be discharged. 

A ‘logical’? method for calculating the size of safety-valve is given in 
The Locomotive, July, 1892, based on the assumption that the actual opening 
should be sufficient to discharge all the steam generated by the boiler. 
Napier’s rule for flow of steam is taken, viz., flow through aperture of one 
sq. in, in lbs. per second = absolute pressure + 70, or in lbs. per hour = 51.43 
* absolute pressure, 

If the angle of the seat is 45°, as specified in the rules of the U. S. Super- 
visors, the area of opening in sq. in. = circumference of the disk x the lift 
* .71, .71 being the cosine of 45°; or diameter of disk x lift « 2.23. 

A. G. Brown in his book on The Indicator and its Practical Working 
(London, 1894) gives the following as the lift of the ordinary lever safety- 
vaive for 100 Ibs. gauge-pressure: 


Digm. of valye..c.. 2a, cae eo Olona | 456, Oo 6 inches. 
Rise of valve.... .0583 .0523 .0507 .0492 .0478 .0462 .0446 .0430 inch. 


The lift decreases with increase of steam-pressure; thus fora 4-inch valve: 
Abs. pressure, lbs. 45 65 Soper lOoper tio 8155 155) 170" 2 19a at 
(jauge-press., lbs... 30 50 70 90 100 120 140 160 180 200 


[RARE AO Slercins abag 1034 .0775 .0620 .0517 .0478 .0413 .0365 .0327 .0296 .0270 
The erfective area of opening Mr, Brown takes at 70% of the rise multiplied 
by the circumference. ; 
An approximate formula corresponding to Mr. Brown's figures for diam- 
eters between 214 and 6 in. and gauge-pressures between 70 and 200 lbs, is 


Lift = (.0603 — 0031d) x ,in which d = diam, of valve in in, 


abs. pressure 


424 THE STEAM-BOILER. 


If we combine this formula with the formule 

Flow in lbs. per hour = area of opening in sq. in. x 51.43 abs. pressure, and 

Area = diameter of valve x lift x 2.28, we obtain the following, which the 
author suggests as probably a more correct formula for the discharging 
capacity of the ordinary lever safety-valve than either of those above given. 

Flow in lbs. per hour = d(.0603 — .0031d) x 115 & 2.28 x 51.43 = d(795 — 41d). 

From which we obtain : 


Diameter, inches.....-1....134....2.,, 2i6.48) -Bi4 sei4 eee OL ee 
Flow, Ibs. per hour.. 754 1100 1426 1738 2016 2882 2524 2950 3294 3556 
Horse-power........ 25 37% 47 58 67 76 84 OS) tal 10 get io 


the horse-power being taken as an evaporation of 30 lbs. of water per hour. 

If we solve the example, above given, of the boiler evaporating 3600 lbs. of 
water per hour by this table, we find it requires one 7-inch valve, or a 214- 
and a 3-inch valve combined. The 7-inch valve has an area of 38.5 sq. in., 
and the two smaller valves taken together have an area of only 12 sq. in.; 
another evidence of the absurdity of considering the area of disk as the 
factor which determined the capacity of the valve. ~ 

It is customary in practice not to use safety-valves of greater diameter 
than 4in. If a greater diameter is called for by the rule that is adopted, 
then two or more valves are used instead of one. 

Spring-loaded Safety=-valves.—Instead of weights, springs are 
sometimes employed to hold down safety-valves. The calculations are 
similar to those for lever safety-valves, the tension of the spring correspond: 
ing to a given rise being first found by experiment (see Springs, page 347). 

The rules of the U. S. Supervisors allow an area of 1 sq. in. of the valve 
to 3 sq. ft. of grate, in the case of spring-loaded valves, except in water-tube, 
coil, or sectional boilers, in which 1 sq. in. to 6 sq. ft. of grate is allowed. 

Spring-loaded safety-valves are usually of the reactionary or ‘*‘ pop’ type, 
in which the escape of the steam is opposed by a lip above the valve-seat, 
against which the escaping steam reacts, causing the valve to lift higher 
than the ordinary valve. 

A. G. Brown gives the following for the rise, effective area, and quantity 
of steam discharged per hour by valves of the ** pop” or Richardson type. 
The effective is taken at only 50% of the actual area due to the rise, on account 
of the obstruction which the lip of the valve offers to the escape of steam. 
































Dia.valve, in. 1 1% 2 246| 3 3844 4 446| 5 6 
Lift, inches. 135 .150| .175 | .200}) .225 | .250} .275| .800] .825 | .875 
Area, sq. in. | .196| .3854] .550| .785 | 1.061 | 1.875 | 1.728 | 2.121 | 2.553 |3.535 
Gauge-pres., Steam discharged per hour, lbs. 
80 lbs. | 474] 856 | 1330 | 1897 | 2563 | 3325 | 4178 | 5128 | 6178] 8578 
50 669 | 1209 | 1878 | 2680 | 3620 | 4695 | 5901 | 7242 | 8718] 12070 
70 861 | 1556 | 2417 | 3450 | 4660 | 6144 | 7596 | 9324 | 11220) 15535 
90 1050 | 1897 | 2947 | 4207 | 5680 | 7370 | 9260 |11365 | 13685) 18945 
100 1144 | 2065 | 38208 | 4580 | 6185 | 8322 |10080 |12375 | 14895] 20625 
120 1832 | 2405 | 8736 | 53832 | 7202 | 9842 |11735 |14410 | 17340) 24015 
140 1516 | 2738 | 4254 | 6070 | 8200 |10635 |13365 |16405 | 19745] 27340 
160 1696 | 3064 | 4760 | 6794 | 9175 |11900 |14955 |18355 | 22095] 30595 
180 1883 | 3400 | 5283 | 7540 |10180 |13250 |16595 |20370 | 24520] 83950 
200 2062 | 8724 | 5786 | 8258 111150 114465 118175 122310 | 26855! 37185 


If we take 30 lbs. of steam per hour, at 100 ibs. gauge-pressure = 1 H.P., 
we have from the above table: 
Diameter, inches... 1 14% 2 2% 3 38% 4 4% 5 6 
Horse-power....... 88 69 107 153 206 277 3836 412 496 687 


A safety-valve should be capable of discharging a much greater quantity 
of steam than that corresponding to the rated horse-power of a boiler, since 
a boiler having ample grate surface and strong draught may generate more 
than double the quantity of steam its rating calls for. 

The Consolidated Safety-valve Co.’s circular gives the following rated 
capacity of its nickel-seat *‘ pop’ safety-valves: 

Size, in ..... Dera tt6 2 4. 8 Bla ae ate G5 BS 
Boiler ; from’ “S° 10%, 20° 85 60°" 75 100 125" 150 - '.1'75) 8200 
H:P. to’ 10 Paiee uso * 50) | (95. 100 “925 eso 995 | 200 Sears 

The figures in the lower line from 2inch to 5 inch,inelusive, correspond to 

the formula H.P. = 50(diameter — 1 inch), ; 


THE INJECTOR, 925 


THE INJECTOR. 
Equation of the Injector, 


Let S be the number of pounds of steam used; 
W the number of pounds of water lifted and forced into the boiler; 
h the height in feet of a column of water, equivalent to the absolute 
pressure in the boiler; 
hy the height in feet the water is lifted to the injector; 
t, the temperature of the water before it enters the injector; 
t, the temperature of the water after leaving the injector; 
H the total heat above 32° F. in one pound of steam in the boiler, in 
heat-units; 
L the lost work in friction and the equivalent lost work due to radia- 
tion and lost heat; 
778 the mechanical equivalent of heat. 


THR W + S)h Wh L 
SLH — (t — 82>)] = Wit, — t) + AES Who tb 


An equivalent formula, neglecting Wh» + L as small, is 
W-+s 144 1 
s=| wite— 4) + d Ds |S 
dita tal W(t, —t,)d + .1851p] 
< ~ [H — (tg — 32°)]d -- .1851p’ 
in which d = weight of 1 cu. ft. of water at temperature ¢,; p = absolute 
pressure of steam, lbs. per sq. in. 


The rule for finding the proper sectional area for the narrowest part of 
the:nozzles is given as follows by Rankine, S. E. p. 477: 


cubic feet per hour gross feed-water, 











Area in square inches = 
800 pressure in atmospheres 


Animportant condition which must be fulfilled in order that the injector 
will work is that the supply of water must be sufficient to condense the 
_ steam. As the temperature of the supply or feed-water is higher, the 
amount of water required for condensing purposes will be greater. 

The table below gives the calculated value of the maximum ratio of water 
to the steam, and the values obtained on actual trial, also the highest admis- 
sible temperature of the feed-water as shown by theory and the highest 
actually found by trial with several injectors. 


) ‘Maximum RaTIO WATER Maximum TEMPERATURE OF 
TO STEAM. FEED-WATER. 


2 Gauge-\T 
Gauge kas Theoretical.| Experi’tal Results. 














res- 
He Actual Expe-| sure, 
pounds|Calculated riment. pounds S oi 
per Sapa per [a8 2° | BE 3° 
Re sg Sq.1n. |Faoleos| w.| p.| M1 8. 
AFI 184 Wh eu SR | ee 
;S S 
10 36.5 BO 391 sercicilion, ht HORST Re edo Sea ee. | Babes 
20 25.6 22,5)19.9)21.5 20 142° 173°| 135°) 120°) 180°; 134 
30 20.9 19.0/17.2/19.0 380 132 TOR, leis Mel cecdee oe ese 
40 17.87 15.8)15.0)15.86 40 126 156 | 140 | 118 }125 | 132 
50 16.2 138.3)14.0)13.3 50 120 ESO Ae se ole te Steet 131 
60 14.7 11.2)11 .2)12.6 60 114 1438 { ....1115 |128 4, 130 
70 13.7 12.3)11.7/12.9 70 109 139 } 141%] ....)123 | 130 
80 12.9 11 4 he oe cas 80 105 134 | 141*} 118 | 122 | 131 
90 ea | seahic é 90 99 129 | .. 33] ucminiees Weloee 
100 11.5 100 95 125 132* 
120 87 117 | .5 chal gree -s 2} 184* 
150 oh 107 ; Peer PAE 











* Temperature of delivery above 212°. Waste-valve closed. 


H, Hancock inspirator; P, Park injector; M, Metrovolitan injector; 8, Sel- 
lers 1876 injector. 


726 ee THE STEAM-BOILER. 


Efficiency of the Injector.—Experiments at Cornell University, 
described by Prof. R. C. Carpenter, in Cassier’s Magazine, Feb. 1892, show 
that the injector, when considered merely as a pump, has an exceedingly 
luw efficiency, the duty ranging from 161,000 to 2,752.000 under different cir- 
cumstances of steam and delivery pressure. Small direct-acting pumps, 
such as are used for feeding boilers, show a duty of from 4 to 8 
million lbs., and the best pumping-engines from 100 to 140 million. When 
used for feeding water into a boiler, however, the injector has a thermal 
efficiency of 100%, less the trifling loss due to radiation, since all the heat re- 
jected passes into the water which is carried into the boiler. 

The loss of work in the injector due to friction reappears as heat which i is 
carried into the boiler, and the heat which is converted into useful work in 
the injector appears in the boiler as stored-up energy. 

Although the injector thus has a perfect efficiency as a boiler-feeder, it is 
nevertheless not the most economical means for feeding a boiler, since it 
can draw only cold or moderately warm water, while a pump ‘ean feed 
water which has been heated by exhaust steam which would otherwise be 
wasted. 

Performance of Injectors.—In Am. Mach., April 13, 1893, are a 
number of letters from different manufacturers of injectors in reply to the 
question: *‘ What is the best performance of the injector in raising or lifting 
water to any height ?”? Some of the replies are tabulated below. 

W. Sellers & Co.—25.51 lbs. water delivered to boiler per lb. of steam; tem- 
perature of water, 64°; steam pressure, 65 Ibs. 

Schaeffer & Budenberg—1 gal. water "delivered to boile~ for 0.4 to 0.8 lb. 
steam, 

Injector will lift by suction water of 

140° F. 186° to 133° 122° to 118° 113° to 107° 
Tf boiler pressure is. 30 to 60lbs. 60to901bs. 90to1201bs. 120 to 150 lbs. 


If the water is not over 80° F., the injector will force against a pressure 75 
lbs. higher than that of the steam. 
Hancock Inspirator Co.: 


ALG IMGCCh LS ast Mekaee Seek uetk ape 22 ae 22 11 
Boiler pressure, absolute, lbs..... 75.8 54.1 95.5 75.4 
Temperature of suction..... .. .. 34.9° 85.4° a7.3° 58.2° 
Temperature of delivery ......... 134° Ties IW ete 131.1 


Water fed per lb. of steam, Ibs... 11.02 13.67 8.18 13.3 


The theory of the injector is discussed in Wood's, Peabody’s, and Ront- - 


gen’s treatises on Thermodynamics. See also ‘‘ Theory and Practice of the 
Injector,” by Strickland L. Kneass, New York, 1895. 

Boiler-feeding Pumps.—Since the direct-acting pump, commonly 
used for feeding boilers, has a very low efficiency, or less than one tenth 
that of a good engine, it is generally better to use a pump driven by belt 
from the main engine or driving shaft. The mechanical work needed to feed 
a boiler may be estimated as follows: If the combination of boiler and en- 
gine is such that half a cubic foot, say 32 lbs. of water, is needed per horse- 
power, and the boiler-pressure is 100 ‘Ibs. per sq. in. , then the work of feed- 
ing the quantity of water is 100 lbs..x 144 sq. in. x 14 ft.-lbs. per hour = 120 
ft.-lbs. per min. = 120/33,000 = .0036 H.P., or less than 4/10 of 1% of the 
power exerted by t the engine. If a direct-acting pump, which discharges its 
exhaust steam into the atmosphere, is used for feeding, and it has only 1/10 
the efficiency of the main engine, then the steam used by the pump will be 
equal to nearly 4% of that generated by the boiler. 

The following table by Prof. D. S. Jacobus gives the relative efficiency of 
steam and power pumps and injector, with and without heater, as used 
upon a boiler with 80 lbs. gauge-pressure, the pump having a duty of 
10,000,000 ft.-lbs. per 100 Ibs. of coal when no heater i is used; the injector 
heating the water from 60° to 150° F. 


Direct-acting pump feeding water at 60°, without a heater............ 1.000 
Injector feeding water at 150°, without a heaters: es: - 985 
Injector feeding water through a heater in which it is heated from 
MOOS: Cio 2OO Oc is eR Oe cells oe are nase ole AUN a ae ae ee trots 2 doe 938 
Direct-acting pump spoging water phroueh a heater, in ‘which it is 
heated from 60° to 200 .879 


Geared pump, run from the engine, feeding ‘water ‘through a heater, 
in which it is heated from 60° to 200° 


—— 


a 


FEED-WATER HEATERS. Meny. 


FEED-WATER HEATERS. 


Percentage of Saving for Each Decree of Increasein Tem=-= 
perature of Keed-water Heated by Waste Steam. 











Pressure of Steam in Boiler, lbs. per sq. in. above 


Tnitial Atmosphere. 


Initial 
Temp. 


| 
0 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 |} 180 } 200 








32° | .0872].0861] .0855} .0851/ .0847] .0844! .0841] .0839] .0837| .0835] .0833) 32 
40 |.0878] .0867| .0861! .0856] .0853} .0850) .0847| .0845] .0843].0841].0839| 40 
50 | .0886| .0875) .0868] .0864] .0860} .0857) .0854] .0852] .0850] .0848] .0846} 50 
60 | .0894| .0883) .0876| .0872] .0867| .0864) .0862! .0S59| .0856] .0855) .0853} 60 
70 | .0902] .0890) .0884) .0879] .0875] .0872) .0869! .0867| .0864].0862).0860} 70 
80 |.0910).0898] .6891) .0887| .0883] .0879, .087'7| .0874| .0872] .0870|.0868] 80 
90 |.0919|.0907) .0900} .0895| .0888] .0887| .0884] .0883] .0879] 0877) 0875} 90 
100 | .0927}.0915} .0908} .0903) .0899] .0895; .0892] 0890) .0887] .0885} .0883} 100 
110 | .0936} .0923] .0916] .0911] .0907] .0903) .0900) .0898] .0895) .0893] .0891} 110 
120 | .0945} .0932} .0925] .0919] .0915) .0911) .0908} .0906] .0903] .0901] .0899| 120 
139 | .0954|.0941]| .0934| .0928] .0924] .0920) .0917] .0914| .0912] .0909| .0907} 1380 
140 | .0963) .0950} .0943)| .0937| .0932| .0929) .0925|. 0923] .0920|.0918).0916) 140 
150 | 0973] .0959} .0951] .0946] .0941] .0937| .0934} .0931] .0929] 0926) .0924) 150 
160 | .0982) .0968! .0961| .0955] .0950} .0946] .0943] .0940} .0937| .0935] .0933} 160 
170 | .0992) 0978] .0970| .0964| .0959) .0955] .0952) .0949] .0946] .0944/.0941) 170 
180 |.1002} .0988] .0981} .0973] .0969] .0965] .0961| .0958] .0955].0953|.0951) 180 
190 | .1012}.0998] .0989/ .0983] .0978} .0974| .0971| .0968] .0964].0962) 0960) 190 
200 | .1022| .1008] .0999] .0993) .0988] .0984) .0980} .0977| .0974] 0972} .0969| 200 
210 |.1033}.1018]. 1009) . 1003] .0998] .0994} .0990} .0987) .0984| .0981|.0979) 210 











ZS ore . 1029] . 1019} . 1013} .1008] . 1004] . 1000] .0997} .0994].0991).0989} 220 
QU ale <antsis 1039] . 1031] .1024] .1018]. 1012} 1010} .1007} .1003].1001].0999} 230 
AO disses’ - 1050} .1041} . 1034] .1029].1024| .1620} .1017].1014].1011|.1009} 240 
OU jdrsiesere 1062]. 1052} . 1045] . 1040]. 1035] . 1031] .1027].1025].1022].1019] 250 


An approximate rulefor the conditions of ordinary practice is a saving 
of 1% is made by each increase of 11° in the temperature of the feed-water. 
This corresponds to .0909% per degree. 

The calculation of saving is made as follows: Boiler-pressure, 100 lbs. 
gauge; total heat in steam above 32° = 1185 B.T.U. Feed-water, original 
temperature 60°, final temperature 209° F. Increase in heat-units, 150. 
Heat-units above 382° in feed-water of original temperature = 28. Heat- 
units in steam above that in cold feed-water, 1185 — 28 = 1157. Saving by the 
feed-water heater = 150/1157 = 12.96%. ‘The same result is obtained by the 
use of the table. Increase in temperature 150° x tabular figure .0864 = 
12.96%. Let total heat of 1lb. of steam at the boiler-pressure = H; total 
heat of 1 lb. of feed-water before entering the heater = h,, and after pass- 
ing through the heater = hg; then the saving made by the heater is en 

. A ap 1 

Strains Caused by Cold Feed=-water.—A calculation is made 
in The Loconotive ot March, 1893, of the possible strains caused in the sec- 
tion of the shell of a boiler by cooling it by the injection of cold feed-water. 
Assuming the plate to be cooled 200° F., and the coefficient of expansion of 
steel to be .0000067 per degree, a strip 10 in. long would contract .0138 in., if it 
were free to contract, To resist this contraction, assuming that the strip is 
firmly held at the ends and that the modulus of elasticity is 29,000,000, would 
require a force of 37,700 lbs. per sq. in. Of course this amount of strain can- 
not actually take place, since the strip is not firmly held at the ends, but is 
allowed to contract to some extent by the elasticity of the surrounding 
metal. But, says The Locomotive, we may feel pretty confident that in the 
case considered a longitudinal strain of somewhere in the neighborhood of 
8v00 or 10,600 lbs. per sq. in. may be produced by the feed-water striking 
directly upon the plates; and this, in addition to the normal strain pro- 
duced by the steam-pressure, is quite enough to tax the girth-seams beyond 
their elastic limit, if the feed-pipe discharges anywhere nearthem. Hence 
it is not surprising that the girth-seams develop leaks and cracks in 99 
eoees out of every 100 in which the feed discharges directly upon the fire- 
sheets, 


728 THE STEAM-BOILER. - 


STEAM SEPARATORS. 


If moist steam flowing at a high velocity in a pipe has its direction sud. 
denly changed, the particles of water are by their momentum projected in 
their original direction against the bend in the pipe or wall of the chamber 
in which the change of direction takes place. By making proper provision 
for drawing off the water thus separated the steam may be dried to a 
greater or less extent, 

For long steam-pipes a large drum should be provided near the engine 
for trapping the water condensed in the pipe. A drum 38 feet diameter, 15 
feet high, has given good results in separating the water of condensation of 
a steam-pipe 10 inches diameter and 800 feet long. 

Efficiency of Steam Separators.—Prof. R. C. Carpenter, in 1891, 
made a series of tests of six steam separators, furnishing them with steam 
containing different percentages of moisture, and testing the quality of 
steam before entering and after passing the separator. A condensed table 
of the principal results is given below. 


Test with Steam of about 10% of 








& B Moistiire, Tests with Varying Moisture. 
a 
os | 
““G | Quality of | Quality of ze Quality of | Quality of | Av’ge 
S ms Steam Steam eeepc Steam Steam Effi- 
op) before. after. P i before. after. ciency. 
B 87.0% 98.8% 90.8 66.1 to 97.5%|97.8 to 99% 87.6 
A 90.1 98.0 80.0 BL Oaot) Gen (995° GOet 76.4 
D 89.6 95.8 59.6 42.2 * 96.4 195.5 °° 98.2 |) GL.7 
C 90.6 93.7 83.0 67.1 ** 96.8 |93.7 ** 98.4 | 63.4 
EH 88.4 90:2 15.5 68.6 ‘S 98.1 |79.3 © 98.5 | 386.9 
F 88.9 92.1 28.8 70.4 °° 97.4 (84.1 § 97.9 || 28.4 





Conclusions from the tests were: 1. That no relation existed between the 
volume of the several separators and their efficiency. 

2. No marked decrease in pressure was shown by any of the separators, 
the most being 1.7 lbs. in E. 

3. Although changed direction, reduced velocity, and perhaps centrifugal 
force are necessary for good separation, still some means must be provided 
to lead the water out of the current of the steam. 

The high efficiency obtained from B and A was largely due to this feature. 
In B the interior surfaces are corrugated and thus catch the water thrown 
out of the steam and readily lead it to the bottom. 

In A, as soon as the water falls or is precipitated from the steam, it comes 
in contact with the perforated diaphragm through which it runs into the, 
space below, where it is not subjected to the action of the steam. 

Experiments made by Prof. Carpenter on a “Stratton’”’ separator in 1894 
showed that the moisture in the steam leaving the separator was less than 
1% when that in the steam supplied ranged from 6% to 21%. 


DETERMINATION OF THE MOISTURE IN STEAM~— 
STEAM CALORIMETERS., 


In all boiler-tests it is important to ascertain the quality of the steam, 
i.e., 1st, whether the steam is ‘‘saturated’’ or contains the quantity 
of heat due to the pressure according to standard experiments; 2d, whether 
the quantity of heat is deficient, so that the steam is wet; and 3d. whether 
the heat is in excess and the steam superheated. The best method of ascer- 
taining the quality of the steam is undoubtedly that employed by a com- 
mittee which tested the boilers at the American Institute Exhibition of 
1871-2, of which Prof. Thurston was chairman, i.e., condensing all the water 
evaporated by the boiler by means of a surface condenser, weighing the 
condensing water, and taking its temperature as it enters and as it leaves 
the condenser; but this plan cannot always be adopted. 

A substitute for this method is the barrel calorimeter, which with careful 
operation and fairly accurate instruments may generally be relied on to 
give results within two per cent of accuracy (that is, a sample of steam 
which gives the apparent result of 2% of moisture may contain anywhere be 
tween 0 and 4%). This calorimeter is described as follows: A sample of the 
steam is taken by inserting a perforated 14-inch pipe into and through the 
main pipe near the boiler, and led by a hose, thoroughly felted, to a barrel, 
holding preferably 400 lbs, of water, which is set upon a platform scale and 


DETERMINATION OF THE MOISTURE IN STEAM. 729 


provided with a cock or valve for allowing the water to flow to waste, and 
with a small propeller for stirring the water. 

To operate the calorimeter the barrel is filled with water, the weight and 
temperature ascertained, steam blown through the hose outside the barrel 
until the pipe is thoroughly warmed, when the hose is suddenly thrust into 
the water, aid the propeller operated until the temperature of the water is 
increased to the desired point, say about 110° usually. The hose is then 
withdrawn quickly, the temperature noted, and the weight again taken. 

An error of 1/10 of a pound in weighing the condensed steam, or an error 
of 16 degree in the temperature, will cause an error of over 1% in the calcu- 
lated percentage of moisture. See Trans. A. S. M. E., vi. 298. 

The calculation of the eee of moisture is made as below: 

1 
= —(hy —h) —-(T—h i: 
Q WoT ah 1 = ¢ 1) 

Q = quality of the steam, dry saturated steam being unity. 

H = total heat of 1 1b. of steam at the observed pressure. 

ess “ee ** water at the temperature of steam of the ob- 

served pressure. 





fic aes cee we © 6eondensing water, original. 
= 13 66 66 (73 6s 66 73 
a final. 
W = weight of condensing water, corrected for water-equivalent of the 


apparatus. 
aw = weight of the steam condensed. 
Percentage of moisture = 1 — Q. 


If Q is greater than unity, the steam is superheated, and the degrees of 
superheating = 2.0833 (dH — 7’) (Q — 1). 

Difficulty of Obtaining a Correct Sam ple.—Recent experiments 
by Prof. D. S. Jacobus, Trans. A. 8. M. E., xvi. 1017, show that it is practi- 
cally impossible to obtain a true average sample of the steam flowing in a ° 
pipe. For accurate determinations all the steam made by the boiler should 
be passed through a separator, the water separated should be weighed, and 
a calorimeter test made of the steam just after it has passed the separator, 

Coil Calorimeters,—Instead of the open barrel in which the steam 
is condensed, a coil acting as a surface-condenser may be used, which is 
placed in the barrel, the water in coil and barrel being weighed separately. 
For description of an apparatus of this kind designed by the author, which 
he has found to give results with a probable error not exceeding 1% per cent 
of moisture, see Trans. A. S. M. E., vi. 294. This calorimeter may be used 
continuously, if desired, instead of intermittently. In this case a continu- 
ous flow of condensing water into and out of the barrel must be estat lished, 
and the temperature of inflow and outflow and of the condensed steam 
read at short intervals of time. 

Throttling Calorimeter.—For percentages of moisture not ex- 
ceeding 3 per cent the throttling calorimeter is most useful and convenient 
and remarkably accurate. In this instrument the steam which reaches it 
in a 14-inch pipe is throttled by an orifice 1/16 inch diameter, opening into a 
chamber which has an outlet to the atmosphere. The steam in this cham- 
ber has its pressure reduced nearly or quite to the pressure of the atmos- 
phere, but the tote] heat in the steam before throttling causes the steam in 
the chamber to be superheated more or less according to whether the 
steam before throttling was dry or contained moisture. The only observa- 
tions required are those of the temperature and pressure of the steam on 
each side of the orifice. 

The author’s formula for reducing the observations of the throttling 
calorimeter is as follows (Experiments on Throttling Calorimeters, Am. 
Mach., Aug. 4, 1892): w= 100 x a Pn eM Sd AG ob in which w = percent- 
age of moisture in the steam; H = total heat, and Z = latent heat of steam 
in the main pipe; 2 = total heat due the pressure in the discharge side of 
the calorimeter, = 11466 at atmospheric pressure: K = specific heat of su- 
perheated steam; 7'= temperature of the throttled and superheated steam 
in the calorimeter; f= temperature due the pressure in the calorimeter, 
= 212° at atmospheric pressure. 

Taking K at 0.48 and the pressure in the discharge side of the calorimeter 
as atmospheric pressure, the formula becomes 


_— oo —_ 9199 
w= 100% A — 1146.6 — 0.48(7 — 212 ) 


L 
From this formula the following table is calculated : 





730 THE STEAM-BOILER. 


MoIsturRE IN STEAM—DETERMINATIONS BY THROTTLING CALORIMETER. 





Gauge-pressures. 


5 | 10 | 20 | 20 | ao 70 





so | a 








zs | s0 | 8 | 90 





T — 212°. 


Per Cent of Moisture in Steam. 


Degree of Super- 
heating 


























Oe CO rt CO 2 OT CO r+ SOO 


























oe | 0.51] 0.90] 1.54] 2.06] 2.50] 2.90] 3.24] 3.56] 3.71] 3.86] 3.99] 4.13 
10° —-| 0.01| 0.39| 1.02] 1.54] 1.97] 2.36| 2.71] 3.02] 3:17] 3.82 3.45] 3.58 
pos Sat Tish s. tuilhas, 51] 1.02] 1.45] 1.83] 2.17| 2.48] 2.63] 2.77] 2.90] 3.03 
apse eee |, ase 00| 50.92] 1.30] 1.64 1.94] 2.09] 2.93) 2.35] 2.49 
agrees, lac viceeane My vol soot "39:77 1.10] 1.40] 1.55} 1.69 1.80] 1.94 
BOON Mla actAlsetl pele ks ke 24) 157] :87] 1.01| 1.15| 1.26] 1.40 
TSG ean he "03| 133] 147/160; .72|  .85 
Lit 24 Rape KA Rn BOAO LAC ODIN Racha Kas 208 wal cs fy | 106 i172]. 231 
Dif. p dee! .0503| .0507| .0515| .0521| .0526| .0531| .0535| .0539| .0541| 0542! .0544| 0546 
RESET AEE DLE TILE GR LLL EBLE, RELI EEN, DIE REET RY ETS, PE ED BE 2ST ROTEL TED ES FS POLE SAT: ET a BE ET RANTLE BAG RE) 
= 
este Gauge-pressures. 
= &o 
yest 
33% | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 | 250 
® 
Se 
Bs Per Cent of Moisture in Steam. 
0° | 4.39 4.63, 4.85) 5.08) 5.29) 5.49) 5.68) 5.87) 6.05| 6.22) 6.80) 7.1 
10° | 3.84 4.08 4.29| 4.52| 4.73] 4:93] 5.12] 5.30) 5.48] 5.65| 5.82] 6.5 
20° | 3.99 3.52) 3.74] 3.96] 4.17] 4.37] 4.56] 4.74] 4.91] 5.08] 5.25| 6.0 
30° | 2.74 2.97| 3.18| 3.41| 3.61| 3.80 3.99] 4.17| 4.34] 4.51] 4.67] 5.4 
40° | 2.19 2.42] 2.63| 2.85| 3.05| 3.24] 3.43] 3.61| 3.78) 3.94] 4.10] 4.8 
50° | 1.64. 1.87| 2.08] 2.29] 2.49| 2.68] 2.87] 3.04| 3.21] 3.37] 3.53) 4.2 
60° | 1.09| 1.32) 1.52] 1.74] 1.93] 2.12| 2.30| 2148) 2.64] 2.80| 2.96] 3.6 
oe «| 155] .77| 97] 1.18] 1.38] 1.56] 1.74] 1.91] 2.07] 2.23] 2.38] 3.0 
goe | 00; 122] 42} .63/ .82| 1.00] 1.18] 1.34] 1.50] 1.66| 1.81] 2.5 
Bae litel tatbrhtsn cite kc. '07| :26| 44] 61] .78| 194] 1.09] 1.24] 1.9 
TOU eWalinsi cals ics (aie, 05] 121) 187] .52] 167] 1.3 
Taped ash lee hha cv.2| oe ote eae lial 10).06.7 
Dif.p.deg_| .0549] .0551| .0554| .0556] .0559| .0561| .0564| .0566| .0568| .0570| .0572 0581 











Separating Calorimeters.—For percentages of moisture beyond 
the range of the throttling calorimeter the separating calorimeter is used, 
which is simply a steam separator on asmali scale. An improved form of 
this calorimeter is described by Prof. Carpenter in Power, Feb. 1893. 

For fuller information on various kinds of calorimeters, see papers by 
Prof. Peabody, Prof. Carpenter, and Mr. Barrus in Trans. A. S. M. E., vols. 
x, xi, xii, 1889 to 1891; Appendix to Report of Com. on Boiler Tests, 
A.S. M. E., vol. vi, 1884; Circular of Schaeffer & Budenberg, N. Y., ‘‘ Calo- 
rimeters, Throttling and Separating,’ 1894. 

Identification of Dry Steam by Appearance of a Jet.— 
Prot. Denton (Trans. A. S. M. E., vol. x.) found that jets of steam show un- 
mistakable change of appearance to the eye when steam varies less than 1% 
er the condition of saturation either in the direction of wetness or super- 
1eating. 

Ifa jet of steam flow from a boiler into the atmosphere under circumstances 
such that very little loss of heat occurs through radiation, etc., and the jet 
be transparent close to the orifice, or be even a grayish-white color, the 
steain may be assumed to be so nearly dry that no portable condensing 
calorimeter will be capable of measuring the amount of water in the steam. 
If the jet be strongly white, tlhe amount of water may be roughly judged up 
to about 2%, but beyond this a calorimeter only can determine the exact 
almnount of moisture. glee “a 


CHIMNEYS. 731 


A common brass pet-cock may be used as an orifice, but it should, if possi- 
ble, be set into the steam-drum of the boiler and never be placed further 
away from the latter than 4 feet, and then only when the intermediate reser- 
voir or pipe is well covered. 

Usual Amount of Moisture in Steam Escaping from a 
Boiler.—In the common forms of horizontal tubular land boilers and 
water-tube boilers with ample horizontal drums, and supplied with water 
free from substances likely to cause foaming, the moisture in the steam 
does not generally exceed 2% unless the boiler is overdriven or the water- 
level is carried too high. ; 


CHIMNEYS. 


Chimney Draught Theory.—The commonly accepted theory of 
chimney draught, based on Peclet’s and Rankine’s hypotheses (see Rankine, 
S. E.), is discussed by Prof. De Volson Wood in Trans. A. S. M. E., vol. xi. 

Peclet represented the law of draught by the formula 

a, fl 
Bi La Gick ; 
in which h is the ‘‘ head,’ defined as such a height of hot gases as, if added 
to the column of gases in the chimney, would produce the 
same pressure at the furnace as a column of outside air, of the 
same area of base, and a height equal to that of the chimney; 
u is the required velocity of gases in the chimney; 
G a constant to represent the resistance to the passage of air 
through the coal; 
i the length of the flues and chimney; 
m the mean hydraulic depth or the area of a cross-section divi- 
ded by the perimeter; 
jf a constant depending upon the nature of the surfaces over which 
the gases pass, whether smooth, or sooty and rough. 


Rankine’s formula (Steam Engine, p. 288), derived by giving certain values 
to the constants (so-called) in Peclet’s formula, is 


To 7) 
“(0.080% 


a 9( 0.084 ) 


H — H = (0.96% —1)H; 


in which H = the height of the chimney in feet; 
T) = 493° F., absolute (temperature of melting ice); 
7, = absolute temperature of the gases in the chimney; 
T. = absolute temperature of the external air. 


Prof. Wood derives from this a still more complex formula which gives 
the height of chimney required for burning a given quantity of coal per 
second, and from it he calculates the following table, showing the height of 
chimney required to burn respectively 24, 20, and 16 lbs. of coal per square 
foot of grate per hour, for the several temperatures of the chimney gases 
given. 











Chimney Gas. Coal per sq. ft. of grate per hour lbs. 
Outside Air. s 
ay Temp. 24 20 16 
Absolute. Fahr, i 
Height H, feet. 

520° 700 239 250.9 157.6 67.8 
absolute or 800 339 172.4 115.8 55.7 
59° FB. 1000 539 149.1 100.0 48.7 
1100 639 148.8 98.9 48.2 
1200 739 152.0 100.9 49.1 
1400 939 159.9 105.7 By 
1600 1139 168.8 111.0 53.5 


2000 1539 206.5 182.2 63.0 


Yas CHIMNEYS. 


Rankine’s formula gives a maximum draught when tr = 2 1/12rg, or 622° F., 
when the outside temperature is 60°. Prof. Wood says: ‘‘ This result is not 
a fixed value, but departures from theory in practice do not affect the result 
largely. There is, then, in a properly constructed chimney, properly work- 
ing, a temperature giving a maximum draught,* and that temperature is not 
far from the value given by Rankine, although in special cases it may be 50° 
or 75° more or less.”’ 

All attempts to base a practical formula for chimneys upon the theoret- 
ical formula of Peclet and Rankine have failed on account of the impos- 
sibility of assigning correct values to the so-called *‘ constants”’ G and f. 
(See Trans. A. S. M. E., xi. 984.) 

Force or Intensity of Draught,—tThe force of the draught is equal 
to the difference between the weight of the column of hot gases inside of the 
chimney and the weight of a column of the external air of the same height. 
It is measured by a draught-gauge, usually a U-tube partly filled with water, 
one leg connected by a pipe to the interior of the flue, and the other open to 
the external air. 

If D is the density of the air outside, d the density of the hot gas inside, 
in lbs. per cubic foot, h the height of the chimney in feet, and .192 the factor 
for converting pressure in lbs. per sq. ft. into inches of water column, then 
the formula for the force of draught expressed in inches of water is, 


F = .192h(D — d). 
The density varies with the absolute temperature (see Rankine). 


d = 20,084; D = 0.0807 —, 
Ty 7 

where Tp is the absolute temperature at 32° F., = 493., 7, the absolute tem- 
perature of the chimney gases and r. that of the external air. Substituting 

these values the formula for force of draught becomes 

Ld lod 4 
FH -192n (22% oi nee) ts re (ses 4 reer 
T2 1 T3 T1 

To find the maximum intensity of draught for any given chimney, the 
heated column being 600° F., and the external air 60°, multiply the height 
above grate in feet by .0073, and the product is the draught in inches of water. 


Height of Water Column Due to Unbalanced Pressure in 
Chimney 100 Feet High. (The Locomotive, 1854.) 




















a 

2 =| Temperature of the External Air—Barometer, 14.7 Ibs. per sq. in. 
ag 

gr 

cad a 0° 10%] 20° | 80% 1402 4} 5091 609A BO *) B02. 4 .90° | 100° 


——q“ |__| | ——— lf _ |_| — | | | | | | 


480 | .810 | .776 | .741) .710 | |678 | 1649 | .620 | 1591 | .566 | .540 | 1515 
500 | .829 | .791 | .760 | .730 | .697 | 16691 1639 | .610.| .586 | .559 | .534 


* Muen confusion to students of the theory of chimneys has resulted from 
their understanding the words maximum draught to mean maximum inten- 
sity or pressure of draught, as measured by a draught-gauge. It here means 
maximum quantity or weight of gases passed up the chimney. The maxi- 
mum intensity is found only with maximum temperature, but after the 
temperature reaches about 622° F. the density of the gas decreases more 
rapidly than its velocity increases, so that the weight is a maximum about 
622° F., as shown by Rankine.—W. K. 


CHIMNEYS. 733 


For any other height of chimney than 100 ft. the height of water-column 
is found by simple proportion, the height of water column being directly 
proportioned to the height of chimney. 

The calculations have been made for a chimney 100 ft. high, with various 
temperatures outside and inside of the flue, and on the supposition that the 
temperature of the chimney is uniform from top to bottom. This is the 
basis on which all calculations respecting the draught-power of chimneys 
have been made by Rankine and other writers, but it is very far from the 
truth in most cases. The difference will be shown by comparing the read- 
ing of the draught-gauge with the table given. In one case a chimney 122 ft. 
high showed a temperature at the base of 320°, and at the top of 230°, 

Box, in his “ Treatise on Heat,” gives the following table: 


DRAUGHT POWERS OF CHIMNEYS, ETC., WITH THE INTERNAL AIR AT 552°, AND 
THE EXTERNAL AIR AT 62°, AND WITH THE DAMPER NEARLY CLOSED. 














wi _ 4. | Theoretical Velocity | 8 a Theoretical Velocity 
oy == 5 | in feet per second. J ° >, == | in feet per second. 
aos | Bag ——_—___] 228 | weg |-——___. 
wma od aa ws 0 uy 
sa | £27 | Cold air | Hot Air} oe" | £22 | Cold air | Hot Air 
ms Asoo | Entering. | at Exit. | 55 ASS | Entering. | at Exit. 
Ra a 
10 073 (as 35.6 80 585 50.6 101.2 
20 146 Pao} 50.6 90 657 53.7 107.4 
30 219 31.0 62.0 100 730 56.5 113.0 
40 292 SoG 71.4 120 87 62.0 124.0 
50 365 40.0 80.0 150 1.095 69.3 138.6 
60 2438 43.8 7.6 175 1.277 74.3 149.6 
7 511 47.3 94.6 200 1.460 80.0 160.0 





Rate of Combustion Due to Height of Chimney.— 
Trowbridge’s ‘‘ Heat and Heat Engines”’ gives the following table showing 
the heights of chimney for producing certain rates of combustion per sq. 
ft. of section of the chimney. It may be approximately true for anthracite 
in moderate and large sizes, but greater heights than are given in the table 
are needed to secure the given rates of combustion with small sizes of 
anthracite, and for bituminous coal smaller heights will suffice if the coal 
is reasonably free from ash—5% or less. 


Lbs. of Coal Lbs. of Coal 
Lbs. of Coal | Burned per ‘Lbs. of Coal | Burned per 
Burned per | Sq. Ft. of Burned per }| Sq. Ft. of 
Heights | Hour per Grate, the § Heights| Hour per Grate, the 
in Sq. Ft. Ratio of i Sq. Ft. Ratio of 
feet of Section |Grate to Sec- of Section |Grate to Sec- 
oO tion of of tion of 
Chimney. | Chimney be- Chimney. | Chimney be- 
ing 8 tol. ing 8 to 1. 
20 60 7.5 126 15.8 
25 68 8.5 131 16.4 
380 76 9.5 135 16.9 
85 84 10.5 139 17.4 
40 , 93 11.6 144 18.0 
45 99 12.4 148 18.5 
50 105 13.1 152 19.0 
55 111 13.8 156 19.5 
60 116 14.5 160 20.0 
65 121 1531 





Thurston’s rule for rate of combustion effected by a given height of chim- 
ney (Trans. A.S. M. H., xi. 991) is: Subtract 1 from twice the square root of 
the height, and the result is the rate of combustion in pounds per square foot 


of grate per hour, for anthracite. Or rate = 2 /i —4, in which h is the 
height in feet. This rule gives the following: t 


ies, 50 60 70 80 90 100 110 12 150 1% 200 
27/h—1=18.14 14.49 15.78 16.89 17.97 19 19.97 21.86 23.49 25.45 27.28 


The results agree closely with Trowbridge’s table given above. In prac- 


734 CHIMNEYS. 


tice the high .a.es 2. v6mbustion for high chimneys given by the formula 
are not generally obtained, for the reason that with high chimneys there are 
usually long horizontal flues, serving many boilers, and the friction and the 
interference of currents from the several boilers are apt to cause the inten- 
sity of draught in the branch flues leading to each boiler to be much iess 
than that at the base of the chimney. The draught of each boiler is also 
usually restricted by a damper and by bends in the gas-passages. In a bat- 
tery of several boilers connected to a chimney 150 ft. high, the author found 
a draught of 34-inch water-column at the boiler nearest the chimney, and 
only 44-inch at the boiler farthest away. The first boiler was wasting fuel 
from too high temperature of the chimney-gases, 90°, having too large a 
grate-surface for the draught, and the last boiler was working below its 
rated capacity and with poor economy, on account of insufficient draught. 
The effect of changing the length of the flue leading into a chimney 60 ft. 
eh and 2 ft. 9 in. square is given in the following table, from Box on 
eat’; 








Tee enebae = Horse-power. ckdey Kansere e Horse-power. 
50 107.6 800 56.1 
100 100.0 1,000 51.4 
200 85.3 1,500 43.3 
400 70.8 2,000 38.2 
600 62.5 3,000 31.7 


The temperature of the gases in this chimney was assumed to be 552° F., 
and that of the atmosphere 62°. 

High Chimmeys not Necessary.—Chimneys above 150 ft. in height 
are very costly, and their increased cost is rarely justified by increased ef. 
ficiency. In recent practice it has become somewhat common to build two or 
more smaller chimneys instead of one large one. A notable example is the 
Spreckels Sugar Refinery in Philadelphia, where three separate chimneys are 
used for one boiler-plant of 7500 H.P, The three chimneys are said to have 
cost several thousand dollars less than a single chimney of their combined 
capacity would have cost. Very tall chimneys have been characterized by 
one writer as ‘*‘ monuments to the folly of their builders.” 

Heights of Chimney required for Different Fuels.—The 
minimum height necessary varies with the fuel, wood requiring the least, 
then good bituminous coal, and fine sizes o7 anthracite the greatest. It 
also varies with the character of the boiler—the smaller and more circuitous 
the gas-passages the higher the stack required; also with the number of 
boilers, a single boiler requiring less height than several that discharge 
into a horizontal flue. No general rule can be given. 


SIZE OF CHIMNEYS. 


The formula given below, and the table calculated therefrom for chimneys 
up to 96 in. diameter and 200 ft. high, were first published by the author 
in 1884 (Trans, A.S. M. E. vi., 81). They have met with much approval 
since that date by engineers who have used them, and have been frequently 
published in boiler-makers’ catalogues and elsewhere. The table is now 
extended to cover chimneys up to 12 ft. diameter and 300 ft. high. The sizes 
corresponding to the given commercial horse-powers are believed to be 
ample for all cases in which the draught areas through the boiler-flues and 
connections are sufficient, say not less than 20% greater than the area of the 
chimney, and in which the draught between the boilers and chimney is not 
checked by long horizontal passages and right-angled bends. 

Note that the figures in the table correspond to a coal consumption of 5 Ibs. 
of coal per horse-power per hour. This liberal allowance is made to cover 
the contingencies of poor coal being used, and of the boilers being driven 
beyond their rated capacity. In large plants, with economical boilers and 
engines, good fuel and other favorable conditions, which will reduce tue 
maximum rate of coal consumption at any one time to less than 5 Ibs. per 
H. P. per hour, the figures in the table may be multiplied by the ratio of 5 to 
the maximum expected coal consumption per H.P. per hour. Thus, with 
conditions which make the maximum coal consumption only 2.5 lbs, per 
hour, the chimney 300 ft. high x 12 ft. diameter nour be sufficient for 6155 
X 2 = 12,310 horse-power. The formula is based on the following data: 


735 


SIZE OF CHIMNEYS. 


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1736 OHIMNEYS. 


x 1. The draught power of the chimney varies as the square root of the 
eight. 

2° The retarding of the ascending gases by friction may be considered as 
equivalent to a diminution of the area of the chimney, or to a lining of the 
chimney by a layer of gas which has no velocity. The thickness of this 
lining is assumed to be 2 inches for all chimneys, or the diminution of area 
equal to the perimeter X 2 inches (neglecting the overlapping of the corners 
of the lining). Let D = diameter in feet, 4 = area, and # = effective area 
in square feet. 


For square chimneys, H = D? — 2 =A- WA. 


For round chimeys, H= : (p — 2) = A — 0.591 WA. 


For simplifying calculations, the coefficient of 4/.A may be taken as 0.6 
for both square and round chimneys, and the formula becomes 


Eo A 06 V7 


8. The power varies directly as this effective area L. 

4. A chimney should be proportioned so as to be capable of giving sufficient 
draught to cause the boiler to develop much more than its rated power, in 
case of emergencies, or to cause the combustion of 5 lbs. of fuel per rated 
horse-power of boiler per hour. 

5. The power of the chimney varying directly as the effective area, H, and 
as the square root of the height, H, the formula for horse-power of boiler for 


a given size of chimney will take the form H.P. = CE WH, in which C is a 

constant, the average value of which, obtained by plotting the results 

obtained from numerous examples in practice, the author finds to be 3.33. 
The formula for horse-power then is 


H.P. = 3.330 /H, or H.P. = 3.33(4 — .6 A) YH. 


If the horse-power of boiler is given, to find the size of chimney, the height 
being assumed, 


E= 0.8 H.P.+-VH.; = 4 — 0.64 A, 
For rouud chimneys, diameter of chimney = diam. of H+ 4”, 


For square chimneys, side of chimney = VE 4. aoe 
If effective area His taken in square feet, the diameter in inches is d = 


13.54 /H +4”, and the side of a square chimney in inches is s = 12 WH+4”. 
2 
If horse-power is given and area assumed, the height H = (ao 4 


In proportioning chimneys the height is generally first assumed, with due 
consideration to the heights of surrounding buildings or hills near to the 
proposed chimney, the length of horizontal flues, the character of coal to be 
used, etc., and then the diameter required for the assumed height and 
horse-power is calculated by the formula or taken from the table. 

An approximate formula for chimneys above 1000 H.P. is H.P. = 
ae Ge VH. This gives the H.P. somewhat greater than the figures in the 

able. 

The Protection of Tall Chimney-shafts from Lightning. 
—C. Molyneux and J. M. Wood (Indusntel Maren 28, 1890) recommend for 
tall chimneys the use of a coronal or heavy band at the top of the chimney, 
with copper points 1 ft. in height at intervals of 2 ft. throughout the cireum- 
ference. The points should be gilded to prevent oxidation. The most ap- 
proved form of conductor is a copper tape about 34 in. by \& in. thick, 
weighing 6 ozs. per ft. If iron is used it should weigh’ not less than 214 lbs. 
per ft. There must be no insulation, and the copper tape should be fastened 
to the chimney with holdfasts of the same material, to prevent voltaic 
action. An allowance for expansion and contraction should be made, say 1 
in. in 40 ft. Slight bends in the tape, not too abrupt, answer the purpose. 
Yor an earth terminal a plate of metal at least 3 ft. sq. and 1/16 in. thick 
should be buried as deep as possible in a damp spot. The plate should be of 
the same metal as the conductor, to which it should be soldered. The best 
earth terminal is water, and when a deep well or other large body of water 
is at hand, the conductor should be carried down into it. Right-angled 
bends in the conductor should be avoided. No bend in it should be over 20°, 


~sy Sr 


SIZE OF CHIMNEYS. vied 


Some Tall Brick Chimneys. 




















;, fy . 
Z| Oniside ]Oapscity by the 
5 Diameter. orice. 
3 3 Pounds 
= 5 $ hig, ol Bode oboe 
ca Fis & hour. 
1. Hallsbriickner Hiitte, Sax.| 460 15/7 33/ 16’ | 18,221 | 66,105 
2. Townsend’s, Glasgow... ...| 454 |...,...... 382 
3. Tennant’s, Glasgow........ 435 13’ 6” 40 9,795 | 48,975 
4. Dobson & Barlow, Bolton, 
iN ee, See CS Mees Se 36714) 187 .2/7 183/10// 8,245 | 41,225 
5. Fall River Iron Co., Boston! 350 11 30 21 5,558 | 27,790 
6. Clark Thread Co., Newark, ; 
ING Disccttt paeeie salataas 335 11 28’ 6’) 14 5,435 | 27,175 
%. Merrimac MilJs, Low’l, Mass}282/9” 12 5,980 | 29,900 
8. Washington Mills, Law- 
rence, Massi#ac scans «ee 250 10 8,839 | 19,195 
9. Amoskeag Mills, Manches- 
UCI EN bale EMorpce eae e 5, 3 = 250 10 8,839 } 19,195 
10. Narragansett E. L. Co., 
Provadence, Ke Le. css. - 238 14 7,515 | 37,575 
11. Lower Pacific Mills, Law- 
PenG@e MWASS so ce et leas sce 214 8 2,248 | 11,240 
12. Passaic Print Works, Pas- 
BONO a oars cn cteatel ites 200 9 2,771 | 13,855 
18. Edison Sta,B’klyn,Twoe’ch| 150 150/’ x 120’ leach! 1.541 7,705 








Notes ON THE AsBovE CHIMNEYS.—1. This chimney is situated near 
Freiberg, on the right bank of the Mulde, at an elevation of 219 feet above 
that of the foundry works, so that its total height above the sea will be 71134 
feet. The works are situated on the bank of the river, and the furnace- 
gases are conveyed across the river to the chimney on a bridge, through a 

ipe 3227 feet in length. It is built throughout of brick, and will cost about 

40,000.—Mfr. and Bldr. 

2. Owing to the fact that it was struck by lightning, and somewhat 
damaged, as a precautionary measure a copper extension subsequently was 
added to it, making its entire height 488 feet. 

1, 2, 3, and 4 were built of these great heights to remove deleterious 
gases from the neighborhood, as well as for draught for boilers. 

5. The structure rests on a solid granite foundation, 55 x 30 feet, and 
16 feet deep. In its construction there were used 1,700,000 bricks, 2000 tons 
of stone, 2000 barrels of mortar, 1000 loads of sand, 1000 barrels of Portland 
cement, and the estimated cost is $40.000. It is arranged for two flues, 9 
feet 6 inches by 6 feet, connecting with 40 boilers, which are to be run in 
connection with four triple-expansion engines of 1350 horse-power each. 

6. It has a uniform batter of 2.85 inches to every 10 feet. Designed 
for 21 boilers of 200 H. P. each. It is surmounted by a cast-iron cop- 
ing which weighs six tons, and is composed of thirty-two sections, 
which are bolted together by inside flanges, so as to present a smooth 
exterior. The foundation is in concrete, composed of crushed lime: 
stone 6 parts, sand 3 parts, and Portland cement 1 part. It is 40 feet 
square and 5 feet deep. Two qualities of brick were used; the outer 
portions were of the first quality North River, and the backing up was of 
good quality New Jersey brick. Every twenty feet in vertical measurement 
an iron ring, 4 inches wide and 3 to Winch thick, placed edgewise, was 
built into the walls about 8 inches from the outer circle. As the chimney 
starts from the base it is double. The outer wall is 5 feet 2 inches in thick- 
ness, and inside of this isa second wall 20 inches thick and spaced off about 
20 inches from main wall. From the interior surface of the main wall eight 
buttresses are carried, nearly touching this inner or main flue wall in 
order to keep it in line should it tend to sag. The interior wall, starting 
with the thickness described, is gradually reduced until a height of about 
90 feet is reached, when it is diminished to 8inches. At 165 feet it ceases, 


738 CHIMNEYS. 


and the rest of the chimney is without lining. The total weight of the chim. 
ney and foundation is 5000 tons. It was completed in September, 1888. 

7. Connected to 12 boilers, with 1200 square feet of grate-surface. Draught- 
gauge 1 9/16 inches. 

8. Connected to 8 boilers, 6’ 8’ diameter x 18 feet. Grate-surface 448 
square feet. 

9. Connected to 64 Manning vertical boilers, total grate surface 1810 sq. ft. 
Designed to burn 18,000 lbs. anthracite per hour. 

10. Designed for 12,000 H.P. of engines; (compound condensing), 

11. Grate-surface 434 square feet; H.P. of boilers (Galloway) about 2500. 

13. Eight boilers (water-tube) each 450 H.P.; 12 engines, each 300 H P. Plant 
designed for 86,000 incandescent lights. For the first 60 feet the exterior 
wall is 28 inches thick, then 24 inches for 20 feet, 20 inches for 80 feet, 16 
inches for 20 feet, and 12 inches for 20 feet. The interior wallis 9 inches 
thick of fire-brick for 50 feet, and then 8 inches thick of red brick for the 
next 30 feet. Illustrated in Iron Age, January 2, 1890. 

A number of the above chimneys are illustrated in Power, Dec., 1890. 

Chimney at Knoxville, Tenn., illustrated in Eng’g News, Nov. 2, 1893. 
G feet diameter, 120 feet high, double wall: 


Exterior wall, height 20feet, 30 feet, 30 feet, 40 feet; 
i * thickness 2114 in.,17in., 13 in,, 844 in.s 
Interior wall, height 85 ft.,85ft., 29 ft., 21 ft.; 
$8 se thickness 131% in., 814 in., 4 in., 0. 


Exterior diameter, 15’ 6” at bottom; batter, 7/16 inch in 12inches from bot- 
tom to 8 feet from top. Interior diameter of inside wall, 6 feet uniform to 
top of interior wall. Space between walls, 16 inches at bottom, diminishing 
to 0 at top of interior wall. The interior wall is of red brick except a lining 
of 4 inches of fire-brick for 20 feet from bottom. 

Stability of Chimmneys.—Chimneys must be designed to resist the 
maximum force of the wind in the locality in which they are built, (see 
Weak Chimneys, below). A general rule for diameter of base, of briclk 
chimneys, approved by many years of practice in England and the United 
States, is to make the diameter of the base one tenth of the height. If the 
chimney is square or rectangular, make the diameter of the inscribed circle 
of the base one tenth of the height. The ‘‘ batter” or taper of a chimney 
should be from 1/16 to 14 inch to the foot on each side. The brickwork 
should be one brick (8 or 9 inches) thick for the first 25 feet from the top, in- 
creasing 14 brick (4 or 4% inches) for each 25 feet from the top downwards. 
If the inside diameter exceed 5 feet, the top length should be 11% bricks; and 
if under 3 feet, it may be 1% brick for ten, feet. 

(From The Locomotive, 1884 and1886.) For chimneys of four feet in diam- 
eter and one hundred feet high, and upwards, the best form is circular, with 
a straight batter on the outside. A circular chimney of this size, in addition 
to being cheaper than any other form, is lighter, stronger, and looks much 
better and more shapely. 

Chimneys of any considerable height are not built np of uniform thickness 
froin top to bottom, nor with a uniformly varying thickness of wall, but the 
wall, heaviest of course at the base, is reduced by a series of steps. 

Where practicable the load ona chimney foundation should not exceed two 
tons per square foot in compact sand, gravel, or loam. Where a solid rock- 
bottom is available for foundation, the load may be greatly increased. If 
the rock is sloping, all unsound portions should be removed, and the face 
dressed to a series of horizontal steps, so that there shall be no tendency to 
slide after the structure is finished. 

All boiler-chimneys of any considerable size should consist of an outer 
stack of sufficient strength to give stability to the structure, and an inner 
stack or core independent of the outer one. This core is by many engineers 
extended up to a height of but 50 or 60 feet from the base of the chimney, 
but the better practice is to run it up the whole height of the chimney; it 
may be stopped off, say, a couple feet below the top, and the outer shel! con- 
tracted to the area of the core, but the better way is to run it up to about 8 
or 12 inches of the top and not contract the outer shell. But under no cir= 
cumstances should the core at its upper end be built into or connected with 
the oute. stack. This has been done in several instances by bricklayers, and 
the resul, has been the expansion of the inner core which lifted the top of 
the outer stack squarely up and crecked the brickwork. 

For a height of 100 feet we would make the outer shell in three steps, the 
first 20 feet high, 16 inches thick, the second 30 feet high, 12 inches thick, the 


—— 


SIZE OF CHIMNEYS. 739 


third 50 feet high and 8 inches thick. These are the minimum thicknesses 
admissible for chimneys of this height, and the batter should be not less 
than 1 in 386 to give stability. The core should also be built in three steps, 
each of which may be about one-third the height of the chimney, the lowest 
12 inches, the middle 8 inches, and the upper step 4 inches thick. This will 
insure a good sound core. The top of a chimney may be protected by a 
cast-iron cup; or perhaps a cheaper and equally good plan is to lay the 
ot eth part in some good cement, and plaster the top with the same 
material, 

Weak Chimmneys.—James B. Francis, in a report to the Lawrence 
Mfg. Co. in 1878 (Eng’g News, Aug. 28, 1880), gives some calculations con- 
cerning the probable effects of wind on that company’s chimney as then 
constructed. Its outer shell is octagonal. The inner shell is cylindrical, 
with an air-space between it and the outer shell; the two shells not being 
bonded together, except at the openings at the base, but with projections in 
the brickwork, at intervals of about 20 ft. in height, to afford lateral sup- 
port by contact of the twoshells, The principal dimensions of the chimney 
are as follows: 


Height above the surface of the ground...............- Ke eae 213 ft. 


Thickness of the outer shell near the base, 6 bricks, or......... 2314 in 
Thickness of the outer shell near the top, 3 bricks, or........... 11% “ 
Thickness of the inner shell near the base, 4 bricks, or.......... 15 “ 
Thickness of the inner shell near the top, 1 brick, or ........... 334 $f 


One tenth of the height for the diameter of the base is the rule commonly 
adopted. The diameter of the inscribed circle of the base of the Lawrence 
Manufacturing Company’s chimney being 15 ft., it is evidently much less 
than is usual in a chimney of that height. 

Soon after the chimney was built, and beforethe mortar had hardened, it 
was found that the top had swayed over about 29 in. toward the east. This 
was evidently due to a strong westerly wind which occurred at that time. 
It was soon brought back to the perpendicular by sawing into some of the 
joints, and other means, ; 

The stability of the chimney to resist the force of the wind depends mainly 
on the weight of its outer shell, and the width of its base. The cohesion of 
the mortar may add considerably to its strength; but it is too uncertain to 
be relied upon. The inner shell will add _a little to the stability, but it may 
be cracked by the heat, and its beneficial effect, if any, is too uncertain to 
be taken into account. 

The effect of the joint action of the vertical pressure due to the weight of 
the chimney, and the horizontal pressure due to the force of the wind is to 
shift the centre of pressure at the base of the chimney, from the axis to- 
ward one side, the extent of the shifting depending on the relative magni- 
tude of the two forces, If the centre of pressure is brought too near the 
side of the chimney, it will crush the brickwork on that side, and the chim- 
ney will fall. A line drawn through the centre of pressure, perpendicular to 
the direction of the wind, must leave an area of brickwork between it and 
the side of the chimney, sufficient to support half the weight of the chim- 
ney; the other half of the weight being supported by the brickwork on the 
windward side of the line. 

Different experimenters on the strength of brickwork give very different 
results. Kirkaldy found the weights which caused several kinds of bricks, 
Jaid in hydraulic lime mortar and in Roman and Portland cements, to fail 
slightly, to vary from 19 to 60 tons (of 2000 Ibs.) per sq. ft. If we take in this 
case 25 tons per at ft., as the weight that would cause it to begin to fail, we 
shall not err greatly. To support half the weight of the outer shell of the 
chimney, or 322 tons, at this rate, requires an area of 12.88 sq. ft. of brick- 
work, From these data and the drawings of the chimney, Mr. Francis cal- 
culates that the area of 12.88 sq. ft. is contained ina portion of the chimney 
extending 2.428 ft. from one of its octagonal sides, and that the limit to 
which the centre of pressure may be shifted is therefore 5.072 ft. from the 
axis. If shifted beyond this, he says, on the assumption of the strength 
of the brickwork, it wil) crush and the chimney will fall. 

Calculating that the wind-pressure can affect only the upper 141 ft. of the 
chimney, the lower 70 ft. being protected by buildings, he calculates that a 
wind-pressure of 44.02 lbs. per sq. ft. would blow the chimney down. 

Rankin iu a paper printed in the transactions of the Institution of Engl« 


740 OHIMNEYS. 


neers, in Scotlanu, for 1867-68, says: ‘It had previously been ascertained 
by observation of the success and failure of actual chimneys, and especially 
of those which respectively stood and fell during the violent storms of 1856, 
that, in order that a reund chimney may be sufficiently stable, its weight 
should be such that a pressure of wind, of about 55 Ibs. per sq. ft. of a plane 
surface, directly facing the wind, or 2714 lbs. per sq. ft. of the plane projec- 
tion of a cylindrical surface, . . . shall not cause the resultant pressure 
at any bed-joint to deviate from the axis of the chimney by more than one 
quarter of the outside diameter at that joint,” 

According to Rankine’s rule, the Lawrence Mfg. Co.’s chimney is adapted 
toa maximum pressure of wind on a plane acting on the whole height of 
18.80 lbs. per sq. ft., or of a pressure of 21.40 lbs. per sq. ft. acting on the 
uppermost 141 ft. of the chimney. 

Steel Chimmeys are largely coming into use, especially for tall chim- 
neys of iron-works, from 150 to 300 feet in height. The advantages claimed 
are: greater strength and safety; smaller space required; smaller cost, by 
80 to 50 per cent, as compared with brick chimneys; avoidance of infiltras 
tion of air and consequent checking of the draught, common in brick chim- 
neys. They are usually made cylindrical in shape, with a wide curved flare 
for 10 to 25 feet at the bottom. A heavy cast-iron base-plate is provided, to 
which the chimney is riveted, and the plate is secured to a massive founda-~ 
tion by holding-down bc\ts. No guys are used. F. W. Gordon, of the Phila. 
Engineering Works, gives the following method of calculating their resist- 
ance to wind pressure (Power, Oct. 1893): 

In tests by Sir William Fairbairn we find four experiments to determine 
the strength of thin hollow tubes. In the table will be found their elements, 
with their breaking strain, These tubes were placed upon hollow blocks, 
ade ate weights suspended at the centre from a block fitted to the inside of 
the tube. 














: : . : Breaking W't 
Clear Thick- | Outside |} Sectional | Breaking ‘9 
Span, InessIron,| Diame- | Area, Weight, Sat MAR AS 
ft. in. in. ter, in. in. lbs. / Constant 1.2 
I, 17 037 12 1.3901 2,704 2,627 
Ir. | 15 71g] <112 12.4 4.8669 113440 9,184 
TII. 23 5 0631 17.68 8.487 6,400 4,302 
IV. 23 5 119 18.18 6.74 14,240 13,910 


Edwin Clarke has formulated a rule from experiments conducted by him 


during his investigations into the use of iron and steel for hollow tube 


bridges, which is as follows : 
Center break- ) _Area of material in sq.in. x Mean depth in in. xX Constant 
ing load,in tons. , ne Clear span in feet. , 


When the constant used is 1.2, the calculation for the tubes experimented 
upon by Mr. Fairbairn are given in the last column of the table. D. K. 
Ulark’s ‘*‘ Rules, Tables, and Data,’ page 513, gives a rule for hollow tubes 
as follows: W=3.14D°TS+L. W = breaking weight in pounds in centre; 
D=extreme diameter in inches; 7 = thickness in inches; L=length be- 
tween supports in inches; S = ultimate tensile strength in pounds per sq. in. 

Taking S, the strength of a square inch of a riveted joint, at 35,000 lbs. 
per. sq. in., this rule figures as follows for the different examples experi- 
mented upon by Mr. Fairbairn : I, 2870; IT, 10,1903; III, 7700; IV, 15,820. 

This shows a close approximation to the breaking weight obtained by 
experiments and that derived from Edwin Clarke’s and D. K. Clark’s rules. 
We therefore assume that this system of calculation is practically correct, 
and that it is eminently safe when a large factor of safety is provided, and 
from the fact that a chimney may be standing for many years without 
receiving anything like the strain taken as the basis of the calculation, viz., 
fifty pounds per square foot. Wind pressure at fifty pounds ver square foot 
may be assumed to be travelling in a horizontal direction, and be of the 
same velocity from the top to the bottom of the stack. This is the extreme 
assumption. If, however, the chimney is round, its effective area would be 
only half of its diameter plane. We assume that the entire force may be 
concentrated in the centre of the height of the section of the chimney 
under consideration. 





SIZE OF CHIMNEYS. 741 


Taking as an example a 125-foot iron chimney at Poughkeepsie, N. Y., the 
average diameter of which is 90 inches, the effective surface in square feet 
upon which the force of the wind may play will therefore be 714 times 125 
divided by 2, which multiplied by 50 gives a total wind force of 23,437 

unds. The resistance of the chimney to breaking across the top of the 

oundation would be 3.14 X 168? (that is, diameter of base) x..25 « 35,000 + 
(750 X 4) = 258,486, or 10.6 times the entire force of the wind. We multiply 
the half height above the joint in inches, 750, by 4, because the chimney is 
considered a fixed beam with a load suspended on oneend. In calculating 
{ts strength half way up, we have a beam of the same character. It is a 
fixed beam at a line half way up the chimney, where it is 90 inches in diam- 
eter and .187 inch thick. Taking the diametrical section above this line, 
and the foree as concentrated in the centre of it, or half way up from the 
point under consideration, its breaking strength is: 3.14 * 902 x .187 « 35,000 
-- (381 & 4) = 109,220; and the force of the wind to tear it apart through its 
cross-section, 714 x 6244 & 50+ 2 = 11,352, or a little more than one tenth of 
the strength of the stack. 

The Babcock & Wilcox Co.’s book ‘* Steam” illustrates a steel chimney 
at the works of the Maryland Steel Co., Sparrow’s Point, Md. It is 225 ft. 
in height above the base, with internal brick lining 13’ 9’7 uniform inside 
diameter. The shell is 25 ft. diam. at the base, tapering in a curve to 17 ft. 
25 ft. above the base, thence tapering almost imperceptibly to 14’ 8’” at the 
top. The upper 40 feet is of 44-inch plates, the next four sections of 40 ft. 
each are respectively 9/382, 5/16, 11/32, and 3g inch, 


Sizes of Foundations for Steel Chimneys, 
(Selected from circular of Phila. Engineering Works.) 


Haur-LInED CHIMNEYS. 
Diameter, clear, feet....... pes; 4 5 6 % 9 11 
Height, feet. .2.006 ceccdeoe 100 100 150 150 150 150 150 
Least diameter foundation... 15/9 16/4 20/4 21/10 92/77 93/87 24/gH 
Least depth foundation..... ai 0% 6/ 9/ 8 9 10’ 10’ 
Height, feet......... a désvetes ase e6, ox 1120s, 4200 200 250 75 300 
Least diameter foundation... .... 18/5 23/8 25 29/8” 33/6” 386’ 
Least depth foundation...... .... 7 10’ 10’ 12’ 42’ 14’ 


Weight of Sheet-iron Smokesstacks per Foot. 
(Porter Mfg. Co.) 








Diam., Thick- Weightj Diam., Thick- Weight# Diam. Thick- Weight 


inches. Wea per ft. er ft. finches.| yw q | per ft. 


























10 No. 16 ® 20 No. 16 : 20 No. 14 18.33 
12 ~ 8.66 28 by 22 =O 20.00 
14 bd 9.58 ks F 24 Co 21.66 
16 S 11.68 No. 14 26 oe 23.33 
20 13.75 2 oe 28 2 25.00 
2 es 15.00 be 30 oe 26.66 
24 a 16.25 ez 
Sheet-iron Chimneys, (Columbus Machine Co.) 
Diameter F Diameter] Length | Thick- ! 
Chimney, Weight, Chimney, Chimney, tenn vee 
inches. inches. feet. |p W_G s. 
10 160 89 40 No. 15 960 
15 240 82 40 se 18 | leOo0 
20 34 40 patti Fag ee 
2 850 386 40 scan 14 1,240 
a4 760 88 40 “ 12] 1,800 
26 826 40 40 12] 1,890 
28 900 











742 THE STEAM-ENGINE, 


THE STEAM-ENGINE. 


Expansion of Steam. Isothermal and Adiabatic.—Accord- 
ing to Mariotte’s law, the volume Of a perfect gas, the temperature being 


kept constant, varies inversely as its pressure, or p« at Buse a constant. 


The curve constructed from this formula is called the isothermal curve, or 
curve of equal temperatures, and is a common or rectangular hyperbola. 
The relation of the pressure and volume of saturated steam, as deduced 
from Regnault’s experiments, and as given in Steam tables, is approxi- 
mately, according to Rankine (S. E., p. 403), for pressures not exceeding 120 
aie led iz 1.0625 
Ibs.,p x —,, orpxv *S or pul? = pu = a constant. Zeuner has 
ute 

found that the exponent 1.0646 gives a closer approximation. 

When steam expands in a closed cylinder, us in an engine, according to 





Rankine (S. E., p. 8385), the approximate law of the expansion is p « or 


~ | 

vs 

pev , or pv 1111 _ g constant. The curve constructed from this for- 
iuula is called the adiabatic cur ve, or curve of no transmission of heat. 

Peabody ‘Therm., p, 112) says: “It is probable that this equation was 
obtained by comparing the expansion lines on a large number of indicator- 
diagrams. ... There does not appear to be any good reason for using an 
exponential equation in this connection,...and the action of a lagged steam- 
engine cylinder is far from being adiabatic. ... For general purposes the 
hyperbola is the best curve for comparison with the expausiou curve of an 
indicator-card. .’ Wolff and Denton, Trans. A. S. M. E., ii. 175, say: 
“From a number of cards examined from a variety of steam- -engines in cur- 
rent use, we find that the actual expansion line varies between the 10/9 
adiabatic curve and the Mariotte curve.’ 

Prof. Thurston (A. 5S. M. E., ii. 203), says he doubts if the exponent ever 
becomes the same in any two engines, or even in the same engines at dif- 
ferent times of the day and under varying conditions of the day. 

Expansion of Steam according to Mariotte’s Law and 
to the Adiabatic Law. (lIrans. A. §. M. a li. 156.)—Mariotte’s law 


pv =P; Values calculated from formula malls == te + hyp log R),in which 


R= vg + Vy, P; = absolute initial pressure, Pm = fa ores mean pressure, 
v= initial volume of steam in cylinder at pressure py, V2 = final volume of 
10 


steam at final pressure. Ge digvatle ive: puv® = p,v,°; values calculated 










from formula -—10R SORT L?. 
Bt 
Ratio of Mean p Ratio of Mean 7 Ratio of Mean 
, to Initial Ratio to Initial Ratio to Initial 
Ratio of Pressure. of Pressure. of Pressure. 
Expan- Expan- Expan- 





siou R. | yar, | Adiab. JO" *:| mar. | Adiab. GSO" *-| mar. | Adiab. 


————_$ | ———____ 4§_—————————_— | | J | | 












2.0 3.7 .624 600 6. 465 438 
1.2 38 .614 .590 6.25 453 425 
1.5 3.9 605 580 6.5 442 413 
1.7 4. 597 mye 6.75 431 403 
2. 4.1 ‘ ce 421 393 
Pde 4.2 4.25 411 383 
2.4 4.3 7.5 402 374 
2.5 4.4 0.05 393 365 
2.6 4.5 8. 385 B57 
2.8 4.6 8.25 BY s 349 
8. 4.7 8.5 369 342 
3.1 4.8 8.75 362 335 
8.2 4.9 9. 855 828 
8.3 5.0 9.25 03849 321 
3.4 5 25, 9.5 842 815 
3.5 5.5 9.75 : 

3.6. 5.78. 10 


4 


MEAN AND TERMINAL ABSOLUTE PRESSURES. %43 


Mean Pressure of Expanded Steam.—For calculations of 
engines it is generally assumed that steam expands according to Mariotte’s 
law, the curve of the expansion line being a hyperbola. The mean pressure. 
measured above vacuum, is then obtained from the formula 


1+ hyp log R 
R 


in which Pm is the absolute mean pressure, p, the absolute initial pressure 
taken as uniform up to the point of cut-off, P¢ the terminal pressure, and R 
the ratioof expansion. If/= length of stroke to the cut-off, LZ = total stroke. 


Pm = Pp, , or Pm = Pil + hyp log R), 


L 
Py! + py! hyp cog> 1+-hyplogR 
Pm = ———;——*; and tra, Pra ae pyres 


Wean and Terminal Absolute Pressures.—Mariotte’s 
Law.—The values in the following table are based on Mariotie’s law, 
except those in tbe last column, which give the-mean pressure of superheated 
steam, which, according to Rankine, expands in a cylinder according to 


the law pa v— 18, These latter values are calculated frum the formula 


—~16R—1T sap 
Pm aa Ae ase may be found by extracting the square root of 4 








Pr 
four times. From the mean absolute pressures given deduct the mean back 
pressure (absolute) to obtain the mean effective pressure. 


Rate Ratio of Ratio of Ratio of | Ratio of Ratio of 





of Cut- Mean to Meanto | Terminai [ Initial Mean to 
Expan-| off. Initial Terminal | to Mean to Mean Initial 
sion. Pressure. | Pressure. | Pressure. | Pressure. |Dry Steam. 
30 0.033 0.1467 4.40 0.227 6.82 0.136 
28 0.036 0.1547 4.33 0.231 6.46 a sictolste eyes e 
26 0.038 0.1638 4.26 0.235 GEILE Sa) lee ttt © 
24 0.042 0.1741 4.18 0.289 DCD t | |'bae eteetacterath 
22 0.045 0.1860 4.09 0.244 DROS Ens ln steclonteasicters 
20 0.050 0.1998 4.00 0.250 5.00 0.186 
18 0.055 0.2161 8.89 0.256 4 O35 pattem nce aes ate 
16 0.062 0.2358 3.77 0.265 AEE) Pale focs crersrate sate 
15 0.066 0.2472 3.71 0.269 A OB ier cancels tne 
14 0.071 0.2599 8.64 0.275 Oe SO Me tlic dese Steere 
13.33 0.075 0.2690 3.59 0.279 8.72 0.254 
13 0.077 0.2742 3.56 0.280 SOD bal Sedative a 
12 0.083 0.2904 3.48 0.287 DAA le eloretalsseaie aicis 
i1 0.091 0.3089 3.40 0.294 ea ieee || a cuctencte oes Ps 
10 0.100 0.3303 3.30 0.303 3.03 0.314 
9 0.112 0.3552 3.20 0.312 aC eaay | eeteiiate eters 
8 0.125 0.3849 3.08 0.321 2.60 0.37 
v 6.143 0.4210 2.95 0.339 Daal, QW ead bacco ts 
6.66 0.150 0.4347 2.90 0.345 2.30 0.417 
6.00 0.166 0.4653 2.79 0.360 Belo (esate aecrepets 
5.71 0.175 0.4807 2.74 0.364 QROS I. baie ae aeutelens 
5.60 0.200 0.5218 2.61 0.383 1.92 0.506 
4.44 0.225 0.5608 2.50 0.400 a ts ean einer is 4 cre 
4.00 0.250 0.5965 2.39 0.419 1.68 0.582 
8.63 0.275 0.6308 2.29 0.487 1.58 Re RE, te 
3.33 0.300 0.6615 2.20 0.454 1.51 0.648 
8.00 0.333 0.6995 2.10 0.476 1243-0 oa th eee ; 
2.86 0.350 0.7171 2.05 0.488 1.39 0.707 
2.66 0.875 €.7440 1.98 0.505 1534 4 0 ee eae oi 
2.50 0.400 0.7664 1.91 0.523 1.31 0.756 
2.22 0.450 0.8095 1.80 0.556 1.24 0.500 
2.00 0.500 0.8465 1.69 0.591 1.18 0.840 
1.82 0.550 0.8786 1.60 0.626 1.14 8.874 
1.66 0 600 0.9066 1.51 0.662 1.10 0.900 
1.60 0.625 0.9187 1.47 0.680 1 ODER RS iss ee 
1.54 0.650 0.9292 1.43 0.699 1.07 0.926 
1.48 0.675 0.9405 1.39 0.718 106 ARR IAR os. 5 ee 3 











744 THE STEAM-ENGINE, 


Caleulation of Mean Effective Pressure, Clearance and 
Compression Considered.—In the above tables no account is taken 
eae - J—} of clearance, which in actual 
steam-engines modifies,the ratio 
of expansion and the mean pres- 
sure; nor of compression and 
back-pressure, which diminish 
the mean effective pressure. In 
the following calculation these 
elements are considered. 

L = length of stroke, 7 = length 
before cut-off, « = length of com- 
pression part of stroke, e = clear- 
ance, p, = initial pressure, py = 
back pressure, Pc = pressure of 
clearance steam at end of com- 
pression. All pressures are abso- 
lute, that is, measured from a 
perfect vacuum. 





Fia. 187. 
Area of ABCD = p,(l-+ (1 -+ hyp ieee +2); 





i+ 
B= p,(L — 2); 


C= pec(1 -+- hyp log 
D = (pi — Pole = PC — py (@ +). 
Area of A= ABCD — (B+C4+D) 


= pil-+o(1+ hyp log >) 


= [pot - %) + Pyle + (1 +-hyp log 22 ) + pic — Pye +0) | 


x+e 
c 








) = Pye +ey(1 + hyp log sd +e); 








Cc 


= pl + o(1-+hyp log Z£2) 





= pp| (L ~ 2) + @+e)hyp log =e | — Pic. 


2 


i area of A 
Mean effective pressure = ——~——> 


L 
ExaMPLe.,—Let DL = 1, l = 0.25, = 0.25, ¢ = 0.1, p, = 60 lbs., py, = 2 lbs. 


Area A = 60(.25 -+ (1 + hyp log za 


—2 [a — .2) + .85 hyp log = - 60x 2 


= 21(1 + 1.145) — 20.75 + 35 x 1.253) — 6 
= 45.045 — 2.377 — 6 = 36.668 = mean effective pressure. 


‘rne actual indicator-diagram generally shows a mean pressure consider 
ably less than that due to the initial pressure and the rate of expansion. The 
causes of loss of pressure are: 1. Friction in the stop-valves and steam- 
pipes. 2. Friction or wire-drawing of the steam during admission and cut- 
off, due chiefly to defective valve-gear and contracted steam-passages. 
8. Liquefaction during expansion. 4. Exhausting before the engine has 
completed its stroke. 5. Compression due to early closure of exhaust. 
6. Friction in the exhaust-ports, passages, and pipes. 

Re-evaporation during expansion of the steam condensed during admis- 
sion, and valve-leakage after cut-off, tend to elevate the expansion line of 
the diagram and increase the mean pressure, 

If the theoretical mean pressure be calculated from the initial pressure 
and the rate of expansion on the supposition that the expansion curve fol- 


EXPANSION OF STEAM. 145 


lows Mariotte’s law, pv = a constant, and the necessary corrections are 
made for clearance and compression, the expected mean pressure in practice 
may be found by multiplying the calculated results by the factor in the 
following table, according to Seaton. 


Particulars of Engine. Factor. 


cut-off valve, cylinder jacketed......... J teri Melee ea 0.94 

dinary valves, cylinders jacketed....0........sceseees -- 0.9 to 0.92 
in general practice, and unjacketed ............... e006 0.8 to 0.85 
der; cylinders jacketed, and with large ports, etc...... 0.9 to 0.92 
Jacketad, ANd -Ga0d Ports, CC... ocsencesacsaiespranraces 0.8 to 0,85 


jackets and expansion-valves..................-2eceeeee 0.7 to 0.8 


in, War-shipg™. 2) <1 dsa nadie sar dp cesses sceccecscocaets . 0.6 10.0.8 


If no correction be made for clearance and compression, and the engine 
is in accordance with general inodern practice, the theoretical mean pres« 
sure may be multiplied by 0.96, and the product by the proper factor in the 
table, to obtain the expected mean pressure, 


Given the Initial Pressure and the Average Pressure, to 
Find the Ratio of Expansion and the Period of Admig» 
sion. 

P = initial absolute pressure in Ibs. per sq. in.3 
P = average total pressure during stroke in lbs. per sq. in.$ 
= length of stroke in inches; 
@ = period of admission measured from beginning of stroke; 
e = clearance in inches} L+ 


R= actual ratio of expansion = Paaoe ri tats es (i) 
P(i+ hyp log R) 
EROS Fhe Tolenng 





Pp 


To find average pressure p, taking account of clearance, 


l Pil hyp log R — 
pa SE tor PUTO bye be Pe ollie Renkin” gb ataegy 
whence pL+ Pe = Pil-+c)(1 + byp log R) 3 
p 
—E+6 
_pL+Pe P 
hyp log R= "Fae = ae 7h oe Vane) 


Given p and P, to find R and 1 (by trial and error).—There being two un- 
known quantities & and l, assume one of them, viz., the period of admission 
i, substitute it in equation (3) and solve for R. Substitute this value of # in 


the formula (1), or? = com c, obtained from formula (1), and find Z. If 


the result is greated than the assumed value of 7, then the assumed value of 
the period of admission is too long; if less, the assumed value is too short. 
Assume a new value of J, substitute it in formula (8) as before, and continue 
Py ee eh ae of trial and error till the required values of # and / are 
obtained. 

EXAmMPLe.—P = 70, p = 42.78, EB = 60”, cz 3, tofind&% Assume l= 21 in. 
Dp 42.78 
pathy va 70 x 60+38 

t+e 21+3 


hyp log R = .653, whence & = 1.92, 





hyp log R = — 1 = 1.653 — 1 = S583 


746 THE STEAM-ENGINE, 


_L+e _ 63 £ 


which is greater than the assumed value, 21 inches. 
Now assume lJ = 15 inches: 








42.78 
7 % 60 + 3 
hyp log R= ib — 1= 1.204, whence R= 3.5; 
i pate oa ice = — 3= 18 — 3 = 15 inches, the value assumed. 


Therefore R = 3.5, and 1 = 15 inches. 


Period of Admission Required for a Given Actual Ratio of Expansion; 


t= “4% _ ¢, in inches . <1aS ae. eiisae eae 
100+-p.ct. clearance 
In percentage of stroke, 1 = ail Maher ius camel p. ct. clearance. . (5) 
. P(iti+c) In 
¥ eet ee ge Se) LS gi tiie careey rere 
Terminal pressure ee R (6) 


Pressure at any other? Point of the Expansion.—Let L, = length of stroke 
up to the given point. 
P(i-+-c) 
Ly + c e . . e e 4 e e e e e e 





Pressure at the given point = 


WORK OF STEAM IN A SINGLE CYLINDER. 


To facilitate calculations of steam expanded in cylinders the table on the 
next page is abridged from Clark on the Steam-enging. The actual ratios 
of expansion, column 1, range from 1.0 to 8.0, for which the hyperbolic 
logarithms are given in column 2. The 8d column contains the periods of 
admission relative to the actual ratios of expansion, as percentages of the 
stroke, calculated by formula (5) above. The 4th column gives the values 
of the mean pressures relative to the initial pressures, the latter being taken 
as 1, calculated by formula (2). In the calculation of columns 3 and 4, clear- 
ance is taken into account, and its amount is assumed at 7% of the stroke. 
The final pressures, in the 5th column, are such as would be arrived at by 
the continued expansion of the whole of the steam to the end of the stroke, 
the initial pressure being equal to 1. They are the reciprocals of the ratios 
of expansion, column 1. The 6th column contains the relative total per- 
formances of equal weights of steam worked with the several actual ratios 
of expansion; the total performance, when steam is admitted for the whole 
of the stroke, without expansion, being equal to 1. They are obtained by 
dividing the figures in column 4 by those in column 5. 

The pressures have been calculated on the supposition that the pressure of 
steam, during its admission into the cylinder, is uniform up to the point of 
eutting off, and that the expansion is continued regularly to the end of the 
stroke. The relative performances have been calculated without any allow- 
ance for the effect of compressive action. 

The calculations have been made for periods of admission ranging from 
100%, or the whole of the stroke, to 6.4%, or 1/16 of the stroke. And though, 
nominally, the expansion is 16 times in the last instance, it is actuadly only 
8 times, as given in the first column. The great difference between the 
nominal and the actual ratios of expansion is caused by the clearance, 
which is equal to 7% of the stroke, and causes the nominal volume of steam 
admitted, namely, 6.4%, to be augmented to 6.4 + 7 = 13.4% of the stroke, or, 
say, double, for expansion. When the steam is cut off at 1/9, the actual 
expansion is only 6 times; when cut off at 1/5, the expansion is 4 times; 
when cut off at 14, the expansion is 2%4 times; and to effect an actual expan- 
sion to twice the initial volume, the steam is cut off at 4614% of the stroke, 
uot at half-stroke, 


WORK OF STEAM IN A SINGLE CYLINDER. Q49 


Expansive Working of Steam—Actual Ratios of Expan- 
sion, with the Relative Periods of Admission, Press- 
ures, and Performance, 


Steam-pressure 100 lbs. absolute. Clearance atfeach end of the cylinder 7% 
of the stroke. 


(SINGLE CYLINDER.) , 











1 2 3 4 6 6 is Salutes 
ado = 4 toe Of ee ee Poe ° aweas mete 
Mose jgea [28 12 |e 1 isse_l 22 |sssizecs 
sess_\iemr [ES la £16 £ aes| "ss gucses s 
core Cm eos ra aie Ss 2 S428 it Mot e!o 5 ot 
=Ores < x si. wn el nM os 5a SE Oo) Bra 
S$ -2S8/Ou% BI) peed NG Shy Sein EL red Tal, bn eet es se ies et neice 
mescesisol Hoste Ale a lwee4iF ss [pe °sls sare 

Sssels o| 2 & Sigeaus 2 [Pu oO TS, 
Ses Rie aS sis! & a ai-s¥slcaa se ules £2 
Beso see siocCl Ess | ees (SESS) SPS [got souks 
Sepseianmalsak| Fse | 55E Seer] Scn |Some|es2 so 

= © ta | 
< fr am < = ea 4 o Z, 

1 .0000 1100 1.000 1.000 1.000 58,273} / 34.0 9.05 . 

1.1 0953 | 90.3 .996 909 1.096 63,850} 31.0 4.45 

1.18 -1698 | 83.3 -986 847 1.164 67,836} 29.2 4.78 

1.23 -2070 | 80 980 813 1.206 70,246] 28.2 4.98 

1.3 2624 | 75.3 969 - 769 1.261 73,513] 26.9 5.26 

1.39 38293 | 70 953 2719 1.325 97,242] 25.6 5.63 

1.45 716 | 66.8 942 690 1.365 79,555] 24.9 5.87 

1.54 4317 | 62.5 925 649 1.425 83,055} 23.8 6.23 

1.6 .4700 | 59 9 913 625 1.461 Soviizol seduce 6.47 

aay 5595 | 54.1 883 orl 1.546 90,115} 22.0 7.08 

1.88 .6314 6 .860 532 1.616 94,200) 21.0 7.61 

2 .0931 | 46.5 . 836 1.672 97.432) 20.3 8.09 

2.28 8241 | 40 787 2439 1.793 | 104,466} 19.0 9.23 

2.4 8755 7.6 766 417 1.837 | 107,050} 18.5 9.71 

2.65 9745 | 33.3 2126 37 4s) ab eee 17.7 10.72 

2.9 1.065 29.9 692 2345 2.006 | 116,885} 16.9 11.74 

8.2 1.163 26.4 -652 2313 2.083 | 121,886} 16.3 12.95 

3.00 1.209 25 637 298 2.129 | 124,066} 16.0 13.56 

3.6 1.281 22.7 608 278 2.187 | 127,450} 15 14.57 

3.8 1.385 21.2 589 263 2.240 | 180,533] 15.2 15.38 

4 1.386 19.7 569 250 2.27 132.770} 14.9 16.19 

4.2 1.4385 18.5 551 238 2.315 ; 134.900} 14.7 17.00 

4.5 1.504 16.8 526 222 2.370 | 138,130] 14.34 18.21 

4.8 1.569 15.3 503 208 2.418 | 140,920) 14.05 19.43 

5 1.609 14.4 -488 -200 2.440 | 142,180} 13.92 20.23 

5.2 1.649 13.6 476 193 2.466 | 143,720) 13.7 21.04 

aya 1.705 12.5 457 182 2.511 | 146,825! 13.53 22.25 

5.8 1.758 11.4 438 172 2.547 | 148,390) 13.34 23.47 

5.9 ACs aw LB | 432 169 2.556 | 148,940) 13.29 23.87 

6.2 1.825 10.3 419 161 2.585 | 150,630) 13.14 25.09 

6.3 1.841 10 0413 159 2.597 | 151,370) 13.08 25.49 

6.6 1.887 9.2 398 2152 2.619 | 152,595) 12.98 26.7 

4 1.946 8.3 381 143 2.664 | 155,200) 12.7 28.33 

7.3 [1.988 hens .3809 0137 2.693 | 156,960} 12.61 29.54 

7.6 2.028 hea 357 132 2.711 | 157,975) 12.53 30.7 

7.8 2.054 6.7 348 128 2.719 | 158,414) 12.50 Slebt 

8 2.079 6.4 .342 «125 2.736 | 159,483! 11.83 82.38 


ASSUMPTIONS OF THE TABLE.—That the initial pressure is uniform; that 
the expansion is complete to the end of the stroke; that the pressure in ex- 
pansion varies inversely as the volume; that there is no back-pressure of 
exhaust or of compression, and that clearance is 7% of the stroke at each 
end of the cylinder. No allowance has been made for loss of steam by cyle 
inder-condensation or leakage, 


Volume of 1 Ib. of steam of 100 1bs, pressure per sq. in., or 14,400 
Ths Peed ftv. 0... CeeR eG cia yeber kes cocea cocuhsiee 4,00 Clune 
Product of initial pressure and VOlUME.....00,-ccocses: vecvqesesO2, 000 Lt,-lbg, 


748 THE STEAM-ENGINE. 


Though a uniform clearance of 7% at each end of the stroke has been 
assumed as an average proportion for the purpose of compiling the table, 
the clearance of cylinders with ordinary slides varies considerably—say 
from 5% to 10%. (With Corliss engines it is sometimes as low as 2%.) With 
the clearance, 7%, that has been assumed, the table gives approximate re- 
sults sufficient for most practical purposes, and more trustworthy than re- 
sults deduced by calculations based on simple tables of hyperbolic loga- 
rithms, where clearance is neglected. 

Weight of steam of 100 lbs. total initial pressure admitted for one stroke, 
per cubic foot of net capacity of the cylinder, in decimals of a pound = 
reciprocal of figures in column 9. 

Total actual work done by steam of 100 Ibs. total initial pressure in one 
stroke per cubie foot of net capacity of cylinder, in foot-pounds = figures 
in column 7% -- figures in column 9. 

Rute 1: To find the net capacity of cylinder for a given weight of steam 
admitted for one stroke, and a given actual ratio of expansion. (Column 9 
of table.)—Multiply the volume of 1 lb. of steam of the ziven pressure by the 
given weight in pounds, and by the actual ratio of expansion. Multiply the 
product by 100, and divide by 100 plus the percentage of clearance. The 
quotient is the net capacity of the cylinder. 

Rue 2: To find the net capacity of cylinder for the performance of a 
given amount of total actual work in one stroke, with a given initial press- 
‘ure and actual ratio of expansion.—Divide the given work by the total 
actual work done by 1 Ib. of steam of the same pressure, and with the same 
actual ratio of expansion; the quotient is the weight of steam necessary to 
do the given work, for which the net capacity is found by Rule 1 preceding. 

Notr.—1. Conversely, the weight of steam admitted per cubic foot of net 
capacity for one stroke is the reciprocal of the cylinder-capacity per pound 
of steam, as obtained by Rule 1. 

2. The total actual work done per cubic foot of net capacity for one stroke 
is the reciprocal of the cylinder-capacity per foot-pound of work done, ag 
obtained by Rule 2. 

3. The total actual work done per square inch of piston per foot of the 
stroke is 1/144th part of the work done per cubic foot. 

4. The resistance of back pressure of exhaust and of compression are to 
be added to the net work required to be done, to find the total actual work. 


APPENDIX TO ABOVE TABLE—MULTIPLIERS FOR NET CYLINDER-CAPACITY, AND 
TOTAL ACTUAL WORK DONE. 


(For steam of other pressures than 100 Ibs. per square inch.) 








Multipliers. Multipliers. 


Total Pres- | ror Col. 7. | For Col. 9. Total Pres: | For Col. 7. | For Col. 9. 
sures per (Total Work] Capacity § Sures fon Total Work Capeelyy 





square inch. | ‘py { lb. of of square by 1 lb. of O 
Steam. Cylinder. Steam. Cylinder. 
Ibs. lbs. 
5 975 1.50 100 1.00 
70 .981 1.40 110 917 
5 986 1.31 120 .843 
80 -988 1,24 18 (81 
85 .991 1.17 140 2730 
90 .995 1.11 150 683 
95 .998 1.05 160 644 








The figures in the second column of this table are derived by multiplying 
the total pressure per square foot of any given steam by the volume in 
cubic feet of 1 lb. of such steam, and dividing the product by 62,352, which 
is the product in foot-pounds for steam of 106 lbs. pressure. The quotient 
is the multiplier for the given pressure. 

The figures in the third column are the quotients of the figures in the 
pean column divided by the ratio of the pressure of the given steam to 100 

s. 

Measures tor Comparing the Duty of Engines.—Capacity is 
measured in horse-powers, expressed by the initials, H.P.: 1 H.P. = 83, 
ft.-lbs. per minute, = 550 ft.-lbs. per second, = 1,980,000 ft.-lbs. per hour. 


ie WORK OF STEAM IN A SINGLE CYLINDER. 749 


1 ft.-lb. = a pressure of 1 Ib. exerted through aspace of 1 ft. Economy is 
measured, 1,in pounds of coal per horse-power per hour; 2, in pounds of 
steam per horse-power per hour. The second of these measures is the more 
accurate and scientific, since the engine uses steam and not coal, and it is 
indepndent of the economy of the boiler. 

In gas-engine tests the common measure is the number of cubic feet 
of gas (measured at atmospheric pressure) per horse-power, but as all gas 
is not of the same quality, it is necessary for comparison of tests to give the 
analysis of the gas. When the gas for one engine is made in one gas-pro- 
ducer, then the number of pounds of coal used in the producer per hour per 
horse-power of the engine is the proper measure of economy. 

Economy, or duty of an engine, is also measured in the number of foot- 
pounds of work done per pound of fuel. As 1 horse-power is equal to 1,980, 
000 ft.-lbs. of work in an hour, a duty of 1 lb. of coal per H.P. per hour 
would be equal to 1,980,000 ft.-lbs. per lb. of fuel; 2 lbs. per H.P. per hour 
equals 990,000 ft.-lbs. per lb. of fuel, ete. 

The duty of pumping-engines is commonly expressed by the number of 
foot-pounds of work done per 100 lbs, of coal. 

When the duty of a pumping-engine is thus given, the equivalent number 
of pounds of fuel consumed per horse-power per hour is found by dividing 
198 by the number of millions of foot-pounds of duty. Thus a pumping: 
engine giving a duty of 99 millions is equivalent to 198/99 = 2 lbs. of fuel pex 
horse-power per hour. 

Efficiency Measured in Thermal Units per Minute.— 
Some writers express the efficiency of an engine in terms of the number of 
thermal units used by the engine per minute for each indicated horse-power, 
instead of by the number of pounds of steam used per hour. 

The heat chargeable to an engine per pound of steam is the difference be- 
tween the total heat in a pound of steam at the boiler-pressure and that in 
a pound of the feed-water entering the boiler. In the case of condensing 
engines, suppose we have a temperature in the hot-well of 101° F., corre- 
sponding to a vacuum of 28 in. of mercury, or an absolute pressure of 1 Ib. 
per sq. in. above a perfect vacuum: we may feed the water into the boiler 
at that temperature. In thecase of a non-condensing-engine, by using a por- 
tion of the exhaust steam in a good feed-water heater, at a pressure a trifle 
above the atmosphere (due to the resistance of the exhaust passages 
through the heater), we may obtain feed-water at 212°. One pound of steam 
used by the engine then would be equivalent to thermal units as follows: 


Pressure of steam by gauge: 
50 75 100 125 150 175 200 


Total heat in steam above 82° : 
1172.8 1179.6 1185.0 1189.5 1198.5 1197.0 1200.2 


Subtracting 69.1 and 180.9 heat-units, respectively, the heat above 32° in 
feed-water of 101° and 212° F., we have— 


Heat given by boiler: 
Feed at 101°...... 10337 1110.5 111559 1120.4 1124.4 1127.9 1131.1 
Heed ati2is°...... 991.9 998.7 1004.1 1008.6 1012.6 1016.1 1019.3 


Thermal units per minute used by an engine for each pound of steam used 
per indicated horse-power per hour : 
Feed at 101°...... 18.40 18.51 18 GON ele Of 218.74 18.80 18.85 
Weed at-o}2°. 28s. 2 01655505 2166p 2916074 416. Si 16.88 16.94 16.99 


EXAMPLES.—A triple-expansion engine, condensing, with steam at 175 Ibs., 
gauge and vacuum 28 in., uses 13 lbs. of water perI.H.P. per hour, and a 
high-speed non-condensing engine, with steam at 100 lbs. gauge, uses 30 
Ibs. How many thermal units per minute does each consume ? 

Ans.—18 X 18.80 = 244.4, and 80 x 16.74 = 502.2 thermal units per minute. 

A perfect engine converting all the heat-energy of the steam into work 
would require 83,000 ft.-lbs. + 778 = 42.4164 thermal units per minute per 
indicated horse-power. This figure, 42.4164, therefcre, divided by the num- 
ber of thermal units per minute per I.H.P. consumed by an engine, gives its 
efficiency as compared with an ideally perfect engine. In the examples 
above, 42.4164 divided by 244.4 and by 502.2 gives 17.35% and 8.45% efficiency, 
respectively. > : 

Total Work Done by One Pound of Steam Expanded in 
a Single Cylinder. (Column 7 of table.)—If 1 pound of water be con- 
verted into steam of atmospheric pressure = 2116.8 lbs. per sq. ft., it occu: 
pies a volume equal to 26.86 cu, ft. The work done is equal to 2116.8 lbs, 


¥ 


750 THE STEAM-ENGINE. 


K 26.36 ft. = 55,788 ft.-Ibs. The heat equivalent of this work is (55,788 +- 778 
=)71.7 units. This is the work of 1 lb. of steam of one atmosphere acting 
on a piston without expansion. 

The gross work thus done on a piston by 1 lb. of steam generated at total 
pressures varying from 15 Ibs, to 100 lbs. per sq. in. varies in round numbers 
from 56,000 to 62,000 ft.-lbs., equivalent to from 72 to 80 units of heat. 

This work of 1 lb. of steam without expansion is reduced by clearance 
according to the proportion it bears to the net capacity of the cylinder. If 
the clearance be %% of the stroke, the work of a given weight of steam with- 
out expansion, admitted for the whole of the stroke, is reduced in the ratio 
of 107 to 100. 

Having determined by this ratio the quantity of work of 1 lb. of steam with. 
out expansion, as reduced by clearance, the work of the same weight of steam 
for various ratios of expansion may be found by multiplying it by the relative 
performance of equal weights of steam, given in the 6th column of the table. 

Quantity of Steam Consumed per Horse-power of Total 
Work per Hour. (Column 8 of table.)—The ‘measure of a horse-power 
is the performance of 33.000 ft.-lbs. per minute, or 1,980,000 ft.-lbs. per hour. 
This work, divided by ‘the work of 1 lb of steam, gives the weight of steam 
required per horse-power per hour. For example, the total actual work 
done in the cylinder by 1 1b. of 100 lbs. steam, without expansion and with 
7% of clearance, is 58,273 ft.-lbs.; and a = 34 lbs. of steam, is the weight 
of steam consumed for the total work done in the cylinder per horse-power 
per hour, For avy shorter period of admission with expansion the weight 
of steam per horse-power is less, as the total work of 1 lb. of steam is more, 
and may be found by dividing 1,980,000 ft.-lbs. by the respective total work 


done; or by dividing 34 lbs. by the ratio of performance, column 6 in the 
table. 





ACTUAL EXPANSIONS, 
With Different Clearances and Cut-offs, 
Computed by A. F. Nagle. 


Per Cent of Clearance. 











Cut- eee 
off. 
0 1 2 3 4 5 6 q 8 9 10 

.01 |100.00| 50.5 |34.0 (25.75 |20.8 {17.5 |15.14 113.88 |12.00 |10.9 /10 
.02 | 50.00] 83.67/25.50 120.60 117.38 115.00 }18.25 |11.89 |10.80 | 9.91 | 9.17 
.03 | 33.33) 25.25)20.40 |17.16 |14.86 |18.12 |11.78 |10.70 | 9.82 | 9.08 | 8.46 
.04 | 25.00) 20.20)17.00 14.71 [18.00 11.66 |10.60 | 9.73 | 9.00 | 8.89 | 7.86 
105 | 20.00) 16.83)14.57 |12.87 |11.55 |10.50 | 9.64 |} 8.92 | 8.381 | 7.79 | 7.33 
.06 | 16.67) 14.43)12.75 |11.44 |10.40 | 9.55 | 8.88 | 8.23 | 7.71 | 7.27 | 6.88 
.O7 | 14.28} 12.62/11.383 |10.30 | 9.46 | 8.75 | 8.15 | 7.64 | 7.20-] 6.81 | 6.47 
.08 | 12.50} 11.22])10.2 9.36 | 8.67 | 8.08 | 7.57 | 7.18 | 6.75 | 6.41 | 6.11 
2098) 1121110210) 9:27 | 8.58 | 8.00 1 7.50 17.07 | 6.69 196.85 196.06 ebro 
.10 | 10.00} 9.18] 8.50 | 7.92 | 7.43 | 7.00 | 6.62 | 6.30 | 6.00 | 5.74 | 5.50 
Baily 9.09} 8.42) 7.84 | 7.36 | 6.93 | 6.56 | 6.24 | 5.94 | 5.68 | 5.45 | 5.24 
.12 | 8.33} 7.78! 7.29 | 6.86 | 6.50 | 6.1 5.89 | 5.63 | 5.40 |] 5.19 | 5.00 
14 7.141 6.73] 6.87 | 6.06 | 5.78 | 5.53 | 5.30 | 5.10 | 4.91 | 4.74 | 4.58 
16) 6.25) 5.94) 5.67 | 5.42 | 5.20 | 5.00 | 4.82 | 4.65 | 4.50 | 4.36 | 4 23 
.20 | 5.00) 4.81) 4.64 | 4.48 | 4.33 | 4.20 | 4.u8 | 3.96 | 3.86 | 3.76 | 3.67 
BD, 4,00| oa. 88iteed0 36.68: | 8.58 | 3.50 | 8.42 198284] Sieg7aiesiet | aaa 
.30 3.05| ‘oe2Olenlomvacte | 8.06] 8.00 12.94 | 2:90" B84 182 80 eea 
.40 2,'50|— 2246/e28430 (e240 | 2.36 | 2.88)] 2.30)]' 2.281 Seb) 25222280 
50 2.00) 1.98} 1.96 | 1.94 | 1.92 | 1.90 | 1.89 | 1.88 | 1.86 | 1.85 | 1.83 
60 1.67) 1.66) 1.65 | 1.64 | 1.63 | 1.615] 1.606] 1.597] 1.588] 1.580) 1.571 
ai 1.43] 1:42] 1.42 | 1.41 | 1.41 | 1.400] 1.395) 1.890) 1.885) 1.880] 1.3875 
80 1525) 1.25) 12244)°12241) 1.238) 1.285) 1.233) 1.2380}.1.227| 1.224) 7.228 
.90 | 1.111] 1.11] 1.109) 1.108) 1.106) 1.105} 1.104] 1.103} 1.102} 1.101] 1.100 

1.00 | yal 1.00} 1.000} 1.000] 1.000) 1.000} 1.000) 1.000} 1.000} 1.000) 1.000 











WORK OF STEAM IN A SINGLE CYLINDER. HOY 


Relative Efficiency of 1 Ib. of Steam with and without 
Clearance; back pressure and ccmpression not considered. 


P(i+ c) + Pii+c) hyp. log. R ~ Pe 


Mean total pressure = p= = 


Let P= 13 7 = 1003 Use 25: om 7. 


107 
; 10r _ 
oe TT Ee 
p= 100 z, 1” a 


If the clearance be added to the stroke, so that clearance becomes zero, 
the same quantity of steam being used, admission Z being then =1+c= 
32, and stroke L+c= 10%. 


632, 


107 
San 82 hyp. log5- = © . 'g9 4. 's2 5¢ 1.209 
P= 107 ee a ee 





= 707. 


That is, if the clearance be reduced to 0, the amount of the clearance 7 
being added to both the admission and the stroke, the same quantity of 
steam will do more work than when the clearance is 7% in the ratio 707 : 637, 
or 11% more. 

Back Pressure Considered.—If back pressure = .10 of P, this 
amount has to be subtracted from p and p, giving p = .537, p, = .607, the 
work of a given quantity of steam used without clearance being greater 
than when clearance is 7 per cent in the ratio of 607 : 587, or 13% more. 

Effect of Compression.—By early closure of the exhaust, so thata 
portion of the exhaust-steam is compressed into the clearance-space, much 
of the loss due to clearance may be avoided. If expansion is continued 
down to the back pressure, if the back pressure is uniform throughout the 
exhaust-stroke, and if compression begins at such point that the exhaust- 
steam remaining in the cylinder is compressed to the initial pressure at the 
end of the back stroke, then the work of compression of the exhaust- steam 
equals the work done during expansion by the clearance-steam. The clear- 
ance-space being filled by the exhaust-steam thus compressed, no new steam 
is required to fill the clearance-space for the next forward stroke, and the 
work and efficiency of the steam used in the cylinder are just the same as if 
there were no clearance and no compression. When, however, there is a 
drop in pressure from the final pressure of the expansion, or the terminal 
pressure, to the exhaust or back pressure (the usual case), the work of com- 
pression to the initial pressure is greater than the work done by the expan- 
sion of the clearance-steam, so that a loss of efficiency results. In this 
case a greater efficiency can be attained by inclosing for compression a less 
quantity of steam than that needed to fill the clearance-space with steam of 
the initial pressure. (See Clark, S. E., p. 399, et seg.; also F. H. Ball, Trans. 
A.S. M. E., xiv. 1067.) It is shown by Clark that a somewhat greater effi- 
ciency is thus attained whether or not the pressure of the steam be carried 
down by expansion to the back exhaust-pressure. As a result of calcula- 
tions to determine the most efficient periods of compression for various 
percentages of back pressure, and for various periods of admission, he gives 
the table on the next page: 

Clearance in Low-and High-speed Engines. (Harris 
Tabor, Am. Mach., Sept. 17, 1891.)\—The construction of the high-speed 
engine is such, with its relatively short stroke, that the clearance must be 
much larger than in the releasing-valve type. The short-stroke engine is, ' 
of necessity, an engine with large clearance, which is aggravated when a 
variable compression is a feature. Conversely, the releasing-valve gear is, 
from necessity, an engine of slow rotative speed, where great power is 
obtainable from long stroke, and small clearance is a feature in its construc. 
tion. In one case the clearance will vary from 8% to 12% of the piston-dis- 
placement, and in the other from 2% to 3%. In the case of an engin? with a 
clearance equalling 10% of the piston-displacement the waste room becomes 
enormous when considered in connection with an early cut-off. The system of 
compounding reduces the waste due to clearance in proportion as the steam 
is expanded to a lower pressure. The farther expansion is carried through 
a train of cylinders the greater will be the reduction of waste due to clear- 
ance. This is shown from the fact that the high-speed engine, expanding 


752 THE STEAM-ENGINE. 


steam much less than the Corliss, will show a greater gain when changed 
from simple to compound than its rival under similar conditions, 


COMPRESSION OF STEAM IN THE CYLINDER. 
Best Periods of Compression; Clearance 7 per cent. 





Total Back Pressure, in percentages of the total initial pressure. 
Cut-off in 

















Percent- 
ages of 244 5 10 | 15 20 25 | 80 | 35 
the 
Stroke 
Periods of Compression, in parts of the stroke. 
10% 65% 57% 44% bys Oe Raed rea aes aosollccuyc sac 
ils 58 52 40 29 QB Gils F5s eke Een chaste ® | steiale seer 
20 52 47 37 27 Dea (Seance ear Acca lletacesa3 2 
25 47 42 34 26 21 L7Ge- | eee pete hea eines 
30 42 39 32 25 20 16 14% 12% 
35 39 35 29 23 19 15 13 11 
40 36 32 7 21 18 14 13 11 
45 383 30 25 20 17 14 12 10 
50 30 27 23 18 16 13 12 10 
55 27 24 21 17 15 13 11 9 
60 24 22 19 15 14 12 11 9 
65 22 20 17 15 14 12 10 8 
70 19 17 16 14 14 12 10 8 
75 17 16 14 13 12 11 9 8 


Notrrs To TaBue.—1. For periods of admission, or percentages of back 
pressure, other than those given, the periods of compression may be readily 
found by interpolation. 

2. For any other clearance, the values of the tabulated periods of com- 
pression are to be altered in the ratio of 7 to the given percentage of 
clearance. 

Cylinder-condensation may have considerable effeet upon the best point 
of compression, but it has not yet (1893) been determined by experiment. 
(Trans. A. S. M. E., xiv. 1078.) 

Cylinder-condensation.—Rankine, S. E., p. 421, says: Conduction 
of heat to and from the metal of the cylinder, or to and from liquid water 
contained in the cylinder, has the effect of lowering the pressure at the be- 
ginning and raising it at the end of the stroke, the lowering effect being on 
the whole greater than the raising effect. In some experiments the quantity’ 
of steam wasted through alternate liquefaction and evaporation in the 
eee: has been found to be greater than the quantity which performed 
the work. 


Pereentage of Loss by Cylinder-condensation, taken at 


Cut-off, (From circular of the Ashcroft Mfg. Co. on the Tabor 
Indicator, 1889.) 


Percent. of Feed-water accounted|Percent. of Feed-water Consump-< 





so) 
o 
Gi yo. 
oe Hi for by the Indicator diagram. | tion due to Cylinder-condensat’n. 
ome) 
vee | pone Obs. he a 
RQ 55 Triple-ex- Triple-ex- 
22 2 | Simple eres” pansion | Simple me) pee pansion 
oO” | Engines. hp eyl. Engines, | Engines. h e. eyl » | Engines, 
eae eee hip, éyit BeSd* | hip. eyl. 
5 ee ae 43 533) BEDS. here dase, 
10 66 (Co ae een 34 SOT OP ts Jee 
15 71 76 ft 2 24 22 
20 74 78 80 26 22 20 
30 78 82 84 22 18 16 
40 82 85 7 18 15 13 
50 86 88 90 14 12 10 








WORK OF STEAM IN A SINGLE CYLINDER, 793 


Theoretical Compared with Actual Water=-consump= 
tion, Simele-cylinder Automatic Cut-off Engines, (From 
the catalogue of the Buckeye Engine Co.)—The following table has been 
prepared on the basis of the pressures that result in practice with a con- 
stant boiler-pressure of 80 lbs. and different points of cut-off, with Buckeye 
engines and others with similar clearance. Fractions are omitted, except 
in the percentage column, as the degree of accuracy their use would seem 
to imply is not attained or aimed at. 








CORY 78 2 
Mean Total ate, : 
tea la Effective | Terminal | lbs. 7 eS 

Pressure. | Pressure. | Per 0.0.0. Act’l Rate.| Per ct. Loss.‘ 





per hour. 

10 18 11 20 382 58 
15 27 15 19 27 41 
20 35 20 .19 25 31.5 

25 42 25 20 25 25 

.30 48 380 2 24 21.8 

35 53 385 21 25 19 

.40 57 38 22 26 16.7 

45 61 43 23 27 15 
50 64 48 24 27 13.6 


2 


It will be seen that while the best indicated economy is when the cut-off 
is about at .15 or .20 of the stroke, giving about 30 lbs. M.H.P., and a termi- 
nal 3 or 4 lbs. above atmosphere, when we come to add the percentages due 
to 2 constant amount of unindicated loss, as per sixth column, the most eco- 
nomical point of cut-off is found to be about .30 of the stroke, giving 48 lbs. 
M.E.P. and 30 lbs. terminal pressure. This showing agrees substantially 
vith modern experience under automatic cut-off regulation. 

Experiments on Cylinder-condensatiomn.—Experiments by 
Major Thos. English (fig’g, Oct. 7, 1887, p. 386) with an engine 10 X 14 in., 
jacketed in the sides but not on the ends, indicate that the net initial con- 
densation (or excess of condensation over re-evaporation) by the clearance 
surface varies directly as the initial density of the steam, and inversely as 
the square root of the number of revolutions per unit of time. The mean 
results gave for the net initial condensation by clearance-space per sq. ft. of 
surface at one rev. per second 6.06 thermal units in the engine when run 
non-condensing and 5.75 units when condensing. 

G. R. Bodmer (Hg’g, March 4, 1892, p. 299) says: Within the ordinary 
limits of expansion desirable in one cylinder the expansion ratio has prac- 
tically no infinence on the amount of condensation per stroke, which for 
simple engines can be expressed by the following formula for the weight 
of water condensed [per minute, probably; the original does not state]: 

S(T— t) 
W= OL ix where 7 denotes the mean admission temperature, ¢ the 
mean exhaust temperature, S clearance-surface (square feet), NV the num. 
ber of revolutions per second, ZL latent heat of steam at the mean admission 
temperature, and Ca constant for any given type of engine: 

Mr. Bodmer found from experimental data that for high-pressure non- 
jacketed engines C = about 011, for condensing non-jacketed engines 0.085 
to 0.11, for condensing jacketed engines 0.085 to 0,053. The figures for jack- 
eted engines apply to those jacketed in the usual way, and not at the ends. 

C varies for different engines of the same class, but is practically con- 
stant for any given engine. For simple high-pressure non-jacketed engines 
it was found to range from 0.1 to 0.112. 

Applying Mr. Bodmer’s formula to the case of a Corliss non-jacketed non- 
condensing engine, 4-ft. stroke, 24 in. diam , 60 revs. per min., initial pres- 
sure 90 lbs. gauge, exhaust pressure 2 lbs., we have 7 — ¢ = 112°, N=1, 
L= 880, S=7sq. ft.; and, a a C= .112 and W = lbs. water condensed 
ee = .09 1b. per minute, or 5.4 lbs. per hour. If 
the steam used per I.H.P. per hour according to the diagram is 20 lbs., the 
pean ye consumption is 25.4 lbs., corresponding to a cylinder condensa< 
tian o : 


per minute, W = 


754 THE STEAM-ENGINE. 


INDICATOR-DIAGRAM OF A SINGLE-CYLINDER 
ENGINE 


Definitions.,—The Atmospheric Line, AB, is a line drawn by the pencil 
of the indicator when the connections with the engine are closed and both 
sides of the piston are open to the atmosphere. 


K 





Fia. 138. 


The Vacuun Line, OX, is a reference line usually drawn about 14 7/10 
pounds by scale below the atmospheric line. 

The Clearance Line, OY, is a reference line drawn at a distance from the 
end of the diagram equal to the same percent of its length as the clearance 
and waste room is of the piston-displacement, 

The Line of Boiler-pressure, JK, is drawn parallel to the atmospheric 
line, and at a distance trom it by scale equal to the boiler-pressure shown 
by the gauge. 

The Admission Line, CD, shows the rise of pressure due to the admission 
of steam to the cylinder by opening the steam-valve. 

The Steam Line, DE, is drawn when the steam-valve is open and steam is 
being admitted to the cylinder. 

The Point of Cut-off, HL, is the point where the admission of steam is 
stopped by the closing of the valve. It is often difficult to determine the 
exact point at which the cut-off takes place. It is usually located where the 
outline of the diagram changes its curvature from convex to concave. 

The Expansion Curve, EF’, shows the fallin pressure as the steam in the 
cylinder expands doing work. 

The Point of Release, F, shows when the exhaust-valve opens. 

The Exhaust Line, FG, represents the change in pressure that takes 
place when the exhaust-valve opens. 

The Back-pressure Line, GH, shows the pressure against which the piston 
acts during its return stroke. 

The Point of Exhaust Closure, H, is the point where the exhaust-valve 
closes. It cannot be located definitely, as the change in pressure is at first 
due to the gradual closing of the valve. 

The Compression Curve, HC, shows the rise in pressure due to the com- 
haga of the steam remaining in the cylinder after the exhaust-valve has 
closed. 

The Mean Height of the Diagram equals its area divided by its length. 

The Mean Effective Pressure is the mean net pressure urging the piston 
forward = the mean height x the scale of the indicator-spring. 

To find the Mean Effective Pressure from the Diayram.—Divide the 
length, LB, into a number, say 10, equal parts, setting off half a part at L, 
half a part at B, and nine other parts between; erect ordinates perpendicu- 
lar to the atmospheric line at the points of division of LB, cutting the dia- 
gram; add together the lengths of these ordinates intercepted between the 
upper aud lower Jines of the diagram and divide by their number. This 


> Sate 


INDICATED HORSE-POWER OF ENGINES. "55 


gives the mean height, which multiplied by the scale of the indicator-spring 
gives the M.E.P. Or find the area by a planimeter, or other means (see 
Mensuration, p. 55), and divide by the length LB to obtain the mean height. 

The Initial Pressure is the pressure acting on the piston at the beginning 
of the stroke. 

The Terminal Pressure is the pressure above the line of perfect vacuum 
that would exist at the end of the stroke if the steam had not been released 
earlier. It is found by continuing the expansion-curve to the end of the 
diagram, 


INDICATED HORSE-POWER OF ENGINES, SINGLE= 
CYLINDER. y 


F PLan 
n se- . Se 
Indicated Horse-power I.H.P 33,000" 
in which P = mean effective pressure in lbs. per sq. in.; IZ = length of stroke 
in feet; a= area of piston in squareinches. For accuracy, one half of the 
sectional area of the piston-rod must be subtracted from the area of the 
piston if the rod passes through one head, or the whole area of the rod if it 
passes through both heads; 2. = No. of single strokes per min. = 2 X No, of 
revolutions. 


PaS 


LS Be Bh ee 33.000" in which S= piston speed in feet per minute, 


PLd?n Pd?S 


= -—— > = ——_ = 221 2 2 
LH.P. 42,017 22.017 .0000238 PLd?n = .0000238Pd28, 
in which d=diam. of cyl. in inches. (The figures 238 are exact, since 
7854 + 33 = 23.8 exactly.) If product of piston-speed * mean effective 
pressure = 42,017, then the horse-power would equal the square of the 
diameter in inches. 

Handy Rule for Estimating the Horse-power ot a 
Single-cylinder Engime.—Square the diameter and diviae by 2. Thisis 
correct Whenever the product of the mean effective pressure and the piston- 
speed = 4% of 42,017, or, say, 21,000, viz., when M.E.P. = 30 and S= 700; 
when M.E.P. =35 and S= 600; when M.E.P. = 38.2 and S = 550; and when 
M.E.P. = 42 and S= 500. These conditions correspond to those of ordinary 
practice with both Corliss engines and shaft-governor high-speed engines. 

Given Wiorse-power, Miean Effective Pressure, and 
Piston-speed, to find Size of Cylinder,— 


__ 38,000 x I.H.P. Her TP. 
Area = ema se owe Diameter = 205, “pg (Exact.) 


Brake Horse-power is the actual horse-power of the engine as 
measured at the tly-wheel by a friction-brake or dynamometer. It is the 
indicated horse-vower minus the friction of the engine. 

Table for Roughiy Approximating the Horse-power of 
a Compound Engine from the Diameter of its Low= 
pressure Cylinder,.—Jhe indicated horse-power of an engine being 
Psd? 
42,017’ 
ft. per min., and d = diam. of cylinder in inches; if s = 600 ft. per min., 
which is approximately the speed of modern stationary engines, and P = 35 
lbs., which is an approximately average figure for the M.E.P. of single- 
cylinder engines, and of compound engines referred to the low-pressure 
cylinder, then I.H.P. = 44d?; hence the rough-and-ready rule for horse-power 
given above: Square the diameter in inches and divide by 2. This applies to 
triple and quadruple expansion engines as well as to single cylinder and 
compound. For most economical loading, the M.E P. referred to the low- 
pressure cylinder of compound engines is usually not greater than that of 
simple engines; for the greater economy is obtained by a greater number of 
expansions of steam of higher pressures, and the greater the number of 
expansions for a given initial pressure the lower the mean effective pressure. 
The following table gives approximately the figures of mean total and effec- 


in which P = mean effective pressure per sq. in., s = piston-speed in 


756 THE STEAM-ENGINE. 


tive pressures for the different types of engines, together with the factor by 
which the square of the diameter is to be multiplied to obtain the horse- 
power at most economical loading, for a piston-speed of 600 ft. per minute. 


























4g w f=} | # -w : D 5 
Zes|8, |-8-l€o Sl8e [Seeigge) ee) ux 
xy ~ rs ~ = . += a 
Type of Engine. Sine 98 ESA EaS ale B Oe cA | sel, oo 
ORs ag sa VpoSs sick! Ia salaod|S9 ieee 
BEPlEk sols ogklae ¥iSreiasFiSerziros 
Non-condensing. 
Single Cylinder.| 100) 5. 20 522 52.2 { 15.5 | 36.7 600 524 
Compound...... 120} 7.5 | 16 402 EAS e 2 lop ioeal “ 467 
"Driplenstes tai sias 160 | 10. 16 .330 52:8) 1 15.51 38733 ef .533 
Quadruple...... 200 | 12.5 16 | .282 | 56.4:] 15.5 | 40.9 of 584 
Condensing Engines. 
Single Cylinder.| 100 | 10. 10 -830 33.0 2 81.0 600 | .443 
Compound......| 120} 15. 8 247 29.6 2 | 27.6 A .390 
Triple... 96a. 160 | 20 8 200 | 32.0 2 | 30.0 a .429 
Quadruple...... 200 | 25 8 .169 | 33.8 2) Olas Saad 








For any other piston-speed than 600 ft. per min., multiply the figures in 
the last column by the ratio of the piston-speed to 600 ft. 


Nominal Horse-power.—The term ‘“‘ nominal horse-power” origi- 
nated in the time of Watt, and was used to express approximately the power 
of an engine as calculated from its diameter, estimating the mean pressure 
in the cylinder at 7 lbs. above the atmosphere. It has long been obsolete in 
America, and is nearly obsolete in England. 

Horse-power Constant of a given Engine for a Fixed 
Speed = product of its area of piston in square inches, length of stroke in 

Lan 
33,000 
= C. The product of the mean effective pressure as found by the diagram 
and this constant is the indicated horse-power. 

Horse-power Constant of a given Engine for Varying 
Speeds = product of its area of piston and length of stroke divided by 
33,000. This multiplied by the mean effective pressure and by the number 
of single strokes per minute is the indicated horse-power. 

Horse-power Constant of any Engine of a given Diam= 

eter of Cylinder, whatever the length of stroke = area of piston + 33,000 
= square of the dianieter of piston in inches X .0000238. A table of constants 
derived from this formula is given below. 

- ‘he constant multiplied by the piston-speed in feet per minute and by 

' the M.E.P. gives the I.H.P. 

Errors of Indicators,—The most common error is that of the spring, 
which may vary from its normal rating; the error may be determined by 
proper testing apparatus and allowed for. But after making this correction, 
even with the best work, the results are liable to variable errors which may 
amount to 2 or 3 per cent. See Barrus, Trans. A. S. M. E., v. 310; Denton, 
A. 8. M. E., xi, 829; David Smith, U. 8S. N., Proc. Eng’g Congress, 1893, 
Marine Division. 

Indicator “ Rigs,’? or Reducing-motions ; Interpretation of Diagrams for 
Errors of Steam-distribution, etc. For these see circulars of manufacturers 
of Indicators; also works on the Indicator. 

Table of Engine Constants for Use in Figuring Horse= 
power.—‘: Horse-power constant” for cylinders from 1 inch to 60 inches in 
diameter, advancing by 8ths, for one foot of piston-speed per minute and one 
pound of M.E.P. Find the diameter of the cylinder in the column at the 
side. If the diameter contains no fraction the constant will be found in the 
column headed Even Inches. If the diameter is not in even inches, follow 
the line horizontally to the column corresponding to the required fraction, 





feet, and number of single strokes per minute divided by 33,000, or 


The constants multiplied by the piston-speed and 


INDICATED HORSE-POWER OF ENGINES. 


horse-power. 


Diameter 


oO 
Cylinder. 


6 +2 Or. Cow 


Even 
Inches. 


0000238 
0000952 
0002142 
-0003808 
0005950 
0008568 
:0011662 
0015282 
0019278 
“0023800 
0028798 
0084272 
0040222 
0046648 
0053550 
0060928 
.0068782 
0077112 
-0085918 
-0095200 
0104958 
“0115192 
0125902 
0137088 
-0148750 
.0160888 
0173502 
“0186592 
0200158 
0214200 
0228718 
0243712 
0259182 
0275128 
0291550 
“0308448 
0325822 
.0343672 
"0361998 
:0380800 
:0400078 
.0419832 
0440062 
:0460768 
0481950 
"0503608 
"0525742 
0548352 
0571438 
0595000 
0619038 
10643552 
0668542 
.0694008 
0719950 
.0746368 
0773262 
.0800632 
0828478 
0856800 





+% 
or 
125. 


.0000301 


.0001074 
0002324 
.0004050 
0006251 
0008929 
.0012082 
.0015711 
0019817 
0024398 
0029456 


.0034990 
.0040999 
.0047484 


0054446 
.0061884 
0069797 


0078187 


.0087052 
.0096393 
.0106211 
0116505 
0127274 
.0138519 
.0150241 





0162439 


0175112 
0188262 
0201887 


.0215988) . 
0232422 
0247535 
0263124) , 
0279189 
0295729 
0312747 
.0330239 
0348209 
0366654 
0385575 
.0404972 
0424845 
.0445194 
.0466019 
0487320 
.0509097 
0531349 
0554079 
0577284 
.0600965 
0625122 
.0649753 
0674864 
.0700449 
.0726510 
0753047 
.0780060 
0807549 
0835514. 
-0863955 | 


0230566 
.0245619 
0261149 
0277155 
0293636 


0310594! 


0328027 
0345937 
0364322 
0383184 
0402521 
0422335 
0442624 
0463389 
0484631 
0506349 
0528542 
.0551212 
0574357 
.0597979 
.0622076 
.0646649 
0671699 
0697225 
0724226 
0749704 
0776657 
.0804087 
.0831992 
0860374 





ae 
or 
25, 


0000372 
.0001205 
.0002514 
0004299 
. 0006560 
0009297 
.0012510 
.0016198 
0020363 
.0025004 
0030121 
0035714 
.0041783 
.0048328 
0055349 
.0062847 
.0070819 
.0079268 
.0088193 
0097594 
.0107472 
0117825 
.0128654 
.0139959 
.0151789 
.0163997 
.0176729| 
.0189939 
0203674) . 
0219588 
0234285 
0249457 


217785 





+56 
or 
375. 





-0000450 
.0001342 
0002711 
. 0004554 
0006876 
.0009672 
.0012944 
.0016693 
.0020916 
.0025618 


0030794 
0036447 
0042576 
.0049181 
. 0056261 
.0063817 
.0071850 
.0080360 
. 0089343 
.0098803 
.0108739 
.0119152 
.0130040 
.0141405 
.0153246 
-0165563 
-0178355 
0191624 


205368 


265106 


0281231 
.0297831 
. 0314908 
0332460 
.0350489 
.0368993 
0387973 
0407430 
0427362 
0447771 
0468655 





.0490016 
0511853 
0534165 
.0556953 
-0580218 
-0603959 


0628175 
.0652867 
.0678036 
.0703681 
0729801 
0756398 
0783476 
.0811019 
0839043 





0867543 


+h 
or 


-0000535 
-0001487 
.0002915 
.0004819 
.0007199 
-0010055 
0013387 
0017195 
0021479 
.0026239 
.0031475 
.0037187 
0043375 
-0050039 
0057179 
.0064795 
.0072887 
0081452 
.0090499 
-0100019 
-0110015 
0120487 
.0131435 
.0142859 
0154759 
.0167135 
.0179988 
-0193316 
-C207119 
0221399 
-0236155 
0251387 
-0267095 
0283279 
0299939 
0317075 
- 0334687 
0352775 
-0371339 
0390379 
.0409895 
0429887 
.0450355 
0471299 
-0492719 
0514615 
. 0536988 
-0559835 
-0583159 
.0606959 
0632235 
0655987 
0681215 
-0705293 
0733099 
0759755 
0786887 
.0814495 











0842579 
08711389 


0874743 


W5T 


by the M.E.P. give the 


.0000628 
.0001640 
.0003127 
.0005091 
.0007530 
.0010445 
0013837 
.0017705 
.0022048 
.0026867 
.0032163 
. 0037934 
.0044182 
.0050906 
.0058105 
.0065780 
.0073932 
. 0082560 
.0091663 
.0101243 
.0111299 
.0121830 
0182837 
-9144321 
.0156280 
.0168716 
.0181627 
.0195015 
.0208879 
.0223218 
0238033 
0253325 
.0269092 
0285336 
. 0302056 
.0319251 
. 0836922 
. 0355070 
.0373694 
.0392793 
0412368 
.0432420 
0452947 
.0473951 
.0495430 
.0517886 
.0539818 
. 0562725 
.0586109 
.0609969 
0634304 
.0659115 
.0684402 
.0710166 
.0736406 
.0763120 
.0790312). 
.0817980 
.0846123 





0821472 
0849675 





0878354 


0000729 
.0001800 
0003347 
0005370 
.0007869 
.0010844 
.0014295 
0018222 
0022625 
-0027502 
0032859 
.0038690 
0044997 
.0051780 
.0059039 
0066774 
-0074985 
0083672 
-0092835 
.0102474 
.0112589 
0123179 
0134247 
.0145789 
-0157809 
0170304 
.0183275 
.0196722 
0210645 
0225044 
0289919 
0255269 
-0271097 
0287399 
.0804179 
0821434 
0339165 
0357372 
0876055 
0395214 
.0414849 
0434959 
0455547 
-0476609 
.0498149 
.0520164 
.0542655 
0565622 
0589065 
.0612984 
06373879 
.0662250 
.0687597 
.0713419 
0739719 
-0766494 


793745 











.0000837 


0001967 


00038574 
.0005656 
0008215 
.0011249 
0014759 
.0018746 
00238209 
-0028147 
0033561 
0039452 
.0045819 
-0052661 
.0059979 
0067774 
0076044 
.00847'91 
.0094013 
.0103712 
.0113886 
0124537 
0185664 
0147266 
.0159845 
.0171899 
.0184929 
.0198436 
.0212418 
0226877 
0241812 
0257222 
0273109 
0289471 
0306309 
0323624 
.0341415 
0359681 
0378424 
0897642 
0417337 
0437507 
.0458154 
0479276 
. 0500875 
.U522949 
.0545499 
0568526 
0592029 
0616007 
.0640462 
0665392 
.0690799 
0716681 
07480389 
0769874 
0797185 
0824971 
0853234 
0881973 


758 


THE STEAM-ENGINE. 


Morse-power per Pound Mean Effective Pressure, 


Formula, 


Area in sq. in. X piston-speed — 





83,000 





Diam. of 
Cylinder, 


inches. 


4 
414 
5 


Speed of Piston in feet per minute. 








100 | 200 | 300 | 400 
~.0881{ .0762} .114z]  . 1523 
.0482} .0964) .1446) .1928 
.0595} .1190) .1785}  .2880 
.0720} .1440; .2160} .2880 
.0857} 1714) 9.2570) =. 8427 
.1006] .2011] .3017! =. 4022 
.1166] .2832) .3499]  .4665 
.1339} .2678} .4016} .5855 
1528] .3046) .4570} = .6098 
1720] .3439} .5159) =. 6878 
.1928| .3856) .5783) .7711 
-2148] .4296) .6444) .8592 
.2380| .4760) .7140} .9520 
.2880} .5760) .8639} 1.1519 
.8427| 6854) 1.0282] 1.3709 
.4022| .8044) 1.2067] 1.6089 
.4665| .9330) 1.3994) 1.8659 
.5355| 1.0710) 1.6065) 2.1420 
.6093| 1.2186) 1.8278} 2.4371 
.6878| 1.2756) 1.9635) 2.6513 
TTL] 1.5422) 2.3134) 8.0845 
8592} 1.7184) 2.5775) 8.4367 
-9520| 1.9040) 2.8560) 3.8080 
1.0496] 2.0992) 3.1488] 4.1983 
1.1519) 2.3038) 3.4558] 4.6077 
1.2590) 2.5180) 3.7771) 5.0361 
1.3709} 2.7418) 4.1126) 5.4835 
1.4875] 2.9750) 4.4625} 5.9500 
1.6089] 3.2178) 4.8266} 6.4255 
1.7350) 3.4700) 5.2051) 6.9401 
1.8659) 3.7318) 5.5978] 7.4637 
2.0016] 4.0033) 6.0047). 8.0063, 
2.1420] 4.2840) 6.4260) 8.5680 
2.2872] 4.5744) 6.8615] 9.1487 
2.4371] 4.8742} 7.3114] 9.7485 
2.5918] 5.1836) 7.7755/10.367 
2.7513] 5.5026) 8.2538/11.005 
2.9155) 5.8310) 8.7465/11.662 
3.0845] 6.1690} 9.2534]12.338 
3.2582) 6.5164) 9.7747/13.033 
8.4367| 6.8734'10.310 |13.747 
3.6200] 7.2400 10.860 |14.480 
3.8080) 7.6160 11.424 15.232 
4.0008) 8.0016/12.002 |16.003 
4.1983] 8.3866 12.585 |16.783 
4.4006] 8.8012/13.202 |17.602 
4.6077] 9.2154 13.823 |18.431 
4.8195) 9.6390\14.459 119.27 
5.0361}10.072 |15.108 |20.144 
5.2574/10.515 |15.772 |21.0380 
5.4835)10.967 16. io 21,934 
5.7144/11.429 |17.148 |22.858 
5.9500|11.900 |17.850 |23.800 
6.1904}12.381 |18.571 |24.762 
6.4355}12.871 |19.3807 |25.742 
6.6854/13.371 |20.056 |26.742 
6.9401)13.880 )20.820 |27.760 
7.1995}14.399 |21.599 |28.798 
7.4637/14.927 |22.391 )29.855 
7 .7326/15.465 |23.198 |30.930 
8. 0063/16.013 |24.019 ]82.025 
8.2849}16.570 |24.854 /33.139 
8,5680}17.136 [25.704 |34.272 








500 | 600 | 700 | 800 | 900 





1904 
2410 
2975 
. 3600 
4284 
5028 
.5831 
.6694 
7616 
8598 
9639 
0740 
.1900 
.4399 
7186 
0111 
8324 
6775 
0464 
3391 
8556 
2959 
7600 
247 

5.7596 
6.2951 
6.8544 
7.4375 
8.0444 
8.675] 
9.3296 
10.008 

10.710 

11.436 

12.186 

12.959 

13.756 


OUR BD 0909 COW W WHS 





14.578 





2285 
2892 
.8570 
43820 
.5141 
6033 
6997 
8033 
.9139 
03817 
1567 
2888 
4280 
“(279 
2.0863 
2.4138 
2.4989 
3.2130 
3.6557 
4.0269 
4.6267 
5.1551 
5.7120 
6.2975 


at ek et 











41.424 


. 2666 
33874 
.4165 
.5040 
.5998 
. 1059 
.8168 
. 9871 
0662 
. 2037 
3495 
5036 


Eap &© GO CO 2 O32 G2 OV HA G9 C5 BD] DD TW Fabs rt Pree 
5 * 
o 
1S) 
o 





54.128 
56.044 





57.993 


42.840 |51. "408 59. 976 





3046 
8856 

760 
.5760 
6854 
8044 
. 9330 
.0710 
2186 
3756 





1 
1 
1 
1 
22| 1.7350 
1 
2 
2 





8427 
4338 
.5355 
.6480 
afin 
- 9050 
.0496 
.2049 
8709 
5476 


9532 





INDICATED’ HORSE-POWER OF ENGINES. 759 


To draw the Clearance-line on the Indicator-diagram, 
the actual clearance not being known.—The clearance-Jine may be obtained 
approximately by drawing a straight line, cbad, across the compression 
curve, first having drawn OX parallel to the atmospheric line and 14.7 lbs. 
below. Measure from a the distance ad, equal to cb, and draw YO perpen- 
dicular to OX through d; then will TB divided by AT be the percentage of 





Fig. 139. 


clearance. The clearance may also be found from the expansion-line by 
constructing a rectangle efhg, and drawing a diagonal gf to intersect the 
line XO. This will give the point O, and by erecting a perpendicular to XO 
we obtain a clearance-line OY. 

Both these methods for finding the clearance require that the expansion 
and compression curves be hyperbolas. Prof. Carpenter (Power, Sept., 
1893) says that with good diagrams the methods are usually very accurate, 
and give results which check substantially. 

The Buckeye Engine Co., however, say that, as the results obtained are 
seldom correct, being sometimes too little, but more frequently too much, 
and as the indications from the two curves seldom agree, the operation has 
little practical value, though when a clearly defined and apparently undis- 
torted compression curve exists of sufficient extent to admit of the applica- 
tion of the process, it may be relied on to give much more correct results 
than the expansion curve. 

To draw the Hyperbolic Curve on the Indicator-dia= 
gram,—Select any point Jin the actual curve, and from this point draw a 
line perpendicular to the line JB, meet- j | c 
jung ihe lattes in the point J. The line ee 2 |e ts = 
JB may be the line of boiler-pressure, 
but this is not material; it may be drawn y 
at any convenient height near the top of 
diagram and parallel to the atmospheric 
line. From J draw a diagonal to K, the 
latter point being the intersection of 
the vacuum and clearance lines; from I 
draw IL parallel with the atmospheric 
line. From JZ, the point of intersection 
of the diagonal’ JK and the horizontal 
line JL, draw the vertical line LM. The 
point M is the theoretical point of cut-off, and LM the cut-off line, Fix 
upon any number of points 1, 2, 3, etce., on the line JB, and from these points 
draw diagonals to K. From the intersection of these diagonals with LM 
draw horizontal lines, and from 1, 2, 3, ete., vertical lines. Where these lines 
meet will be points in the hyperbolic curve. 

Pendulum Indicator Big.—Power (Feb. 1893) gives a graphical 
representation of the errors in indicator-diagrams, caused by the use of ine 





Fie. 140. 


760 THE STEAM-ENGINE. 


correct form i the pendulum rigging. It is shown that the “ brumbo” 
pulley on the pendulum, to which the cord is attached, does not gener- 
ally give as good a reduction as a simple pin 
E attachment. When the end of the pendulum is 
: slotted, working in a pin on the crosshead, the 
error is apt to be considerable at both ends of 
the card. With a vertical slot in a plate fired 
to the crosshead, and a pin on the pendulum 
working in this slot, the reduction is perfect, 
when the cord is attached to a pin on the pen- 
dulum, a slight error being introduced if the 
brumbo pulley is used. With the connection 
between the pendulum and the crosshead made 
by means of a horizontal link, the reduction is 
nearly perfect, if the construction is such that 
the connecting link vibrates equally above and 
Fig. 141. below the horizontal, and the cord is attached 
by apin. If the link is horizontal at mid-stroke 
a serious error is introduced, which is magnified if a brumbo pulley also is 
used. The adjoining figures show the two forms recommended. 
Wheoretical Water-consumption calculated from the 
Indicator-card.—The following method is given by Prof. Carpenter 
{Power, Sept. 1893): yj = mean effective pressure, 1 = length of stroke in 
feet, a = area of piston in square inches, a -+- 144 = area in square feet, c = 
percentage of clearance to the stroke, b = percentage of stroke at point 
where water rate is to be computed, = number of strokes per minute, 
60n = number per hour, w = weight of a cubic foot of steam having a pres. 
sure as shown by the diagram corresponding to that at the point where 
water rate is required, w’ = that corresponding to pressure at end of com-« 
pression. 





b+cec\ a 





Number of cubic feet per stroke = 1( 





100 144° 
Corresponding weight of steam per stroke in lbs. = (rte erie 
! lea 
Volume of clearance = 14,400 : 
“ ; ‘ __ leaw 
Weight of steam in clearance = 14,400" 


Total weight of} _,f/%¥-+e¢\wa  Icaw’  _ila 
steam per Stroke | ia 100 / 144 ~ 14,400 ~ Tom © + c)w — cw’ |. 
Total weight of steam 60nla 
from diagram per one = 74,400 [ + cw — cw |. 


_The indicated horse-power is p 1 a n + 33,000. Hence the steam-consump: 
tion per hour per indicated horse- power is 





60nla 
+ jaa00L. + ow ew" | 197 59 ; 
faa niat ae eae [@ + c)w — cw |. 
33,000 


Changing the formula to a rule, we have: To find the water rate from the 
indicator diagram at any point in the stroke. 

Ruie.—To the percentage of the entire stroke which has been completed 
by the piston at the point under consideration add the percentage of clear- 
ance. Multiply this result by the weight of a cubic foot of steam, having a 
pressure of that at the required point. Subtract from this the product of 
percentage of clearance multiplied by weight of a cubic foot of steam hav- 
ing a pressure equal to that at the end of the compressioii. Multiply this 
result by 137.50 divided by the mean effective pressure.* 

Notr.—This method only applies to points in the expansion curve or be- 
tween cut-off and release. 
ee as oe I Pe, 

* For compound or triple-expansion engines read: divided by the equiva- 


lent mean effective pressure, on the supposition that all work is done in one 
cylinder, 


COMPOUND ENGINES. TOL 


The beneficial effect of compression in reducing the water-consumption of 
an engine is clearly shown by the formula. . [f the compression is carried to 
such a poinu that it produces a pressure equal to that at the point under 
consideration, the weight of steam per cubic foot is equal, and w= w’. In 
this case the effect of clearance entirely disappears, and the formula 


“ 
becomes (bw). 
In case of no compression, w’ becomes zero, and the water-rate = 
137 5 
ip -[(B + c)w]. 


Prof. Denton (Trans. A. S. M. E., xiv. 1363) gives the following table of 
theoretical water-consumption for a perfect Mariotte expansion with steam 
at 150 lbs. above atmosphere, and 2 lbs. absolute back pressure: 





Lbs. of Water per hour 


Ratio of Expansion, 7. | M.E.P., lbs. per sq. in. per horse-power, W. 














10 52.4 9.68 
15 38.7 8.74 
20 30.9 8.20 
25 25.9 4.84 
30 22.2 4.63 
35 19.5 G45 





The difference between the theoretical water-consumption found by the 
formula and the actual consumption as found by test represents ‘* water not 
accounted for by the indicator,” due to cylinder condensation, leakage 
through ports, radiation, etc. 

Leakage of Steam,—Leakage of steam, except in rare instances, has 
60 little effect upon the lines of the diagram that it can scarcely be detected. 
The only satisfactory way to determine the tightness of an engine is to take 
it when not in motion, apply a full boiler-pressure to the valve, placed in a 
elosed position, and to the piston as well, which is blocked for the purpose at 
some point away from the end of the stroke, and see by the eye whether 
leakage occurs. The indicator-cocks provide means for bringing into view 
steam which leaks through the steam-valves, and in most cases that which 
leaks by the piston, and an opening made in the exhaust-pipe or observa- 
tions at the atmospheric escape-pipe, are generally sufficient to determine 
the fact with regard to the exhaust-valves. 

The steam accounted for by the indicator should be computed for both 
the cut-off and the release points of the diagram. If the expansion-line de- 
parts much from the hyperbolic curve a very different result is shown at 
one point from that shown at the other. In such cases the extent of the 
loss occasioned by cylinder condensation and leakage is indicated in a much 
more ‘ese manner at the cut-off than at the release. (Tabor Indicator 
Circular.) 


COMPOUND ENGINES. 


Compound, Triple=- and Quadruple-expansion Engines, 
—A couipound engine is one having two or more cylinders, and in which 
the steam after doing work in the first or high-pressure cylinder completes 
its expansion in the other cylinder or cylinders. 

The term ‘‘compound” is commonly restricted, however, to engines in 
which the expansion takes placeintwo stages only—high and low pressure, 
the terms triple-expansion and quadruple-expansion engines being used when 
the expansion takes place respectively in three and four stages. The number 
of cylinders may be greater than the number of stages of expansion, for 
constructive reasons; thus in the compound or two-stage expansion engine 
the low-pressure stage may be effected in two cylinders so as to obtain the 
advantages of nearly equal sizes of cylinders and of three cranks at angles of 
120°. In triple-expansion engines there are frequently two low-pressure ~ 
cylinders, one of them being placed tandem with the high-pressure, and the 
other with the intermediate cylinder, as in mill engines with two cranks at 
90°. In the triple-expansion engines of the steamers Campania and Lucania, 


762 THE STEAM-ENGINE. 


with three cranks at 120°, there are five cylinders, two high, one intermedi-« 
ate. and two low, the high-pressure cylinders being tandem with the low. 
Advantages of Com pounding.—The advantages secured by divid- 
ing the expansion into two or more stages are twofold: 1. Reduction of wastes 
of steam by cylinder-condensation, clearance, and leakage; 2. Dividing the 
pressures on the cranks, shafts, etc., in large engines so as to avoid excessive 
pressures and consequent friction. The diminished loss by cylinder-conden- 
sation is effected by decreasing the range of temperature of the metal sur- 
faces of the cylinders, or the difference of temnperature of the steam at 
admission and exhaust. When high-pressure steam is admitted into a single- 
cylinder engine a large portion is condensed by the comparatively ccld 
metal surfaces; at the end of the stroke and during the exhaust the water 
is re-evaporated, but the steam so formed escapes into the atmosphere or 
into the condenser, doing no work; while if it is taken into a second 
cylinder, as in acompound engine, it does work. The steam lost in the first 
cylinder by leakage and clearance also does work in the second cylinder. 
Also, if there is a second cylinder, the temperature of the steam exhausted 
from the first cylinder is higher than if there is only one cylinder, and the 
metal surfaces therefore are not cooled to the same degree. The difference 
in temperatures and in pressures corresponding to the work of steam of 
150 lbs. gauge-pressure expanded 20 times, in ane, two, and three cylinders, 
i Se in the following table, by W. H. Weightman, Am. Mach., July 28, 





are ie Compound Triple-expansion 
inder.|. Cylinders. Cylinders. 
Diameter of cylinders, in..| 60 33 61 28 46 61 
ATeapratiOs icc crectieslsl cutee weia. telestd 1 8.416] 1 2.70 4.7493 
WX MANSIONS He wis ieflie cH ven-(leet1) 20 5 4 2.714, 2.714) 2.714 
Initial steam - pressures— 
absolute—pounds .. ....| 165 165 33 165 60.8 22.4 


Mvan pressures, pounds. .| 82.96 | 86.11 |] 19.68 | 121.44 | 44.75 | 16.49 


Mean effective pressures, 
pounds.... 28.96 |} 53.11 | 15.68 | 60.64} 22.385] 12.49 


Steam temperatures into 


GYINAErsy.5 «02 Ope seek 866° 366° 259° .9 | 366° 298°.5 | 234°.1 
Steam temperatures out of 
the cylinders.... ....2.. 184°.2 | 2599.9 | 184°.2 | 2989.5 | 2349.1 | 1849.2 


Difference in temperatures} 181.8 | 106.1 "5? G20 59.4 49.9 
Horse-power developed...| 800 399 403 269 268 264 
Speed of piston............| 822 290 290 238 238 238 
Total initial pressures on 
pistons, pounds....... .. 455.218 | 112.900 | 84,752 | 64.162 | 68.817 | 53,773 


66 Woolf?) and Receiver Types of Compound Engines.— 
The compound steam-engine, consisting of two eylinders, is reducible to two 
forms, 1, in which the steam from the h.p. cylinder is exhausted direct into 
the 1. p. cylinder, as in the Woolf engine; and 2, in which the steam from the 
h. p. cylinder is exhausted into an intermediate reservoir, whence the steam 
is supplied to, and expanded in, the 1. p. cylinder, as in the “‘ receiver- 
engine. 

If the steam be cut off in the first cylinder before the end of the stroke, 
the total ratio of expansion is the product of the ratio of expansion in the 
first cylinder, into the ratio of the volume of the second to that of the first 
eylinder; that is, the product of the two ratios of expansion. 

Thus, let the areas of the first and second cylinders be as 1 to 3%, the 
strokes being equal, and let the steam be cut off in the first at 44stroke; then 


Expansion in GnoueeceyliNder..... ....sececneaverinescsantineemmmenmreses, - cOye 
ie hee! — 2d se Seer eS eeeS eset eSeeeseseose: eegeeeeeee* e@uwee 1 to 3l4 


————-- 


Total or combined expansion, the product of the two ratios... 1to7 


Woolf Engine, without Clearance—Ideal Diagrams,— 
The diagrams of pressure of an ideal Woolf engine are shown in Hig. 142, ag 
they would be described by the indicator, according to the arrows. In these 
diagrams pq is the atmospheric line, mn the vaenum line. ¢d the admissiop 


COMPOUND ENGINES. 763 


line, dg the hyperbolic curve of expansion in the first cylinder, and gh the con- 
secutive expansion-line of back pressure 
for the return-stroke of the first piston, 
and of positive pressure for the steam- 
stroke of the second piston. Atthe point 
h, at the end of the stroke of the second 
piston, the steam is exhausted into the 
condenser. and the pressure falls to the 
level of perfect vacuum, m0. 

The diagram of the second cylinder, 
below gh, is characterized by the absence 
of any specific period of admission; the 
whole of the steam-line gh being expan- 
sional, generated by the expansion of 
the initial body of steam contained in 
the first cylinder into the second. When 
the return-stroke is completed, the 
pie of ae steam transferred cia n re 
the first is shut into the second cylin- ia a4 oy eA ag 
der. The final pressure and volume of Fig. ete eG Mp Me 
the steam in the secend cylinder are the 1 ‘ 7 
same as if the whole of the initial steam had been admitted at once into the 
second cylinder, and then expanded to the end of the stroke in the manner 
of a single-cylinder engine. Bet isore 

The net work of the steam is also the same. according to both distributions. 

Receiver-engine, without Clearance—Ideal Diagrams.— 
In the ideal receiver-engine the pistons of the two cylinders are con- 
nected to cranks at right angles to each other on the same shaft. The 
receiver takes the steam exhausted from the first cylinder and supplies it to 
the second, in which the steam is cut off and then expanded to the end of 
the stroke. On the assumption that the initial pressure in the second cylin- 
der is equal to the final pressure in the first, and of course equal to the pres- 
sure in the receiver. the volume cut off in the second cylinder must be 
equal to the volume of the first cylinder, for the second cylinder must admit 
as much steam at each stroke as is discharged from the first cylinder. 

In Fig. 143 cd is the line of admission and hg the exhaust-line for the first 


dc 








Fic. 148.—RECEIVER-ENGINE, IDEAL Fia. 144.—ReEcEIVER ENGINE, IDEAL 
INDICATOR-DIAGRAMS., DIAGRAMS REDUCED AND COMBINED. 


cylinder; and dg is the expansion-curve and pq the atmospheric line. In 
the region below the exhaust-line of the first cylinder, between it and the 
line of perfect vacuum, ol, the diagram of the second cylinder is formed; hi, 
the second line of admission, coincides with the exhaust-line hg of the first 
cylinder, showing in the ideal diagram no intermediate fall of pressure, and 
ik is the expansion-curve. The arrows indicate the order in which the dia- 
grams are formed. : : j 

In the action of the receiver-engine, the expansive working of the steam, 
though clearly divided into two consecutive stages, is, as in the Woolf 
engine, essentially continuous from the point of cut-off in the first cylinder 
to the end of the stroke of the second cylinder, where it is delivered to the 
condenser; and the first and second diagrams may be placed together and 


764 THE STEAM-ENGINE. 


combined to form a continuous diagram. For this purpose take the second 
diagram as the basis of the combined diagram, namely, hiklo, Fig. 144. The 
period of admission, hz, is one third of the stroke, and as the ratios of the 
cylinders are as 1 to 3, hi is also the proportional length of the first diagram 
as applied to the second. Produce oh upwards, and set off oc equal to the 
total height of the first diagram above the vacuum-line; and, upon the 
shortened base hi, and the height hc, complete the first diagram with the 
steam-line cd, and the expansion-line di. 

It is shown by Clark (S. E., p. 432, et seq.) in a series of arithmetical cal- 
culations, that the receiver-engine is an elastic system of compound engine, 
in which considerable latitude is afforded for adapting the pressure in the 
receiver to the demands of the second cylinder, without considerably dimin- 
ishing the effective work of the engine. In the Woolf engine, on the 
contrary, it is of much importance that the intermediate volume of space; 
between the first and second cylinders, which is the cause of an interme- * 
diate fall of pressure, should be reduced to the lowest practicable amount. 

Supposing that there is no loss of steam in passing through the engine, 
by cooling and condensation, it is obvious that whatever steam passes 
through the first cylinder must also find its way through the second cylin- 
der. By varying, therefore, in the receiver-engine, the period of admission 
in the second cylinder, and thus also the volume of steam admitted for each 
stroke, the steam will be measured into it at a higher pressure and of a less 
bulk, or at a lower pressure and of a greater bulk; the pressure and density 
naturally adjusting themselves to the volume that the steam from the re- 
ceiver is permitted to occupy in the second cylinder. With a sufficiently ; 
restricted admission, the pressure in the receiver may be maintained at the 
pressure of the steam as exhausted from the first cylinder. On the con- 
trary, with a wider admission, the pressure in the receiver may fall or 
“‘drop’’ to three fourths or even one Wai of the pressure of the exhaust- 
steam from the first cylinder. 

(For a more complete discussion of the action of steam in the Woolf and 
receiver engines, see Clark on the Steam-engine.) 

Combined Diagrams of Compound Engines,.—tThe only way 
of making a correct combined diagram from the indicator-diagrams of the 
several cylinders ina compound engine is to set off all the diagrams on the 
same horizontal scale of volumes, adding the clearances to the cylinder ca- 

. 6 





pacities proper. When this is attended to, the successive diagrams fall ex- 
actly into their right places relatively to one another, and would compare 
properly with any theoretical expansion-curve, (Prof. A. B. W. Kennedy, 
Proc. Inst. M. E., Oct. 1886.) 


COMPOUND ENGINES. 765 


This method of combining diagrams is commonly adopted, but there are 
objections to its accuracy, since the whole quantity of steam consumed in 
the first cylinder at the end of the stroke is not carried forward to the 
second, but a part of it is retained in the first cylinder for compression. Fer 
a method of combining diagrams in which compression is taken account of, 
see discussions by Thomas Mudd and others, in Proc. Inst. M. E., Feb., 
1887, p. 48. The usual method of combining diagrams is also criticised by 
Frank H. Ball as inaccurate and misleading (Am. Mach., April 12, 1894; 
Trans, A. S. M. E., xiv. 1405, and xv. 403). 

Figure 145 shows a combined diagram of a quadruple-expansion engine, 
drawn according tothe usual method, that is, the diagrams are first reduced 
in length to relative scales that correspond with the relative piston-displace- 
ment of the three cylinders. Then the diagrams are placed at such distances 
from the clearance-line of the proposed combined diagram as to correctly 
represent the clearance in each cylinder. 


Calculated Expansions and Pressures in Two-cylinder 
Compound Engines, (James Tribe, Am. Mach., Sept. & Oct. 1891.) 


TWO-CYLINDER COMPOUND NON-CONDENSING. 
Back pressure 14 lb. above atmosphere. 





Initial gauge- | 
pressure....... 100 ;.110 | 120 130 | 140 | 150 {| 160 | 170 | 17% 


Initial absolute 
pressure....... 115 125 135 145 155 165 175 185 190 


Total expansion.| 7.39 | 7.84 | 8.41 9 | 9.61 {10.24 |10.89 [11.56 ]11.9 
Hxpansionsin 

each cylinder..j| 2.7 | 2.8 | 2.9 8 | 3.10] 3.2 | 3.3 | 3.4 | 3.45 
Hyp. log. plus 1.] 1.993} 2.029) 2.064; 2.098) 2.131] 2.163) 2.193] 2.223] 2.238 
Forward § High./84.8 {90.5 101.4 106.5 |111.5 {116.3 |120.9 123.2 
ressures ) Low..|31.3 |82.3 1 133.7 184.38 |84.8 (85.2 (35.6 [85.7 
ack High.}42.5 |44.6 .5 148.3 |50 sul aaye vss} 54.4 155 
pressures ( Low..]15.5 /15.5 |15.5 |15.5 [15.5 [15.5 115.5 |15.5 /15.5 


Mean 4 
MN SHigh.|42.3 |45.9 {49.5 [53.1 |56.5 |6o 63.3 166.5 |6s.2 
estetive } Fer 15.8 |16.8 |17.6 |18.2 |18.8 119.3 19.7 |20:1 [20.9 


Ratio-cylinder 
BYOAN oc is as antes 2.67 | 2.73 | 2.81 | 2.91 | 3 3.11 | 3.21 | 3.31 | 3.37 


TWO-CYLINDER COMPOUND CONDENSING. 
Back pressure, 6.5 lbs. above vacuum , 


Initial gauge-pressures........ 90 | 100 | 110 {| 120 | 180 | 140 | 150 
Initial absolute pressures...... 105°} 115 \°125 7} 135.) 145 155 | 165 
Probable per cent of loss....../ 2.6 | 2.9 | 3.3 | 3.6 | 3.8 | 4.0 | 4.3 
Total expansions.............. [15.7 |17 18.5 '29 21.5 [22.7 124.2 
Exps. in each cylinder. .......] 3.96 | 4.13 | 4.3 | 4.47 | 4.64 | 4.77 | 4.92 
Hyp. log. plusl.... ... ese ar 2.376] 2.418) 2.458] 2.497) 2.534] 2.562) 2.593 
Mean forward ; AI Snes esec cae 62.9 (67.3 |71.4 |%5.4 179.8 (83.2 187 
pressures LOW ...006.--. 15.25 15.55 (15.9 ]16.2 |16.5 [16.75 |17.05 
Mean back 4 Fpeptaaer ae Pires 2c ey Pies an eH!) 80.2 (31.4 |82.4 |33.5 
reyes LOW cccedncros it Omen neon acon | 4.0. | ded.) ao 
ean ‘ 

; High..............|86.4 {89.5 42.4 |45.2 [47.9 [50.8 [53.5 
earned LOW . cee. see cee. {10.95 [11.25 ]11.6 {11.9 [12.2 [12.45 ]12-75 
Terminal § High.............. {26.5 /27.8 (29.0 {80.2 |81.4 |82.4 [33.5 
Vressures | OW ce weet ase 6.4 | 6.45 | 6.45 | 6.5 | 6.55 | 6.55 | 6.6 
Initial pressure in 1. p. cyl.....]25.3 26.6 127.8 |29 80.2 [381.4 {82.4 
Ratio of cylinder areas........ 3.32 | 3.51 | 3.66 | 3.8 | 3.92 | 4.08 | 4.19 


The probable percentage of loss, line 3, is thus explained: There is always 
a loss of heat due to condensation, and which increases with the pressure of 
steam. The exact percentage cannot be predetermined, as it depends 
largely upon the quality of the non-conducting covering used on the cylin- 
der, receiver, and pipes, etc., but will probably be abont as shown. 

Proportions of Cylinders in Compound Engines,—Authori- 
ties differ as to the proportions by volume of the high and low pressure 


cylinders v and V. Thus Grashof gives V +2 = 0.85 77; Hrabak, 0.90 4/7; 


%66 THE STEAM-ENGINE. 


3 
Werner, Vr; and Rankine, 4/72, r being the ratio of expansion. Busley 
makes the ratio dependent on the boiler-pressure thus: 


Lbatper ea) inc ssaas coos wee ee eae 0, 90 105 «120 
A Pie eS etey Ae Bae SOR AL Ba ty ee ee tra 4 4.5 5 


(See Seaton’s Manual, p. 95, ete., for analytical method; Sennett, p. 496, 
ete.; Clark’s Steam-engine, p. 445, ete; Clark, Rules, Tables, Data, p. 849, etc.) 

Mr. J. McFarlane Gray states that he finds the mean effective pressure in 
the compound engine reduced to the low-pressure cylinder to be approxi- 
mately the square root of 6 times the boiler-pressure. 

Approximate Horse-power of a Modern Compound 
Miarinmne-engime, (Seaton.)—The following rule will give approximately 
the horse-power developed by a compound engine made in accordance with 

)2 / 
modern marine practice, Estimated H.P. = DXA MEXS. 
D = diameter of |.p. cylinder; p = boiler-pressure by gauge; 
R = revs. per min.; S = stroke of piston in feet. 


Ratio of Cylinder Capacity in Compound Marine En= 
gines. (Seaton.)—The low-pressure cylinder is the measure of the power 
of a compound engine, for so long as the initial steam-pressure aud rate of 
expansion are the same, it signifies very little, so far as total power only is 
concerned, whether the ratio between the low and high-pressure cylinders 
is 3 or 4; but as the power developed should be nearly equally divided be- 
tween the two cylinders, in order to get a good and steady working engine, 
there is a necessity for exercising a considerable amount of discretion in 
fixing on the ratio. 

In choosing a particular ratio the objects are to divide the power evenly 
and to avoid as much as possible ‘‘ drop ”’ and high initial strain. 

If increased economy is to be obtained by increased boiler-pressures, the 
rate of expausion should vary with the initial pressure, so that the pressure 
at which the steam enters the condenser should remain constant. In this 
case, with the ratio of cylinders constant, the cut-off in the high-pressure 
cylinder will vary inversely as the initial pressure. 

Let R be the ratio of the cylinders; r, the rate of expansion; », the initial 
pressure: then cut-off in high-pressure cylinder = R +r; r varies with p,, 
so that the terminal pressure pn is constant. and consequently r =p, + pn} 
therefore, cut-off in high-pressure cylinder = R X pn~+ py. 

Ratios of Cylinders as Found in Marine Practice,—The 
rate of expansion may be taken at one tenth of the boiler-pressure (or about 
one twelfth the absolute pressure), to work economically at full speed.’ 
Therefore, when the diameter of the low-pressure cylinder does not exceed 
100 inches, and the boiler-pressure 70 lbs., the ratio of the low-pressure to 
the high-pressure cylinder should be 3.5; for a boiler-pressure of 80 lbs., 3.755 
for 90 lbs., 4.0; for 100 lbs., 4.5. If these proportions are adhered to, there 
will be no need of an expansion-valve to either cylinder. If, however, to 
avoid ‘‘drop,”’ the ratio be reduced, an expansion-valve should be fitted to 
the high-pressure cylinder. 

Where economy of steam is not of first importance, but rather a large 
power, the ratio of cylinder capacities may with advantage be decreased, 
so that with a boiler-pressure of 100 Ibs. it may be 3.75 to 4. 

In tandem engines there is no necessity to divide the work equally. The 
ratio is generally 4, but vw hen the steam-pressure exceeds 90 lbs. absolute 4.5 
is better, and for 100 lbs. 5.0. 

When the power requires that the 1. p. cylinder shall be more than 100 in, 
diameter, it should be divided in two cylinders. In this case the ratio of the 
combined capacity of the two]. p. cylinders to that of the h. p. may ke 3.0 
for 85 Ibs. absolute. 3.4 for 95 lbs., 8.7 for 105 lbs., and 4.0 for 115 Ibs. 

Receiver Space in Compound Engines should be from 1 to 
1.5 times the capacity of the high-pressure cylinder, when the cranks are at 
an angle of from 90° to 120°. When the cranks are at 180° or nearly this, 
the space may be very much reduced. In the case of triple-compound en- 
gines, with cranks at 120°, and the intermediate cylinder leading the high- 
pressure, a very small receiver will do. The pressure in the receiver should 
never exceed half the boiler-pressure. (Seaton.) 


COMPOUND ENGINES, 767 


formula for ee eet the Expansion anu the Work 
of Steam in Compound Engines, 


(Condensed from Clark on the “ Steam-engine.’} 


@ = area of the first cylinder in square inches; 

a’ = area of the second cylinder in square inches; 

¥ = ratio of the capacity of the second cylinder to that of the first; 

J. = length of stroke in feet, supposed to be the same for both cylinders; 
t= period of admission to the first cylinder in feet, excluding clearance; 
€ = clearance at each end of the cylinders, in parts of the stroke, in feet: 

L’ = length of the stroke plus the clearance, in feet; 

v= peLon of admission plus the clearance, in feet; 

Ss = length of a given part of the stroke of the second cylinder, in feet; 

P = total initial pressure in the first cylinder, in lbs. per square inch, sup- 
posed to be uniform during admission; 

Ff’ = total pressure at the end of the given part of the stroke s3 

ls = average total pressure for the whole stroke; 

= nominal ratio of expansion in the first cylinder, or L + 2; 

= actual ratio of expansion in the first cylinder, or LD’ + 2’; 

= actual Comings ratio of expansion, in the first and second cylinders 
together; 

n = ratio of the final pressure in the first cylinder to any intermediate 
fall of pressure between the first and second cylinders; 

WV = ratio of the volume of the intermediate space in the Woolf engine, 
reckoned up to, and including the clearance of, the second piston, 
to the capacity of the first cylinder plus its clearance. The value 
of N is correctly expressed by the actual ratio of the volumes as 
stated, on the assumption that the intermediate space is a vacuum 
when it receives the exhaust-steam from the first cylinder. In point 
of fact, there is a residuum of unexhausted steam in the interme- 
diate space, at low pressure, and the value of N is thereby prac- 


tically reduced below the ratio here stated. N= = a 7 3. 





w = whole net work in one stroke, in foot-pounds. 
Ratio of expansion in the second cylinder: 


( r 4 +N 
In the Woolf engine, a nad Sted 


In the receiver-engine, @ — 1, 


Total actual ratio of expansion = product of the ratios of the thr3e con- 
secutive expansions, in the first cylinder, in the intermediate space, and 
in the second cylinder, 


L 
In the Woolf engine, R’ ( "7 4 N), 


In the receiver-engine, re, or rR’. 
Combined ratio of expansion behind the pistons = ele rR’ = RM", 





Work done in the two cylinders for one stroke, with a given cut-off and & 
given combined actual ratio of expansion: 


Woolf engine, w = aP[l’(1+ hyp log R”) — c); 
Receiver engine, w= aP| (1 +- hyp log R”) ~ o(1 +75), 


when there is no intermediate fall of pressure. 

When there is an intermediate fall, when the pressure falls to 34, %, 34 of 
the final pressure in the 1st cylinder, the reduction of work is 0.2%, 1.0%, 4.6% 
of that when there is no fall. 


"68 THE STEAM-ENGINE. 


Total work in the two cylinders of a receiver-engine, for one stroke for 
any intermediate fall of pressure, 


w= aply(2+! + hyp log R”) - e(1 +2=de-»)] : 


Exampis.—Let a = 1 sq. in., P = 63 Ibs., ’ = 2.42 ft., n= 4, R” = 5.969, 
c= .42ft., r= 3, R’ = 2.658; | 


w = 1 x 63| 2.42(5/4 hyp log 5.969) — 4214 2X" 


4X 2.653 


Calculation of Diameters of Cylinders of a compound con- 
densing engine of 2000 H.P. at a speed of 4UU feet per minute, with 100 lbs. 
boiler-pressure. q 

100 Ibs. gauge-pressure = 115 absolute, less drop of 5 lbs, between boiler 
and cylinder = 110 lbs. initial absolute pressure. Assuming terminal pres- 
sure inl, p. cylinder = 6 lbs., the total expansion of:steam in both cylinders 
= 110-+6 = 18.33. Hyp log 18.33 = 2.909. Back pressure in 1, p. cylinder, 
3 lbs. absolute. 

The following formule are used in the calculation of each cylinder : 


as H.P. x 33,000 

NOE aeons Sa pats “M.E.P. X piston-speed’ 

(2) Mean effective pressure = mean total pressure — back pressure. 

(3) Mean total pressure = terminal pressure X (1+ hyp log Rk). | 

(4) Absolute initial pressure = absolute terminal pressure X ratio of ex- 
pansion. ‘ . 

First calculate the area of the low-pressure cylinder as if all the work 
were done in that cylinder. 

From (3), mean total pressure = 6 X (1 + hyp log 18.38) = 23.454 Ibs. 

From (2), mean effective pressure = oy — 3= 20.454 lbs. 

. 2009 X 33, as ' Pha ae : 
From (1), area of cylinder = 20.454 ¢ 700 = 4610 sq. ins. = 76.6 ins. diam. 


If half the work, or 1000 H.P., is done in the 1. p, cylinder the M.E.P. will 
be half that found above, or 10.227 lbs., and the mean total pressure 10.227 +- 
3 = 13.227 lbs. 

From (3), 1-- hyp log R = 13.227 + 6 = 2.2045. 

Hyp log R = 1.2045, whence # inl. p. cyl. = 3.835. 

Irom (4), 3.335 x 6 = 20.01 Ibs. initial pressure in l. p. cyl. and terminal 
pressure in h. p. cyl., assuming no drop between cylinders. 

1lu + 20.01 = 18.33 + 8.335 = 5.497, # in h. p. cyl. 

From (3), mean total pres. in h. p.cyl. = 20.01 x (1 + hyp log 5.497) = 54.11. 

From (2), 54.11 — 20.01 = 34.10, M.E.P. in h. p. cyl. 

From (1), area of h. p. cyl. = Ne = 1882 sq. ins. = 42 ins. diam. 

Cylinder ratio = 4610 -- 1382 = 3.336. 

The area of the h. p. cylinder may be found more directly by dividing the 
area of the l. p. cyl. by the ratio of expansion in that cylinder. 4610 + 
3.330 = 1382 sq. ins. 

In the above calculation no account is taken of clearance, of compression, 
of drop between cylinders, nor of area of piston-rods. It also assumes that 
the diagram in each cylinder is the full theoretical diagram, with a horizontal 
steam-line and a hyperbolic expansion line, with no allowance for round- 
ing of the corners. ‘lo make allowance for these, the mean effective pres- 
sure in each cylinder must be multiplied by a diagram factor, or the ratio 
of the area of an actual diagram of the ciass of engine considered, with the 
given initial and terminal pressures, to the area of the theoretical diagram. 
Such diagram factors will range from 0.6 to 0.94, as in the table on p. 745. 

Best Ratios of Cylinders.—The question what is the best ratio of 
areas of the two cylinders of a compound engine is still (1901), a disputed 
one, but there appears to be an increasing tendency in favor of large ratios, 
even as great as 7 or 8 to 1, with considerable terminal drop in the high- 
pressure cylinder. A discussion of the subject, together with a description 
of a new method of drawing theoretical diagrams of multiple-expansion 
engines, taking into consideration drop, clearance, and compression, will be 
found in a paper by Bert C, Ball, in Trans. A. §, M. E,, xxi. 1002. 


— 


)| = 421.55 ft.-Ibs. 





TRIPLE-EXPANSION ENGINES. 769 


TRIPLE-EXPANSION ENGINES, 


Proportions of Cylinders.—H. H. Suplee, Mechanics, Nov. 1887, 
gives the following method of proportioning cylinders of triple-expansion 
engines: 

As in the case of compound engines the diameter of the low-pressure 
cylinder is first determined, being made large enough to furnish the entire 
power required at the mean pressure due to the initial pressure and expan- 
sion ratio given; and then this cylinder is only given pressure enough to per- 
form one third of the work, and the other cylinders are proportioned so as to 
divide the other two thirds between them. 

Let us suppose that an initial pressure of 150 Ibs. is used and that 900 H.P. 
is to be developed at a piston-speed of 800 ft. per min., and that an expan- 
sion ratio of 16 is to be reached with an absolute back pressure of 2 lbs. 

The theoretical M.E.P. with an absolute initial pressure of 150 + 14.7 = 
164.7 lbs, initial at 16 expansions is 


14h Tt 
PO t hyp tog 19) — 164.7 x 2.7126 = 28.83, 


less 2 Ibs. back pressure, = 38.83 — 2 = 36.83. 

In practice cernly about 0.7 of this pressure is actually attained, so that 
36.83 X ae = 25.781 lbs. is the M.E.P. upon which the engine is to be pro- 
portioned. 

To obtain 900 H.P. we must have 33,000 * 900 = 29,700,000 foot-pounds, and 
this divided by the mean pressure (25.78) and by the speed in feet (800) will 
aire 1440 sq. in. for the area of the l. p. cylinder, about equivalent to 43 in. 

iam. 

Now as one third of the work is to be done in the ]. p. cylinder, the M.E.P, 
in it will be 25.78 + 3 = 8.59 lbs. 

The cut-off in the high-pressure cylinder is generally arranged to cut off 
at 0.6 of the stroke, and so the ratio of the h. p. to the 1. p. cylinder is equal 
to 16 X 0.6 = 9.6, and the h. p. cylinder will be 1440+-9.6 = 150 sq. in. area, or 
about 14 in. diameter, and the M.H.P. in the h. p. cylinder is equal to 
9.6 X 8.59 = 82.46 Ibs. 

If the intermediate cylinder ts made a mean size between the other two, 
its size would be determined by dividing the area of the 1, p. cylinder by the 
square root of the ratio between the low and the high; but in practice this is 
found to give a result too large to equalize the stresses, so that instead the 
area of the int. cylinder is found by dividing the area of the 1. p. piston by 
1.1 times the square root of the ratio of 1. p. to h. p. cylinder, which in this 


case is 1440 + (1.1 4/9.6) = 422.5 sq. in., or alittle more than 23 in. diam. 

The choice of expansion ratio is governed by the initial pressure, and is 
generally chosen so that the terminal pressure in the l. p. cylinder shall be 
about 10 lbs. absolute. 

Formuls for Proportioning Cylinder Areas of Triple=- 
Expansion Engines.—tThe following formule are based on the method 
ot first finding the cylinder areas that would be required if an ideal hyper- 
bolic diagram were obtainable from each cylinder, with no clearance, com- 
pression, wire-drawing, drop by free expansion in receivers, or loss by 
cylinder condensation, assuming equal work to be done in each cylinder, 
and then dividing the areas thus found by a suitable diagram factor, such as 
those given on page 745, expressing the ratio which the area of an actual 
diagram, obtained in practice from an engine of the type under considera- 
tion, bears to the ideal or theoretical diagram. It will vary in different classes 
of engine and in different cylinders of the same engine, usual values ranging 
from 0.6 to 0.9. When any one of the three stages of expansion takes place 
in two cylinders, the combined area of these cylinders equals the area found 
by the formule. 


NOTATION. 
Pp, = initial pressure in the high pressure cylinder. 
ps = terminal ** *¢ ** Jow pressure + 
Py = back “ 66 66 6 be “6 
Pq = term. press. in h. p. cyl. and initial press. in intermediate cyl. 
Dgizear' At "ANA wie 5° 3 OL, Dae Vale 


R,. Ro, Rg, ratio of exp. inh, p. int. and 1. p. cyls. 
R = total ratio of exp. = Ry xR. x Rs. ; 
mean effec. press. of the combined ideal diagram, referred to the 


Wt 


Do 
I. p. cyl. 


770 THE STEAM ENGINE. 


P,, Pg, Ps =m. e. p. in the h. p., int., and 1. p. cyls. 
HP = horse-power of the engine = PLA,N + 33,000. 

LZ = length of stroke in feet; N = number of single strokes per min. 
Ay, Ag, Az, areas (sq ins.) of h. p. int. and 1. p. cyls. (ideal). 

W = work done in one cylinder per foot of stroke. 

Yg = ratio of dg to Aj; 73 = ratio of A; to Aj. 
F,, Fo, F3, diagram factors of h. p. int. and 1. p. cyl. 
Gy, Ag, Mg, areas (actual) of ry Pabeaniitise Aah aa peen ae 


Formule, 
(1) R = pj + pt. 
(2) P = pt + byp. log. R) — pb. 
(3) Ps = 4%P 


(4) Hyp. log. Rs = (P; — p, + pb) + py, 
(5) RR, = R = P33 FR, = Re = VRIRS 


(6) ps = pt x Rg 
(7) Pa =DP3 x Ry. 
8) py =p2 x Rf). 
(9) Po = pa(hyp. log. R,) = sR. 
(10) P; = pa(hyp. log. Rj) = PRs. 
(11) W = 11,000 HP + LN. 
(12) A, =W-+P; Ag = W+ Po; Aga W + Py. 


(13) m = Ag+ 41 => P, + Po = R, or Rg; 13 = Ag Ay = Py + Ps. 
(14) a3 =A) +43 Og = 4g + FQ; a3 = 43+ Fs. 
From these formule the figures in the following tables have been 
calculated: 


THEORETICAL MEAN EFFECTIVE PRESSURES, CYLINDER RATIOS, ETC., OF TRIPLE 
EXPANSION ENGINES. 


Back pressure, 3lbs. Terminal pressure, 8 Ibs. (absolute). 


Pi. R. Le P3. Rs. 


120 | 15 26.66} 8.89 1.626 | 3.037 | 13.01} 89.51] 14.45] 43.39] 4.939 
1.712 | .8.197 | 13.70) 43.79) 15.92] 50.89] 5.472 

é 1.790 | 3.843 | 14.32) 47.86] 17.29) 57.76) 5.980 

180 | 22.5 | 29.91 9.97 1.861 | 3.477 | 14.89) 51.77) 18.55] 64.52) 6.471 
1 

1 














.928 | 8.601 | 15.42) 55.54) 19.76) 71.16] 6.942 . 
: : .990 |} 3.718 | 15.91) 59.16] 20.90} 77.69) 7.397 
240 | 80 82.21] 10.7 2.049 | 3.826 | 16.39] 62.72] 22.00} 84.16] 7.839 


Back pressure, 3 lbs. Terminal pressure, 10 Ibs. (absolute). 





( 
Pi- B. Ned P3. Rs3. "a P3- Pr Po- Jaa V3. 





1 2.890 | 14.36] 41.50] 15.24] 44.04) 4.148 
140 | 14 | 83.39) 11.138 | 1 3.044 } 15.11] 45.99} 16.82) 51.20) 4.600 
160 | 16 | 34.73} 11.58} 1 3.182 | 15.80} 50.28] 18.29) 58.20] 5.027 
180 | 18 | 85.90) 11.97 en gee 16.43} 54.38] 19.66} 65.09} 5.439 
1 3 
1 











120 | 12 | 31.85} 10.62 


200 | 20 | 36.96) 12.32 428 | 17.02) 58.384) 20.97] 71.88] 5.884 
220 | 22 | 87,91) 12.64 : 3.538 | 17.57] 62.15) 22.20) 78.54] 6.215 
240 | 24 | 38.78} 12.93 -809 | 3.642 | 18.09) 65.88] 23.38] 85.15] 6.587 








Given the required H.P. of an engine, its speed and length of stroke, and 
the assumed diagram factors F’,, /,, #, for the three cylinders, the areas of 
the cylinders may be found by using formule (11), (12), and (14), and the 
values of P,, P,, and P, in the above table, 


TRIPLE-EXPANSION ENGINES. rypi 


A Common Rule for Proportioning the Cylinders of mu}- 
uple-expansion engines is: for two-cylinder compound engines, the cylinder 
ratiois the square root of the number of expansions, and for triple-expansion 
engines the ratios of the high to the intermediate and of the intermediate 
to the low are each equal to the cube root of the number of expansions, the 
ratio of the high to the low being the product of the two ratios, that is, the 
square of the cube root of the number of expansions. Applying this rule to 
the pressures above given, assuming a terminal pressure (absolute) of 10 Ibs. 
and 8 lbs. respectively, we have, for triple-expansion engines: 














ie Terminal Pressure, 10 lbs. Terminal Pressure, 8 lbs. 
Boiler- 
pressure a Raa SEL SERSES Teo 
(Absolute). | No. of Ex- | Cylinder Ratios, | No. of Ex-| Cylinder Ratios, 
pansions. areas. pansions, areas. 
130 13 1 to 2.35 to 5.53 16144 1 to 2.53 to 6.42 
140 14 1 to 2.41 to 5.81 171% 1 to 2.60 to 6.74 
150 15 1 to 2.47 to 6.08 1834 1 to 2.66 to 7.06 
160 16 1 to 2.52 to 6.35 20 1 to 2.71 to 7.37 











The ratio of the diameters is the square root of the ratios of the areas, and 
the ratio of the diameters of the first and third cylinders is the same as the 
ratio of the areas of first and second. 

Seaton, in his Marine Engineering, says: When the pressure of steam em- 
ployed exceeds 115 lbs. absolute, it is advisable to employ three cylinders, 
through each of which the steam expands in turn. The ratio of the low- 
pressure to high-pressure cylinder in this system should be 5, when the 
steain-pressure is 125 lbs. absolute; when 135 lbs. absolute, 5.4; when 145 
lbs. absolute, 5.8; when 155 Ibs. absolute, 6.2; when 165 lbs. absolute, 6.6. 
The ratio of low-pressure to intermediate cylinder should be about one half 
that between low-pressure and high-pressure, as given above. That is, if 
the ratio of |. p. to h. p. is 6, that of |. p. toint. should be about 3, and conse- 
quently that of int. to h. p. about 2. In practice the ratio of int. to h.p. is 
nearly 2.25, so that the diameter of the int. cylinder is 1.5 that of the h.p. 
The introduction of the triple-compound engine has admitted of ships being 
propelled at higher rates of speed than formerly obtained without exceeding 
the consumption of fuel of similar ships fitted with ordinary compound 
engines; in such cases the higher power to obtain the speed has been devel- 
oped by decreasing the rate of expansion, the low-pressure cylinder being 
only 6 times the capacity of the high-pressure, with a working pressure of 
170 lbs. absolute. It is now a very general practice to make the diameter of 
the low pressure cylinder equal to the sum of the diameters of the h. p. and 

jnt. cylinders; hence, 


Diameter of int. cylinder = 1.5 diameter of h. p. cylinder; 
Diameter of 1. p. cylinder = 2.5 diameter of h. p. cylinder. 


In this case the ratio of 1. p. to h. p. is 6.25; theratio of int. to h. p. is 2.25; 
and ratio of 1. p. to int. is 2.78. 

Ratios of Cylinders for Different Classes of Engines, 
(Proc. Inst. M. E., Feb. 1887, p. 86.)—As to the best ratios for the cylinders 
in a triple engine there seems to be great difference of opinion. Considera- 
ble latitude, however, is due to the requirements of the case, inasmuch as 
it would not be expected that the same ratio would be suitable for an eco- 
nomical land engine, where the space occupied and the weight were of 
minor importance, as in a war-ship, where the conditions were reversed. In 
the land engine, for example, a theoretical terminal pressure of about 7 
lbs. above absolute vacuum would probably be aimed at, which would give 
a ratio of capacity of high pressure to low pressure of 1 to 844 or 1 to 
9; whilstin a war-ship a terminal pressure would be required of 12 to 13 lbs. 
which would need a ratio of capacity of 1 to 5; yet in both these instances 
the cylinders were correctly proportioned and suitable to the requirements 
of the Paro It is obviously unwise, therefore, to introduce any hard-and- 
fast rule. 

Wypes of Three-stage Expansion Engines,.—1. Three cranks 
at 120 deg. 2. Two cranks with Ist and 2d cylinders tandem. 3. Two 
eranks with ist and 3d cylinders tandem. The most common type is the 
first, with cylinders arranged in the sequence high, intermediate, low. 


AUR THE STEAM-ENGINE. 


Sequence of Cranks.—Mr. Wyllie (Proc. Inst. M. E., 1887) favors the 
sequence high, low, intermediate, while Mr. Mudd favors high, intermediate, 
low. The former sequence, high, low, intermediate, gave an approximately 
horizontal exhaust-line, and thus minimizes the range of temperature and 
the initial load; the latter sequence, high, intermediate, low, increased the 
range and also the load. 

Mr. Morrison, in discussing the question of sequence of cranks, presented 
a diagram showing that with the cranks arranged in the sequence high, 
low, intermediate, the mean compression into the receiver was 1914 per cent 
of the stroke; with the sequence high, intermediate, low, it was 57 per cent, 

In the former case the compression was just what was required to keep 
the receiver-pressure practically uniform; in the latter case the compression 
ee a variation in the receiver-pressure to the extent sometimes of 
2216 lbs. 

Velocity of Steam through Passages in Compound 
Engines, (Proc. Inst. M. E., Feb. 1887.)—In the SS. Para, taking the area 
of the cylinder multiplied by the piston-speed in feet per second and 
dividing by the area of the port the velocity of the initial steam through 
the high-pressure cylinder port would be about 100 feet per second; the ex- 
haust would be about 90. In the intermediate cylinder the initial steam 
had a velocity of about 180, and the exhaust of 120. In the low-pressure 
cylinder the initial steam entered through the port with a velocity of 250, 
and in the exhaust-port the velocity was about 140 feet per second. 


QUADRUPLE-EXPANSION ENGINES, 


H. H. Suplee (Trans. A. S. M. E., x. 583) states that a study of 14 different 
quadruple-expansion engines, nearly all intended to be operated at a pres- 
sure of 180 lbs. per sq. in., gave average cylinder ratios of 1 to 2, to 3.78, ta 
7.70, or nearly in the proportions 1, 2, 4, 8. 

If we take the ratio of areas of any two adjoining cylinders as the fourth 
root of the number of expansions, the ratio of the 1st to the 4th will be the 
enbe of the fourth root. On this basis the ratios of areas for different pres- 
sures and rates of expansion will be as follows: 








Gauge- Absolute Terminal Ratio of Ratios of Areas 
pressures. Pressures. | Pressures. | Expansion. of Cylinders. 
12 14.6 be Os SSL eee 
160 175 10 17.5 1:2.05:4.518; 8.55 
8 21.9 1 2.16:9,4568 210312 
12 16.2 1é3 23013 4502218107 
180 195 10 19.5 1: 2.10: 4.42:. 9.28 
8 24.4 1: 2.22: 4.94: 10.98 
12 17.9 We eOGtadeee nese 
200 215 10 21.5 1: 2.15: 4.64: 9.98 
8 26.9 1:3, 2828/55, 19 7011 384 
12 19.6 1:2.10: 4.48: 9.381 
220 235 10 2050 1: 2.20: 4.85: 10.67 
8 29.4 It 2208 5.42 12 62 





_ Seaton says: When the pressure of steam employed exceeds 190 lbs. abso- 
iute, four cylinders should be employed, with the steam expanding through 
each successively; and the ratio of l. p. toh. p. should be at least 7.5, and 
if economy of fuel is of prime consideration it should be 8; then the ratio 
of first intermediate to h. p. should be 1.8, that of second intermediate to 
first int. 2, and that of 1. p. to second int. 2.2. 

In a paper read before the North East Coast Institution of Engineers and 
Shipbuilders, 1890, William Russell Cummins advocates the use of a four- 
cylinder engine with four cranks as being more suitable for high speeds 
than the three-cylinder three-crank engine. The cylinder ratios, he claims, 
should be designed so as to obtain equal initial loads in each cylinder. The 
ratios determined for the triple engine are 1, 2.04, 6.54, and for the quadru- 
. ple, 1, 2.08, 4.46, 10.47. He advocates long stroke, high piston-speed, 100 rev- 
olutions per minute, and 250 Ibs. boiler-pressure, unjacketed cylinders, and 
separate steam and exhaust valves. 


QUADRUPLE-EXPANSION ENGINES. 773 


Diameters of Cylinders of Recent Tripie-expansion 
Engines, Chiefly Marine. 


Compiled from several sources, 1890--1893. 


Diam. in inches: H = high pressure, J = intermediate, L = low pressure. 


vel I L H of L H I L Tae I I 


an er ef 


| 
| 
| 
| 
| 











3 5 B16.) 85-6), 41 Ton lhe { 49 36 | 58 | 94 
494) 7.5] 13 | 164) 2376) 38.9 40 | 38 | 61.5) 100 
5 23 | 38 | 61 f 2 

6.5| 10.5} 16.59 26-5) 24-5 +31 3.51 38 | 60 38 ¢ 56 | 86 
pot g«| issn a7 | or | 44 Pea] 37° 1-56 9 89 | 61.1. 97 
7.1] 11.8! 18.98 17 | 26.5} 42 | 25 | 40 | 64 | 40 | 59 | 88 
75] 12 | 19 | 17 | 28 | 45 | 2 42 | 69 | 40 7 | 106 
g | 11.5 16 § 18 | 27 | 40 §-26 | 42.51 70 | 40 | 66 | 100 
9 | 14.51 22.58 18 | 299 | 48 f es | 44 | v2 9 41 | 66 | 101 
9.8| 15.7] 25.69 18 | 305.| 51 | 293 44 | 7 4156 67 | 10634 





11.5] 17.5) 30.5 "11 36 33 58 88 $82.5 gg | 1857 
12 19.2) 30.7 20 33 2 33.9] 55.1] 84.6932 af 185.7 
13 92 33.58 21 32 48 34 54 85 47 5 81.5 
14 22.4] 36 21 36 51 34 50 90 1 81.5 
14.5] 24 39 21.7] 33.5} 49.29 34.5] 51 85 it rg 98 
15 24 39 21.9] 34 57 34.5] 57 92 87 ‘ 4 98 





Where the figures are bracketed there are two cylinders of a kind. Two 
28’// = one 39.6’, two 31’ = one 43.8”, two 32.5’ = one 46.0’, two 36’’ = one 
50.9", two 37’ = one 52.3’, two 40/7 = one 56.6’, two 81.5’ = one 115”, two 
85.77 = one 121/’, two 98/7 = one 140’. The average ratio of diameters of 
cylinders of all the engines in the above table is nearly 1 to 1.60 to 2.56 and 
the ratio of areas nearly 1 to 2.56 to 6.55. 

The Progress in Steam-engines between 1876 and 1893 is shown 
in the following comparison of the Corliss engine at the Centennial Exhibi- 
tion in 1876 and the Allis-Corliss quadruple-expansion engine at the Chicago 
Exhibition. 


Q eid : 1876. 
: uadruple- : 
PEP UIED £5. . Gain.1h seal eoinic oa Sees wee oe Seiehin oe Usie a eres Simple 
Cylinders, NUM bEer tae. ese oecles aciees acdc 4 2 

es diameter...........00. Risale chalga 24, 40, 60, 70 in. 40 in. 

es SULOKGL ys swomticiedis de oe. asieite see 72 in. 120 in. 
Why=wheel vdiametery 0s cs seis.c 0410 ceies01s.0 30 ft. 30 ft. 

¢ WICC Of fACC.e. salrms sits oe aiiiaiae 76 in. 24 in. 

ss WIDTH ee ak oe codes ans kes 136,000 Ibs. 125,440 Ibs. 
Revolutions per minute..........c00-+00. 60 86 
Capacity, economical............... Seba 2000 H.P. 1400 H.P. 

od ANLARAMUNI, veers one veer ooutiee 3000 H.P. 2500 H.P. 
"Total weit 23 acate caer scws tod seen eee 650,000 lbs. 1,860,é88 Ibs, 


The crank-shaft body or wheel-seat of the Allis engine has a diameter of 
91 inches, journals 19 inches, and crank bearings 18 inches, with a total 
length of 18 feet. The crank-disks are of cast iron 2nd are 8 feet in diam- 
eter. The crank-pins are 9 inches in diameter by 9 inches long. 

A Doubile-tandem Tripie-expansionu Kungime, built by Watts, 
Campbell & Co., Newark, N. J., is described in Am. Mach., April 26, 1894. 
It is two three-cylinder tandem engines coupled to one shaft, cranks at 90°, 
cylinders 21, 32 and 48 by 60 in. stroke, 65 revolutions per minute, rated H.P. 
2000; fly-wheel 28 feet diameter, 12 ft. face, weight 174,000 lbs.; main shaft 
92 in. diameter at the swell; main journals 19 x 38 in.; crank-pins 9144 x 10 
in.; distance between centre lines of two engines 24 ft. 7 in.; Corliss 
valves, with separate eccentrics for the exhaust-valves of the ],p, cylinder. 


THE STEAM-ENGINE, 


774 


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ECONOMIC PERFORMANCE OF STEAM-ENGINES. %75 


ECONOMIC PERFORMANCE OF STEAM-ENGINES, 


fLeonomy of Expansive Working under Various Condi- 
tions, Single Cylinder. 
(Abridged from Clark on the Steam Engine.) 


1. SINGLE CYLINDERS WITH SUPERHEATED STEAM, NONCONDENSING.—In- 
side cylinder locomotive, cylinders and steam-pipes enveloped by the hot 
gases in the smoke-box. Net boiler pressure 100 lbs.; net maximum press- 
ure in cylinders 80 Ibs. per sq. in. 


Cut-off, per cent....... . 20 25 30 35 40 50 60 70 80 
Actual ratio of expansion 3.91 3.31 2.87 2.53 2.26 1.86 1.59 1.89 1.23 
Water per I.H.P. per hour, 

SYST Ast eee eee Ope 19.4 20 pede tenes. ote Orn lt wae O OO Menmes 


2. SINGLE CYLINDERS WITH SUPERHEATED STEAM, CONDENSING.—The best 
results obtained by Hirn, with a cylinder 2334 x 67 in, and steam super- 
heated 150° F., expansion ratio 334 to 444, total maximum pressure in cylin- 
der 63 to 69 lbs. were 15.63 and 15.69 lbs. of water per I.H.P. per hour. 

38. SINGLE CYLINDERS OF SMALL Size, 8 OR 9 IN. DIAM., JACKE”ED, Non- 
CONDENSING.—The best results are obtained at a cut-off of 20 per cent, with 
75 lbs. maximum pressure in the cylinder; about 25 lbs, of water per I.H.P. 
per hour. 

4. SINGLE CYLINDERS, NOT STEAM-JACKETED, CONDENSING.—Best results. 


~ 











Total 
: Maxi- |Water as 
yy Actual | “mnum_ | Steam 
Engine. * | Cut-off. <P Pressure per 
ca sion | in Qylin-| I.H.P 
Stroke. Ratio. y Bart ae 
. der per |per hour. 
sq. in. x 
ins. per cent.| ratio. lbs. Ibs. 
Corliss and Wheelock...| 18 x 48 12.5 6.95 104.4 19.58 
FEVIRTIRIN Os) O stale'oters Gielen erate 2334 X 67 16.3 5.84 61.5 19.93 
Mair Ma.% 5... ISSGCAAB AS: 52 X 66 24.6 3.84 54.5 26.46 
BAC Oherms trie tels sle/siee's Re | Deo eed 15.5 5.32 hers 26.25 
MDOXUO Rites cree cialels oveisin a nals 26 X 386 18.3 4.46 80.4 23.86 
Dallas..... aicis wienaieaisters seaete 36 X 30 13.3 5.07 46.9 26.69 
Gallatin..... oh tele ens 30.1 X 30 15.0 4.94 81.7 21.89 
SamME ENGINES, AVERAGE RESULTS. 

Long Stroke. Inches. | Cut-off, Per cent, Lbs. Lbs. 
Corliss and Wheelock...| 18 x 48 12.5 104.4 19.58 
15 Ob 30k, Was IOSES eos 2334 X 67 16.3 61.5 19.93 

Short Stroke. 2 
BSCS ohx cds eae sink deeae 25 X 24 #3 aan : 87.7 26.25 

.0 to 33. 
Dexter, Nos. 20, 21, 22, 23] 26 x 36 average 3 ' 79.0 24.05 
13.3 to 26.4 | . 
ae ae pean 4 36 X 30 , ay erage 19.8 { 46.8 26.86 
allatin, Nos, 24, i ‘ 2.8to 18.5 
O6 n  2e.k, Re Un | Seg re eats 138t @.2 23.50 








Feed-water Consumption of Different Types of Engines, 
—The following tables are taken from the circular of the Zabor Indicator 
(Ashcroft Mfg. Co., 1889). In the first of the two columns under Feed-water 
required, in the tables for simple engines, the figures are obtained by 
computation from nearly perfect indicator diagrams, with allowance for cyl- 
inder condensation according to the table on page 752, but without allow- 
ance for leakage, with back-pressure in the non-condensing table taken at 16 
Jbs. above zero, and in the condensing table at 3 lbs. above zero. The com- 
pression curve is supposed to be hyperbolic, and commences at 0.91 of the 
return-stroke, with a clearance of 3% of the piston-displacement. 

Table No. 2 gives the feed-water consumption for Jacketed compound-con- 


776 THE STEAM-ENGINE, 


densing engines of the best class. The water condensed in the jackets is 
included in the quantities given. The ratio of areas of the two cylinders are 
as 1 to 4 for 120 lbs. pressure; the clearance of each cylinder is 3%; and the 
cut off in the two cylinders occurs at the same point of stroke. The initial 
pressure in the 1. p. cylinder is 1 lb. per sq. in. below the back-pressure of the 
h. p. cylinder. The average back pressure of the whole stroke in the |. p. 
cylinder is 4.5 lbs. for 10% cut-off; 4.75 lbs. for 20% cut-off; and 5 lbs. for 30% 
cut-off. The steam accounted for by the indicator at cut-off in the h. p. 
cylinder (allowing a small amount for leakage) is .74 at 10% cut-off, .78 at 
20%, and .82 at 30% cut-off. The loss by condensation between the cylinders 
is such that the steam accounted for at cut-off in the 1. p. cylinder, ex- 
pressed in proportion of that shown at release in the h. p. cylinder, is .85 at 
10% cut-off, .87 at 20% cut-off, and .89 at 30% cut-off. 

The data upon which table No. 3 is calculated are not given, but the feed- 
water consumption is somewhat lower than has yet been reached (1894), the 
lowest steam consumption of a triple-exp. engine yet recorded being 11.7 lbs. 















ABLE No. 1. 
FEED-WATER CONSUMPTION, SIMPLE ENGINES. 
NON-CONDENSING ENGINES. CONDENSING ENGINES. 
n o Feed-water Re- n oO Feed-water Re- 
“ 5 quired per I.H.P. S s quired per I.H.P. 
& Q per Hour. s n per Hour. 
oO o —. 
hy oy 
oO ee) ia ' x ® 1 . ‘ro ‘ s 
SRL: ape het pst gs |e | #4 | SBE 
° as <q8 5 tw ce) Ad qs oe 
2 tC) ea Bas 2 ® i gas 
* 3 > ° © mi ° es] > ° ose 
& ees PO SS a's & “4 - oO Poss 
oO sob) ~~ =A {<>} ~ 
: = 3) wa wd OF oO] f 3) =| wd oO 
2 3 D aq Ano Fi! s ® fq ondH 
Ss | my | &. ares —SO0,8 5 | au | & pre mBHle 
oO ais Lia ire Cane Oo no “z Cas hat C355 
oO | Feb b6 g5oc 2 |} SE g =e 
veh ih wee Cue o 23.0 eh As Res OB Sue 
Sec d a ee ce Leen ewe ee ae | €uba 
CO) S8 (ee) 28h | ea Mie ss | eg] £88 | fat 
a r= kee os 5 tos epee 5 =e o2 5 &s ee | 
Aa | = 6) 6) | = é) 6) 














| 











aed 
oS 
re 
x) 
oo 
ve) 
co co 
on 
© 
Velen 
vers 
woe 
Sc 
Mu 


80 | 16.07] 27.61 29.88 
90 | 19.76] 25.43 27.43 
100 | 23.45] 23.90. | 25.73 


60 | 21.12) 27.55 29.43 
GO | 26.57) 25.44 27.04 
80 | 82.02} 21.04 25.68 
90 | 37.47; 23.00 24.57 
100 | 42.92) 22.25 23.77 
60 | 30.47| 27.24 29.10 
j 27.43 
§ 24. 26.29 
90 | 50.73) 23.91 25.88 
100 7.49) 28.27 - 24.68 
60 Yeerth 27.92 29.63 - 
70 | 45.50) 26.66 28.18 
80 | 53.25) 25.76 Citi al We 
90 | 61.01) 25.03 26.35 
100 | 68.76) 24.47 25.73 


60 | 48.42] 28.94 | 30.66 
70, | 51.94) 27.79 | 29.31 
80 | 60.44] 26.99 | 28.38 
90 | 68.96] 26.32 | 27.62 
100 | 77.48} 25.78 | 26.99 


_ 
oS 


a ee Oe eee eee Se Or OS OS Or 
cost 
oo 
ree 
Co =? 

ra) 
~Fe 
ww 0% 
Or 
=) 
=o 


or 


2 
Oo 
—_— 
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5 


fs 4) 
oO 


CALCULATED PERFORMANCES OF STRAM-ENGINES. 777 























TABLE No. 2. 
FEED-WATER CONSUMPTION FOR COMPOUND CONDENSING ENGINES. 
Initial Pressure above | Mean Bios Press- Woedtwater 
Sete ott. Atmosphere. Atmosphere. Remured 
per cent. per J.H.P. per 
PLP IOs ine. Cylon HP ey, WLP: Cyl 
lbs. lbs. ibs. lest ore 
“80. 4.0 11.67 | 2.65 16.92 
10 100 7.3 15.33 3.87 15.00 
120 11.0 18.54 5.23 13.86 
80 4.3) 26.73 5.48 14.60 
20 100 8.1 eoale 7 56 13.67 
120 [oat 39.29 9.74 13.09 
80 4.6 . 7 37761 7.48 14.99 
30 100 8.5 46.41 10.10 14.21 
120 ular 56.00 12.26 13.87 


TABLE No. 3. 
FEED-WATER CONSUMPTION FOR TRIPLE-EXPANSION CONDENSING ENGINES. 


———i 








Initial Pressure above 














Cut-off. Atmosphere. Mean Effective Pressure. pire cp 
per per I.H.P. 
cent. |H.P. Cyl.,| I. Oyl., |L.P. Cyl.,/H.P. Cyl.,| I. Cyl.,|L.P. Cyl.,| per Hour, 
lbs. lbs. lbs. lbs. lbs. lbs. lbs. 
120 | 37.8 | 1.3 38.5 | 17.1 6.5 12.05 
30 140 43.8 2. 46.5 18.6 ok 11.4 
160 49.3 3.8 55.0 20.0 8.0 10,7 
120 388.8 2.8 DIED 22.8 8.6 165 
40 140 45.8 3.9 59.5 ga 9.1 11.4 
160 51.3 ise} 70.0 25.5 10.0 10.85 
120 39.8 S%. 60.5 26.7 10.1 12.2 
50 1 140 46.8 4.8 70.5 28.0 10.8 11.6 
160 52.8 6.3 82.5 39.0 11.8 Tks) 8a) 


Most Economical Point of Cut-off in Steam-engines, 
(See paper by Wolff and Denton, Trans. A. S. M. E., vol. ii. p. 147-281; also, 
Ratio of Expansion at Maximum Efficiency, R. H. Thurston, vol. ii. p. 128.) 
—The problem of the best ratio of expansion is not one of economy of con- 
sumption of fuel and economy of cost of boiler alone. The ‘question of 
interest on cost of engine, depreciation of value of engine, repairs of engine, 
etc., enters as well; for as we increase the rate of expansion, and thus, 
within certain limits fixed by the back-pressure and condensation of steam, 
decrease the amount of fuel required and cost of boiler per unit of work, 
we have to increase the dimensions of the cylinder and the size of the en- 
gine, to attain the required power. We thus increase the cost of the engine, 
ete., as we increase the rate of expansion, while at the same time we de- 
crease the fuel consumption, the cost of boiler, ete. So that there is in 
every engine some point of cut-off, determinable by calculation and graphi- 
cal construetion, which will secure the greatest efficiency for a given expen- 
diture of money, taking into consideration the cost of fuel, wages of engineer 
and firemen, interest on cost, depreciation of value, repairs to and insurance 
of boiler and engine, and oil, waste, etc., used for engine. In case of freight- 
carrying vessels, the value of the room occupied by fuel should be consid- 
ered in estimating the cost of fuel. 

Sizes and Calculated Performances of Vertical Highe 
speed Engines.—tThe following tables are taken from a circular of the 
Field Engineering Co., New York, describing the engines made by the Lake 
Erie Engineering Works, Buffalo, N. Y. The engines are fair representatives 
of the type now coming largely into use for driving dynamos directly with- 
out belts. The tables were calculated by E. F. Williams, designer of the 
engines. They are here somewhat abridged to save space: 


¢78 


THE STEAM-ENGINE. 


Simple Engines—Non-condensing,. 














BS Phe tie ee 
> od oma 
63\ 3 (8 
ws q fe 
om | cm o 
> 3 + 
mn 
se| £ | 55 
=) oD) fa 
71% 10 37 
816 12 318 
1044 | 14 | 277 
12 16 246 
1344} 18 | 222 
16 20 181 
18 24 158 
22 28 138 
2416 | 32 | 120 
27 34 112 


Mean eff. press.lb. 


Ratio of expans’n. 
Terminal pressure 
(about) 


lbs.}17 





9 


Cyl.condensat’n, %| 26 


Steam per J.H.P. 
per hour..... lbs. 


32.9 











H.P. when | H.P. when | H.P. when wont = g 
Cutting off | Cutting off | Cutting off Wheel Shee: [ates 
at 1/5 stroke.| at 14 stroke.| at 14 stroke.| " mi alg = Pat 
diam. face| y 
oe | ee B 
70 | 80| 90] 70 | 80 | 90] 70| 80] 90] wm In| $ | 4 
lbs. /Ibs. |Ibs.|Ibs.|Ibs.|Ibs.|Ibs.|Ibs.|Ibs.| ~ “ [|] 2} 3 
20) 25) 30) 26) 381] 36) 32 “| 43) 4 4 | 244] 3 
27) 382} 39) 34] 41] 47) 41) 48) 56; 416] 5 | 284) 844 
41; 49} 60} 52) 62) 1) 63) 74] 85) 5/9’’|614] 8l4) 4 
53] 64) 77| 67; 81} 93] 82) 96) 111] 6/871 9| 4 | 41% 
66; 80) 96] 84} 100) 116) 102) 120) 138] 7144 |11 | 4 | 5 
95| 115} 138] 120) 144} 106} 146) 172] 198] 8/4’/|15 | 414] 6 
119} 144) 173} 151} 181) 208) 188) 215) 248)10 19 1:5 Gane 
179} 216) 261) 227} 272) 313) 276) 324) 373)11/8/7/28 | 6 8 
221| 267) 322] 281] 336} 3886) 840) 400} 460)13’4/7/34 | 7 | 9 
269} 325] 392] 342] 409} 470} 414} 487] 560)/14/2’’"\41 | 8 {10 
2 a sy e ‘ 2 ay 5 
24 | 29 | 85 |80.5/36.5] 4 387 [48.5] 50 NO pe! The 
5 4 3 nominal-power 


rating of the en- 


20 |22.3/22.4! 25 |27.6/29.8/33.3136.8/Sines is at 80 Ibs. 


26 
380 


26 | 24 


24 | 24 | 21 
27.4]31.2/29.0|27.9] 32 |31.4] 30 |/4 Stroke. 


‘ oj |\gauge pressure, 
BL det steam cut-off at 





Compound Engines — Non-condensing — High = pressure 
Cylinder and Receiver Jacketed. 








Diam. D 
Cylinder, | 3 
inches. a 
oD 
ad 
9 
4 2 
Pi |} Ay | ay | 2 
Tim) 4 
534] 616/12 | 10 
6364] 7146|138146| 12 
734| 9/1616] 14 
9 }1014)19 | 16 
1014/12 “|2214] 18 
12 ee sone 20 
1314} 1514) 2814] 24 
16 "|1814/3314| 28 
18 2014/88 | 32 
20 (2212/43 | 34 
2416/2816 /52 42 
2814/33 |60 | 48 


Mean effec. press...lbs} 3.3 6.8 





Revolutions per 
Minute 


Ratio of expansion.... 


Cyl. condensation, 


Ter. press. (about) .lbs.| 7.3) 7.7 


ae 


Loss from expanding 


below atmosphere, %| 34 


St. perI.H.P. p. hr.|bs. 


The original table contains figures of horse-power, etc., for 110 and 120 lbs., 
cylinder ratio of 4 to 1; and 140 lbs., ratie 414 to 1. 





H.P.when cutting 
off at 14 Stroke 


in h.p. Cylinder. 


Cyl. 
Ratio, 


344:1,. 


Cyl. 
Ratio, 
416: 1. 





H.P.whencutting| H.P.when cutting 
off at 14 Stroke | off at 14 Stroke 
in h.p. Cylinder .| in h.p, Cylinder. 


Cyl. Cyl. Cyl. Cyl. 
Ratio, | Ratio, | Ratio, | Ratio, 
844:1.| 44:1.) 344: 1.] 44: 1. 


80 | 90 | 180] 150} 80 | 90 | 1380] 150 - 





.|lbs.|lbs.|lbs.|lbs.|llbs.|lbs.}lbs.|lbs. 














1215) 1508 
1589} 1973 


29 | 36 


880 
1151 


16 | 21 


838] 1048 
1096} 1370 


20 | 25 

















1314 





1334 634 914 





14 | 14 





SIS Weg 


10 | 10 
14 115.5) 
0 


12 | 13 | 13 
-2/10.4)10.5) 12 


1 


119 |e 
14.6)17.8 








55 | 42 





B10 70) (aCe 0| 0 
33.3]27.7/28.7]25.4] 30 |26.2) 21 | 20 


CALCULATED PERFORMANCES OF STEAM-ENGINES, 779 


Compound-engines—Condensing—S team-jacketed. 


H.P.when cutting|H.P.when cutting|H.P.when cutting 





mrles off at 144 Stroke | off at 4 Stroke | off at 4 Stroke 

Diam. 2 |& jin h.p. Cylinder. | in h.p. Cylinder, | in h.p. Cylinder, 
JERSE, 8 OU Si a ee 
Inches. m los Cyl. Cyl. Cyl. Cyl. Cyl. Cyl. 
eae Ratio, | Ratio, | Ratio, | Ratio, | Ratio, | Ratio, 

“ se | de:h |] 421. | ged. | 4:1. | 8gs1.] 4:1. 
A |S a a 
ala a n 80 | 110] 115 | 125} 80 ) 110) 115] 125] 80 | 110] 115} 125 
mf | Ibs. |lbs. Ibs. |Ibs.jIbs.|1bs.}lbs.}1bs. |Ibs, |lbs. j1bs.|Ibs. 
6 | 6144)12 | 10] 870} 44} 59) 53) 62) 55) 70; 68} %5| 70} 97) 95] 106 
614) 744|13814| 12 | 818 | 56) 76) 67; 78} 70} 90) 87} 95) 90] 123] 120) 134 
-814| 9 |1616} 14 | 277 83} 112} 100} 116] 104} 133} 129] 141] 138] 183] 179} 2U0 
946)1016)19 | 16 | 246 | 109) 147) 131] 152) 136) 174) 169] 185] 174] 239) 284] 261 
11 =(|12 = |2216) 18 | 222 | 156} 210) 187) 218) 195) 250] 242] 265} 250) 343) 385) 37 
1216/1816 }25 20 | 185 } 192] 260) 231) 269} 241) 308] 298] 327) 3808} 423] 414] 462 
14 |1516/2844] 24 | 158 | 258] 348} 310} 361] 323) 413] 400] 439} 4128) 568) 555) 619 
17 |1846/3314] 28 | 188 | 346} 467) 415) 484) 433) 554) 536] 588) 554 761) 744] 830 
19 |2016|388 82 | 120 | 446) 602) 5385] 624) 558] 714) 691) 758) 714} 981) 959)1070 
21 (2216/43 34 | 112 72) 772) 686} 801) 715] 915) 887) 972) 915)1258)1230)1573 
26 |284/52 | 42 93 | 838)1131/1006) 1174) 1048) 18411299] 1425) 13841}1844/ 1801/2012 
30 3 {60 48 80 |1096}1480/1316) 1534] 1370) 1757] 1699] 1863/1 757|2411/2356) 26382 
Mean effec. press..Ibs.| 20 | 27 | 24 | 28 | 25 | 32 | 31 | 34 | 32 | 44 | 43 | 48 

Ratio of Expansion...} 1344 1614 oo Be — 814 
Cyl. condensation, %...| 18 | 18 | 20 | 20 | 15 18 14 | 14 








St. per 1.H.P. p. hr.lbs.|17.3/16.6/16.6]15.2/17. olt64|16 3/15. 8117. “sli? *olte-sl16-0 


The original table contains figures for 95 lbs., cylinder ratio 3144 to 1; and 
120 lbs , ratio 4 to 1. 





Triple-expansion Engines, Non-condensing.—Receiver 


only Jacketed,. 


Horse-power 


Horse-power 


Horse-power 



































al 
i n|% when Cutting | when Cutting | when Cutting 
peiniace a a off at 42 per off at 50 per off at 67 per 
inches, Sia | cent of Stroke | cent of Stroke | cent of Stroke 
k -—|2 | in First Cylin- | in First Cylin- | in First Cylin- 
g|S5 der. der. der. 
TS TAS os Meat dlne commana eae) | OB «tellin d woke meal iiblalieir is 28 BAR fo 
£\e= 
js ad ag gs oy Ba Se 2 180 Ibs.| 200 lbs.| 180 lbs.} 200 Ibs. | 180 lbs.} 200 Ibs, 
434 | 74 | 12 {10} 370 55 64 70 84 95 108 
5l4 | 8l6 | 18% |12) 318 70 81 90 106 120 137 
614 | 1044 | 1644 |14] 277] 104 121 133 158 179 204 
4% | 12 19 16] 246 136 158 174 207 234 267 
2 1414 | 2214 {18} 222 195 226 250 296 335 382 
10 16 25 20} 185} 241 279 808 366 414 47 
1114 | 18 2814 |24) 158] 323 374 413 490 555 632 
13 22 3314 |28) 1388) 433 502 554 657 744 848 
15 2414 | 88/32] 120) 558 647 714 847 959 1093 
17 27 43 24) 112) °W15 829 915 1089 1230 1401 
20 33 52/42) +93) 1048 1215 1341 1592 1801 2053 
2314 | 38 60 (48} 80) 1370 1589 1754 2082 2856 2685 
Mean effective press., Ibs. 25 29 32 38 43 | 49 
No. of expansions.. 16 13 10 
Per cent cyl. condens.... 14 12 10 
Steam p. 1.H.P. p.hbr.,Ibs.| 20.76 | 19.36 | 19.25 {17.00 | 17.89 | 17.20 
Lbs. coal at 8lb. evap. lbs.| 2.59 2.39 2.40 2.12 2.23 2.15 


780 THE STEAM-ENGINE. 


Vriple-expansion Engines—Condensing—Steame 
Jacketed. 








Horse-power|Horse-power|Horse-power | Horse-power 





Diameter :, | When Cut- | when Cut- | when Cut- | when Cut- 
Cylinders, | a |&, ting off at 14|ting off at l4|ting off at 14| ting off at 34 
inches. 2 a Stroke in Stroke in Stroke in Stroke in 

ofa First Cylin- | First Cylin- | First Cylin- | First Cylin~ 

£29 der. der. der. der. 

g 22} ———_|--_——_ ——__ | __ 
Bla fAale eS 120; 140); 160] 120) 140) 160} 120} 140) 160} 120] 140} 160 
apa ie PRY RETA 2 Ibs.| Ibs.|Jbs.|1bs.} lbs.| Ibs.| lbs.| lbs.} 1bs.| lbs.] lbs.} Ibs. 





434| 714/12 | 10 | 810) 35) 42) 48) 44] 58) 59] 57] 72] 84] 81 Met O's 
5lg| 816]1314] 12 | 318] 45) 53! 62] 56) 67| 76) 78| 92) 107] 104] 123) 140 
619)1014/1614) 14 } 207) 67) 79} 92) 83} 100) 112] 108] 137] 159] 154) 183} 208 
The/12 19 | 16 | 246] 87) 103] 120] 109} 1381) 147) 141] 180] 208] 201] 239] 272 
9 }1446)2216} 18 | 222) 125) 148) 172) 156) 187) 211) 203] 257) 299] 289) 843} 390 
10 {16 |25 | 20 | 185) 154) 183) 212} 192) 231] 260) 250) 317] 868] 856) 423] 481 
1144]18 |2814] 24 | 158] 206) 245) 284] 258! 310} 348) 835] 426] 494] 477) 568) 645 
13 |22 |83)6} 28 | 138) 277| 3829) 381] 346] 415) 467) 450) 571] 663) 640} 761] 865 
15 |2416/88 | 32 | 120) 357) 424) 491} 446] 535) 602) 580) 736] 854] 825] 981/1115 
17 |27 143 | 84 { 112] 458) 543) 629) 572) 686] 772 744) 944]1095| 1058) 1258] 1430 
20 |33 [52 | 42] 93) 670 796) 922) 838)1006)1131/ 1089] 1383] 1605 | 1551} 1844/2096 
2314/38 |60 | 48 { 80) 877/1041/1206) 1096/1316 1480 1424 1808} 2099 | 2028) 2411 |2740 


-——— | —— i | | | | 


Mean effec. press.,lbs.| 16! 19] 22) 20] (24) 27) 26| 33/88.3) 37] 44] 50 
No. of expansions.... 26.8 20.1 13.4 8.9 






































Per cent cyl. condens.| 19 | 19 ) 19 | 16 | 16 | 16 | 12] 12 | 12 2S aaae 
St. p. LH.P. p. hr., Ibs.|14.7]18. 9/13.3]14.3)18.98]/13.2 14.3]13.6]13.0]15.7/14.9/14.2 
Coal at 8lb. evap., lbs.} 1.8]1.73/1.66/1.78]1.74]1.65 1.78]1.70]1.62]1.96/1.86]1.77 





Wype of Emgine to be used where Exhaust-steam is 
needed for Meating.—In many factories more or less of the steam 
exhausted from the engines is utilized for boiling, drying, heating, ete. . 
Where all the exhaust-steam is so used the question of economical use of 
steam in the engine itself is eliminated, and the high-pressure simple engine 
is entirely suitable. Where only part of the exhaust-steam is used, and the 
quantity so used varies at different times, the question of adopting a simple, 
a condensing, or a compound engine becomes more complex. This problem 
is treated by C. T. Main in Trans. A. S. M. E., vol. x. p. 48. He shows that 
the ratios of the volumes of the cylinders in compound engines should vary 
according to the amount of exhaust-steam that can be used for heating. A 
case is given in which three different pressures of steam are required or 
could be used, as in a worsted dye-house: the high or boiler pressure for 
the engine, an intermediate pressure for crabbing, and low-pressure for 
* boiling, drying, ete. If it did not make too much complication of parts in 
the engine, the boiler-pressure might be used in the high-pressure cylinder, 
exhausting into a receiver from which steam could be taken for running 
small engines and crabbing, the steam remaining in the receiver passing 
into the intermediate cylinder and expanded there to from 5 to 10 lbs. above 
the atmosphere and exhausted into a second receiver. From this receiver 
is drawn the low-pressure steam needed for drying, boiling, warming mills, 
etc., the steam remaining in receiver passing into the condensing cylinder. 


Comparison of the Economy of Compound and Single- 
cylinder Corliss Condensing Engines, each expanding 
about Sixteen Times, (D. 5S. Jacobus, Trans. A. S. M. E., xii. 943.) 


The engines used in obtaining comparative results are located at Stations 
I. and II. of the Pawtucket Water Co. 

The tests show that the compound engine is about 30% more economical 
than the single-cylinder engine. The dimensions of the two engines are ag 
follows: Single 20’ x 48’, compound 15” and 38014’ x 30’”.. The steam 
used per horse-power per hour was: single 20.35 lbs., compound 13.73 lbs. 

Both of the engines are steam-jacketed, practically on the barrels only, 
with steam at full boiler-pressure, viz. single 106.3 lbs., compound 127.5 lbs. 


PERFORMANCES OF STEAM-ENGINES, got 


The steam-pressure in the case of the compound engine is 127 lbs., or 21 
Ibs. higher than for the single engine. If the steam-pressure be raised thig 
amount in the case of the single engine, and the indicator-cards be increased. 
accordingly, the consumption for the single-cylinder engine would be 19.97 
lbs. per hour per horse-power. F 

Two-cylinder vs. Three-cylinder Compound Engine,— 
A Wheelock triple-expansion engine, built for the Merrick Thread Co., 
Holyoke, Mass., is constructed so that the intermediate cylinder may be cut 
out of the circuit and the high-pressure and low-pressure cylinders run as @ 
two-cylincer compound, using the same conditions of initial steam-pressure 
and load. The diameters of the cylinders are 12, 16, and 2433 inches, the 
stroke of the first two being 36 in. and that of the low-pressure cylinder 48 
in, The results of a test reported by S. M. Green and G.I. Rockwood, Trans. 
A.5S.M. E., vol. xiii. 647, are as follows: In lbs. of dry steam used per I.H.P. 
per hour, 12 and 2443 in. cylinders only used, two tests 13.06 and 12.76 lbs., 
average 12.91. All three cylinders used, two tests 12.67 and 12.90 Ibs., average 
12.79. The difference is only 1%, and would indicate that more than two cylin- 
ders are unnecessary in a compound engine, but it is pointed out by Prof, 
Jacobus, that the conditions of the test were especially favorable for the 
two-cylinder engine, and not relatively so favorable for the three cylinders. 
The steam-pressure was 142 lbs. and the number of expansions about 25. 
(See also discussion on the Rockwood type of engine, Trans. A.S. M. E., vol. 
xvi.) 

Effect of Water contained in Steam on the Efficiency of 
the Steam-engine,. (From a lecture by Walter C. Kerr, before the 
Franklin Institute, 1891.)-—Standard writers make little mention of the effect 
of entrained moisture on the expansive properties of steam, but by common 
cousent rather than any demonstration they seem to agree that moisture 
produces an ill effect simply to the percentage amount of its presence. 
That is, 5% moisture will increase the water rate of an engine 5%. 

Expefiments reported in 1893 by R. C. Carpenter and L. S. Marks, Trans. 
A.S. M. E., xv., in which water in varying quantity was introduced into the 
steam-pipe, causing the quality of the steam to range from 99% to 58% dry, 
showed that throughout the range of qualities used the consumption of dry 
steam per indicated horse-power per hour remains practically constant, and 
indlcated that the water was an inert quantity, doing neither good nor harm. 

Relative Commercial Economy of Best Wodern Types of 
Compound and Triple-expansion Engines. (J. 1. Venton, 
American Machinist, Dec. 17, 1891.)\—The following table and deductions 
show the relative commercial economy of the compound and triple type for 
the best stationary practice in steam plants of 500 indicated horse-power. 
The table is based on the tests of Prof. Schréter, of Munich, of engines built 
at Augsburg, and those of Geo. H. Barrus on the best plants of America, and 
of detailed estimates of cost obtained from several first-class builders. 


Trip motion, or Corliss engines of [ 
the twin-compound-receiver con- | 


densing type, expanding 16 times. HP : 
Mielec tz) ; .P., assuming 8.5 lbs. 1.60 1.65 
Boiler pressure 120 Ibs. actual evaporation. 


Trip motion, or Corliss engines of { Lbs. water per hour per 
the triple-expansion four-cylin- H.P., by measurement. 
der-receiver condensing type, ex- + Lbs. coal per hour per 
panding 22 times. Boiler pressure, H.P., assuming 8.5 lbs. 1.48 1.50 
150 Ibs. actual evaporation. 


Lbs. water per hour per 
H.P., by measurement, t 18.6 14,0 
Lbs. coal per hour per 


1 12.56 12.80 


The figures in the first column represent the best recorded performance 
(1891), and those in the second column the probable reliable performance. 

The table on the next page shows the total annual cost of operation, with 
coal at $4.00 per ton, the plant running 300 days in the year, for 10 hoursand 
for 24 hours per day. 


Increased cost of triple-expansion plant per horse-power, including 
boilers, chimney, heaters, foundations, piping and erection. ........ $4.50 
Taking the total cost of the plants at $33.50, $36.50 and $41 per horse- 

power respectively, the figures in the table imply that the total annual sav- 

ing is as follows for coal at $4 per ton: 

1, A compound 500 horse-power plant costs $18,250, and saves about $1630 
for 10 hours’ service, and $4885 for 24 hous’ service, per year over a single 
plant costing $16,750, That is, the compound saves its extra cost in 10-hour 
service in about one year, or in 24-hour service in four months, 


« 


182 THE STHAM-ENGINE. 


2, A triple 500 horse-power plant costs $20,500, and saves about $114 per 
year in 10-hour service, or $826 in 24-hour service, over a compound plant, 
thereby saving its extra cost in 10-hour service in about 1934 years, or in 
24-hour service in about 234 years. 


Hours TUnnINE PEL iCayss ser siviee o'sielcie'e ssiaien ese 10 24 


Expense for coal. Compound plant.......... $9.90 $28.50 
Expense for coal. Triple plant... ........... 9.00 25.92 
Annual saving of triple plant in fuel....... .. 0.90 2.60 
Annual interest at 5% on $4.50. ................ $0.23 $0.23 
Annual depreciation at 5% on $4.50...-....... 0.23 0.23 
Annual! extra cost of oil, 1 gallon per 24-hour 
day, at $0.50, or 15% of extra fuel cost....... OF 1D 0.36 
Annual extra cost of repairs at 3% on $4.50 per 
Oa WOUPSsciccte See ehte Meta tne eines y tides nad 0.06 0.14 
$0.67 $0.96 
ANDUAL SAVINGS DET EH bestia oreo he Sees cise crew $0.23 $1.64 


Highest Economy of Pumping Engines, 1900. (Eng. Newss 
Sept. 27, 19v0.) 








Name of Builder............... SZ. P. Allis Co. ead Mfg. 
oO. 
OCAUOM Ny cca’ sie sth gajtsioriere- / ChestnutHill,| St. Louis Wildwood, Pa. 
Boston. (No. 10). 
ES ANSLOMNS kes cele eles eae Triple. Triple. Quadruple. 
Cyls. diam. and stroke, in..... 30, 56, 87. x 66/34, 62, 92 x 72)19},293,493,57¢ x42 
Plungers, diam., in............ 42 29 143 
Revs. per min...... oA Eni Hie 16.43 86.5 
Steam pressure, lbs. per sq. in. 187.4 180.2 199.9 
Vacuum, lbs. per sq. in........ 13.8 14.04 18.11 
Ind. horse-power..... Ate dhatete OM 801.6 801.6 712 
Capacity, million gals..,...... 30 15 6 
FUOUAIGMEAG wits ce te ces ne ose teiee 140.35 292.11 504.06 
Duty per million B.T.U....... 157,052,500 * | 158,077,324 162,948,824 
Dry steam per I.H.P. hour, lbs. 10.335 10.676 12.26 
B.T.U. per I.H.P. per min..... 196.08 * 201 .96 185.96 
Thermal efficiency, per cent... 21.63 * 21.003 22.81 
Friction, per cent.............. 6.71 3.16 6.12 
Ratio of expansion, about..... 42 23.4 24 


* These figures do not include the heat saved by the economizer; including 
this they are 163,912,800; 187.8; 22.58. The Nordberg engine had a series of 
feed-water heaters taking steam respectively from the exhaust, from the 
low-pressure cylinder, and from the third, second, and first receivers. The 
feed-water was thereby treated successively to 105°, 136°, 193°, 260°, and 
811° F. The coal consumption of the Chestnut Hill engine was 1.062 lbs. 
per I.H.P. per hour, including the coal used by the fan, stoker, and econo- 
mizer engines, This is the lowest figure yet recorded. 


Steam Consumption of Sulzer Compound and Triple- 
expansion Engines with Superheated Steam. 


The figures on the next page were furnished to the author (Aug., 1902) 
by Sulzer Bros., Winterthur, Switzerland. They are the results of official 
tests by Prof. Schréter of Munich, Prof. Weber of Zurich, and other emi- 
nent engineers. : 


PERFORMANCES OF STEAM-ENGINES, 


433 


Notrs.—A, B, C, D, tandem engines at electrical stations’ A, Frank- 


fort a/M.; B, Zurich; C, 


Mannheim; D, 


Mayence. 


E, F, tandem engine 


with intermediate superheater: H, Metallwarenfabrik, Geislingen, Wiirtem- 
berg; F, Neue Baumwoll-Spinnerei, Hof, Bavaria. i 
cal stations, Berlin’ G, Moabit station, horizontal 4-cyl.; H, Louisenstrasse, 


4-cyl. vertical. 


COMPOUND ENGINES, 


G, H, engines at electri- 










































































Se 















































a : “J Steam Consump- | Pci 
6 Coal : 2 tion in Pounds. Ehoteno? 
Zl elie i8 |3 | 
8 | |Dimensions iS zie 2 oy : 
a - ERO, ea : ; : 5 ) 
= a C finders w | Ee fy A mM) a 3: : = |2 g 
q Ni Oi oe foe Ns) Silene ye er arse = s a q 
° ao Inches. on Siig aa aS Mx 7H uy B00 leis 
2 me -|e zoel Be ee sienem sey q 3 f 
3 8 2 /S S| ge) 2 6 ° Oo} @ |§am 
his 2 la FA) se oid (a jas Oy tlre yey aA 
H|4 Sis |e > Ay Ay Ay C. i) 
|__| |- | fe ill Sel EER Te A Se Tea ek 
A |1500] 30.5 and | 85/130/356/26.4; 850/13.3 |14.90/21.30/0.895|0.851 
to |49.2x59.1 132/428)26.4| 842}12.05/13.52/19.48)0.891/0.842 
1800 122) 482)26 .6]1719)12.42/13.24/18.72/0.939/0.903 
B |1050} 26.8 and |100| 108/455/26.8/1167|13.10)13.77|19.72/0.951|0.C04 
to |43.3xX51.2 
1250 
C | 800} 24 and 83} 136) 357/28 481|13.00/14.68/21.30/0.886/0.830 
to |40.4x51.2 134] 356/28 750|13.10/14.14/20.35|0.926|/0.877 
1000 135] 356/27 .6|1078/14.10)14.95)21.30/0.932/0.892 
135| 547/28 515]11.32112.70}18.69]0.894|/0.824 
132| 533/27 .8| 788/11.52/12.38]17.90/0.931/0.875 
134] 545/27 .2/1100/11.88)12.50)17.92}0.951|0.902 
D | 950! °26 and 86| 130] 358/28 .2}1076|14.10)14.82/21.25/0.951]0.902 
fon/42539<51 52 129) 358/28 |1316|14.50/15.10/21.55)0.960/0.915 
1150 132] 496/28 .3)1071)11.73/12.33/17.70/0.951/0.903 
do., non-cond’g} 136| 527 1021)15.37)16.30/23.4010.943'0.893 
E |400} 17.7 and |110/135|577/26.4| 519'10:80'Intermediate ) 349°F. 
to |80.5X35.4 135| 554/26.4] 347/10.35| superheating, | Solos 
500 temp. of steam 
at entrance of } 
ep De iteaid Dy eee E } 
A OOO\ 26.9 and Oot a Gone Mec l Soin oo lsllebenemeaeticysl ois) <1) si'6 BL SU vametie 
to |47.2X66.9 VA CNGGA 2 Leela OG tS arch ae h ee etedes 31 oe sas 
1200 128] 572|27.1| 788)10.70 
TRIPLE-EXPANSION ENGINES. 
g - oO : Pl 
i a F | | BaF 
B ‘ 3 a2 a) Be ‘ Bi 
° Dimensions Of ee ® ve Dn. a Ay fel 
Bac | Gyliaders, | Se ae | oe | gh | a |Shs 
Bes : Of = 5 : 80 Sh — gq 
=e aime Ais) ao 5.8 =} 
ae < alee |S gh 5 
Z = A | = aE 
G 3000 |321,474,58x59| 85 188 606 28 2860 8.97 
190 397 274 | 2880 | 11.28 
H 38000 | 34,49.61 x51 834 189 613 Digi 2908 9.41 
196 381 264 |-38040 | 11.57: 








784 THE STEAM-ENGINE, 


Relative Economy of Compound Non-condensing Ene 
gines under Variable Loads.—F. M. Rites. in a paper on the Steam 
Distribution in a Form of Single-acting Engine (Trans. A. 8. M. E., xiii. 537), 
discusses an engine designed to meet the following problem: Given an 
extreme range of conditions as to load or steam-pressure, either or both, to 
fluctuate together or apart, violently or with easy gradations, to construct 
an engine whose economical performance should be as good as though the 
engine were specially designed for a momentary condition —the adjustment 
to be complete and automatic. In the ordinary non-condensing compound 
engine with light loads the high-pressure cylinder is frequently forced to 
supply all the power and in addition drag along with it the low-pressure 
piston, whose cylinder indicates negative work. Mr. Rites shows the 
peculiar value of a receiver of predetermined volume which acts as a clear- 
ance chamber for compression in the high-pressure cylinder. The Westing- 
house compound single-acting engine is designed upon this principle. The 
following results of tests of one of these engines rated at 175 H.P. for most 
economical load are given : 


WATER RATES UNDER VARYING LOADS, LBS. PER H.P. PER HOUR. 


Horse: pOWer: ss. 4-052 210 170 140 115 100 80 50 
Non-condensing.......... 22.6 21.9 22.2 22.2 22.4 24.6 28.8 
Condensing Jo. fiona bb 64) A982 98.2 618.2. 18.8 eas Seo 


Efficiency of Non-condensing Compound Engines. (W. 
Lee Church, Am. Mach., Nov. 19, 1891.)—The compound engine, non-con- 
densing, at its best performance will exhaust from the low-pressure cylin- 
der at a pressure 2 to 6 pounds above atmosphere. Such an engine will be 
limited in its economy to a very short range of power, for the reason that 
its valve-motion will not permit of any great increase beyond its rated 
power, and any material decrease below its rated power at once brings the 
expansion curve in the low-pressure cylinder below atmosphere. In other 
words, decrease of load tells upon the compound engine somewhat sooner, 
and much more severely, than upon the non-compound engine. The loss 
commences the moment the expansion line crosses a line parallel to the 
atmospheric line, and at a distance above it representing the megn effective 
pressure necessary to carry the frictional load of the engine. Wien expan- 
sion falls to this point the low-pressure cylinder becomes an air-pump over 
more or less of its stroke, the power to drive which must come from the . 
high-pressure cylinder alone. Under the light loads common in many 
industries the low-pressure cylinder is thus a positive resistance for the 
greater portion of iis stroke. A careful study of this problem revealed the 
functions of a fixed intermediate clearance, always in communication with 
the high-pressure cylinder, and having a volume bearing the same ratio to 
that of the high-pressure cylinder that the high-pressure cylinder bears to 
the low-pressure. Engines laid down on these lines have fuily confirmed 
the judgment of the designers. 

The effect of this constant clearance is to supply sufficient steam to the 
low-pressure cylinder under light loads to hold its expansion curve up to 
atmosphere, and at the same time leave a sufficient clearance volume in the 
high-pressure cylinder to permit of governing the engine on its compression 
under light loads. 

Economy of Engines under Varying Loads. (From Prof. 
W. C. Unwin’s lecture before the Society of Arts, London, 1892.)—The gen- 
eral result of numerous trials with large engines was that with a constant 
load an indicated horse-power should be obtained with a consumption of 
144 pounds of coal per indicated horse-power for a condensing engine, and 
134 pounds for a non-condensing engine, figures which correspond to about 
134 pounds to 21g pounds of coal per effective horse-power. It was much more 
difficult to ascertain the consumption of coal in ordinary every-day work, 
but such facts as were known showed it was more than on trial, 

In electric-lighting stations the engines work under a very fluctuating 
load, and the results are far more unfavorable. An excellent Willans non- 
condensing engine, which on full-load trials worked with under 2 pounds 
per effective horse-power hour, in the ordinary daily working of the station ° 
used 7144 pounds per effective H.P. hour in 1886, which was reduced to 4.3 
pounds in 1890 and 3.8 pounds in 1891. Probably in very few cases were the 
engines at electric-light stations working under a consumption of 444 pounds 
per effective H.P. hour, In the case of small isolated motors working with 
a fluctuating load, still more extravagant results were obtained. 


PERFORMANCES OF STEAM-ENGINES. ~ WS5 


ENGINES IN ELECTRIC CENTRAL STATIONS. 


LVOAT Et ee Be Miriamisciiscclae celeste oe a baldnscas csi acer bLCCUs LOOUs mouse 
Coal used per hour per effective H.P........... 8.4 5.6 4.9 
ae Eye pS er LLLOLGALOCE <; welsiec a accoteo.s 6.5 4.85 3.8 


At electric-lighting stations the load factor, viz., the ratio of the average 
load to the maximum, is extremely small, and the engines worked under 
very unfavorable conditions, which largely accounted for the excessive fuel 
consumption at these stations. 

In steam-engines the fuel consumption has generally been reckoned on 
the indicated horse-power. At full-power trials this was satisfactory 
enough, as the internal friction is then usually a small fraction of the total. 

Experiment has, however, shown that the internal friction is nearly con- 
stant, and hence, when the engine is lightly loaded, its mechanical efficiency 
is greatly reduced. At full load small engines have a mechanical efficiency 
of 0.8 to 0.85, and large engines might reach at least 0.9, but if the internal 
friction remained constant this efficiency would be much reduced at low 
powers. Thus, if an engine working at 100 indicated horse-power had an effi- 
ciency of 0.85, then when the indicated horse-power fell to 50 the effective 
horse-power would be 35 horse-power and the efficiency only 0.7. Similarly, 
at 25 horse-power the effective horse-power would be 10 and the efficiency 
0.4. 

Experiments on a Corliss engine at Creusot gave the following results : 
Effective power at fullload: ........ sce la OS 0:50 92 0-25 Olio 
Condensing, mechanical efficiency...... 0.82 0.79 0.74 0.63 0.48 
Non-condensing, ‘°‘ . fice: O86 0.83 0.78 0.67 0.52 


At light loads the economy of gas and liquid fuel engines fell off even 
more rapidly than in steam-engines. The engine friction was large and 
nearly constant, and in some cases the combustion was also less perfect at 
light loads. At the Dresden Central Station the gas-engines were kept 
working at nearly their full power by the use of storage-batteries. The 
results of some experiments are given below: 

Brake load,per Gas-engine, cu.ft. Petroleum Eng., Petroleum Eng., 


cent of full of Gas per Brake Lbs.of Oil per Lbs. of Oil per 
Power. H.P. per hour, B.H.P. per hr. B.H.P. per hr. 
100 22.2 0.96 0.88 
75 23.8 1.11 0.99 
59 28.0 1.44 1.20 
20 40.8 2.38 1.82 
1214 66.3 4.25 3.07 


Steam Consumption of Engines of Various Sizes.—W. C. 
Unwin (Cassier’s Magazine, 1894) gives a table showing results of 49 tests of 
engines of different types. In non-condensing simple engines, the steam 
consumption ranged from 65 lbs. per hour in a 5-horse-power engine to 22 
lbs. in a 134-H.P. Harris-Corliss engine. In non-condensing compound en- 
gines, the only type tested was the Willans, which ranged from 27 lbs. in a 
10 H.P. slow-speed engine, 122 ft. per minute, with steam-pressure of 84 lbs. 
to 19.2 lbs. in a 40-H.P. engine, 401 ft. per minute, with steam-pressure 165 
lbs. A Willans triple-expansion non-condensing engine, 39 H.P., 172 Ibs. 
pressure, and 400 ft. piston speed per minute, gave a consumption of 18.5 lbs. 
In condensing engines, nine tests of simple engines gave results ranging only 
from 18.4 to 22 lbs., and, leaving out a beam pumping-engine running at slow 
speed (240 ft. per minute) and low steam-pressure (45 lbs.), the range is only 
from 18.4 to 19.8 lbs. In compound-condensing engines over 100 H.P., in 13 
tests the range is from 13.9 to 20 lbs. In three triple-expansion engines the 
figures are 11.7, 12.2, and 12.45 lbs., the lowest being a Sulzer engine of 360 
H.P. In marine compound engines, the Fusiyama and Colchester, tested 
by Prof. Kennedy, gave steam consumption of 21.2 and 21.7 lbs.; and the 
Meteor and Tartar triple-expansion engines gave 15.0 and 19.8 lbs. 

Taking the most favorable results which can be regarded as not excep- 
tional, it appears that in test trials, with constant and full load, the expen- 
diture of steam and coal is about as follows: 

Per Indicated Horse- Per Effective Horse 








power Hour. power Hour. 
Kind of Engine, -——- 4 - “a aaal 
Coal, Steam, Coal, Steam, 
lbs. lbs. lbs. lbs. 
Non-CONnGensilig’.....)...% ce: useeee ou 16.5 2.00 18.0 


Condensing....,.... eo occ ch beg mmneee 13.5 1.75 15.8 


786 THE STEAM-ENGINE. 


These may be regarded as minimum values, rarely surpassed by the most 
efficient machinery, and only reached with very good machinery in the 
favorable conditions of a test trial. 

Small Engines and Engines with Fluctuating Loads are 
usually very wasteful of fuel. The following figures, illustrating their low 
economy, are given by Prof. Unwin, Cassier’s Magazine, 1894. 


CoaL CONSUMPTION PER INDICATED HORSE-POWER IN SMALL ENGINES. 


In Workshops in Birmingham, Eng. 


Probable I.H.P. at fullload... 12 45 60 45 75 60 60 
Average I.H.P. during obser- 


VAtlonasy)ut ehtycatie tls rivets 2.96 7.87 8.2 8.6 23.64 19.08, 20.08 
Coal per I.H.P. per hour dur- 
ing observation, lbs......... 386.0... 21.25, 22:61) . 18.18 12368569253) 98i50 


It is largely to replace such engines as the above that power will be dis- 
tributed from central stations. 


Steam Consumption in Small Engines, 


Tests at Royal Agricultural Society’s show at Plymouth, Eng. Hngineer- 
ing, June 27, 1890. 


Diam. of | Per Brake H.P.,| 2 





Com- | Cylinders.| ot, Max. er hour, | S2¢ 

Rated H.P.| pound or Reems pao’ Steam- iz ie aah aa 
Simple. h.p. | l.p. pressure.) Coal.| Water. RO 

5 simple 12 AES 10 75 12.12] 78.1 Ibs.|6.1 Ib. 

3 compound, 3 6 6 110 4.82} 42.03 ° |8.72°* 

2 simple 44 |..05. 114 75 DIRT SOS OES: Be Gae 








Steam-consumption of Engines at Various Speeds. 
(Profs. Denton and Jacobus, Trans, A.S. M. E., x. 722)—17 x 380in. engine, 
non-condensing, fixed cut-off, Meyer valve. 


STEAM-CONSUMPTION, LBS. PER 1.H.P. PER Hour. 
Figures taken from plotted diagram of results. 


Revs. per min..... tej IBS alloy P48) 24 32 40 48 56 W2 88 
¥g cut-off, lbs..... 39) 30) Oe 900). 298 29 = 828 28D coro Meco oket 
4 ie 1 Sa 39) 34 ol 29 On coe eb cd. Fr e8n Orb Ove eben G 
44 oa Rares 389 36 34 33 382 380.8 29.8 29.2) 28:8 28.7 


STEAM-CONSUMPTION OF SAME ENGINE; FIXED Spzep, 60 Revs. PER Min. 


Varying cut-off compared with throttling-engine for same horse-power 
and boiler-pressures: 


Cut-off, fraction of stroke 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 
Boiler-pressure, 90. los... 29. 2b elo 2am 27.2 2782835 eye eee 
ze 60: lbs... ° 89 y- 84.2:98212531 503154) 31) Gusee2 34 te30 ps9 


THROTTLING-ENGINE, % CUT-OFF, FOR CORRESPONDING HORSE- POWERS. 


Boiler-pressure, 90 lbs... 42 387 388.8 81.5 29.8 .... 
be GOMDS <0: see SO N49 SAG Sie44 (Gaedd 


Some of the principal conclusions from this series of tests are as follows: 

1. There is a distinct gain in economy of steam as the speed increases for 
14, 14, and \4 cut-off at 90 lbs. pressure. The loss in economy for about 14 
cut-off is at the rate of 1/12 lb. of water per H.P. for each decrease of a 
revolution per minute from 86 to 26 revolutions, and at the rate of 5 lb. of 
water below 26 revolutions. Also, at all speeds the 144 cut-off is more eco- 
nomical than either the 4% or 4 cut-off. 

2. At 90 lbs. boiler-pressure and above 14 cut-off, to produce a given H.P. 
reauitee about 20% less steam than to cut off at 7% stroke and regulate by the 
throttle. 

3. For the same conditions with 60 Ibs. boiler-pressure, to obtain, by 
throttling, the same mean effective pressure at 7 cut-off that is obtained by 


PERFORMANCES OF STEAM-ENGINES, "87 


curing off about 14, requires about 30% more steam than for the latter 
condition. 

High Piston-speed in Engines. (Proc. Inst. M. E., July, 1883, p. 
321).—The torpedo boat is an excellent example of the advance towards 
high speeds, and shows what can be accomplished by studying lightness 
and strength in combination. In running at 2244 knots an hour, an engine 
with cylinders of 16 in. stroke will make 480 revolutions per minute, which 
gives 1280 ft. per minute for piston-speed; and it is remarked that engines 
running at that high rate work much more smoothly than at lower speeds, 
and that the difficulty of lubrication diminishes as the speed increases. 

A High-speed Corliss Engine.—aA Corliss engine, 20 x 42 in., has 
been running a wire-rod mill at the Trenton Iron Co.’s works since 1877, at 
160 revolutions or 1120 ft. piston-speed per minute (Trans. A. S. M. E., ii. 
72). A piston-speed of 1200 ft. per min. has been realized In locomotive 
practice. 

Whe Limitation of Engine-speed. (Chas. T. Porter, in a paper 
on the Limitation of Engine-speed, Trans. A. 8. M. E., xiv. 806.)—The 
practical limitation to high rotative speed in stationary reciprocating steam - 
engines is not found in the danger of heating or of excessive wear, nor, as 
is generally believed, in the centrifugal force of the fly-wheel, nor in the 
tendency to knock in the centres, nor in vibration. He gives two objections 
to very high speeds: First, that ‘‘engines ought not to be run as fast as 
they can be ;’’ second, the large amount of waste room in the port, which 
is required for proper steam distribution. In the important respect of 
economy of steam, the high-speed engine has thus far proved a failure. 
Large gain was looked for from high speed, because the loss by condensa- 
tion on a given surface would be divided into a greater weight of steam, but 
this expectation has not been realized. For this unsatisfactory result we 
have to lay the blame chiefly on the excessive amount of waste room. The 
ordinary method of expressing the amount of waste room in the percentage 
added by it to the total piston displacement, is a misleading one. It should 
be expressed as the percentage which it adds to the length of steam admis- 
sion. For example, if the steam is cut off at 1/5 of the stroke, 8% added by 
the waste room to the total piston displacement means 40% added to the 
volume of steam admitted. Engines of four, five and six feet stroke may 
properly be run at from 700 to 800 ft. of piston travel per minute, but for 
ordinary sizes, says Mr. Porter, 600 ft. per minute should be the limit. 

Influence of the Steam-jacket.—Tests of numerous engines with 
and without steam-jackets show an exceeding diversity of results, ranging 
all the way from 30% saving down to zero, or even in some cases showing an 
actual loss. The opinionsof engineers at this date (1894) is also as diverse as 
the results, but there is a tendency towards a general belief that the jacket is 
not as valuable an appendage to an engine as was formerly supposed. An ex- 
tensive résumé of facts and opinions on the steam-jacket is given by Prof. 
Thurston, in Trans. A. 8S. M. E., xiv. 462. See also Trans. A. S. M. E., xiv. 
873 and 1340; xiii. 176; xii. 426 and 1340; and Jour. F.1., April, 1891, p. 276. 
The following are a few statements selected from these papers. 

The results of tests reported by the research committee on steam-jackets 
appointed by the British Institution of Mechanical Engineers in 1886, indi- 
cate an increased efficiency due to the use of the steam-jacket of from 1% to 
over 30%, according to varying circumstances. 

Sennett asserts that ‘tit has been abundantly proved that steam- 
jackets are not only advisable but absolutely necessary, in order that high 
rates of expansion may be efficiently carried out and the greatest possible 
economy of heat attained.” 

Isherwood finds the gain by its use, under the conditions of ordinary 
practice, as a general average, to be about 20% on small and 8% or 9% on 
large engines, varying through intermediate values with intermediate sizes, 
it being understood that the jacket has an effective circulation, and that 
both heads and sides are jacketed. 

Professor Unwin considers that ‘in all eases and on all cylinders the 
jacket is useful; provided, of course, ordinary, not superheated, steam is 
used; but the advantages may diminish to an amount not worth the interest 
on extra cost.”” 

Professor Cotterill says: Experience shows that a steam-jacket is advan- 
tageous, but the amount to be gained will vary according to circumstances. 
In many cases it may be that the advantage is small. Great caution is 
necessary in drawing conclusions from any special set of experiments on 
the influence of jacketing. 


788 THE STEAM-ENGINE. 


Mr. E. D. Leavitt has expressed the opinion that, in his practice, steam- 
jackets produce an increase of efficiency of froim 15% to 20%. 

In the Pawtucket pumping-engine, 15 and 3014 x 30 in., 50 revs. per min., 
steam-pressure 125 lbs. gauge, cut-off 144 in h.p. and 14 in l1.p. cylinder, the 
barrels only jacketed, the saving by the jackets was from 1% to 4%, 

The superintendent of the Holly Mfg. Co. (compound pumping-engines) 
says: ‘‘In regard to the benefits derived from steam-jackets on our steam- 
cylinders, Iam somewhat of a skeptic. From data taken on our own en: 
gines and tests made I am yet to be convinced that there is any practical 
value in the steam-jacket.” . . . ‘‘ You might practically say that there 
is no difference.” 

Professor Schréter from his work on the triple-expansion engines at Augs- 
burg, and from the results of his tests of the jacket efficiency on a small 
engine of the Sulzer type in his own laboratory, concludes: (1) The value 
of the jacket may vary within very wide limits, or even become nega- 
tive. (2) The shorter the cut-off the greater the gain by the use of a 
jacket. (8) The use of higher pressure in the jacket than in the cylinder 
produces an advantage, The greater this difference the better. (4) The 
high-pressure cylinder may be left unjacketed without great loss, but the 
others should always be jacketed. 

The test of the Laketon triple-expansion pumping-engine showed a gain 
of 8.38% by the use of the jackets, but Prof. Denton points out (Trans. A. .S 
M. E., xiv. 1412) that all but 1.9% of the gain was ascribable to the greater 
range of exnansion used with the jackets. 

West of a Compound Condensing Engine with and with= 
out Jackets at different Loads. (R. C. Carpenter, Trans. A. S. 
M, H., xiv. 428.)—Cylinders 9 and 16 in. x14 in. stroke; 112 lbs. boiler-pressure; 
rated capacity 100H.P.; 265revs.per min. Vacuum, 23in. From the results 
of soveral tests curves are plotted, from which the following principal figures 
are taken. 


Indicated H.P....,. .»+ a0. 40 50° 60° 70 80 90 100 110 120° "Jah 
Steam per I.H.P. per hour: 

With jackets, lbs... .. 22.6 21.4 20.38 19.6 19 18.7 18.6 18.9 19.5 20.4 21.0 

Without jackets, lbs.. .... out gutes en eee teU- Del, 219 oot O ek Ol ome meme 


Saving Dy Jacket, D;.C..j..+e..2s0+ cee, 10.9. 7.3 4:6. 5.11.0 —1. 051 oe 


This table gives aclue to the great variation in the apparent saving due to 
the steam-jacket as reported by different experimenters. With this par- 
ticular engine it appears that when running at its most economical rate of 
100 H.P., without jackets, very little saving is made by use of the jackets. 
When running light the jacket makes a considerable saving, but when over- 
loaded it is a detriment. 

At the load which corresponds to the most economical rate, with no steam 
in jackets, or 100 H.P., the use of the jacket makes a saving of only 1%; but 
at a load of 60 H.P. the saving by use of the jacket is about 11%, and the 
shape of the curve indicates that the relative advantage of the jacket would 
be still greater at lighter loads than 60 H.P. 

Counterbalancing Enginmes.—Prof. Unwin gives the formula for 
counterbalancing vertical engines: 


r 
W, => ides qe fe 6" (on oF Re oe ae tne (1) 


in which W, denotes the weight of the balance weight and p the radius to 
its centre of gravity, W2 the weight of the crank-pin and half the weight of 
the connecting-rod, and 7 the length of the crank. For horizontal engines: 


Wi=H(Wat Wa to MWet Wy ... - s @ 


in which W, denotes the weight of the piston, piston-rod, cross-head, and 
the other half of the weight of the connecting-rod. 

The American Machinist, commenting on these formule, says: For hori- 
zontal engines formula (2) is often used; formula (1) will give a counter- 
balance too light for vertical engines. We should use formula (2) for 
computing the counterbalance for both horizontal and vertical engines, 
excepting locomotives, in which the counterbalance should be heavier. 


PERFORMANCES OF STEAM-ENGINES, 789 


Preventing Vibrations of Engines.—Many suggestions have 
been made for remedying the vibration and noise attendant on the working 
of the big engines which are employed to run dynamos. A plan which has 
given great satisfaction is to build hair-felt into the foundations of the 
engine. An electric company has had a 90-horse-power engine removed 
from its foundations, which were then taken up to the depth of 4feet. A 
layer of felt 5 inches thick was then placed on the foundations and run up 2 feet 
on all sides, and on the top of this the brickwork was built up.—Safety Valve. 

Steam-engine Foundations Embedded in Air.—In the sugar- 
refinery of Claus Spreckels, at Philadelphia, Pa., the engines are distributed 
practically all over the buildings, a large proportion of them being on upper 
floors. Some are bolted to iron beams or girders, and are consequently 
innocent of all foundation. Some of these engines ran noiselessly and satis- 
factorily, while others produced more or less vibration and rattle. To cor- 
rect the latter the engineers suspended foundations from the bottoms of the 
engines, so that, in looking at them from the lower floors, they were literally 
hanging in the air.—Ivron Age, Mar. 13, 1890. 

Cost of Coal for Steam-power.—The following table shows the 
amount and the cost of coal per day and per year for various horse-powers, 
from 1 to 1000, based on the assumption of 4 lbs. of coal being used per hour 
per horse-power. It is useful, among other things, in estimating the saving 
that may be made in fuel by substituting more economical boilers and 
engines for those already in use. Thus with coal at $3.00 per ton, a saving 
of $9000 per year in fuel may be made by replacing a steam plant of 1000 
1p el Ey gehen: 4 lbs. of coal per hour per horse-power, with one requiring 
only 2 lbs. 








Coal Consumption, at 4 Ibs. 


er H.P. per hour; 10 hoursa $1.50. $2.00. $3.00. 4.00. 
5 day ; 300 days in a Year. ; 








a es 
oO 

= Ti Tons. Short Per Per Per Per 

Q ce? payer! Tons. Short Ton.| Short Ton, | Short Ton. {Short Ton. 
S| ——} —A | _] — J — |] 

me 

S Cost in Cost in Cost in Cost in 
q Dollars. | Dollars. Dollars. Dollars. 


Per | Per | Per | Per] Per 
Day. | Day. | Year. | Day.| Year 





Per | Per| Per] Per !' Per | Per Per | Per 
Day.| Year| Day.| Year.| Day.| Year. | Day.| Year 

















i 40] .0179! 5.357) 02 6} = .03 9} = 04 12) .06 18 .08 24 
10 400] .1786) 53.57) = .20 60] 30 90| .40 120; .60 180 80} 240 
25) 1,000] .4464) 133.92] .50} 150) _.75) 225] 1.00 300} 1.50 450 | 2.00} 600 
50; 2,000} .8928] 267.85) 1.00) 300; 1.50) 450; 2.00 600} 3.00 900.) 4,00} 1,200 
| 3,000] 1.3393] 401.78} 1.50] 450] 2.25] 675] 3.00 900} 4.50] 1,350 | 6.00) 1,800 
100| 4,000] 1.7857] 535.71) 2.00} 600} 3.00} 900) 4.00} 1,200] 6.00) 1,800 | 8.00! 2,400 
150) 6,000] 2.6785| 803.56] 3.00) 900] 4.50} 1,350) 6.00) 1,800] 9.00} 2,700 | 12.00] 3,600 
200} 8,006] 3.5714|1,071.42) 4.00] 1,200] 6.00] 1,800) 8.00) 2,400] 12.00) 3,600 | 16.00) 4,800 
250| 10,000] 4.4642/1,339.27] 5.00] 1,500) 7.50} 2,250) 10.00/ 3,000] 15.00} 4,500 | 20.00| 6,000 
300) 12,000] 5.3571/1,607.13] 6.00; 1,800] 9.00) 2,700) 12.00} 3,600) 18.00) 5,400 | 24.00) 7,200 
350} 14,000] 6.2500)1,874.98] 7.00] 2,100) 10.50) 3,150) 14.00) 4,200} 21.00] 6,200 | 28.00) 8,400 
400| 16,000] 7.1428]/2,142.84] 8.00] 2,400] 12.00) 3,600) 16.00] 4,800} 24.00] 7,200 | 32.00; 9,600 
450| 18,000] 8.0356|2,410.69| 9.00) 2,700} 13.50} 4,050} 1800) 5,400] 27.00) 8,100 | 36.00) 10,800 
500] 20,000] 8.9285)2,678.55) 10.00] 3,000) 15.00) 4,500} 20.00} 6,000} 30.00} 9,000 | 40.00/12,000 
600| 24,000]10.7142/3,214.26| 12.00] 3,690] 18.00} 5,400] 24.00] 7,200] 36.00] 10,800 | 48.00]14,400 
700} 28,000|12.4999|5,749.97| 14.00] 4,200] 21.00} 6,300] 28.00] 8,400} 42.00] 11,600 | 56.00)16,800 
800] 32,000|14.2856|4,285.68] 16.00) 4,800) 24.00] 7,200] 32.00) 9,600] 48.00] 12,400 | 64,00/19,200 
900} 36,000|16.0713/4,821.39] 18.00] 5,400) 27.00} 8,100} 36.00] 10,800} 54.00) 14,200 | 72.00/21,600 
1,000| 40,000'17.8570|5,357.10' 20.00] 6,000! 30.00! 9,000’ 40.00' 12,000{ 60.00! 18,000 ] 80.00'24,000 
ee ee ee 











Storing Steam Heat,.—There is nosatisfactory method for equalizing 
the load on the engines and boilers in electric-light stations. Storage-batteries 
have been used, but they are expensive in first cost, repairs, and attention. 
Mr. Halpin, of London, proposes to store heat during the day in specially 
constructed reservoirs. As the water in the boilers is raised to 250 lbs. pres- 
sure, it is conducted to cylindrical reservoirs resembling English horizontal 
boilers, and stored there for use when wanted. In this way a comparatively 
small boiler-plant can be used for heating the water to 250 lbs. pressure all 
through the twenty-four hours of the day, and the stored water may be 

_ drawn on at any time, according to the magnitude of the demand The 


7599 THE STEAM-ENGINE. 


steam-enpines are to be worked by the steam generated by the releasé of 
pressure from this water, and the valves are to be arranged in such a way 
that the steam shall work at 130 lbs. pressure. A reservoir 8 ft. in diameter 
aud 30 ft. long, containing 84,000 lbs. of heated water at 250 lbs. pressure, 
would supply 5250 lbs. of steam at 130 lbs. pressure. As the steam consump- 
tion of a condensing electric-light engine is about 18 lbs. per horse-power 
hour, such a reservoir would supply 286 effective horse-power hours. In 
1878, in France, this method of storing steam was used on a tramway. 
M. Francq, the engineer, designed a smokeless locomotive to work by steam- 
power supplied by a reservoir containing 400 gallons of water at 220 lbs, 
pressure. The reservoir was charged with steam from a stationary boiler 
at one end of the tramway. 

Cost of Steam-power, (Chas. T. Main, A. S.M.E., x. 48.)—Estimated 
costs in New England in 1888, per horse-power, based on engines of 1000 H.P. 


Compound Condens- Non-con- 


OV WH 

















; = densing 
Engine. ing Engine. Engine. 
1. Cost engine and piping, complete.......... $25.00 $20.00 $17.50 
2. Engine-house........ Saseteacsen sda sicecice eae Os00 7.50 7.50 
8 Engine foundations 2.2... cocesccccecce 7.00 5.50 4.50 
4. Total engine plant....cceccseceres 40.00 83.00 29.50 
5. Depreciation, 4% on total cost.........00.-- 1.60 1,32 1.18 
6. Repairs, 2% pie ta th cagack ess css cnet 0.66 0.59 
%. Interest, 5% JON Wits SS aeenoesdcasan «AUD 1.65 1.47 
8. Taxation, 1.5% on 34 Costs. ch. .ccscccneses 0.45 0.271 0.3 
9. Insurance on engine and house........-.. 0.165 0.138 0.12 
70. Total of lines 5, 6, 7,6,9...cee20. 5.015 4.139 8.702 
11. Cost boilers, feed-pumps, etc......ceeeeees 9.88 13.33 16.00 
12. Boiler-house........ Sauces cs tie den tiesttee meres 4.17 5.00 
13., Chimney. ANG MMES Nemec sscce oo siceeicses pe cnmEOTlE %.30 8.00 
1 4. Total boiler-plant. e@eoreeereeooce2ceee 18.36 24.80 29.00 
15. Depreciation, 5% on total cost......eceeoee. 0.918 1.240 1.450 
16. Repairs, 2% ABM, Se? oY. BREE Orr 367 -496 -580 
17. Interest, 5% eb ihicles hc ey | oeae wel toners pas fF FS 1.240 1,450 
"18. Taxation, 1.5% on 34 Cost....... 2.0. .ccccece 207 279 3826 
19. Insurance, 0.5% on total cost...... Hodonased 092 124 «145 
20. Total of lines 15 to 19 ....ceee-ce0e 2.502 3.87 8.951 
21, Coal used per I.H.P. per hour, Ibs......... 1.75 2.50 3.00 
22, Cost of coal per I.H.P. per day of 1014 _ ets. cts. ets. 
hours at $5.00 per ton of 2240 Ibs........ 4.00 5.72 6.86 
23. Attendance of cnginc per day.....-...e00- 0,60 0.40 0.35 
24. Ny Saabollers' °° = $! Tees: eter seaneelOo 0.%5 0.90 
25. Oil, waste, and supplies, per day.......... 0.25 0.22 0.20 
26. Total daily expense........eecee. 5.88 7.09 8.31 
27. Yearly running expense, 308 days, per ° 
SPT OWE te. YSs Per g16.570 «21.837 —-$25.895 
28. Total yearly expense, lines 10, 20, and 27.. 24.087 29.355 83.248 
29. Total yearly expense per I.H.P. for power 
if 50% of exhaust-steam is used for heat- 
mers. cs BE oi Gone OREeee se peak CRN’ 14,907 16.663 
80. Total if all ex.-steam is used for heating... 8.624 3.916 7.700 


When exhaust-steam or a part of the receiver-steam is used for heating, or 
if part of the steam in a condensing engine is diverted from the condenser, 
and used for other purposes than power, the value of such steam should - 
be deducted from the cost of the total amount of steam generated in order 
to arrive at the cost properly chargeable to power. The figures in lines 29 


ROTARY STEAM-ENGINES. 791 


and 30 are based on an assumption made by Mr. Main of losses of heat 
amounting to 25% between the boiler and the exhaust-pipe, an allowance 
which is probably too large. 

See also two papers by Chas. E. Emery on “ Cost of Steam Power,” Trans. 
A.5S. C. E., vol. xii, Nov. 1883, and Trans. A. I. E. E., vol. x, Mar. 1893. 


ROTARY STEAM-ENGINES, 


Steam Turbines.—The steam turbine is a small turbine wheel which 
runs with steam as the ordinary turbine does with water. (For description 
of the Parsons and the Dow steam turbines see Modern Mechanism, p. 298, 
etc.) The Parsons turbine is a series of parallel-flow turbines mounted side 
by side on a shaft; the Dow turbine is a series of radial outward-flow tur- 
bines, placed like a series of concentric rings in a single plane, a stationary 
guide-ring being between each pair of movable rings. The speeds of the 
steam turbines enormously exceed those of any form of engine with recip- 
rocating piston, oreven of the so-called rotary engines. The three- and four- 
cylinder engines of the Brotherhood type, in which the several cylinders 
are usually grouped radially about a common crank and shaft, often exceed 
1000 revolutions per minute, and have been driven, experimentally, above 
2000; but the steam turbine of Parsons makes 10,000 and even 20,000 revolu- 
tions, and the Dow turbine is reputed to have attained 25,000. (See Trans. 
A. S. M. E., vol. x. p. 680, and xii. p. 888; Trans. Assoc. of Eng’g Societies, 
vol. viii. p. 583; Hng’g, Jan. 13, 1888, and Jan. 8, 1892; Hng’g News, Feb. 27, 
1892.) A Dow turbine, exhibited in 1889, weighed 68 lbs., and developed 10 
H.P., with a consumption of 47 Ibs. of steam per H.P. per hour, the steam 
pressure being 70 lbs. The Dow turbine is used to spin the fly-wheel of the 
Howell torpedo. The dimensions of the wheel are 13.8 in. diam., 6.5 in. 
width, radius of gyration 5.57 in. The energy stored in it at 10,000 revs. 
per min. is 500,000 ft.-Ibs. 

The De Laval Steam Turbine, shown at the Chicago exhibition, 
1893, is a reaction wheel somewhat similar to the Pelton water-wheel. The 
steam jet is directed by a nozzle against the plane of the turbine at quite a 
small angle and tangentially against the circumference of the medium 
periphery of the blades. The angle of the blades is the same at the side of 
' admission and discharge. The width of the blade is constant along the 
entire thickness of the turbine. 

The steam is expanded to the pressure of the surroundings before arriv- 
ing at the blades. This expansion takes place in the nozzle, and is caused 
simply by making its sides diverging. As the steam passes through this 
channel its specific volume is increased in a greater proportion than the 
cross section of the channel, and for this reason its velocity is increased, 
and also its momentum, till the end of the expansion at the last sectional 
area of the nozzle. The greater the expansion in the nozzle the greater its 
velocity at this point. A pressure of 75 lbs. and expansion to an absolute 
pressure of one atmosphere give a final velocity of about 2625 ft. per second. 

Expansion is carried further in this steam turbine than in ordinary steam- 
engines. This is on account of the steam expanding cumpletely during its 
work to the pressure of the surroundings. 

For obtaining the greatest possible effect the admission to the blades must 
be free from blows and the velocity of discharge as low as possible. These 
conditions would require in the steam turbine an enormous velocity of 
periphery—as high as 1300 to 1650 ft..per second. The centrifugal force, 
nevertheless, puts a limit to the use of very high velocities. In the 5 horse- 

ower turbine the velocity of periphery is 574 ft. per second, and the num- 
er of revolutions 30,000 per minute. 

However carefully the turbine may be manufactured it is impossible, ou 
account of unevenness of the material, to get its centre of gravity to corre- 
spond exactly to its geometrical axle of revolution; and however small this 
difference may be, it becomes very noticeable at such high velocities. De 
Laval has succeeded in solving the problem by providing the turbine with a 
flexible shaft. This yielding shaft allows the turbine at the high rate of 
speed to adjust itself and revolve around its true centre of gravity, the 
centre line of the shaft meanwhile describing a surface of revolution. - 

In the gearing-box the speed is reduced from 30,000 revolutions to 3008 
by means of a driver on the turbine shafts, which sets in motion a cog- 
wheel of 10 times its own diameter. These gearings are provided with spiral 


cogs placed at an angfe of about 45°, 
For descriptions of the most recent forms of steam turbines, see circles 
Of obo Westinghouse Machine Co. Pistsbure, Pa., and the De Lava! Steam 


G92 rail THE STEAM-ENGINE. 


Turbine Co., Trenton, N. J.; also paper by Dr. R. H. Thurston in Trans, 
AS. MAES vols xis, p. 2170: 

Rotary Stcam-engines, other than steam turbines, have been 
invented by the thousands, but not one has attained a commercial success, 
as regards economy of steam. ‘The possible advantages, such as saving of 
space, to be gained by a rotary engine are overbalanced by its waste of 
steam. Rotary engines are in use, however, for special purposes, such as 
steam fire-engines and steam feeds for sawmills, in which steam economy is 
not a matter of importance. 


DIMENSIONS OF PARTS OF ENGINES. 


The treatment of this subject by the leading authorities on the steam-en- 
gine is very unsatisfactory, being a confused mass of rules and formule 
based partly upon theory and partly upon practice. The practice of builders 
shows an exceeding diversity of opinion as to correct dimensions. The 
treatment given below is chiefly the result of astudy of the works of Rankine, 
Seaton, Unwin, Thurston, Marks, and Whitham, and is largely a condensa- 
tion of a series of articles by the author published in the American Mas< 
chinist, in 1894, with many alterations and much additional matter. In or- 
der to make a comparison of many of the formulg they have been applied 
to the assumed cases of six engines of different sizes, and in some cases 
this comparison has led to the construction of new formule. , 

Cylinder. (Whitham.)—Length of bore = stroke + breadth of piston- 
ring — 1g to 14 in; length between heads = stroke + thickness of piston 
sum of clearances at both ends; thickness of piston = breadth of ring 
bettas of flange on one side to carry the ring-+-thickness of follower- 
plate. ; 


Thickness of flange or follower.... 34 to Win. 34in, lin. 
For cylinder of diameter...... ...-- 8toi0in. 36 in. 60 to 100 in, 


Clearance of Piston. (Seaton.)—The clearance allowed varies with 
the size of the engine from 14 to 8 in. for roughness of castings and 1/16 to 
(s in. for each working joint. Naval and other very fast-running engines 

ave a larger allowance. Ina vertical direct-acting engine the parts which 
wear so as to bring the piston nearer the bottom are three, viz., the shaft 
journals, the erank-pin brasses. and piston-rod gudgeon-brasses. ; 

Thickmess of Cylimder. (Thurston.)—For engines of the older 
types and under moderate steam-pressures, some builders have for many 
years restricted the stress to about 2550 lbs. per sq. in. 


t =ap,;D+b. 0%. 00 Ole ee Se ELS (1) 


1s acommon proportion; f, D, and b being thickness, diam., and a constant 
added quantity varying from 0 to (3 in., allininches; p, is the initial unbal- 
anced steam-pressure per sq. in. In this expression 6 is made larger for 
horizontal than for vertical cylinders, as, for example, in large engines 0.5 
in the one case and 0,2 in the other, the one requiring re-boring more tham 
the other. The constant a is from 0.0004 to 0.0005; the first value for verti- 
cal cylinders, or short strokes; the secoml for horizontal engines, or for 
long strokes. 4 

Whickmess of Cylinder and its Connections for Marine 
Engines, (Seaton).—D = the diam. of thecylinder in inches; p = load on 
the safety-valves in lbs. per sq. in.; f, a constant multiplier = thickness of 
barrel + .25 in. 

Thickness of metal of cylinder barrel or liner, not to be less than p X D + 
8000 when of cast iron a e ° ° ° a . e e e . e e e e e a e e ° (2) 


Thickness of cylii.der-barrel = EX? +06 in, sic 0 6 @ 0 0 0 « &) 
MS chk 52) i RC Riga (4) 


Thickness of liner when of steei p & D -- 6000 +- 0.5 
ie metal of steam-ports ax 0.6. %< J. 
ue valve-box sides = 0.65 xf. 





* When made of exceedingly good material, at least twice melted, tho 
thickness may be 0.8 of that given by the above rules, 


DIMENSIONS OF PARTS OF ENGINES. @93 


Thickness of metal of valve-box covers = 0.7 X & 
of * _eylinder bottom = 1.1 x f. if single thickness. 
te eS =O. Go Kafe ik double a 
ce se S covers = 1.0 x f, if single cb 
se ss ss “ =0.6 xf, if double ris 
“ cylinder flange = 1.4) X<.f: 
= * _ cover-flange =1.3 xf. 
Be SHepvalve-box: 9 = 1.0 (x f. 
“ ss door- flange == OO Xie 
- «face over ports = 1.2 Xf. 
“ de 8 ‘“ =1.0 xf, when thereisa false-face, 
a “  false-face =0.8 x f, when cast iron. 
ne be of =0.6 X/, when steel or bronze. 


Whitham gives the following from different authorities: 


Van Buren: { t = 0.0001Dp + 0.15 VD; e 3 eeee (5) 
¢ = 0.03 Dp. «06,18. 6 ©. eb rortetien CO! 


gp (D+2.B)p: 
Tredgold: (pee 1900 cin). @u1bt; veitvw Diatblel cenerainenyias ) 


Weisbach: ¢=0.8+ 0.00038pD, . « « © e e oe e (8) 
Seaton: $= 0.5+0.0004pD. « «ee eee (9) 


. §t= 0.000IpD+ 1% (vertical); . 2. « « « (10) 
Haswell: ee 0.0005pD-+ 1 (horizontal). . . . » (11) 


Whitham recommends (6) where provision is made for the reboring, and 
where ample strength and rigidity are secured, for horizontal or vertical 
cylinders of large or small diameter; (9) for large cylinders using steam 
under 100 lbs. gauge-pressure, and ® 


t = 0.003D 4/p for small cylinders. . . e (12) 
Marks gives t = 0.00028pD. Oy etal 6 a yothaey eke te Bie 3 


This is a smaller value than is given by the other formuls# quoted; but 
Marks says that it is not advisable to make a steam-cylinder less than 0.75 
in. thick under any circumstances. 

The following table gives the calculated thickness of cylinders of engines 
of 10, 30, and 50 in. diam., assuming p the maximum unbalanced pressure on 
the piston = 100 Ibs. per sq.in. As the same engines will be used for calcu- 
jation of other dimensions, other particulars concerning them are here 
given for reference, 


DIMENSIONS, ETC., OF ENGINES. 


PN CING NOsccecistessisiacicises ware cece 1 and 2. 3 and 4. 5 and 6. 





Indicated horse-power...... I.H.P 50 450 1250 
Dian, OL.CYL Silo eae dees scene D 10 30 50 
Stroke, Leet... cesocestics scccess ce eee ies Ge A eee 
Revs. per min.............. o eee ebO o2.0) 9225)130. ... 65. 90 ....) 45 
Piston speed, ft. per min.........S 600 650 700 
Area of piston, sq. in............. a 98.54 706.86 1963.5 
Mean effective pressure....M.E.P. 42 32.3 30 
Max. total unbalanced press..... 1g 7854 70,686 196,350 


Max. total per sq. in.........02++.p 100 100 ’ 100 


794 THE STEAM-ENGINE. 


a eS 








THICKNESS OF CYLINDER Vand 2 Zand 4. 5 and 6. 
BY FORMULA. : 5 

(1) .00049D + 0.5, short stroke... 2.50 
(1) .0005pD + 0.5, long stroke.... 3.00 
DN OOOSE DID) sade oieletcele Apo ocearoe 1 67 
& (O002D DFO. Grados eecss seed 1.66 
(5) .0001pD + .15 /D ....ceseseese 1.56 
(OVEOS ty Dorcce sean sce eoeete nn: 2.12 
(“) ane8) ee@eeereeeeeeeee Bese 2.96 
(8) .00088pD +4-.0.8...06cccccccecces 2.45 
FROM dd ete 0. Dina uisee hone g sens 2.50 
(10) .0004pD +- 1 (vertical). ...... 2.138 
(11) .0005p D -- ¥g (horizontal) ..... 2.63 
(12) .003D 4p (small engines)...... at 

(TSS PO0O2B Dies Me retcteteelske. acl 1.40(?) 
Average of first eleven. ........ 2.26 








The average corresponds nearly to the formula tf = .000837Dp + 0.4 in. A 
convenient approximation is t= .0004Dp + 0.3 in., which gives for 


Diameters f.55..5 65. 10 20 30 40 50 60 in. 
Thicknesses........... ii 1.10 1.50 1.90 2.30 2.70 in. 


The last formula corresponds to a tensile strength of cast iron of 12,500 
Ibs., with a factor of safety of 10 and an allowance of 0.3 in. for reboring. 

Cylinder-heads.—Thurston says: Cylinder-heads may be given a 
thickness, at the edges and in the flanges, exceeding somewhat that of the 
cylinder. An excess of not less than 25% is usual. It may be thinner in the 
middle. Where made, as is usual in large engines, of two disks with inter- 
mediate radiating, connecting ribs or webs, that section which is safe 
against shearing is probably ample. An examination of the designs of 
experienced builders, by Professor Thurston, gave 


Dp 


t = x09 1 4 inch, sehen dh. blake bbedates belt 
D being the diameter of that circle in which the thickness is taken. 
Thurston also gives tas O0SD 4/p.-+0.2Ba yan oil elltnen Seana 
Marks gives £20008 D4. 6 UY Det a Te eee ae 


He also says a good practical rule for pressures under 10¢ Ibs. per sq. in. is” 
to make the thickness of the cylinder-heads 114 times that of the walls; and 
applying this factor to his formula for thickness of walls, or .00028pD, we 
have 
t = -00035p D. ° ° e e ° e ° e a . (4) 
Whitham quotes from Seaton, 
+ PD +500 
~ 2000 
Seaton’s formula for cylinder bottoms, quoted above, is 
t= 1.1f, in which f = .0002pD + .85 inch, or t = .00022pD-+ .93. . (6) 
Applying the above formule to the engines of 10, 30. and 50 inches diame- 


ter, with maximum unbalanced steam-pressure of 100 lbs. per sq. in., w6 
have 


» Which is equal to .0005pD-+ .25inch. . . . (5) 








Cylinder diameter, inches = 10 380 50 
(1) t= .00083Dp + .2 = 58 1.2 1.82 
2) t= .00DVp+.% = 4% 1.75 ats 
(8) £ = .003D Vp = .30 90 1.50 
(4) t = .00035Dp = 85 Yul OSE AS 
(5) t = .0005Dp + .25 =). 76'). tC ean. 
(6) t= .00022Dp + .93 = 1.15 1.59 2.08 


| : 


Average Of 6 sereeresser-coe 069 9 1.8 


= 
~~ 
S 


DIMENSIONS OF PARTS OF ENGINES. 795 


' The average fs expressed by the formulat = .00036Dp +- .81 inch. 
Meyer’s ** Modern Locomotive Construction,” p. 24, gives for locomotive 
eylinder-heads for pressures up to 120 lbs. 


For diameters, in........ 19t022 16to18 14to15 11to13 9to010 
Thickness, in... ...0..00. 114 1 1 % 34 


Taking the pressure at 120 Ibs. per sq. in., the thicknesses 114 in. and 34 in. 
for cylinders 22 and 10 in. diam., respectively, correspond to the formula 
t = .00035Dp + .33 inch. 

Webs-stifiencd Cylinder-covers.—Seaton objects to webs for 
stiffening cast-iron cylinder-covers as a source of danger. The strain on 
the web is one of tension, and if there should be a nick or defect in the 
outer edge of the web the sudden application of strain is apt to start a 
erack. He recommends that high-pressure cylinders over 24 in. and low- 
pressure cylinders over 40 in. diam. should have their covers cast hollow, 
with two thicknesses of metal. The depth of the cover at the middle should 
be about 44 the diam. of the piston for pressures of 80 lbs. and upwards, 
and that of the low-pressure cylinder-cover of a compound engine equal to 
that of the high-pressure cylinder. Another rule is to make the depth at 
the middle not less than 1.3 times the diameter of the piston-rod. In the 
British Navy the cylinder-covers are made of steel castings, 34 to 114 in. 
thick, generally cast without webs, stiffness being obtained by their form, 
which is often a series of corrugations. 

Cylinder-head Bolts.—Diameter of bolt-circle for cylinder-head = 
diameter of cylinder + 2 X thickness of cylinder + 2 X diameter of bolts. 
The bolts should not be more than 6 inches avart (Whitham). 


yi 2. 2: 
Marks gives for number of bolts b = ioe = ooois7iP, in whiche= 


area of a single bolt, p = boiler-pressure in lbs. per sq. in.; 5000 lbs. is taken 
as the safe strain per sq. in. on the nominal area of the bolt. 

Seaton says: Cylinder-cover studs and bolts, when made of steel, should 
be of such a size that the strain in them does not exceed 5000 Ibs. per sq. in. 
When of less than % inch diameter it should not exceed 4500 lbs. per sq. in. 
When of iron the strain should be 202 less. 

Thurston says: Cylinder flanges are made a little thicker than the cylin- 
der, and usually of equal thickness with the flanges of the heads. Cylinder- 
bolts should be so closely spaced as not to allow springing of the flanges 
and leakage, say, 4 to 5 times the thickness of the flanges. Their diameter 
should be proportioned for a maximum stress of not over 4000 to 5000 lbs. 
per square inch. ; 

If D = diameter of cylinder, p = maximum steam-pressure, b = number 
of bolts, s = size or diameter of each bolt, and 5000 Ibs. be allowed per sq. 
in. of nominal area of the bolt, .7854D2p = 392%bs3; whence bs? = .0002D2p; 


-d= 0002; s = .01414D / + For the three engines we have: 
Diameter of cylinder, inches........ 10 80 


50 
Diameter of bolt-circle, approx..... 13 35 57.5 
Circumference of circle, approx.... 40.8 110 180 
Minimum No. of bolts, circ. + €...., 


Diam. of bolts, s = op4/®..... %in. 1.00 1.29 


The diameter of bolt for the 10-inch cylinder i3 0.54 in. by the formula, 
but 34 inch is as small as should be taken, on account of possible overstrain 
by the wrench in screwing up the nut. 

The Piston. Details of Construction of Ordinary Pis« 
tons. (Seaton.)—Let D be the diameter of the piston in inches, p the effec- 
tive pressure per square inch on it, # a constant multiplier, found as follows: 


D = 


796 THE STEAM-ENGINE. 


The thickness of front of piston near the boss = %.2 Xz 
iy ee $ rim» = 0.27 < @ 
. back sf = 0.18 x &, . 
Gy boss around the rod =0.38 xXx 
= flange inside packing-ring =10128 >< te 
« “at edge = 0.25 x @, 
ba acking-ring ==.0.15-X 9, 
Med a inl-Ane at edge PE tS i arm 
a) < inside packing-ring = 0.21 x a 
- * at bolt-holes =e th. Goo oes 
it metal around piston edge = 0105 30:46. 
The breadth of packing-ring = QO Ganx ae 
“* depth of piston at centre abl Aue oe os 
“ lap of junk-ring on the piston = 0.45 X x. 
“ ‘space between piston body and packing-ring = 0.3 X a, 4 
** diameter of junk-ring bolts =0.1 xa + 0.25 in. 
** pitch se Oe id = 10 diameters. 
** number of webs in the piston = (D + 20) + 12, 
“ thickness ‘ a “6 = 0.18 X & 


4 

Marks gives the approximate rule: Thickness of piston-head= id, in 
which / = length of stroke, and d = diameter of cylinder in inches. Whit- 
ham saysina horizontal engine the rings support the piston, or at least a 
part of it, under ordinary conditions. The pressure due to the weight of 
the piston upon an area equal to 0.7% the diameter of the cylinder X 
breadth of ring-face should never exceed 200 lbs. per sg. in. He also gives 
a formula much used in this country: Breadth of ring-face = 0.15 x diam- 
eter of cylinder. 


For our engines we have diameter = ....cecsss-eee 10 30 50 


Thickness of piston-head. 


4 
Marks, VD; JONO'StYOHG’.7 Vscactentscccceaaeee 8.31 5.48 7.00 
Marks, ‘* 3; short stroke......... se eva rsoas GOWN 6.51 8.32 
Seaton, depth at centre = 1.4%...... aisloaelwacelan en 4.30 9.80 15.40 
Seaton, breadth of ring = .68a.......c.0c0evceces 1.89 4.41 6.93 
Whitham, breadth of ring = ID PE es cease ecee 1.50 4.50 7.50 


Diameter of Piston Packing-rings,. — These are generally 
turned, before they are cut, about 14 inch diameter larger than the cylinder, 
for cylinders up to 20 inches diameter, and then enough is cut out of the ring 
to spring them to the diameter of the cylinder. For larger cylinders the 
rings are turned proportionately larger. Seaton recommends an excess 
of 1% of the diameter of the cylinder. 

Cross-section of the Rings.—The thickness is commonly made 
1/30th of the diam. of cyl. + 4inch, and the width = thickness + inch. 
¥or an eccentric ring the mean thickness may be the same as for a ring of - 
uniform thickness, and the minimum thickness = 2% the maximum. 

A circular issued by J. H. Dunbar, manufacturer of packing-rings, 
Youngstown, O., says: Unless otherwise ordered, the thickness of rings will 
be made equal to .08 x their diameter. This thickness has been found 
to be satisfactory in practice. It admits of the ring being made about 3/16” 
to the foot larger than the cylinder, and has, when new, a tension of about 
two pounds per inch of circumference, which is ample to prevent leakage, 
if the surface of the ring and cylinder are smooth. 

As regards the width of rings, authorities *“‘ scatter”? from very narrow to 
very wide, the latter being fully ten times the former. For instance, Unwin 
gives W=d .014 + .08. Whitham’s formula is W=d.15. In both for. 
mule W is the width of the ring in inches, and d the diameter of the cylinder 
in inches. Unwin’s formula makes the width of a 20” ring W = 20 x .014 
+ .08 = .86’, while Whitham’s is 20 x .15 = 3” for the same diameter of 
ring. There is much less difference in the practice of engine-builders in this 
respect, but there fs still room for a standard width of ring. It is believed 
that for cylinders over 16” diameter 34” is a popular and practical width, 
and 14” for cylinders of that size and under, 

Fit of Piston-rod into Piston. (Seaton.)—The most convenient 
and reliable Dig cae is to turn the piston-rod end with a shoulder of 1/16 
inch for sma/l engines, and 4g inch for large ones, make the tapar s in. te 


DIMENSIONS OF PARTS OF ENGLNES, "97 


the foot until the section of the rod 1s thrze fourths of that of the body, then 
turn the remaining fart parallel; the rod should then fit into the piston se 
as to leave 1g inch between it and the shoulder for large. pistons, and 1/16 in. 
for small. The shoulder prevents the rod from splitting the piston, and 
pen of the rod being turned true after long wear without encroaching on 
the taper. 

The piston is secured to the rod by a nut, and the size of the rod should 
be such that the strain on the section at the bottom of the thread does not 
exceed 5500 lbs, per sq. in. for iron, 7000 Ibs. for steel. The depth of this nut 
need not exceed the diameter which would be found by allowing these 
strains. The nut should be locked to prevent its working loose, 

Diameter of Piston-rods.— Unwin gives 


a” = bD V0, e e a e e 2 e ° ° e e (1 


in which D is the cylinder diameter in inches, » is the maximum unbalanced 
pressure in lbs. per sq. in., and the constant b = 0.0167 for iron, and b = 
0.0144 for steel. Thurston, from an examination of a conside:abie number 


of rods in use, gives 
4/D2pL3 
arm 4/ PEE + 2, nearly, a. O88 6 eerste) 


(L in feet, D and din inches), in which a = 10,000 and upward in the various 
types of engines, the marine screw engines or ordinary fast engines on 
shore given the lowest values, while *‘low-speed engines’’ being less 
liable to accident from shock give a = 15,000, often. 

Connections of the piston-rod to the piston and to theecrosshead should 
have a factor of safety of at least 8or10, Marks gives 


” =0.0179D fp, foriron; forsteeld’”  =0.0105D/p;. . (3) 
é 4 
_and d’ == 0.03901 / D2l2p, for iron; for steel d’” = 0.03525 7 D%l2p, (4) 


in which 2 is the length of stroke, all dimensions in inches. Deduce the 
diameter of piston-rod by (8), and if this diameter is less than 1/121, then use 
s é , Diameter of cylinder 

Seaton gives: Diameter of piston-rod = SF tr a ee TET aa Vp. 


The following are the values of F’ 


return connnecting-rod, 2 rods..... oo = 80 

Mercantile ordinary stroke, direct-acting............. F = 50 
$6 ong ‘s ry ape Snes Acro. 2 Geese! 

KS very long “ ts Bnteers bicce stele = 45 

ve medium stroke, oscillating .. ........... P= 45 


Notrre.—Long and very long, as compared with the stroke usual for the 
power of engine or size of cylinder. 

In considering an expansive engine p, the effective pressure should be 
taken as the absolute working pressure, or 15 lbs. above that to which the 
boiler safety-valve is loaded; fora compound engine the value of p For the 
high-pressure piston should be taken as the absolute pressure, less 15 lbs., 
or the same as the load on the safety-valve; for the medium-pressure the 
load may be taken as that due to half the absolute boiler-pressure; and for 
the low-pressure cylinder the pressure to which the escape-valve is loaded 
+ 15 lbs., or the maximum absolute pressure, which can be got in the re- 
ceiver, or about 25 lbs. It is an advantage to make all the rods of a com- 
pound engine alike, and this is now the rule. ; ; 

Applying the above formule to the engines of 10, 30, and 50 in, diameter, 
both short and long stroke, we have: 


798 ; THE STEAM-ENGINE. 


Diameter of Piston-rods, 





Diameter of Cylinder, inches.......... 10 30 50 


SELOKOsINCHES. ecjosccuwecciscomcese fcc] tLe 24 30 60 48 96 
Unwin, iron, .0167D Y/p..... seeseee-.| 1.67 | 1.67 | 5.01 | 5.01 | 8.35 | 8.35 
Unwin, steel, .0144D /p......-see000-| 1-44 | 1.44 | 4.82 | 4.82 | 7.20 | 7.20 


Pin ees 
D*pL2 , D : 
——— — +. _ | > Pea a Ree geste ac Hy B27 beth iE hl a5 0 Yap : 
Thurston / 10,000 + 30 (ZL in feet).| 1 5.10 
Thurston, same with a = 15,000.......)...... 140 em SV RRi lee a a 6.35 
Marks, iron, .0179D WOE ius thee oes 1.% Ee Ne 5.37 5.37 8.95 8.95 
Marks, iron, .03901 VD2%p. seorseeeeeel yan | 491 | 3.70 | 5.13 | 6.04 | 8.54 
‘Marks, steel, .0105D DT eee Nie. Ie (3: 15yh os ca (5.25) eee es 
Marks, steel, .03525 W Des uals ces 1.22 | 1.73 | 3.34 | 4.72 | 5.46 | 7.72 
: D-~ 
Seaton, naval engines, ¢5 /p....-. bae- [1280 4 vaueR G01 s| Wena 8,852) cox, 
; D 
Se ee eee ia) Dp actuseas: |e 2.22]... 6.67.1 0s iat 
Average of four for iron..... secieeat 1.49 | 1.82 | 4.801 5.26 | 7.11 | 8.74 





The figures in brackets opposite Marks’ third formula would be rejected 
stnce they are less than 1g of the stroke, and the figures derived by his 
fourth formula would be taken instead. The figure 1.79 opposite his first 
formula would be rejected for the engine of 24-inch stroke. 

An empirical formula which gives results approximating the abovs aver- 
ages is d’’ = .013 Y Dip. 

The calculated results from this formula, for the six engines, are, respec- — 
tively, 1.42, 1.88, 3.90, 5.61, 6.37, 9.01. 

Piston=-rod Guides.—The thrust on the guide, when the connecting- 
rod is at its maximum angle with the line of the piston-rod, is found from 
the formula: Thrust = total load on piston X tangent of maximum angle 
of connecting-rod = ptan@. This angle, 6, is the angle whose sine = half 
stroke of piston + length of comnecting-rod. 


Ratio of length of connecting-rod to stroke..... 2 214 3 
Maximum angle of connecting-rod with line of 
piston-rod.........6 sitiele clo on rentemicnt Sino ee em ae 20" 11° 33” 9° 36" 


Wan weno teeherangle ic.icccsaccccssesisetes eeeeest) .2D8 .204 .169 
Secant of the angle ............. saitames cmvetronte 1.0327 1.0206 1.014 


Seaton says: The area of the guide-block or slipper surface on which the 
thrust is taken should in no case be less than will admit of a pressure of 400 
lbs. on the square inch; and for good working those surfaces which take the 
thrust when going ahead should be sufficiently large to prevent the maxi- 
mum pressure exceeding 100 lbs. per sq. in. When the surfaces are kept 
well lubricated this allowance may be exceeded. 

Thurston says: The rubbing surfaces of guides are so proportioned that 
if V be their relative velocity in feet per minute, and p be the intensity of 
pressure on the guide in lbs. per sq. in., pV < 60,000 and pV > 40,000. 

The lower is the safer limit; but for marine and stationary engines it is 
allowable to take p = 60,000-- V. According to Rankine, for locomotives, 


P=F 20 where pis the pressure in lbs. per sq. in. and V the velocity of 


rubbing in feet per minute. This includes the sum of al) pressures forcing 
the two rubbing surfaces together. 
Some British builders of portable engines restrict the pressure between 
the guides and cross-heads to less than 40, sometimes 35 lbs. per square inch. 
For a mean velocity of 600 feet per minute, Prof. Thurston’s formulas 
give, p < 100, p > 66.7; Rankine’s gives » = 72.2 lbs. per sq. in, | 


2 
co 
(So 


DIMENSIONS OF PARTS OF ENGINES. 


Whitham gives, 
P _ _-%854d%p, 


PoVn?—1 po V¥n?—1 


in which P = total unbalanced pressure, », = pressure per square inch 
on piston, d = diameter of cylinder, ») = pressure allowable per square inch 
on slides, and m = length of connecting-rod -~ length of crank. This is 
equivalent to the formula, A = P tan 6+ po. For n=5,p; = 100 and po 
= 80, A = .2004d?. For the three engines 10, 30 and 50 in. diam., this would 
give for area of slides, 4 = 20, 180 and 500 sq. in., respectively. Whitham 
says: The normal pressure on the slide may be as high as 500 lbs. per sq. in., 
but this is when there is good lubrication and freedom from dust. Station- 
ary and marine engines are usually designed to carry 100 lbs. per sq. in., 
and the area in this case is reduced from 50% to 60% by grooves. In locomo- 
tive engines the pressure ranges from 40 to 50 lbs. per sq. in. of slide, on ac- 
count of the inaccessibility of the slide, dirt, cinder, etc. 

There is perfect agreement among the authorities as to the formula for 
area of the slides, 4 = P tan 6 + pg; but the value given to pp, the allow: 
able pressure per square inch, ranges all the way from 35 lbs. to 500 lbs. 

he Connecting-rod. fatio of length of connecting-rod to length 
of stroke.—Experience has led generally to the ratio of 2 or 244 to 1, the 
latter giving a long and easy-working rod, the former a rather short, but 
yet a manageable one (Thurston). Whitham gives the ratio of from 2 to 4%, 
and Marks from 2 to 4. 

Dimensions of the Connecting-rod.—The calculation of the diameter of 
a connecting-rod on a theoretical basis, considering it as a strut subject to 
both compressive and bending stresses, and also to stress due to its inertia, 
in high-speed engines, is quite complicated. See Whitham, Steam-engine 
Design, p. 217; Thurston, Manual of 8. E., p.100. Empirical formulas are as 
follows: For circular rods, largest at the middie, D = diam. of cylinder, 1 = 
length of connecting-rod in inches, p = maximum steam-pressure per sq. in. 


A = area of slides in square inches = 


(1) Whitham, diam. at middle, d’” = 0.0272 VW DIYp. 
(2) Whitham, diam. at necks, d/’ = 1.0 to 1.1 X diam. of piston-rod. 


(3) Sennett, diam. at middle, @’’ =2 Vp. 


(4) Sennett, diam. at necks, d’” = “ Vp. 


(5) Marks, diam., d’”” = 0.0179D //p. if diam. is greater than 1/24 length. 


(6) Marks, diam., d’’ = 0,02758 V Di Vp if diam. found by (5) is less than 
1/24 length. 


(7) Thurston, diam. at middle, d’” =a VDL {/p + C, D in inches, L in 
feet, a = 0.15 and C = ¥ inch for fast engines, a = 0.08 and C = 34 inch for 
moderate speed. 

(8) Seaton says: The rod may be considered as a strut free at both ends, 
and, calculating its diameter accordingly, 


VR + 4ar2) 
48.5 ? 


where R = the total load on piston P multiplied by the secant of the maxi 
mum angle of obliquity of the connecting-rod. 
For wrought iron and mild steel a is taken at 1/3000. The following are 
the values of r in practice: 
Naval engines—Direct-acting r=9 toll; 
a i Return connecting-rod + = 10 to 138, old; 
$s ie wi iY r=8 to9, modern; 
he ss Trunk 7 = 11.5 to 18. 
Mercantile ‘* Direct-acting, ordinary r= 12. 
3 ag td long stroke r = 18 to 16. 
(9) The following empirical formula is given by Seaton as agreeing closely 
with good modern practice: 
Diameter of connecting-rod at middle = 71K + 4, 1 = length of rod in 
inches, and K = 0.03 #/effective load on piston in pounds, 


diameter at middle = 





800. THE STEAM-ENGINE. 


The diam. at the ends may be 0.875 of the diam. at the middle. 
Seaton’s empirical formula when translated into terms of Dand p is the 


same as the second one by Marks, viz., d’/’ = 0.02758 W Di Vp. Whitham’s 
(1) is also practically the same. 

(10) Taking Seaton’s more complex formula, with length of connecting- 
rod = 2.5 X length of stroke, and 7 = 12 and 16, respectively, it reduces to: 
Diam. at middle = .02294 4//P and .02411 4/P for short and long stroke en- 
gines, respectively. * 

Applying the above formulas to the engines of our list, we have 


Diameter of Connecting=-rods, 











Diameter of Cylinder, inches......... 10 30 50 
StTOMOmINGHES cela ie «itera temecitae sities 12 24 30 | 60. 48 96 
Length of connecting-rod l..... 9 atelier 30 60 75 150 120 | 240 
(3) d” = = Wp = .0182D H/p....0006. 1.82 | 1.82 } 5.46 | 5.46 | 9.09 | 9.09 
(6) a! = 0179D VD saien.csvewecenat se 1.79 Jrre-s- 5.87 |....-. 8.95 |...-. 
(6) d”’ = 0258 Dl Vp Seske of rer edaig tS Kei Ae Ut pea 585 tous 9.51 
(Adis VARA DEL VirliId. waves ach Olin # O0Atea: Phair eNews ; 
(2) a” = 0.08V DL Vp + 8h... v.esvee|i-ceeee] 2054 |... ee d 8, BB dasorsaye 8.75 
(9) d’? = 03 YP......... Pees ioe aS 2.67 | 2.67 | 7.97 | 7.97 |13.29 [13.29 
(10) a” = .02294 /P; .02411 /P....... 2.03 | 2.14 | 6.09 | 6.41 |10.16 |10.68 
AV@Lrage ......e00 . veeueescecesceel 2.24 | 2.26 | 6.38 | 6.27 {10.52 {10.26 


Formule 5 and 6 (Marks), and also formula 10 (Seaton), give the larger 
diameters for the long-stroke engine; formule 7 give the larger diameters 
for the short-stroke engines. The average figures show but little difference 
in diameter between long- and short-stroke engines; this is what might be 
expected, for while the connecting-rod, considered simply as a column, 
would require an increase of diameter for an increase of length, the load 
remaining the same, yet in an engine generally the shorter the connecting- . 
rod the greater the number of revolutions, and consequently the greater the 
strains due to inertia. The influences tending to increase the diameter 
therefore tend to balance each other, and to render the diameter to some 
extent independent of the length. The average figures correspond nearly 


to the simple formula d’’ = .021D Wp. The diameters of rod for the three 
diameters of engine by this formula are, respectively, 2.10, 6.30, and 10.50 in, 
Since the total pressure on the piston P = .7854D2p, the formula is equiva- 


lent to d’ = .0287 1/P. 

Connecting-rod Ends.—For a connecting-rod end of the marine 
type, where the end is secured with two bolts, each bolt should be propor- 
tioned for a safe tensile strength equal to two thirds the maximum pull or 
thrust in the connecting-rod. 

The cap is to be proportioned as a beam loaded with the maximum pull 
of the connecting-rod, and supported at both ends. The calculation should 
be made for rigidity as well as strength, allowing a maximum deflection of 
1/100 inch. Forastrap-and-key connecting-rod end the strap is designed for 
tensile strength, considering that two thirds of the pull on the connecting- 
rod may come on onearm. At the point where the metal is slotted for the 
key and gib, the straps must be thickened to make the cross-section equal 
to that of the remainder of the strap. Between the end of the strap and the 
slot the strap is liable to fail in double shear, and sufficient metal must be 
provided at the end to prevent such failure. 

.The breadth of the key is generally one fourth of the width of the strap, 
and the length, parallel to the strap, should be such that the cross-section 
will have a shearing strength equal to the tensile strength of the section of 
the strap, The taper of the key is generally about § inch to the foot, 


DIMENSIONS OF TARTS OF ENGINES. 801 


PWapered Connecting-rods.—In modern high-speed engines it is 
customary to make the connecting-rods of rectangular instead of circular 
section, the sides being parallel, and the depth increasing regularly from 
the crosshead end to the crank-pin end. According to Grashof, the bending 
action on the rod due to its inertia is greatest at 6/10 the length from the 
crosshead end, and, according to this theory, that is the point at which the 
section should be greatest, although in practice the section is made greatest 
at the crank-pin end. 

Professor Thurston furnishes the author with the following rule for tapered 
connecting-rod of rectangular section: Take the section as computed by the 


formula d” = 0.1 VDL Vp + 3/4 for a circular section, and for a rod 4/3 the 
actual length, placing the computed section at 2/3 the length from the small 
end, and carrying the taper straight through this fixed section to the large 
end. This brings the computed section at the surge point and makes it 
heavier than the rod for which a tapered form is not required. 

Taking the above formula, multiplying L by 4/3, and changing it to7 in 


inches, it becomes d = 1/30 V Dl ¥ »+8/4". Taking a rectangular section 
of the same area as the round section whose diameter is d, and making the 
depth of the section A = twice the thickress ¢, we have .7854d? = ht = 2¢?, 


whence ¢t = .627d = .0209 V Di Vp +-.47’’, which is the formula for the thick- 
ness or distance between the parallel sides of the rod. Making the depth at 
the crosshead end = 1.5t, and at 2/3 the length = 2¢, the equivalent depth at 
the crank end is 2.25¢. Applying the formula to the short-stroke engines of 
our examples, we have 





Diameter of cylinder, incheS.......cccccccseccccesss| 10 30 50 
Stroke, BCHES MAM REY. Saisie ake Basra alee baeeaielhen 12 80 48 
Length Of connecting-rod , csisessecectsios sssevcteoss|,, 00 (5) 120 


Thickness, ¢ = .0209 VDI /p-L 4% u...-- oveeee-| 1.6f | 8.60 | 5.59 


Depth at crosshead end, 1.5¢ =..........ceccreosses-| 3,42 8.41 8.39 
Depth at crank end, 2147....... apo Me ciawsiclsie Views s Relay: ehoy Ore 8.11 12.58 


The thicknesses ¢, found by the formula t = .0209 4/ Di Vp +. .47, agree 


closely with the more simple formula t = .01D 1p + .60”, the thicknesses 
ealeulated by this formula being respectively 1.6, 3.6, and 5.6 inches. 

Whe Crank-pin.—A crank-pin should be designed (1) to avoid heating, 
(2) for strength, (8) forrigidity. The heating of a crank-pin depends on the 
pressure on its rubbing-surface, and on the coefficient of friction, which 
latter varies greatly according to the effectiveness of the lubrication. It also 
depends upon the facility with which the heat produced may be carried 
away: thus it appears that locomotive crank-pins may be prevented to some 
degree from overheating by the cooling action of the air through which they 
pass at a high speed. 


Marks gives / = .0000247 fpND? = 1.03g¢ EF Sete as te oclee ees 


Whitham gives lf = 0.9075f cer), e e e ° e e eo @ e 6 e e Q) 


in which I = length of crank-pin journal in inches, f = coefficient of friction, 
which may be taken at .03 to .05 for perfect lubrication, and .08 to .10 for im- 
perfect; p = mean pressure in the cylinder in pounds per square inch; D 
= diameter of cylinder in inches; N = number of single strokes per minute}; 
LH.P. = indicated horse-power; LZ = Jength of stroke in feet. These 
formule are independent of the diameter of the pin, and Marks states as a 
general law, within reasonable limits as to pressure and speed of rubbing, 
the longer a bearing is made, fora given pressure and number of revoiutions, 
the cooler it will work; and its diameter Las no effect upon its heating. 
Both of the above formule are deduced empirically from dimensions of 
crank-pins of existing marine engines. Marks says that about one-fourth 
the length required for crank-pins of propeller engines will serve for the pins 
ot side-wheel engines, and one tenth for locomotive engines, making the 


802 THE STEAM-ENGINE. 


formula for locomotive crank-pins | = .00000247/pND?, or if p = 150, 
= .06, and NV = 600, l = .018D2. 

Whitham recommends for pressure per square inch of projected area, for 
naval engines 500 pounds, for merchant engines 400 pounds, for paddle-wheel 
engines 800 to 900 ee 

Thurston says the pressure should, in the steam-engine, never exceed 500 
or 600 pounds pre square inch for wrought-iron pins, or about twice that 
figure for steel. He gives nue ae hee ops Be of a steel pin, in inches, 

= ks a4 « : . « e e e . 9 . 

in which P and R are the mean total load on the pin in pounds, and the 
number of revolutions per minute. For locomotives. the divisor may be 
taken as 500,000. Where iron is used this figure should be reduced to 300,000 
and 250,000 for the two cases taken. Pins so proportioned, if well made and 
well lubricated, may always be depended upon to run cool; if not well 
formed, perfectly cylindrical, well finished. and kept well oiled, no crank-pin 
can be relied upon. It is assumed above that good bronze or white-metal 
bearings are used. 

Thurston also says: The size of crank-pins required to prevent heating of 
the journals may be determined with a fair degree of precision by either of 
the formule given below : 


= EY 4 0) ; 

i= 44,8000 (Rankine, 1865); «4 8) feesene sae tre (H 

- PY e 

iO ee ee 8 ete “otis ® 
PN 


i CVan Buren, 1866). 6-6 eee oO) 


850,000 

The first two formule give what are considered by their authors fair work- 
ing proportions, and the last gives minimum length for iron pins. (V = 
velocity of rubbing-surface in feet per minute.) 

Formula (1) was obtained by observing locomotive practice in which great 
liability exists of annoyance by dust, and great risk occurs from inaccessi- 
bility while running, and (2) by observation of crank-pins of naval screw- 
engines. The first formula is therefore not well suited for marine practice. 

Steel can usually be worked at nearly double the pressure admissible with . 
ivon running at similar speed. 

Since the length of the crank-pin will be directly as the power expended 
upon it and inversely as the pressure, we may take it as 


I.H.P: 
loan g¢ ° e e e e e e e e e (G9) 


in which a Is a constant, and ZL the stroke of piston, in feet. The values of 
the constant, as obtained by Mr. Skeel, are about as follows: a = 0.04 where 
water can be constantly used; a = 0.045 where water is not generally used; 
a = 0.05 where water is seldom used; a = 0.06 where water is never needed. 
Unwin gives 


i=a 


pe seein oe Wer. o He. (6G © bye tme (ashy e: @) 
fr ? 
in which r = crank radius in inches, a = 0.8 toa = 0.4 for iron and for marine 
engines, and a = 0.066 to a = 0.1 for the case of the best steel and for loco- 
motive eis where it is often necessary to shorten up outside pins as much 
as possible. 
J. B. Stanwood (£ng’g, June 12, 1891), in a table of dimensions of parts of 
American Corliss engines from 10 to 80 inches diameter of cylinder, gives 
sizes of crank-pins which approximate closely to the formula 


EarotoD” +. 5 ins td uz? ees ss wee 


By calculating lengths of iron crank-pins for the engines 10, 80, and 50 inches 
diameter, long and short stroke, by the several formule above given, it is 
found that there is a great difference in the results, so that one formula in 
certain cases gives a length three times as great as another. Nos. (4), (F \ and 
(6) give lengths much greater than the others. Marks (1), Whitham (2), 
Thurston (7), 2 = .061.H.P. + ZL, and Unwin (8),/=041LH.P. +7, give re 
a@ults which agree more closely. 


DIMENSIONS OF PARTS OF ENGINES, 803 


The calculated lengths of iron crank-pins for the several cases by formule 
(1), (2), CO, and (8) areas follows: 


Length of Crank=-pins,. 











Diameter of cylinder. ..5..0.6.2552..1. D| 10 10 30 | 30 50 50 
SEP OK Se 2 tes See ETA tele 6 o-eeecds (£63) 1 2 2144 5 4 8 
Revolutions per minute.............. R| 250 125 | 1380; 65 90 45 
Horse vpowersitisc: soue 4. cheer. 1.H.P.| /50 50 | 450 450} 1,250; 1,250 
Maximum pressure..............5- lbs.| 7,854! 7,854]70, 686|70,686! 196,350] 196.350 
Mean pressure per cent of max....... 42 42 | 32.38 | 82.3 | 30 30 
IMGaNDreESSUTE fas ict rte eit oseicy once a) cia als P.| 3,299] 3,299}22,832/22,832]58,905/58, 905 


Length of crank-epinas tae. tee oss te 














(1) Whitham, J = .9075 X .051.H.P.+ LU.) 2.18 | 1.09 | 8.17) 4.08 | 14.18] 7.09 
(2) Marks, i= 1.038 X .051.H.P.-+ L.| 2.59 | 1.30 | 9.34) 4.67 | 16.22) 8.11 
(7) Thurston, /= .06 L.H.P.+L.. ..... 3.00 | 1.50 | 10.80} 5.40 | 18.75) 9.38 
(8)Unwin, J=.41H.P.+7r......... | 3.33 | 1.67 | 12.0 | 6.0 | 20.83] 10.42 
(3) 22 ES Sal ls hy 2s SS eernenr oe 2.50} 1.25] 9.0/4.5 | 15.62) 7.81 
PAWOLA LS pixils 3 Wo kay aadowdions Miedo ed pen 2.72 | 1.36 | 9.86) 4.93 | 17.12] 8.56 
(8) Unwin, best steel, 2 = athe: steagiel ea |, oSe. Oak. 1130 viLOngh enon 
(@ Thurston, steel, 1=—~*.......) 1.87! .69 | 4.95 | 2.47 | 8.84 | 4.42 
5 $ + 600,000" e ee ° . . . . 





The calculated lengths for the long-stroke engines are too low to prevent 
excessive pressures. See ‘‘ Pressures on the Crank-pins,”’ below. 

Whe Strength of the Crank-pin is determined substantially as is 
that of the crank. In overhung cranks the load is usually assumed as 
carried at its extremity, and, equating its moment with that of the resist- 
ance of the pin, 


WPI = 1/32trd?, and d= 4) ae 


in which d = diameter of pin in inches, P = maximum load on the piston, 
~ = the maximum allowable stress on a square inch of the metal. For iron 
it may be taken at 9000 lbs. For steel the diameters found by this formula — 
may be reduced 10%. (Thurston.) 

Unwin gives the same formula in another form, viz.: 


3 Bl sy 5.1 nay? 


the last form to be used when the ratio of length to diameter is assumed. 
For wrought iron, ¢ = 6000 to 9000 lbs. per sq. in., 


Vi = .0947 to 087; 4/ % = .0291 to 0238, 


For steel, ¢ = 9000 to 13,000 Ibs. per sq. In., 


; “+ = .0827 to .07235 = = .0238 to .0194. 


5 Speen ——_---— 
Whitham gives d = 0.0827 Pi = 2.10587/ cciilee 


d = 0.0405 PIs for rigidity, and recommends that the diameter be calculated 
by both formule, and the largest result taken. The first is the same as 
Unwin’s formula, with ¢ taken at 9000 lbs. per sq. in. The second is based 
upon an arbitrary assumption of a deflection of 1-300 in. at the centre of 
pressure (one third of the length from the free end). 





for strength, and 


804 : THE STEAM-ENGINE,. : 


Marks, calculating the diameter for rigidity, gives 


PST i be 
d = 0.0664/plED? = 0.945 {/ SD 


= maximum steam-pressure in pounds per square inch, D = diameter of 
cylinder in inches, L = length of stroke in feet, NV = number of single strokes 
per minute. He says there is no need of an investigation of the strength of 
a crank-pin, as the condition of rigidity gives a great excess of strength. 

Marks’s formula is based upon the assumption that the whole load may be 
concentrated at the outer end, and cause a deflection of .01 inch at that 

oint. 
i It is serviceable, he says, for steel and for wrought iron alike. 

Using the average lengths of the crank-pins already found, we have the 
following for our six engines : 


Diameter of Crank-pins, 





Diameter of cylinder.....0...+..+-+0..| 10 10 | 30 30 50 50 
PUIOKe {boca tees ee eee ee uislele sles cow's cues 1 2 24 5 4 8 
Length of crank-pin......-.ccccececoses! 2.42 | 1.36 | 9.86 | 4.98 | 17.12) 8.56 





a Va 2.29 | 1.92 | 7.84 | 5.82 | 12.40] 9.84 


Marks, d = .066 VEDI n ccetenaee) 1.389 | .85 | 6.44 | 3.78 | 12.41| 7.39 


Pressures on the Crank=pins,—If we take the mean pressure upon 
the crank-pin = mean pressure on piston, neglecting the effect of the vary: 
ing angle of the connecting-rod, we have the following, using the average 
lengths already found, and the diameters according to Unwin and Marks: 





Finpine NO sen op «<iov slog acess sok ty <r 1 2 3 4 5 6 
Diameter of cylinder, inches.......... 10 10 30 30 50 50 
Stroke, Leet, . ctw ey pat peneisa sie ser te mee 1 2 246 5 4 8 
Mean pressure on pin, pounds........| 3,299 | 8,299 |22,8382/22, 832/58, 905/58, 905 
_ Projected area of pin, Unwin...... oe-.| 6.23 | 236 | 72.4 | 28.7 | 212.3) 84.2 
ee TM oe MALES, vs. oteen 8.78 | 1.16 | 63.5 | 18.6 | 212.5) 63.3 
Pressure per square inch, Unwin..... 530 | 1,898} 315 | 7964 2774 700° 
Ts ahs .— er. Marksseeere 873 | 2,845} 360 | 1,228] 277] 930 





The results show that the application of the formule for length and diam- 
eter of crank-pins give quite low pressures per square inch of projected 
area for the short-stroke high-speed engines of the larger sizes, but too high 

ressures for all the other engines. It is therefore evident that after calcu- 

ating the dimensions of a crank-pin according to the formule given that the 
results should be modified, if necessary, to bring the pressure per square 
inch down to a reasonable figure. 

In order to bring the pressures down to 500 pounds per square inch, we 
‘ divide the mean pressures by 500 to obtain the projected area, or product 

of length by diameter. Making / = 1.5d for engines Nos, 1, 2, 4 and 6, the 
revised table for the six engines is as follows: 


Hngine; Now... %.>22:: ». hes 5, esia's ais 1 2 3 4 5 6 
Length of crank-pin, inches....... 8.15 8.15 9.86 8.37 17.12 13.30 
Diameter of crank-pin............. 2.10 2.10 7.34 5.58 12.40 8.87 


Crosshead=pin or Wrist-pin.—Whitham says the bearing surface 
for the wrist-pin is found by the formula for crank-pin design. Seaton says 
the diameter at the middle must, of course, be sufficient to withstand the 
bending action, and generally from this cause ample surface is provided for 
good working; but in any case the area, calculated by multiplying the diam- 
eter of the journal by its length, should be such that the pressure does not 
exceed 1200 lbs. per sq. in., taking the maximum load on the piston as the 
total pressure on it, 


For small engines with the gudgeon shrunk into the jaws of the connect- 


DIMENSIONS OF PARTS OF ENGINES. BOS 


ing-rod, and working in brasses fitted into a recess in the piston-rod end ana 
secured by a wrought-iron cap and two bolts, Seaton gives: 


Diameter of gudgeon = 1.25 x diam. of piston-rod, 
Length of gudgeon = 1.4 x diam. of piston-rod. 


If the pressure on the section, as calculated by multiplying tength by 
diameter, exceeds 1200 Ibs. per sq. in., this length should be increased. 

J. B. Stanwood, in his ‘*‘ Ready Reference” book, gives for length of 
crosshead-pin 0.25 to 0.3 diam. of piston, and diam. = 0.18 to 0.2 diam. of 
piston. Since he gives for diam. of piston-rod 0.14 to 0.1% diam. of piston, 
bis dimensions for diameter and length of crosshead-pin are about 1.25 and 
1.8diam. of piston-rod respectively. Taking the maximum allowable press- 
ure at 1200 lbs. per sq. in. and making the length of the crosshead-pin = 


4/3 of its diameter, we have d = 4/ P+ 40, l= /P + 80, in which P = max- 
imum total load on piston in Ibs., d = diam. and ? = length of pin in inches, 
For the engines of our example we haves 


Diameter of piston, inches........ccvccsesce-eoe 10 80 50 
Maximum load on piston, IDS......ccccecccesoee %854 40,686 196,350 
Diameter of crosshead-pin, inches........cocece 2622 6.65 11.08 
Length of crosshead-pin, inches.... ......... 2.96 8.86 14.77 
Stanwood’s rule gives diameter, inches....... 1.8to2 5.4to6 9.0 to 16 
Stanwood’s rule gives length, inches............ 2.5t08 %7.5to9 12.5to15 
Stanwood’s largest dimensions give pressure 

DCL SQHIM. SIDS eataicuecccteccaeseetecsceces| , 209 1329 1809 


Which pressures are greater than the maximum allowed by Seaton. 

The Crankearm.—The crank-arm is to be treated as a lever, so that 
if a is the thickness in direction paratel to the shaft-axis and bits breadth 
at a section x inches from the crank-pin centre, then, bending moment M 
at that section = Px, P being the thrust of the connecting-rod, and f the 
safe strain per square inch, 


fab? axb? 7 CTH gaia 1/68 
Eo ae em and r pe or ais xy? b= 4/ i. 


If a crank-arm were constructed so that b varied as /x (as given by the 
above rule) it would be of such a curved form as to be inconvenient to man- 
ufacture, and consequently it is customary in practice to find the maxi- 
mum value of b and draw tangent lines to the curve at the points; these 
lines are generally, for the same reason, tangential to the boss of the crank- 
arm at the shaft. 

The shearing strain is the same throughout the crank-arm; and, conse- 
quently, is large compared with the bending strain close to the crank-pin 3 
and soitis not sufficient to provide there only for bending strains. The 
section at this point should be such that, in addition to what is given by the 
calculation from the bending moment, there is an extra square inch for 
every 8000 lbs. of thrust on the connecting-rod (Seaton). 

The length of the boss h into which the shaft is fitted is from 0.75 to 1.0 
of the diameter of the shaft D, and its thickness e must be calculated from 
the twisting strain PL. (L = length of crank.) 

For different values of length of boss kh, the following values of thickness 
of hoss e are given by Seaton: 


Whenh= D, __ thene = 0,35 D; if steel, 0.3. 
h = 0.9 D, then e = 0.38 D, if steel, 0.32, 
h = 0.8 D, then e = 0.40 D, if steel, 0.83, 
h = 0.7 D, then e = 0,41 D, if steel, 0.84. 


The crank-eye or boss into which the pin is fitted should bear the same 
relation to the pin that the boss does to the shaft. 

The diameter of the shaft-end onto which the crank is fitted should be 
1.1 « diameter of shaft. 

Thurston says: The empirical proportions adopted by builders will com- 
mouly be found to fall well within the calculated safe margin. These pro- 
portions are, from the practice of successful designers, about as follows : 

For the wrought-iron crank. the hub is 1.75 to 1.8 times the least diameter 
of that part of the shaft carrying full load; the eye is 2,0 to 2.25 the diame- 
ter of the inserted portion of the pin, and their depths are, for the hub, 1.¢ 
to 1.2 the diameter of shaft, and for the eye, 1.25 to 1.5 the diameter of pin. 


806 THE STEAM “NGINE, 


'The web is made V0.7 to 0.75 the width 9: 20,j2v<20t hub or eye, and is given a 
depth of 0.5 to 0.6 that of adjacent hub or oye. A Riser 
or the cast-iron crank the hub and eye are 2 Hitile larger, ranging in 

diameter respectively from 1.8 to 2 and from 2 to 2.2 udines the diameters of 
shaft and pin. The flanges are made at either ena of mearly the full depth 
of hub or eye. Cast-iron has, however, fallen very generalsy into disuse. 

The crank-shaft is usually enlarged at the seat of the crank to about 1.1 
its diameter at the journal. The size should be nicely adjusted vc allow for 
the shrinkage or forcing on of. the crank. A difference of diameter of one 
fifth of 1%, will usually suffice; and a common rule of practice #'ve8 an 
allowance of but one half of this, or .001, : ; 

The formule given by different writers for crank-arms practically 427¥ee, 
since they all consider the crank as a beam loaded at one end and fixed av 
the other. The relation of breadth to thickness may vary according to the 
poe of the designer. Calculated dimensions for our six engines are ag fo/ 
OWS 8 

Dimensions of Crank-arms, 





Diam, of cylinder, ins...| 10 10 80 30 50 50 
Stroke S, ins: css. oes 12 24 30 60 48 96 
Max. pressure on pin P, 
(approx.) lbs ... ......| 7854 | 7854 | 70,686 | 70,686 196,350 bien 
Ob 


Diam. crank-pin d.......] 2.10 | 2.10 7.04 5.58 12.40 

*/TELP. 
Diam.shaft,a R P\\e.74) 3.46] 7.70 9.70 | 12.55 | 15.82 
(a = 4.69, 5.09 and 5.22).. 
Length of boss, .8D..... 2.19 | 2.77 6.16 7.76 10.24 12.65 
Thickness of boss, .4D..{ 1.10 | 1.39 | 38.08 8.88 6.02 6.32 
Diam. of boss, 1.8D......] 4.93 | 6.23 | 13.86 17.46 22.59 28.47 
Length crank-pineye, .8d} 1.76 | 1.76] 5.87 4.46 9.92 7.10 
Thickness of crank-pin 

OVCRCIG OSM Se es hoe 288 88 2.94 2.23 4.46 38.55 
Max. mom. T at distance 

1464S — 14D from centre 

of pin, inch-lIbs........ 37, 149/80, 661} 788,149 | 1,848,439 | 3,479,322 | 7,871,672 
Thickness of crank-arm 

Dy hota Dy Oise ABS baer see eOD ues00 Ws Daas 2.28 9.41 11.87 
Greatest breadth, 

eer ae J 
6b = 9000a 8.48 4.55 9.54 3 13.0 ABA 21.0 


Min.mom. 7p at distance 
d from centre of pin= Pd! 16,493)16, 493} 528,835 | 394,428 | 2,484,740 | 1,741,625 
Least breadth, 





6To i 
b= 4/ d000g| 2-82 | 2-06 | 7.81 6.01%) 9198.48 9.89 


Whe Shaft.—Twisting Resistance,.—From the general formula 
d3S = .19685d8S, whence d = V = 





for torsion, we have: TJ= 7 a in which 


T = torsional moment in inch-pounds, d = diameter in inches, and S = the 
shearing resistance of the material in pounds per square inch. 

If a constant force P were applied to the crank-pin tengentially to its path, 
the work done per minute would be 


9 
PxLx a x RB = 83,000 x LH.P., 


in which Z = length of crank in inches, and R = revs. per min., and the 
mean twisting moment T = x 63,025. Therefore 





& 


PR ly 821, 4271.H.P, ° / 
J 8 — oo apes e: 





DIMENSIONS OF PARTS OF ENGINES. 807 


This may take the form 


3 8 ‘ 
a= 4/tEE x Bord =a peer 








in which F’and a are factors that depend on the strength of the material 
and on the factor of safety. Taking S at 45,000 pounds per square inch for 
wrought iron, and at 60,000 for steel, we have, for simple twisting by a uni- 
form tangential force, 


Factor of safety = & 6 8 10 5 6 8 10 
Tron...... # = 35.2% 42.8 57.1 71.4 a 8 
Steel..... F== 26.8 32.1 42.8 53.5 a 


Unwin, taking for safe working strength of wrought iron 9000 Ibs., steel 
13,500 lbs., and cast iron 4500 lIbs., gives a = 3.294 for wrought iron, 2.877 for 
steel, and 4.15 for castiron. Thurston, for crank-axles of wrought iron, 
gives a = 4.15 or more. 

Seaton says: For wrought iron, f, the safe strain per square inch, should 
not exceed 9000 Ibs., and when the shafts are more than 10 inches diameter. 
8000 lbs. Steel, when made from the ingot and of good materials, will ad- 
mit of a stress of 12,000 lbs. for small shafts, and 10,000 lbs. for those above 
10 inches diameter. 

The difference in the allowance between large and small shafts is to com- 
pensate for the defective material observable in the heart of large shafting, 
owing to the hammering failing to affect it. 


The formula d = a / I.H.P, 





R assumes the tangential force to be uniform 
and that it is the only acting force. For engines, in which the tangential 
force varies with the angle between the crank and the connecting-rod, and 
with the variation in steam-pressure in the cylinder, and also is influenced 
by the inertia of the reciprocating parts, and in which also the shaft may be 
subjected to bending as well as torsion, the factor a must be increased, to 
provide for the maximum tangential force and for bending. 

Seaton gives the following table showing the relation between the maxi- 
mum and mean twisting moments of engines working under various condie 
eons the momentum of the moving parts being neglected, which is allow- 
able: 





aia ; 
Wis 
at Cube 
Steam Cut-off Diviged Root 
Description of Engine, at Mean | of the 
Twist Ratio. 
Mome’t 
Single-crank expansive....c.ceccecceesees 0.2 2.625 | 1.38 
the Co eee 202080202008 S202 0.4 2 125 1 29 
he oe @eeeroesveeoeeeee eeeeee 0.6 1 835 1 22 
Me ee @eG@eeeoe+e?* eo 8eeeeee 0.8 1 698 1 20 
Two-cylinder expansive, cranks at 90°.... 0.2 1.616 | 1.17 
ee se % eines 0.3 1.415 eae 
ne iy a coos 0.4 1.298 1.09 
a ms bes By ee 0.5 1.256 | 1.08 
p - “ eset: 0.6 1.270 | 1.08 
es = - Rees 0.7 1.329 | 1.10 
Me had C- Lasest 0.8 TS5Cc be 
Three-cylinder compound, cranks 120°....} h.p.0.5, l.p. 0.66/ 1.40 1.12 
=e ae 1. p. cranks t 66 66 1 26 1 08 
opposite one another, and h.p. midway ; : 


Seaton also gives the following rules for ordinary practice for ordinary 
two-cylinder marine engines? 


s THP 3 
Diameter of the tunnel-shafts = { if. ie x F, or a a 





808 THE STEAM-ENGINE, 


Compound engines, cranks at right angles: 


Boiler pressure 70 lbs., rate of expansion 6 to 7, F = 70, a = 4,12 
Boiler pressure 80 Ibs., rate of expansion 7 to 8, #’ = 72, a = 4.16, 
Boiler pressure 90 lbs., rate of expansion 8 to 9, #’ = 7%, a = 4.22, 


Triple compound, three cranks at 120 degrees; 


Boiler pressure 150 Ibs., rate of expansion 10 to 12, F = 62, a = 3.96, 
Boiler pressure 160 lbs., rate of expansion 11 to 13, #' = 64, a = 4. 
Boiler pressure 170 lbs., rate of expansion 12 to 15, #’ = 67, a = 4.06. 


Expansive engines, cranks at right angles, and the rate of expansion 5, 
boiler-pressure 60 lbs., #’ = 90, a = 4.48. 

Single-erank compound engines, pressure 80 lbs,, #’ = 96, a = 4.58. 

For the engines we are considering it will be a very liberal allowance for 
ratio of maximum to mean twisting moment if we take it as equal to the 
ratio of the maximum to the mean pressure on the piston, The factor a, 
then, in the formula for diameter of the shaft will be multiplied by the cube 


Wier rs 2) See eee 
root of this ratio, or ” =1.34, 1 = 1.45, and ee = 1.49 for the 
42 82.3 80 


10, 30, and 50-in. engines, respectively. Taking a = 3.5, which corresponds 
to a shearing strength of 60,000 and a factor of safety of 8 for steel, or to 
45,000 and a factor of 6 for iron, we have for the new coefficient a, in the 


8 
formula d, = aug/ aa, the values 4.69, 5.08, and 5.22, from which we 





obtain the diameters of shafts of the six engines as follows: 


Engine No...... TPE OOS, aa! 2 3 4 5 6 
DAM Ol CVlce nn seek ceser en taeee eel O 10 30 380 50 50 
Horse-power, EE oe ciaeee eee @eevee 50 50 450 450 1250 1250 
HVS: DOLMMINs. | Fees erste eee Hane Neues eek HEN, 65 90 45 


9° /LH.P. 
Diam. of shatt d = a,4/' eae 274. 3146 7587 9:00 To BS ances 





These diameters are calculated for twisting only. When the shaft is also 
subjected to bending strain the calculation must be modified as below: 

Hesistance to Bending.—tThe strength of a circular-section shaft 
to resist bending is one half of that to resist twisting. If Bis the bending 
moment in inch-lbs., and d the diameter of the shaft in inches, 


3 : 
B= Te xsrand d= 4/2 x 10.2; 


J is the safe strain per square inch of the material of which the shaft is 
composed, and its value may be taken as given above for twisting (Seaton). 

Equivalent Twisting Zomemt.—When a shaft is subject to 
both twisting and bending simultaneously, the combined strain on any sec< 
tion of it may be measured by calculating what is called the equivalent 
twisting moment; that is, the two strains are so combined as to be treated 
as a twisting strain only of the same magnitude and the size of shaft cal- 
culated accordingly. Rankine gave the following solution of the combined 
action of the two Strains. 

Tf T = the twisting moment, and B =the bending moment on a section of 


a shaft, then the equivalent twisting moment 7, = B+ YB? + 7°. 

Seaton says: Crank-shafts are subject always to twisting, bending, and 
shearing strains; the latter are so small compared with the former that 
they are usually neglected directly, but allowed for indirectly by means of 
the factor f. 

The two principal strains vary throughout the revolution, and the maxi- 
mum equivalert twisting moment can only be obtained accurately by a 
series of calculations of bending and twisting moments taken at fixed inter 
vals, and from them constructing a curve of strains. 

Considering the engines of our examples to have overhung cranks, the 
maximum bending moment resulting from the thrust of the connecting rod 
on the crank-pin will take place when the engine is passing its centres 
(neglecting the effect of the inertia of the reciprocating parts), and it will 
be the product of the total pressure on the piston by the distance between 


DIMENSIONS OF PARTS OF ENGINES. 809 


two parallel lines passing through the centres of the crank-pin and of the 
shaft bearing, at right angles to their axes; which distance is equal to 
44 length of crank-pin bearing + length of hub+ 4% length of shaft-bearing + 
any clearance that may be allowed between the crank and the two bearings. 
for our six engines we may take this distance as equal to 14 length of 
crank-pin + thickness of crank-arm-—+1.5 x the diameter of the shaft as 
already found by the calculation for twisting. The calculation of diameter 
is then as below: 


Engine No. 1 2 3 4 5 6 
Diam. of cyl., in... 10 10 30 30 50 50 
Horse-power....... 50 50 450 450 1250 1250 
Revs. per min.. .. 250 125 130 65 90 45 


Max.press. on pis, P|} 7,854 7.854 70,686 70,686 196,350 | 196,350 
Leverage,* Lin....| 6.382 7.94 22.20 26.00 36.80 42,25 
Bd.mo.PL=Bin.-lb} 49,637 | 62,3611 1,569,222 | 1,837,886 | 7,225,680} 8,295,788 
Twist. mom. 7...... 47,124 | 94,248} 1,060,290 | 2,120,580 | 4,712,400] 9,424,800 
Equiv.Twist. mom. 

T,=B+ VB?+T? 

(ABDIOX:) 4. cb b5.- 118,000 |! 175,000 ! 3,463,000 | 4,647.000 ! 15,840,000! 20.850,000 


* Leverage = distance between centres of crank-pin and shaft bearing = 
L6l + 2.25d. 


Having already found. the diameters, on the assumption that the shafts 
were subjected to a twisting moment 7 only, we may find the diameter for 
resisting combined bending and twisting by multiplying the diameters 
already found by the cube roots of the ratio 7, + 7, or 


2 AAG EAT ee 1 AG, ohh n, LOE se. 1.00 
Giving corrected diameters d, =... 3.84 4.39 11.85 12.99 20.58 21.52 


By plotting these results, using the diameters of the cylinders for abscissas 

' and diameters of the shafts for ordinates, we find that for the long-stroke 
engines the results lie almost in a straight line expressed by the formula, 
diameter of shaft = .43 x diameter of cylinder; forthe short-stroke engines 
the line is slightly curved, but does not diverge far from a straight line 
whose equation is, diameter of shaft = .4 diameter of cylinder. Using these 
two formulas, the diameters of the shafts will be 4.0, 4.3, 12.0, 12.9, 20.0, 21.5. 

J. B. Stanwood, in Engineering, June 12, 1891, gives dimensions of shafts 
of Corliss engines in American practice for cylinders 10 to 30 in. diameter. 
The diameters range from 4 15/16 to 1415, 16, following precisely the equation, 
diameter of shaft = 1% diameter of cylinder — 1/16 inch. 

Fly-wheel Shafts.—Thus far we have considered the shaft as resist- 
ing the force of torsion and the bending moment produced by the pressure 
on the erank-pin. In the case of fly-wheel engines the shaft on the opposite 
side of the bearing from the crank- pin has tu be designed with reference te 
the bending moment caused by the weight of the fly -wheel, the weight of 
the shaft itself, and the strain of the belt. For engines in which there is an 
outboard bearing, the weight of fly-wheel and shaft being supported by 
two bearings, the point of the shaft at which the bending moment is a 
maximum may be taken us the point midway between the two bearings or 
at the middle of the fly-wheel hub; and the amount of the moment is the 
product of the weight supported by one of the bearings into the distance 
from the centre of that bearing to the middle point of the shaft. The shaft 
is thus to be treated asa beam supported at the ends and loaded in the 
middle. In the case of an overhung fly-wheel, the shaft having only one 
bearing, the point of maximum moment should be taken as the middle of 
the bearing, and its amount is very nearly the product of half the weight 
of the fly-wheel and the shaft into the distance from the middle of its hub 
from the middle of the bearing. The bending moment should be calculated 
and combined with the twisting moment as above shown, to obtain the 
equivalent twisting moment, and the diameter necessary at the point of 
maximum moment calculated therefrom. 

In the case of our six engines we assume that the weights of the fly- 
wheels, together with the shaft, are double the weight of fly-wheel rim 


2 
obtained from the formula} W = 785,400 sede (given under Fly-wheels); 


810 THE STEAM-ENGINE. 


that the shaft is supported by an outboard bearing, the distance between 
the two bearings being 214, 5, and 10 feet for the 10-in., 80-in., and 50-in. 
engines, respectively. The diameters of the fly-wheels are taken such 
that their rim velocity will be a little less than 6000 feet per minute. 


HN EINE-N Oss hs «cle a sey eeel er yeaa 3 3 4 5 6 

Diam. of cyl., inches......... 10 10 30 380 50 50 

Diam. of fly-wheel, ft........ Go | 15 14.5 29 21 42 

ROVE DEL WMMNS: mona cae PAD ait) 130 65 90 45 

Half wt.fly-wh’land shaft,lb. 268 536 aye 11,9386 26,384 52,769 
3 * 


Lever arm for max.mom.,in. 15 15 é 30 60 60 
Max. bending moment, in.-lb. 4020 8040 179,040 858,080 1,583,070 38,166,140 


As these are very much less than the bending moments calculated from 
the pressures on the crank-pin, the diameters already found are sufficient 
for the diameter of the shaft at the fly-wheel hub. 

In the case of engines with heavy band fly-wheels and with long fly-wheel 
shafts it is of the utmost importance to calculate the diameter of the shaft 
with reference to the bending moment due to the weight of the fly-wheel 
and the shaft. 

B. H. Coffey (Power, October, 1892) gives the formula for combined bend- 
ing and twisting resistance, 7 = .196d3S, in which T, = B+ VB24+ 72; T 
being the maximum, not the mean twisting moment; and finds empirical 
working values for .196S as below. He says: Four points should be consid- 
ered in determining this value: First, the nature of the material; second, 
the manner of applying the loads, with shock or otherwise; third, the ratio 
of the bending moment to the torsional moment—the bending moment in a 
revolving shaft produces reversed strains in the material, which tend to rup- 
ture it; fourth, the size of the section. Inch for inch, large sections are 
weaker than small ones. He puts the dividing line between large and small 
sections at 10 in. diameter, and gives the following safe values of S < .196 for 
steel, wrought iron, and cast iron, for these conditions. 


VALUE OF S X .196. 





Light shafts with F 

: Heavy Shafts Light Shafts 

Ratio. ‘ Shock. Heavy i 
with Shock. Shafts No Shock. No Shock. 





a) 4 
Wro’t] Cast Steel Wro’t' Cast Steel Wro’t}| Cast 








B to T. Steel. Tron. | Iron. ‘| Iron. | Iron. ‘| Iron. |Iron, 
3 to 10 or less...... 1045 | 880 | 440 | 1566 | 13201 660 | 2090 | 1760 | sso 
3to5orless ......| 941 | 785 | 393 | 1410 | 1179 | 589 | 1882 | 1570 | 785 
1 tol orleas....... 855 | 715 | 358 | 1281 | 1074 | 537 | 1710 | 1430 | 715 
B greater than 7..| 784 | 655} 328| 1176} 984 | 492 | 1568 | 1310 | 655 


Mr. Coffey gives as an example of improper dimensions the fly-wheel 
shaft of a 1500 H.P. engine at Willimantic, Conn., which broke while the en- 
gine was running at 425 H.P. The shaft was 17 ft.5in. long between centres 
of bearings, 18 in. diam. for 8 ft. in the middle, and 15 in. diam. for the re- 
mainder, including the bearings. It broke at the base of the fillet connect- 
ing the two large diameters, or 5644 in. from the centre of the bearing. He 
calculates the mean torsional moment to be 446,654 inch-pounds, and the 
maximum at twice the mean; and the total weight on one bearing at 87,530 
lbs., which, multiplied by 561 in., gives 4,945,445 in.-lbs. bending moment at 


the fillet. Applying the formula 7, = B+ /B?%+ T?, gives for equivalent 
twisting moment 9,971,045 in.-lbs. Substituting this value in the formula 
T, = .196, Sd3 gives for S the shearing strain 15,070 lbs. per sq. in., or if the 
metal had a shearing strength of 45,000 lbs., a factor of safety of only 3. 
Mr. Coffey considers that 6000 lbs. is all that should be allowed for S under 
these circumstances. This would give d = 20.25 in. If we take from Mr. 
Coffey’s table a value of .196S = 1100, we obtain d* = 9000 nearly, or d = 20.8 
in.. instead of 15 in., the actual diameter. 

Length of Shaft-bearings.—There is as great a difference of 
opinion among writers, and as great a variation in practice concerning length 
of journal-bearings, as there is concerning crank-pins. The length of a 


DIMENSIONS OF PARTS OF ENGINES. 811 


journal being determined from considerations of its heating, the ooserva- 
tions concerning heating of crank-pins apply also to shaft-bearings, and the 
formule for .ength of crank-pins to avoid heating may also be used, using. 

efor the total load upon the bearing the resultant of all the pressures brought 
upon it, by the pressure on the crank, by the weight of the fly-wheel, and by 
the pull of the belt. After determining this pressure, however, we must 
resort to empirical values for the so-called constants of the formule, really 
variables, which depend on the power of the bearing to carry away heat, 
and upon the quantity of heat generated, which latter depends on the pres- 
sure, on the number of square feet of rubbing surface passed over in a 
minute, and upon the coefficient of friction. This coefficient is an exceed.. 
ingly variable quantity, ranging from .01 or less with perfectly polished 
journals, having end-play, and lubricated by a pad or oil-bath, to .10 or more 
with ordinary oil-cup lubrication. 

For shafts resisting torsion only, Marks gives for length of bearing 1 = 
0000247 fp N D2, in which f is the coefficient of friction, p the mean pressure 
in pounds per square inch on the piston, NV the number of single strokes per 
minute, and D the diameter of the piston. For shafts under the combined 
stress due to pressure on the crank-pin, weight of fly-wheel, etc., he gives 
the following: Let Q = reaction at bearing due to weight, S = stress due 
steam pressure on piston, and #,= theresultant force; for horizontal engines, 


R, = VQ? + S?, for vertical engines R, = Q + S, when the pressure on the 
crank is in the same direction as the pressure of the shaft on its bearings, 
and Rk, = Q — S when the steam pressure tends to lift the shaft from its 
bearings. Using empirical values for the work of friction per square inch 
of projected area, taken from dimensions of crank-pins in marine vessels, 
he finds the formula for length of shaft-journals 1 = .0000325fR,N. and 
recommends that to cover the defects of workmanship, neglect of oiling, 
and the introduction of dust, f be taken at .16 or even greater. He says 
that 500 Ibs. per sq. in. of projected area may be allowed for steel or wrought- 
tron shafts in brass bearings with good results if a less pressure is not attain- 
able without inconvenience. Marks says that the use of empirical rules that 
do not take account of the number of turns per minute has resulted in bear- 
ings much too long for slow-speed engines and too short for high-speed 
engines. 

Whitham gives the same formula, with the coefficient .00002575. 

Thurston says that the maximum allowable mean intensity of pressure 


may be, for all cases, computed by his formula for journals, / = OL, 


se PUV + 20) 
py Rankine’s, l = 44,8000” 
V the velocity of rubbing surface in feet per minute, and d the diameter of 
the shaft in inches. It must be borne in mind, he says, that the friction work 
on the main bearing next the crank is the sum of that due the action of the 
piston on the pin, and that due that portion of the weight of wheel and 
shaft and of pull of the belt which is carried there. The outboard bearing 
carries practically only the latter two parts of the total. The crank-shaft 
journals will be made longer on one side, and perhaps shorter on the other, 
than that of the crank-pin, in proportion to the work falling upon each, i.e., 
to their respective products of mean total pressure, speed of rubbing sur. 
faces, and coefficients of friction. : 

Unwin says: Journals running at 150 revolutions per minute are often 
only one diameter long. Fan shafts running 150 revolutions per minute have 
journals six or eight diameters long. The ordinary empirical mode of pro- 
portioning the length of journals is to make the length proportional to the 
diameter, and to make the ratio of length to diameter increase with the 
speed. For wrought-iron journals: 


Revs. per min. = 50 100 150 200 250 500 1000 


Length + diam. = 1.2 1.4 1.6 1.8 2.0 3.0 5.0. 


Cast-iron journals may havel + d = 9/10, and steel journals 1+ d = 1%, 
of the above values. nage 


Unwin gives the following, calculated from the formula 1 = i 


which r is the crank radius in inches, and H.P. the horse-power transmitted 
to the crank-pin, : i 


60,000d 


in which P isthe mean total pressure in pounds, 


= .004F + 1. 


(oH a 


812 THE STEAM-ENGINE. 


YASORETICAL JOURNAL LENGTH IN INCHES, 














Load on Revolutions of Journal per minute. . 
Journal a 
in 
pounds. 50 100 200 800 500 1000 
1,000 By su! 8 1.2 26 4 
2,000 teh 8 1.6 2.4 4, 8. 
4,000 8 1.6 8.2 4.8 P 16. 
5,000 1.0 2s 4. 6. 10. 20. 
10,009 oN 4 8 12. 20. 40. 
15,000 3. 6. 12. 18. 30. BAe 
20,000 4. 8 16 24. 40. sari 
30,000 6. es 24. 36. minnie n 
40,000 8. 16 32. ee se 
50,00¢ 10. 20 40. , aoe 





Applying these different form]uz to our six engines, we have? 


ee I a eg a ee ne ae A ER PR TES SI A a ET Ae 


Engine No....... weenie’ Mises baits oa 1 2 3 4 5 6 
Diam. cyl.......... fe. WA Pe1e? Pb aorseosod Seb Leaoienm 
TIOLSS POWEP ei cccece sce nites Cee eee HT. DO 50 | 450 { 450 1,250} 1,250 
Revs. pervmin 2 FAS. ee 250 125 130 65 90 45 


Mean pressure on crank-pin = S.....| 3,299 | 2,299 | 23,185} 23,185] 58,905) 58,905 
Half wt. of fly-wheel and shaft = Q..] 268 | 536 5,968} 11,936] 26,470) 52,940 
Resultant press. on bearing 

VQ? +S? = Ry.| 3,310 | 3,335 | 23,924] 26,194] 64,580) 79,200 


Diam. of shaft journal................ 3.84 | 4.39 | 11.85) 12.99} 20.58) 21.52 
Length of shaft journal: 


Marks, 1 = .0000325fR,N( f=.10) | 5.38 | 2.71 } 20.87| 11.07] 37.78] 23.17 
Whitham, 2 = .0000515/R,R( f= 10).| 4.27 | 2.15 | 16.53] 8.77] 29.95] 18.35 


epens Ve 
Thurston, b= 69 yygqeree fis boy 83.61 | 1.82 | 14.00] 7.43] 25.86) 15.85 
he eek + 20) 
Freeney Tag ROdd: bei: 5.22 | 2.78 | 21.70| 10.85] 35.16) 22.47 
Unwin, AS eatin I)d..... ++. 7.68 | 6.59 | 17.25] 16.36] 27.99] 25.39 
LLG nh be Sa am RECS 3.33 | 1.60 | 12.00] 6.00| 20.83) 10.42 
Average.................. .....1 4.92 | 2.99 | 17.051 10.00] 29.541 19.22 


If we divide the mean resultant pressure on the bearing by the projected 
area, that is, by the product of the diameter and length of the journal, using 
the greatest and smallest length out of the seven lengths for each journal 


Na above, we obtain the pressure per square inch upon the bearing, as 
ollows: 


Se pe ee eee eee 
Hngine No Gear sec meeiac teks. os3. 2558 1 2 3 4 5 6 











——<— | —____..- | _-___ _. 


Pressure per sq. in., shortest journal.| 259 | 455] 1761 836} 151 | 353 


Lengest journal. soreeemipeseso es. sis. 112 115 97 } 123 83 | 145 
AVeraze JOULNA! Face MeieE <> cic\s ss. 175 | 254], 124] 202] 106 | 191 
Journal of length = diam........... » ot te [PL 03s eee Rae ee. 1%5 


Many of the formulee give for the long-stroke engines a length of journal 
Jess than the diameter, but such short journals are rarely used. in practice, 
The last line in the above table has been calculated ou the supposition thag 


DIMENSIONS OF PARTS OF ENGINES. 813 


the journals of the long-stroke engines are made of a length equal to the 
lameter. 

In the dimensions of Corliss engines given by J. B. Stanwood (Eng., June 
12, 1891), the lengths of the journals for engines of diam. of cyl. 10 to 20 in, 
are the same as the diam. of the cylinder, and a little more than twice the 
diam. of the journal. For engines above 20 in. diam. of cyl. the ratio of 
tength to diam. is decreased so that an engine of 30 in. diam. has a journal 
26 in. long, its diameter being 1443 in. These lengths of journal are greater 
than those given by any of the formule above quoted. 

There thus appears to be a hopeless confusion in the various formule for 
ength of shaft journals, but this is no more than is to be expected from the 
variation in the coefficient of friction, and in the heat-conducting power of 
journals in actual use, the coefficient varying from .10 (or even .16 as given 

y Marks) down to.01, according to the condition of the bearing surfaces 


and the efficiency of lubrication. Thurston’s formula, 1 = sound" reduces to 
9 


the form 1 = .000004363PR, in which P = mean total load on journal, and 
Rk = revolutions per minute. This is of the same form as Marks’ and 
Whitham’s formule, in which, if f the coefficient of friction be taken at .10, 
the coefficients of PR are, respectively, .0000065 and .00000515. Taking the 
mean of these three formule, we have J = .0000053PR, if f = .10 or l= 
.000053fPR for any other value of f. The author believes this to be as safe 
a formula as any for length of journals, with the limitation that if it brings 
a result of length of journal less than the diameter, then the length should 
be made equal to the diameter. Whenever with f = .10 it gives a length 
which is inconvenient or impossible of construction on account of limited 
space, then provision should be made to reduce the value of the coefficient 
of friction below .10 by means of forced lubrication, end play, etc., and to 
carry away the heat, as by water-cooled journal-boxes. The value of P 
should be taken as the resultant of the mean pressure on the crank, and the 
load brought on the bearing by the weight of the shaft, fly-wheel, etc., as 


calculated by the formula already given, viz., Ry = 7 Q? + S? for horizontal 
engines, and Rk, = Y-+ S for vertical engines. 

For our six engines the formula / = ,0000053PR gives, with the limitation 
for the long-stroke engines that the length shall not be less than the diam- 
eter, the following: 





PIM BTHOINO 7,00) cncc oan cceaceroccaesnecT Me 2 8 4 5 6 
Length of journal........ .s,secs-acee 4.39 4.39 16.48 12.99 30.80 21.52 
Pressure per square inch on journal.. 196 173 128 155 102 = 171 


Crank «shafts with Centre-crank and Double-crank 
Arms,—In centre-crank engines, one of the crank-arms, and its adjoining 
journal, called the after journal, usually transmit the power of the engine 
to the work to be done, and the journal resists both twisting and bending 
moments, while the other journal is subjected to bending moment only. 
For the after crank-journal the diameter should be calculated the same as 
for an overhung crank, using the formula for combined bending and twist- 
ing moment, T; = B-+ 7b? + T?,in which 7, is the equivalent twisting 
moment, B the bending moment, and 7 the twisting moment, This value 


3 
of 7, is to be used in the formula diameter = {/ = The bending mo- 


ment is taken as the maximum load on piston multiplied by one fourth of 
the length of the crank-shaft between middle points of the two journal 
bearings, if the centre crank is midway between the bearings, or by one 
half the distance measured parallel to the shaft from the middle of the 
crank-pin to the middle of the after bearing. This supposes the crank- 
shaft to be a beam loaded at its middle and supported at the ends, but 
Whitham would make the bending moment only one half of this, consider- 
ing the shaft to be a beam secured or fixed at the ends, with a point of con- 
trafiexure one fourth of the length from the end. The first supposition is 
the safer, but since the bending moment will in any case be much less than 
the twisting moment, the resulting diameter will be but little greater than 
if Whitham’s supposition is used. For the forward journal, which is sub- 


3/10.2E 
fected to bending moment only, diameter of shaft = We med , in which B 


“« 





814 THE STEAM-ENGINE. 


is the maximum bending moment and S the safe shearing strength of the 
metal per square inch. 

For our six engines, assuming them to be centre-crank engines, and con- 
sidering the crank-shaft to be a beam supported at the ends and loaded in 
the middle, and assuming lengths between centres of shaft bearings as 
given below, we have: 





FBinigine NOs ce setseasa ae os intl 2 8 q 8 6 


eer | ae mee | a | ee OS -- 


Length of shaft, assumed, 
AN CWGS tel get ores toe ee st me 20 24 48 60 %6 96 
Max. press. oncrank-pin,P| 7,854] 7,854] 70,686) 0,686] 196,350} 196,350 

Max. bending moment 





B= 14PL, inch-lbs... aNd 89,270] 49,637) 848,232) 1,060,290)3,729,750| 4,712,400 
Twisting moment, T...... 47,124| 94,248) 1,060,290) 2,120,580) 4,712,400) 9,424,800 
Equiv. twisting moment, 

B+ VBI+T? ....n. ee. 101,000] 156,000) 2,208,000) 3,430,000} 9,740,000) 15,240,000 


Diameter of after journal, 


df cos sssees 3.98] 4.60] 21.15 | 18.00 | 18.25 | 21.20 
8000 


Diam. of forward journal, 


$ 
Qe ........0-] 8.68] 8.99} 10.98 | 11.16} 16.82] 18.18 








The lengths of the journals would be calculated in the same manner as in 
the case of overhung cranks, by the formula / = .000053fPR, in which P is 
the resultant of the mean pressure due to pressure of steam on the piston, 
and the load of the fly-wheel, shaft, etc.,on each of the two bearings. 
Unless the pressures are equally divided between the two bearings, the 
calculated lengths of the two will be different; but it is usually customary 
to make them both of the same length, and in no case to make the length 
less than the diameter. The diameters also are usually made alike for the 
two journals, using the largest diameter found by calculation. 

‘The crank-pin for a centre crank should be of the same length as for an 
overhung crank, since the length is determined from considerations of 
heating, and not of strength. The diameter also will usually be the same, 
since it is made great enough to make the pressure per square inch on the 
projected area (product of length by diameter) small enough to allow of 
free lubrication, and the diameter so calculated will be greater than is re. 
quired for strength. 

Crank:sshaft with Two Cranks coupled at 90°.—If the 
whole power of the engine is transmitted through the after journal of the 
after crank-shaft, the greatest twisting moment is equal to 1.414 times the 
maximum twisting moment due to the pressure on one of the crank-pins. 
If 7 = the maximum twisting moment produced by the steam-pressure on 
one of the pistons, then 7, the maximum twisting moment on the after part 
of the crank-shaft, and on the line-shaft, produced when each crank makes 
an angle of 45° with the centre line of the engine, is 1.4147. Substituting 
this value in the formula for diameter to resist simple torsion, viz.,d@ = 


3/r47n 3 ne 
4/°2, wonaved = 4/%1 217, Af, d= 1.082 4/Z, in which 7 is 


the maximum twisting moment produced by one of the pistons, @ = diam- 
eter in inches, and S=safe working shearing strength of the material. 
For the forward journal of the after crank, and the after journal of the 
forward crank, the torsional moment is that due to the pressure of steam 
on the forward piston only, and for the forward journal of the forward 
crank, if none of the power of the engine is transmitted through it, the 
torsional moment is zero, and its diameter is to be calculated for bending 
moment only. 

For Combined Torsion and Fliexure,.—Let B, = bending mo- 
ment on either journal of the forward crank due to maximum pressure on 





DIMENSIONS OF PARTS OF ENGINES. 815 


forward piston, B, = bending moment on either journal of the after crank 
due to maximum pressure on after piston, 7, = maximum twisting moment 
on after journal of forward crank, and T, = maximum twisting moment on 
after journal of after crank due to pressure on the after piston. 

Then equivalent twisting moment on after journal of forward crank = B, 


+ VB2+ 7;3, 
On forward journal of after crank = By + WB? + 7,2. 
On after journal of after crank = By + V Bq? + (7, + T2)*. 


These vames of equivalent twisting moment are to be used in the formula 


pees tkes 
for diameter of journals d= ae For the forward journal of the 


10.2B, 
S 


It is customary to make the two journals of the forward crank of one 
diameter, viz., that calculated for the after journal. 

For a Three-cylinder Engine with cranks at 120°, the greatest 
twisting moment on the after part of the shaft, if the maximum pressures 
on the three pistons are equal, is equal to twice the maximum pressure on 
any one piston, and it takes place when two of the cranks make angles of 
80° with the centre line, the third crank being at right anglestoit. (For de- 
monstration, see Whitham’s ‘‘ Steam-engine Design,” p. 252.) For combined 
torsion and fiexure the same method as above given for two crank engines 
is adopted for the first two cranks; and for the third, or after crank, if all 
the power of the three cylinders is transmitted through it, we have the 


equivalent twisting moment on the forward journal = B,-+- 7 Bs?+(7,4+75)2, 


and on the after journal = Bs; + 4 #3*-+ (7; + 7, + 13)?, Bs and 73 being 
respectively the bending and twisting moments due to the pressure on the 
third piston. i, 

Crank «shafts for Triple-expansion Marine Engines, 
according to an article in The Hngineer, April 25, 1890, should be made 
' larger than the formulee would call for, in order to provide for the stresses 
due to the racing of the propeller in a sea-way, which can scarcely be cal- 
culated. A kind of unwritten law has sprung up for fixing the size of a 
crank-shaft, according to which the diameter of the shaft is made about 
0.45D, where D is the diameter of the high-pressure cylinder. This is for 
solid shafts. When the speeds are high, as in war-ships, and the stroke 
short, the formula becomes 0 4D, even for hollow shafts. 

The Valve-stem or Valve-rod.—tThe valve-rod should be designed 
to move the valve under the most unfavorable conditions, which are when 
the stem acts by thrusting, as a long column, when the valve is unbalanced 
{a balanced valve may become unbalanced by the joint leaking) and when it 
is imperfectly lubricated. The load on the valve is the product of the aroa 
into the greatest unbalanced pressure upon it per square inch, and the co- 
efficient of friction may be as high as 20%. The product of this coefficient 
and the load is the force necessary to move the valve, which equals the 
maximum thrust on the valve-rod. From this force the diameter of the 
valve-rod may be calculated by Hodgkinson’s formula for columns. An 


3 
forward crank-shaft d = 4/ 


empirical formula given by Seaton is: Diam. of rod = d = a , in which 


= length and 6 = breadth of valve, in inches; p = maximum absolute 
pressure on the valve in Ibs. per sq. in., and F’a coefficient whose values are, 
for iron: long rod 10,000, short 12,000; for steel: long rod 12,000, short 14,500. 

Whitham gives the short empirical rule: Diam. of valve-rod = 1/30 diam. 
of cy). = % diam. of piston-rod. 

Size of Slotelink, (Seaton.)—Let D be the diam. of the valve. rod 


i lbp , 
2 =4/ 12,000° 


then Diameter of block-pin when overhung = D, 
se “s “secured at bothends = 0.75 x D, 
La eccentric-rod pins =0.7 xD. 
be suspension-rod pins = 0.55 x D. 
2 ee? “pin when overhung = 0,%5 x D, 


816 THE STEAM-ENGINE. 


Breadth of link =0.8t00.9 < DB. 
Length of block = 1.8to1.6 x D, 
Thickness of bars of link at middJe os 1" 


If a single suspension rod of round section, its diameter = 0.7 X D. 
If two suspension rods of round section, their diameter = 0.55 x Dd: 


Size of Double-bar Links.—When the distance between centres of 
eccentric pins = 6 to 8 times throw of eccentrics (throw = eccentricity = 
half-travel of valve at full gear) D as before: 


Depth of bars = 125 x D+% in 
Thickness of bars =05 x D+%4 in. 
Length of sliding-block = 25 10.8. >(P: 
Diameter of eccentric-rod pins = 0.8 x D+ 4% in 
* centre of sliding-block = 1.8 < D. 
When the distance between eccentric-rod pins = 5 to 5% times throw of 
eccentrics: 
Depth of bars = 1:25 XD ar Vy in. 
Thickness of bars =05 X D+ “A in. 
Length of sliding-block = 2.5 to3 X 
Diameter of eccentric-rod pins = 0.75 x D. 


Diameter of eccentric bolts (top end) at bottom of thread = 0.42 x D when 
of iron, and 0.88 « D when of steel. 

The Eccentric.-—Diam. of eccentric-sheave = 2.4 X throw of eccentric 
+ 1.2 xX diam. of shaft. Das before 


Breadth of the sheave at the shaft...............0.. = 1.15 & D+ 0.65 inch 
Breadth of the sheave at the strap...... stefeitherste' et etore = D+ 0.6ineh 
Thickness of metal around the shaft ...........e- = 0.7 x D+ 0.5 inch 
Thickness of metal at circumference ..........-..-. = 0.6 X D+ 0.4 inch. 
PAPE ACUI OL, REY: > fiat a scale cos o% 6 5 cspietieeusiesias eeueee = 0.7 X D+ 0.5 inch 
MANIC TIGSSIOL KE Y)- 2 .coniscr haas cece ouleers ote Soni = 0.25 x D+. 0.5 inch. 
Diameter of bolts connecting parts of ‘strap.. = 0.6 X D+ 0.1 inch. 


THICKNESS OF ECCENTRIC-STRAP. 


When of bronze or malleable cast iron: 


Thickness of eccentric-strap at the sae eoeesee. = 0.4% D+-0.6 inch. | 
ef sidess. .c..61... = 0.38 % D015 Meh, 
When of wrought iron or cast steel: 
Thickness of eccentric- str ‘ap at the middle..... Shr Ac D+ 0.5 inch, 
Ob ou’ SIGS, Jetee tae ye ar se D+ 0.4 inch 


Whe Eccentric-rod.—The diameter of the eccentric-rod in the body 
and at the eccentric end may be calculated in the same way as that of the 
connecting-rod, the length being taken from centre of strap to centre of 
pin. Diameter at the link end = 0.8D + 0.2 inch. 

This is for wrought-iron; no reduction in size should be made for steel. 

Eecentric-rods are often ‘made of rectangular section. 

Reversing=gear should be so designed as to have more than sufficient 
strength to withstand the strain of both the valves and their gear at the 
same time under the most unfavorable circumstances; it will then have the 
stiffness requisite for good working. 

Assuming the work done in reversing the link-motion, W, to be only that 
due to overcoming the friction of the valves themselves ‘through their whole 
travel, then, if 7 be the travel of valves in inches; for a compound engine 


a. = PX OLX PY, 
Ss) + pee 
i!, b! and p! being ie Pe. and maximum steam-pressuré On valve 
of the second cylinder; and for an expansive fies 
Wa2ext(XOX?): o Zaxoxp. 


To provide for the friction of link-motion, eccentrics and other gear, and 
for abnormal conditions of the same, take the work at one and a half times 
the above amount. 


FLY-WHEELS. 817 


To find the strain at any part of the gear having motion when reversing, 
divide the work so found by the space moved through by that part in feet; 
the quotient is the strain in pounds; and the size may be found from the 
ordinary rules of construction for any of the parts of the gear. (Seaton.) 

Engine-frames or Bed-plates.—No definite rules for the design 
of engme-frames have been given by authors of works on the steam-engine. 
The proportions are left to the designer who uses “rule of thumb,”’ or 
copies from existing engines. F. A. Halsey (Am. Mach., Feb. 14, 1895) has 
made a comparison of proportions of the frames of horizontal Corliss 
engines of several builders. The method of comparison is to compute from 
Yhe measurements the number of square inches in the smallest cross-sec- 
tion of the frame, that is, immediately behind the pillow-block, also to 
compute the total maximum pressure upon the piston, and to divide the 
latter quantity by the former. The result gives the number of pounds 
pressure upon the piston allowed for each square inch of metal in the 
frame. He finds that the number of pounds per square inch of smallest 
section of frame ranges from 217 for a 10 X 380-in. engine up to 575 for a 
28 < 48-inch. A 80 X 60-inch engine shows 350 lbs., and a 32-inch engine 
which has been running for many years shows 667 lbs. Generally the 
strains increase with the size of the engine, and more cross-section of metal 
is allowed with relatively long strokes than with short ones. 

From the above Mr. Halsey formulates the general rule that in engines 
of moderate speed, and having strokes up to one and one-half times the 
diameter of the cylinder, the load per square inch of smallest section 
should be for a 10-inch engine 3800 pounds, which figure should be increased 
for larger bores up to 500 pounds for a 30-inch eylinder of same relative 
stroke, For high speeds or for longer strokes the load per square inch 
should be recuced. 


FLY-W HEELS. 


The function of a fly-wheel is to store up and to restore the periodical fluc- 
tuations of energy given to or taken from an engine or machine, and thus 
to keep approximately constant the velocity of rotation. Rankine calls the 


quantity a= the coefficient of fluctuation of speed or of unsteadiness, in 


which Ey is the mean actual energy, and AF the excess of energy received or 
of work performed, above the mean, during a given interval. The ratio of 
the periodical excess or deficiency of energy AF to the whole energy exerted 
in one period or revolution General Morin found to be from 1/6 to 44 for 
single-cylinder engines using expansion; the shorter the cut-off the higher 
the value. Fora pair of engines with cranks coupled at 90° the value of the 
ratio is about 14, and for three engines with cranks at 120°, 1/12 of its value 
for single cylinder engines. For tools working at intervals, such as punch- 
ing, slotting and plate-cutting machines, coining-presses, etc., AH is nearly 
equal to the whole work performed at each operation. 


A P ; 
A fly-wheel reduces the coefficient a to a certain fixed amount, being 


0 

about 1/32 for ordinary machinery, and 1/50 or 1/60 for machinery for fine 

urposes. } } 
4 If m be the reciprocal of the intended value of the coefficient of fluctua- 
tion of speed, 4# the fluctuation or energy, J the moment of inertia of the 
fly-wheel alone, and a, its mean angular velocity, J = wg a 
a fly-wheel is usually heavy in comparison with the arms, J may be taken 
to equal Wr?, in en = bhatt of rim in pounds, and x the radius of the 

4 gd ie 

wheel; then W = oe = S if v be the velocity of the rim in feet per 
second. The usual mean radius of the fly-wheel in steam-engines is from 
three to five times the length of the crank. The ordinary values of the prod 
uct mg, the unit of time being the second, lie between 1000 and 2000 feet. 
cAbridged from Rankine, S E., p. 62.) 

Thurston gives for engines with automatic valve-gear W = 250,00 


ae , in which A = area of piston in square inches, S = stroke in feet, p= 
Ft 

n.een steam-pressure in Ibs. persq.in., R = revolutions per minute, D = out 
side diameter of wheel in feet. Thurston also gives for ordinary forms of 


As the rim of 








818 . THE STEAM-ENGINE. 


non-condensing engine with a ratio of expansion between $8 and 5, W = 


ae in which a ranges from 10,000,000 to 15,000,000, averaging 12,000,000, 
For gas-engines, in which the charge is fired with every revolution, the Amer: 
ican Machinist gives this latter formula, with a doubled, or 24,000,000. 
Presumably, if the charge is fired every other revolution, a should be again 


doubled. 
Rankine (‘‘ Useful Rules and Tables,”* p. 247) gives W = 475,000 2 ; 


which V is the variation of speed per cent. of the mean speed. Thurston's 
first rule above given corresponds with this if we take V at 1.9 per cent. 
Hartnell (Proc. Inst., M. E. 1882, 427) says: The value of V, or the 
variation permissible in portable engines, should not exceed 3 per cent. with 
an ordinary load, and 4 per cent when heavily loaded. In fixed engines, for 
ordinary purposes, V = 24 to 3 per cent. For good governing or special 
purposes, such as cotton-spinning, the variation should not exceed 114 to 2 


per cent. i 
F. M. Rites shad A.§. M. E., xiv. 100) develops a new formula for weight 


in 





of rim, viz., W = Ra pe and weight of rim per horse-power = Pann in 

which C varies from 10,000,000,000 to 20,000,000,000; also using the latter value 

of C, he obtains for the energy of the fly-wheel Mer Loe, Sie anise 
BY vy 2 — 64.4 8600 


CxH.P.(8.14)2D2R?2 — 850,000 H.P. . - 850,000 
Rp? x 64.4 50 3000 = . Fly-wheel energy per H.P. = RT 

The limit of variation of speed with such a weight of wheel from excess of 
power per fraction of revolution is less than _.0028. 

The value of the constant C given by Mr. Rites was derived from practice 
of the Westinghouse single-acting engines used for electric-lighting. For 
double-acting engines in ordinary service a value of C = 5,000,000,000 would 
probably be ample. : 

From these formule it appears that the weight of the fly-wheel for a given 
horse-power should vary inversely with the cube of the revolutions and the 
square of the diameter. 

J. B. Stanwood (#ng’g, June 12, 1891) says: Whenever 480 feet is the 
lowest piston-speed probable for an engine of a certain size, the fly-wheel 
weight for that speed approximates closely to the formula 








a2s 
W = 700,000 ERT 
W = weight in pounds, d = diameter of cylinder in inches, s = stroke in 
inches, D = diameter of wheel in feet, R = revolutions per minute, corre 
sponding to 480 feet piston-speed. 

In a Ready Reference Book published by Mr. Stanwood, Cincinnati, 1892, 
he gives the same formula, with coefficients as follows: For slide-valve en- 
gines, ordinary duty, 350,000; same, electric-lighting, 700,000; for automatic 
high-speed engines, 1,000,000; for Corliss engines, ordinary duty 700,000, 
electric-lighting 1,000,000. 


Thurston’s formula above given, W = ane with @ = 12,000,000, when re- 
2 
duced to terms of d and sin inches, becomes W = 785,400 a 
If we reduce it to terms of horse-power, we have I.H:P. = setts 


in which P = mean effective pressure. Taking this at 40 Ibs., we obtain 
W = 5,000,000,000 Re Di . If mean effective pressure = 80 Ibs., then W= 
LH.P, 
R3 D2 * 
Emil Theiss (Am. Mach., Sept. 7 and 14, 1893) gives the following values 


ot d, the coefficient of steadiness, which is the reciprocal of what Rankine 
calls the coefficient of fluctuation : * 








6,666,000,000 


FLY-WHEELS. 819 


Yor engines operating—~ 


Hammering and crushing machinery......esre0.. A= 
Pumping and shearing machinery........e.0.-46. @= to 3 
Weaving and paper-making machinery......-.... @ = 40 
Milling machinery. ee ee ee ee ee 2 oe ey d = 50 
Spinning machinery..... doe web ceneee b cometionecs ... d@= 50 to 100 


Ordinary driving-engines (mounted on bed-plate), 
HeOlHOLANSMIISSION cae cee nacie se ceuls oe te cssiocecte eC; = 
Gear-wheel transmission......ccccccccscccscccccsee OG = 0 
A : . 35,4X1,F.P, 
Mr, Theiss’s formula for weight of fly-wheelin poundsis W=ix Vas 
where d is the coefficient of steadiness, V the mean velocity of the fly- 
wheel rim in feet per second, » the number of revolutions per minute, i = 
a coefficient obtained by graphical solution, the values of which for dif 
ferent conditions are given in the following table. In the lines under ‘‘ cut- 
off,’’ p means ‘‘ compression to initial pressure,” and O “‘ no compression *’: 


VALUES OF 7. SINGLE-CYLINDER NON-CONDENSING ENGINES. 





= | Cutoff, 1/6. | Cut-off, 4. Cut-off, 14. Cut-off, 14. 
®o 
= 5.3 Comp. 0) 6 ls Oo i en O CoP oO 





200 272,690; 218,580} 242.010] 209,170] 220,760] 201,920) 193,340) 182,846 
400 240,810} 187.430) 208,200] 179,460) 188,510] 170,040) 174,630) 167,860 
600 194,670} 145,400} 168,590) 186,460] 165,210) 146,610]........]........ 
800 158:200/S108:6001 2 162,.070) 13,260) Mitat ese Uo aracki|~'s/- bir es a OOF 





SINGLE-CYLINDER CONDENSING ENGINES. 





























24] Cut-off, 4 | Cut-off, 1/6. | Cut-off, 14. | Cut-off, 14. | Cut-off, 14. 
° . 
oO | RR Re 
no 3 
a © 5|Comp Comp. Comp. Comp. Comp. 
ea ra A Ry on ea Pla Fi 2 GR ca aaa Petty Oe 
200. }265,560)176,560|224, 160) 173,660/204,210 167,140 189, 600] 161,830]172, 690] 156,990 
400 }194,550)117,870|174,380)118,350)164,720)133,080)174,630]151,680].......J.....-6 
GBOOH148)780/140, 090 eee ee ee We Prete tverereselel «mused taliceie ate eves ota ene 
TWwO-CYLINDER ENGINES, CRANKS AT 90°. 
gad | Cut-off, 1/6. Cut-off, 14. | Cut-off, 14. Cut-off, %. 
hehe trea Tiere ee 
nodD, j 
a23 | Comp. o |Comp.| g |Comp.; g |Comp.| g 
nm p p p Pp 
200 71,980 59,420 | 49.279 | 
400 70,160 Mean) 57,000 Mean 49.150 Mean] 87,920 | t Mean 
49'220 | ( 50,000 36,950 











35,000 | 





THREE-CYLINDER ENGINES, CRANKS AT 120°. 


22s | Cut-off, 1/6. | Cut-off, 14. Cut-off, 34. Cut-off, 14. 
sya SS ee ee 
a 2.3, Comp | oO rae O Comp. O Comp O 


ee} ee ey 





32,240 | 83.810 | 35,500 | 34,540 | 33,450 | 35,960 | 32,370 
31,570 | 85,140 | 33,810 | 36,470 | 32.850 | 33-810 | 32/370 





200 
800 80,190 


As a mean value of 7 for these engines we may use 83,870. 


880 THE STHAM-ENGINE. 


Centrifagal Foree in Fly-wheels.—Let W = weight of rim in 
pounds; R = mean radius of rim in feet; 7 = revolutions per minute, g = 
82.16; v = velocity of rim in feet per Second = 27kr = 60, 

Contrifieal tence wicw rele rene ymin mn a 

entrifug c ole ring = == oR = 36009 

The resultant, acting at right angles to a diameter of half of this force, 
tends to disrupt one half of the wheel from the other half, and is resisted by 
the section of the rim at each end of the diameter. The resultant of half the 


radial forces taken at right angles to the diameter is 1 + lgn7 = e of the sum 


of these forces; hence the total force Fis to be divided by 2 x 2 x 1.5708 
= 6.2832 to obtain the tensile strain on the cross-section of the rim, or, total 
strain on the cross-section = S = .0000542i1WRr?, The weight W, of a 
rim of cast iron 1 inch square in section is 27k X 3.125 = 19.685R pounds, 
whence strain per square inch of sectional area of rim = 8, = .0010656A71 
= .0002664D2r2 = .0000270V2, in which D = diameter of wheel in feet, and V 
4s aoe of rim in feet per minute. S, = .0972v2, if vis taken in feet per 
second. 


= .000341 W R72. 


For wrought iron.......... S, = .0011866R2r2 = .0002842D272 = .0000288 V 2. 
Om BVCEM ie. o0e ste ane sicisls S, = .00115938R272 = .0002901 D272 = .0000294 V2. 
For wood....... Soa coT0 c10.3 S, = .0000888A272 = .0000222D272 = .00000225V 2, 


The specific gravity of the wood being taken at 0.6 = 37.5 lbs. per cu. ft., 
or 1/12 the weight of cast iron. 

Example.—Required the strain per square inch in the rim of a cast-iron 
wheel 30 ft. diameter, 60 revolutions per minute. 

Answer. 15? x 602 & .0010656 = 863.1 Ibs. 

Required the strain per square inch in a cast-iron wheel-rim running a 
mile a minute. Answer. .000027 « 5280? = 752.7 lbs. 

In cast-iron fly-wheel rims, on account of their thickness, there is difficulty 
in securing soundness, and a tensile strength of 10,000 lbs. per sq. in. is as 
much as can be assumed with safety. Using a factor of safety of 10 gives a 
maximum allowable strain in the rim of 1000 lbs. per sq. in., which corre- 
sponds to a rim velocity of 6085 ft. per minute, ; 

For any given material, as cast iron, the strength to resist centrifugal force 
depends only on the velocity of the rim, and not upon its bulk or weight. 

Chas. E. Emery (Cass. Mag., 1892) says: By calculation half the strength 
of the arms is available to strengthen the rim, or a trifle more if the fly- 
wheel centres are relatively large. The arms, however, are subject to. trans- 
verse strains, from belts and from changes of speed, and there is, moreover, 
no certainty that the arms and rim will be adjusted so as to pull exactly, 
together in resisting disruption, so the plan of considering the rim by itself 
and making it strong enough to resist disruption by centrifugal force within 
safe limits, as is assumed in the calculations above, is the safer way. 

It does not appear that fly-wheels of customary construction should be 
unsafe at the comparatively low speeds now in common use if proper 
materials are used in construction. The cause of rupture of fly-wheels that 
have failed is usually either the ‘“‘running away ”’ of the engine, such as may 
be caused by the breaking or slackness of a governor-belt, or mecorrect 
design or defective materials of the fly-wheel. 

Chas. T. Porter (Trans. A. S. M. E., xiv. 808) states that no case of the 
bursting of a fly-wheel with a solid rim in a high-speed engine is known. He 
attributes the bursting of wheels built in segments to insufficient strength 
of the flanges and bolts by which the segments are held together. (See also 
Thurston, *‘ Manual of the Steam-engine,”’ Part II, page 413, etc.) 

Arms of Fly-wheels and Pulleys. — Professor Torrey (Am. 
Mach., July 30, 1891) gives the following formulafor armis of elliptical cross- 
section of cast-iron wheels: : 

W = load in pounds acting on one arm; S = strain on belt in pounds per 
inch of width, taken at 56 for single and 112 for double belts; v = width of 
belt in inches; 21 = number of arms; L = length of arm in feet; b = breadth 


of arm at hub: d= depthof arm at hu both’in dpches: Wot 


v9 i) 
b= le The breadth of the arm is its least dimension = minor axis of 
the ellipse, and the depth the major axis. This formula is based on a factor 
of safety of 10. 


FLY-WHERELS. 821 


{n using the formula, first assume some depth for the arm, and calculate 
the required breadth to go with it. If it gives tooround an arm, assume 
the depth a little greater, and repeat the calculation, A second trial will 
almost always give a good section. 

The size of the arms at the hub having been calculated, they may be 
somewhat reduced at the rim end. The actual amount cannot be calculated, 
as there are too many unknown quantities. However, the depth and 
breadth can be reduced about one third at the rim without danger, and this 
will give a well-shaped arm. 

Pulleys are often cast in halves, and bolted together. When this is done 
the greatest care should be taken to provide sufficient metal in the bolts. 
This is apt to be the very weakest point in such pulleys. The combined area 
of the bolts at each joint should be about 28/100 the cross-section of the pul 
ley at that point. (Torrey.) 


3/BD 
Unwin gives d= o.oaar4/ for single belts ; 


3 / BD 
d = 0.798 4/ ~;, for double belts; 


D being the diameter of the pulley, and B the breadth of the rim, beth in 
inches. These formule are based on an elliptical section of arm in which 
b = 0.4d or d = 2.56 on a width of belt = 4/5 the width of the pulley rim, 
a maximum driving force transmitted by the belt of 56 lbs. per inch of width 
for a single belt and 112 lbs, for a double belt, and a safe working stress of 
cast iron of 2250 lbs. per square inch. 

If in Torrey’s formula we make b = 0.4d, it reduces to 


3/WL 3/WL 
Sia ee OTM 


Exumple.—Given a pulley 10 feet diameter; 8 arms, each 4 feet long; face, 
36 inches wide; belt, 30 inches: required the breath and depth of the arm at 
the hub. According to Unwin, 


3/BD s /36 x 120 >i ; 
6) 0.6337 4, 1 = 0.6834/ ~—g = 5.16 for single belt, b = 2.06; 


3s /BD 3 /36 X 120 
d = 0.798 hn = 0.7984/ ——g-— = 6.50 for double belt, b = 2.60. 


According to Torrey, if we take the formula b = Mee and assume d =5 


and 6.5 inches, respectively, for single and double belts, we obtain b = 1.08), 
and 1.33, respectively, or practically only one half of the breadth according 

to Unwin. and, since transverse strength is proportional to breadth, an arm 

only one half as strong. 

Torrey’s formula is said to be based on a factor of safety of 10, but this 
factor can be only apparent and not real, since the assumption that the 
strain on each arm is equal to the strain on the belt divided by the number 
of arms, is, to say the least, inaccurate. It would be more nearly correct to 
say that the strain of the belt is divided among half the number of arms. 
Unwin makes the same assumption in developing his formula, but says it is 
only in arough sense true, and that a large factor of safety must be allowed. 
He therefore takes the low figure of 2250 lbs. per square inch for the safe 
working strength of cast iron. Unwin says that his equations agree well 
with practice. 

Diameters of Fly-wheels for Various Speeds.—If 6000 feet 
per minute be the maximum velocity of rim allowable, then 6000 = mRD, in 
which & =revolutions per minute, and D= diameter of wheel in feet, 


whence ee Soe y 


822 : THE STEAM-ENGINE, 


Maximum DIAMETER OF FLY-WHEEL ALLOWABLE FOR DIFFERENT NUMBERS 
OF REVOLUTIONS. 





Assuming Maximum Speed of | Assuming Maximum Speed 





: 5000 feet per minute. of 6000 feet per minute, 
Revolutions not SA ee a ie BL et BSL 
per minute. : 

Circum. ft. Diam. ft. Circum. ft. Diam. ft. 
40 125 39.8 150. 47.7 
50 100 31.8 120. 38.2 
60 83.3 26.5 100. 31.8 
7 71.4 22.7 85.72 27.3 
80 62.5 19.9 75.00 2519 
90 55.5 § Wit 66.66 21.2 
100 50. 15.9 60.00 19.1 
120 41.67 13.3 50.00 15.9 
140 35.7 11.4 42.86 13.6 
160 31.25 9.9 37.5 11.9 
180 27.77 8.8 33.38 10.6 
200 25.00 8.0 30.00 9.6 
220 22.4 G2 27.27 8.7 
240 20.83 6.6 25.00 8.0 
260 19.23 6.1 23.08 7.3 
280 17.86 5.7 21.43 6.8 
300 16.66 5.3 20.00 6.4 
350 14.29 4.5 17.14 Lobh 
400 12.5 4.0 15.00 4.8 
450 11.11 3.5 13.38 4.2 
500 10.00 3.2 12.00 3.8 





Strains in the Rims of Fly-band Whee’s Produced by 
Centrifugal Foree. (James B. Stanwood, Trans. A. §S. M. E., xiv. 251.) 
—Mr. Stanwood mentions one case of a fly-band wheel where the periphery 
velocity ona 17’ 9’ wheel is over 7500 ft. per minute. 

In band saw-mills the blade of the saw is operated successfully over 
wheels 8 and 9 ft. in diameter, at a periphery velocity of 9000 to 10,000 ft. per 
minute. These wheels.are of cast iron throughout, of heavy thickness, with 
a large number of arms. 

In shingle-machines and chipping-machines where cast-iron disks from 2 to 
5 ft. in diameter are employed, with knives inserted radially, the speed is 
frequently 10,000 to 11,000 ft. per minute at the periphery. 

If the rim of a fly-wheel alone be considered, the tensile strain in pounds 


per square inch of therim section is T= Ho nearly, in which V = velocity 


in feet per second; but this strain is modified by the resistance of the arms, 
which prevent the uniform circumferential expansion of the rim, and induce 
a bending as well as a tensile strain. Mr. Stanwood discusses the strains in 
band-wheels due to transverse bending of a section of the rim between a 
pair of arms. 

When the arms are few in number, and of large cross-section, the ring 
will be strained transversely to a greater degree than with a greater number 
of lighter arms. To illustrate the necessary rim thicknesses for various 
rim velocities, pulley diameters, number of arms, etc., the following table 
is given, based upon the formula 


oe 5a 
u F 1° 
py peti et 
=} V2 «10 


in which ¢ = thickness of rim in inches, d = diameter of pulley in inches, 
N = number of arms, V = velocity of rim in feet per second, and F' = the 
greatest strain in pounds per square inch to which any fibre is subjected 
The value of Fis taken at 6000 lbs. per sa. in, 


FLY-WHEELS. 823 


Thickness of Rims in Solid Wheels, 








Diameter of Velocity of Velocity of No. of 





: Ree tate Thickness in 
Pulley in Rim in feet per|Rim in feet per Arms. : 

inches. second. minute, inches, 

24 50 8,000 6 2/10 

24 88 5,280 6 15/32 

48 88 5,280 6 j5/16 
108 184 11,040 16 214 
108 184 11,040 36 b 


Tf the limit of rim velocity for all wheels be assumed to be 88 ft. per sec- 
ond, equal to1 mile per minute, #’= 60001bs., the formula becomes 


_ Aid ae. 
67N2 ~ ** N2 


When wheels are made in halves or in sections, the bending strain may 
be such as to make # greater than that given above. Thus, when the joint 
comes half way between the arms, the bending action is similar to a beam 
supported simply at the ends, uniformly loaded, and ¢ is 50% greater. Then 
the furmula becomes 

eo 112d ; 
1 


aa 


or for a fixed maximum rim velocity of 88 ft. per second and F’ = 6000 Ibs., 


1 
t= ase In segmental wheels it is preferable to have the joints opposite 
the arms. Wheels in halves, if very thin rims are to be employed, should 
have double arms along the line of separation, 

Attention should be given to the proportions of large receiving and tight- 
ening pulleys. The thickness of rim for a 48-in. wheel (shown in table) with 
a rim velocity of 88 ft. per second, is 15/16 in. Many wrecks have been 
caused by the failure of receiving or tightening pulleys whose rims have beex 
too thin. Fly-wheelis calculated for a given coefficient of steadiness are fre- 
quently lighter than the minimum safe weight. This is true especially of 
large wheels. A rough guide to the minimum weight of wheels can be de- 
duced from our formule. The arms, hub, lugs, etc., usually form from one 
quarter to one third the entire weight of the wheel. If 6 represents the rim 
of a whee] in inches, the weight of the rim (considered as a simple annular 
ring) will be w = .82dtb Ibs. If the limit of speed is 88 ft. per second, then 
for solid wheels ¢ = 0.7d - N?. For sectional wheels (joint between arms) 
~¢=1.05d-= N?, Weight of rim for solid wheels, w = .57d2b =- N? in pounds. 
Weight of rim in sectional wheels with joints between arms, w = .86d2b ~ 
NN? in pounds. Total weight of wheel: for solid wheel, W = .76d2b - N? to 
.86d2b -- N2,in pounds. For segmental wheels with joint between arms, 
W = 1.05d2b -- N2 to 1.38d2b -— N2, in pounds. 

(This subject is further discussed by Mr. Stanwood, in vol. xv., and by 
Prof. Gaetano Lanza, in vol. xvi., Trans. A. 8S. M. E. 

A Wooden Rim Fly-wheel, built in 1891 for a pair of Corliss en- 
gines at the Amoskeag Mfg. Co.’s mill, Manchester, N. H., is described by 
Cc. H. Manning in Trans. A.S. M.E., xiii. 618. It is 30 ft. diam. and 108 in. face. 
The rim is 12 inches thick, and is built up of 44 courses of ash plank, 2, 3, 
and 4 inches thick, reduced about % inch in dressing, set edgewise, so as to 
break joints, and glued and bolted together. There are two hubs and two 
sets of arms, 12 in each, all of castiron. The weights are as follows: 





Weicht (calculated) of ash rim...... dcddacdccesccce: OL CDOS. 
‘ of 24 arms (foundry 45,020). ... .seccccccecee: 40,849 *%* 
ae sei TiS: (iamerge Bis i cicnta on 00 seas). Olg00 tees 

Counter-weights in 6arms............. Bieieis ois bis 215% ays 664 ne’ 

Total, excluding bolts and screws..... pera tantas 2 1042624 ** 


The wheel was tested at 76 revs. per min., being a surface speed of nearly 
7200 feet per minute. a 


824 THE STEAM-ENGINE. 


Mr. Manning discusses the relative safety of cast iron and of wooden 
wheels as follows: As for safety, the speeds being the same in botb 
cases, the hoop tension in the rim per unit of cross-section would be directly 
as the weight per cubic unit; and its capacity to stand the strain directly as’ 
the tensile strength per square unit; therefore the tensile strengths divided 
by the weights will give relative values of different materials. Cast iron 
weighing 450 Ibs. per cubic foot and with a tensile strength of 1,440,000 lbs. 
per square foot would give a value of 1,440,000 + 450= 3200, whilst ash, of 
which the rim was made, weghing 34 lbs. per cubie foot, and with 1,152,000 
lbs. tensile strength per square foot, gives a result 1,152,000 + 84 = 33,882, 
and 33,882 -- 3200 = 10.58, or the wood-rimmed pulley is ten times safer 
than the cast-iron when the castings are good. This would allow the wood- 


rimmed pulley to increase its speed to 410.58 = 3.25 times that of a sound 
cast-iron one with equal safety. 

‘Wooden Fly-wheel of the Willimantic Linen Co, (Illlus- 
trated in Power, March, 1893.)—Rim 28 ft. diam., 110 in. face. ‘The rim is 
carried upon three sets of arms, one under the centre of each belt, with 12 
arms in each set. 

The material of the rim is ordinary whitewood, % in. in thickness, cut into 
segments not exceeding 4 feet in length, and either 5 or 8 inches in width. 
These were assembled by building a complete circle 18 inches in width, first 
with the 8 inch inside and the 5-inch outside, and then beside it another cir- 
cle with the widths reversed, so as to break joints. Each piece as it was 
added was brushed over with glue and nailed with three-inch wire nails to 
the pieces already in position. The nails pass through three and into the 
fourth thickness. At the end of each arm four 14-inch bolts secure the 
rim, the ends being covered by wooden plugs glued and driven into the face 
of the wheel. 

Wire-wound Fly-wheels for Extreme Speeds. (Fng’g News, 
August 2, 1890.)—The power required to produce the Mannesmann tubes is 
very large, varying from 2000 to 19,000 H.P., according to the dimensions of 
the tube. Since this power is only needed for a short time (it takes only 36 
to 45 seconds to convert a bar 10 to {2 ft. long and 4 in. in diameter into a 
tube). and then some time elapses before the next bar is ready, an engine of 
1200 H.P. provided with a large fly-wheel for storing the energy will supply 
power enough for one set of rolls. These fly-wheels are so large and run at 
such great speeds that the ordinary method of constructing them cannot be 
followed. A wheel at the Mannesmann Woarks, made in Komotau, Hungary, 
in the usual manner, broke at a tangential velocity of 125 ft. per second. 
The fly-wheels designed to hold at more than double this speed consist of a 
cast-iron hub to which two steel disks, 20 ft. in diameter, are bolted; around 
the circumference of the wheel thus formed 70 tons of No. 5 wire are wound 
under a tension of 50 lbs. In the Mannesmann Works at Landore, Wales, 
such a wheel makes 240 revolutions a minute, corresponding to a tangential 
velocity of 15,080 ft. or 2.85 miles per minute, 





THE SLIDE-VALVE. 


Definitions.—Tavel = total distance moved by the valve. 

Throw of the Eccentric = eccentricity of the eccentric = distance from the 
eentre of the shaft to the centre of the eccentric disk = % the travel of the 
valve. (Some writers use the term ‘ throw ”’ to mean the whole travel of 
the valve.) 

Lap of the valve, also called outside lap or steam-lap = distance the outer 
pr steam edge of the valve extends beyond or laps over the steam edge of 
the port when the valve is in its central position. 

Inside lap, or exhaust-lap = distance the inner or exhaust edge of the 
valve extends beyond or laps over the exhaust edge of the port when the 
valve is in its central position. The inside lap is sometimes made zero, or 
even negative, in which latter case the distance between the edge of the 
valve and the edge of the port is sometimes called exhaust clearance, or 
inside clearance. 

Lead of the valve = the distance the steam-port is opened when the engine 
is on its centre and the piston is at the beginning of the stroke. 

Lead-angle = the angle between the position of the crank when the valve 
begins to be opened and its position when the piston is at the beginning of 
the stroke, 

The valve is said to have lead when the steam-port opens before the pirton 


THE SLIDE-VALVE. 825 


begins its stroke. If the piston begins its stroke before the admission of 
steam begins the valve is said t have negative lead, and its amount is the 
lap of the edge of the valve over the edge of the port at the instant when 
the piston stroke begins. 

Lap-angle = the angle through which the eccentric must be rotated to 
yanee the steam edge to travel from its central position the distance of the 
ap. 
Angular advance of the eccentric = lap-angle + lead angle. 
Linear advance = lap + lead. 
Effect of Lap, Lead, etc., upon the Steam Distribution.— 
Given valve-travel 234 in., lap 34 in., lead 1/16 in., exhaust-lap \ in., re- 
quired crank position for admission, cut-off, release and compression, and 
greatest port-opening. (Halsey on Slide-valve Gears.) Draw a circle of 
diameter fh = travel of valve. From Othe centre set off Oa = lap and ab 
= Jead, erect perpendiculars Oe, ac, bd; then ec is the lap-angle and cd the 
lead-angie, measured as ares. Set off fg=cd, the lead-angle, then Og is 
the position of the crank for steam admission. Set off 2ec-++ cd from h to 7; 
then Oi is the crank-angle for cut-off, and fk --jfh is the fraction of stroke 
completed at cut-off. Set off Ol = exhaust-lap and draw im; em is the 
exhaust-lap angle. Set off hn = ec+cd — em, and On is the position of 
crank at release. Set off fp = ec-+cd+ em, and Op is the position of crank 
for compression, fo + fh is the fraction of stroke completed at release, and 
hq +hf is the fraction of the return stroke completed when compression 
begins; Oh, the throw of the eccentric, minus Oa the lap, equals ah the 
maximum port-opening. 

If a valve has neither lap nor lead, the line joining the centre of the eccen- 


e 7m 


exces ees am ae oe oe = —f- — 





Fia. 146. 


tric disk and the centre of the shaft being at right angles to the line of the 
crank, the engine would follow full stroke, admission of steam beginning at 
the beginning of the stroke and ending at the end of the stroke. 

Adding lap to the valve enables us to cut off steam before the end of the 
stroke; the eccentric being advanced on the shaft an amount equal to the 
lap-angle enables steam to be admitted at the beginuing of the stroke, as 


826 THE STEAM-ENGINE,. 


before lap was added. and advancing it a further amount equal to the lead 
angle causes steam to be admitted before the beginning of the stroke. 

Having given lap to the valve, and having advanced the eccentric on the 
shaft from its central position at right angles to the crank, through the 
angular advance = lap-angle and lead-angle, the four events, admission, 
cut-off, release or exhaust-opening, and compression or exhaust-closure, 
take place as follows: Admission, when the crank lacks the lead-angle of 
having reached the centre; cut-off, when the crank lacks two lap-angles and 
one lead-angle of having reached the centre. During the admission of 
steam the crank turns through a semicircle less twice the lap-angle. The 
yreatest port-opening is equal to half the travel of the valve less the lap. 
Therefore for a given port-opening the travel of the valve must be in- 
creased if the lapis increased. When exhaust-lep is added to the valve it 
delays the opening of the exhaust and hastens its closing by an angle of 
rotation equal to the exhaust-lap angle, which is the angle through which 
the eccentric rotates from its middle position while the exhaust edge of the 
valve uncovers its lap. Release then takes place when the crank lacks one 
lap-angle and one Jlead-angle minus one exhaust-lap angle of having reached 
the centre, and compression when the crank lacks lap-angle + lead-angle + 
exhaust-lap angle of having reached the centre. 

The above discussion of the relative position of the crank, piston, and 
valve for the different points of the stroke is accurate only with a connect- 
ing-rod of infinite length. 

For actual connecting-rods the angular position of the rod causes a 
distortion of the position of the valve, causing the events to take place too 
late in the forward stroke and too early in the return. The correction of 
this distortion may be accomplished to some extent by setting the valve so 
as to give equal lead on both forward and return stroke, and by altering 
the exhaust-lap on one end so as to equalize therelease and compression. 
F. A. Halsey, in his Slide-valve Gears. describes a method of equalizing the. 
cut-off without at the same time affecting the equality of the lead. In 
designing slide-valves the effect of angularity of the connecting-rod should 
be studied on the drawing-board, and preferably by the use of a model. 

Sweet’s Valve-diagram,.—To find outside and inside lap of valve 
for different cut-offs and compressions (see Fig. 147): Draw a circle whose 





Fic. 147.—Sweet’s Valve-diagram. 


diameter equals travel of valve. Draw diameter BA and continue to <A}, 
50 that the length AA! bears the same ratio to XA as the length of con- 
necting-rod does to length of engine-crank. Draw small circle K with a 
radius equal to lead. Lay off AC so that ratio of AC to AB= eut-off in 
parts of the stroke. Erect perpendicular CD. Draw DL tangent to K; 
draw XS perpendicular to DL; XS is then outside lap of valve. 

To find release and compression: If there is no inside lap, draw FE 
through X parallelto DL. F' and EF will be position of crank for release 
and compression. If there is an inside lap, draw a circle about X, in which 
radius XY equals inside lap. Draw HG tangent to this circle and parallel 
to DL; then H and G@ are crank position for release and compression. 
Draw HN and MG, then AN is piston position at release and AM piston 
position at compression, AB being considered stroke of engine. 

To make compression alike on each stroke it igs necessary to increase the 
inside lap on crank end of valve, and to decrease by the same, amount the 


THE SLIDE-VALVE. 827 


inside lap on back end of valve. To determine this amount, through M with 
a radius MM! = AA}, draw are M P, from P draw PT perpendicular to AB, 
then TM is the amount to be added to inside lap on crank end, and to be 
deducted from inside lap on back end of valve, inside lap being XY. 

For the Bilgram Valve Diagram, see Halsey on Slide-valve Gears. 

Whe Zeuner Valve-diagram is given in most of the works on the 
steam-engine, and in treatises on valve-gears, as Zeuner’s, Peabody’s, and 





Fia. 148.—Zeuner’s Valve-diagram. 


Spangler’s. The following is condensed from Holmes on the Steam-engine: 
Describe a circle, with radius OA equal to the half travei of the valve. 
From O measure off OB equal to the outside lap, and BC equal to the lead. 
When the crank-pin occupies the dead centre A, the valve has already 
moveg to the right of its central position by the space OB + BC. From C 
erect the perpendicular CH and join OH. Then will OF be the position 
occupied by the line joining the centre of the eccentric with the centre of 
the crank-shaft at the commencement of the stroke. On the line O# as 
diameter describe the circle OCH; then any chords, as Oe, OF, Oe’, will 
represent the spaces travelled by the vaive from its central position when 
the crank-pin occupies respectively the positions opposite to D, H, and F. 
Before the port is opened at all the valve must have moved from its central 
position by an amount equal to thelap OB. Hence, to obtain the space by 
which the port is opened, subtract from each of the ares Oe. OH, etc., a 
length equal to OB This is represented graphically by describing from 
centre O a circle with radius equal to the lap OB ; then the spaces fe, gE, 
ete., intercepted between the circumferences of the lap-circle Bfe’ and the 
valve-circle OCE, will give the extent to which the steam-port is opened. 
At the point k, at which the chor! Ok is common to both valve and lap 
circles, it is evident that the valve has moved to the right by the amount of 
the lap, and is consequently just on the point of opening the steam-port. 
Hence the steam ‘is admitted before the commencement of the stroke, when 
the crank occupies the position OH, and while the vortion HA of the revo 


828 x THE STEAM-ENGINE. 


lution still remains to be accomplished. When the crank-pin reaches the 
position A, that is to say, at the ..mmencement of the stroke, the port is 
already opened by the space OC — OB= BC, called the lead. From this 
point forward till the crank occupies the position OH the port continues to 
open, but when the crank is at OF the valve has reached the furthest limit 
of its travel to the right, andthen commences to return, till when in the 
position OF’ the edge of the valve just covers the steam-port, as is shown 
by the chord Oe’, being again common to both lap and valve circles. Hence 
when the crank occupies the position OF the cut-off takes place and the 
steam commences to expand, and continues to do so till the exhaust opens. 
For the return stroke the steam-port opens again at H’ and closes at F’. 

There remains the exhaust to be considered. When the line joining the 
centres of the eccentric and crank-shaft occupies the position opposite to 
OG at right angles to the line of dead centres, the crank is in the line OP at 
right angles to OH; and as OP does not intersect either valve-circle the 
valve occupies its central position, and consequently closes the port by the 
amount of the inside lap. The crank must therefore move through such 
an angular distance that its line of direction OQ must intercept a chord on 
the valve-circle OK equal in length to the inside lap before the port can be 
opened to the exhaust. This point is ascertained precisely in the same 
manner as for the outside lap, namely, by drawing a circle from centre O, 
with a radius equal to the inside lap; this is the small inner circle in the 
figure. Where this circle intersects the two valve-circles we get four points 
which show the positions of the crank when the exhaust opens and closes 
during each revolution. Thus at Q the valve opens the exhaust on the side 
of the piston which we have been considering, while at R the exhaust closes 
and compression commences and continues till the fresh steam is read- 
mitted at H. . 

Thus the diagram enables us to ascertain the exact position of the crank 
when each critical operation of the valve takes place. Making a résumé of 
these operations of one side of the piston, we have: Steam admitted before 
the commencement of the stroke at H. At the dead centre A the valve is 
already opened by the amount BC. At £ the port is fully opened, and 
valve has reached one end of its travel. At # steam is cut off, consequently 
admission lasted from H to F. At Pvalve occupies central position, and 
ports are closed both to steam and exhaust. At Q exhaust opened, conse- 
quently expansion lasted from F'to 9. At K exhaust opened to maximum 
extent, and valve reached the end of its travel to the left. At R exhaust 
closed: and compression begins and continues till the fresh steam is admitted 
at H. 

PROoBLEM.—The simplest problem which occurs is the following: Given 
the length of throw, the angle of advance of the eccentric, and the laps of 
the valve, find the angles of the crank at which the steam is admitted and 
cut off and the exhaust opened and closed. Draw the line OF, representing 
the half-travel of the valve or the throw of the eccentric at the given angle 
of advance with the perpendicular OG. Produce OF to K. On OH and OK 
as diameters describe the two valve-circles. With centre and radii equal to 
the given laps describe the outside and inside lap-circles. Then the inter- 
section of these circles with the two valve-circles give points through which 
the lines OH, OF, OQ, and OR can be drawn. These lines give the required 
positions of the crank. 

Numerous other problems will be found in Holmes on the Steam-engine, 
including problems in valve-setting and the application of the Zeuner dia- 
gram to link motion and to the Meyer valve-gear. 

Port Opening.—The area of port opening should be such that the ve- 
locity of the steam in passing through it should not exceed 6000 ft. per min. 
py ratio of port area to piston area will then vary with the piston-speed as 

ollows: 


For speed of piston, 
ft. per min. t 100 200 300 400 500 600 700 800 900 1000 1200 


Port ee Pier .017 083 .05 .067 .088 .1 .107 183 .15 .167 .2 


rea, 
For a velocity of 6000 ft. per min., 
sq. of diam. of cyl. * piston-speea 
7639 . 

The length of the port opening may be equal to or something less than the 
diameter of the cylinder, and the width = area of port opening + its length. 

The bridge between steam and exhaust ports should be wide enough to 
prevent a leak of steam into the exhaust due to overtravel of ‘the valve, 





Port area = 


THE SLIDE-VALYE. 829 


Auchincloss gives: Width of exhaust port = width of steam port -+- 
16 travel of valve — width of bridge. 

Lead. (From Peabody’s Valve-gears.)—The lead, or the amount that 
the valve is open when the engine is on a dead point, varies, with the type 
and size of the engine, from a very small amount, or even nothing, up to 3 
of aninch or more. Stationary-engines running at slow speed may have 
from 1/64 to 1/16 inch lead. The effect of compression is to fill the waste 
space at the end of the cylinder with steam; consequently, engines having 
much compression need less lead. Locomotive-engines having the valves 
controlled by the ordinary form of Stephenson link-motion may have 
a small lead when running slowly and with along cut-off, but when at speed 
with a short cut-off the lead is at least 144 inch; and locomotives that have 
valve-gear which gives constant lead commonly have 4% inch lead. The 
lead angle is the angle the crank makes with the line of dead points at 
admission. It may vary from 0° to 8°. 

Emside Lead.—Weisbach (vol. ii. p. 296) says: Experiment shows that 
the earlier opening of the exhaust ports is especially of advantage, and in 
the best engines the lead of the valve upon the side of the exhaust, or the 
inside lead; is 1/25 to 1/15; i.e., the slide-valve at the lowest or highest posi- 
tion of the piston has made an opening whose height is 1/25 to 1/15 of the 
whole throw of the slide-valve. The,outside lead of the slide-valve or the 
lead on the steam side, on the other hand, is much smaller, and is orten 
only 1/100 of the whole throw of the valve. 


Effect of Changing Outside Lap, Inside Lap, Travel 
and Angular Advamee. (Thurston.) 



































Admission Expansion Exhaust Compression 
Incr. is later, occurs earlier, : begins at 
O.L.} ceasessooner {continues longer is unchanged same point 


incr 


3 unchanged begins as before,| occurs later, begins sooner, 
LL. 


continueslonger| ceases earlier | continues longer 


Iner.| begins sooner, begins later, begins later, begins later, 
YT. |continues longer} ceases sooner ceases later ends sooner 
Incr.| begins earlier, | begins sooner, | begins earlier, | begins earlier, 


A.A.! period unaltered] per. tho same | per. unchanged | p2r. the same 


Zeuner gives the following relations (Weisbach-Dubois, vol. ii. p. 307): 


If 3 = travel of valve, p = maximum port opening; 
i, = steam-lap, / = exhaust-lap; 


& = ratio of steam-lap to half travel = $3 La z= xX 83 
xr = ratio of exhaust lap to half travel = _ l= 5 x S3 


Bs2y eb ae Rk BR: S= 


If ec = angle HOF between positions of crank at admission and at cut-off, 
and 6 = angle QOR between positions of crank at release and at 


: _ 1, sin(i80°— a), ___, sin (180° — 8 
compression, then R = Pat aiige 3 r= sindgau a 


Ratio of Lap and of Port-opening to Valve-travel.—The 
table on page 831, giving the ratio of lap to travel of valve and ratio of travel 
to port opening, is abridged from one given by Buel in Weisbach-Dubois, 
vol. ii. It is calculated from the above formule. Intermediate values may 
be found by the formule, or with sufficient accuracy by interpolation from 
the figures in the table. By the table on page 830 the crank-angle may be 
found, that is, the angle between its position when the engine is on the 
centre and its position at cut-off, release, or compression, when these are 
known in fractions of the stroke. To illustrate the use of the tables the 
following example is given by Buel: width of port = 2.2 in.; width of port 
opening = width of port 4+ 0.3 in.; overtravel = 2.5 in.; length of connect- 
ing-rod = 214 times stroke; cut-off = 0.75 of stroke; release = 0.95 of 
stroke ; lead-angle, 10°, From the first table we find cranksangle = 114.6, 


830 THE STEAM-ENGINE, 


add lead-aagle, making 121.6.° From the second table, for angle between 
admission and cut-off, 125°, we have ratio of travel to port-opening = 3.72, 
or for 124.69 = 3.74, which, multiplied by port- roe 2.5, gives 9.45 in 
travel. The ratio of lap to travel, by the table, is .2324, or 9.45 & .2324 = 2.2 
in. lap. For exhaust-lap we have, for release at 95, crank-angle = 151.3; 
add lead-angle 10° = 161.39, From the second table, by inter polation, ratio 
of lap to travel = .0811, and .0811 x 9.45 = 0.77 in., the exhaust-lap. 


Lap-angle = 1% (180° — lead-angle — crank-angle at cut-off); 
1g (180° - 10 — 114.6) = 27.7°. 
Angularadvance = lap-angle + lead- santos = 27.7 + 10 = 37.79. 
Exhaust lap-angle = crank-angle at release -++ lap-angle -+ lead- -angle — 180°; 
== 151.3 + 27.7 + 10 — 180° = 9°, 


Crank-angle at com- 
pression measured if 180° -- lap-angle — lead-angle — exhaust lap-angle; 
on return stroke 
= 180 — 27.7 — 10 —9 = 183.8° 3 corresponding, by 
table, to a piston position of .81 of the return stroke; or 
Crank- angle at compression «x 180° — Gusie at release — angle at cut-off) 
+ lead-angle; 
= 180 -, (151.3 — 114. 6k 10 = 182.8°, 


The positions determined above for cut-off and release are for the forward 
stroke of the piston. On the return stroke the cut-off will take place at 
the same angle, 114.6°, corresponding by table to 66.6% of the return 
stroke, instead of %5%. By a slight adjustment of the angular advance 
and the length of the eccentric rod the cut-off can be equalized. The 
width of the bridge should be at least 2.5 + 0.25 — 2.2 = 0.55 in. 


Crank Angles for Connecting-rods of Different Length. 
FoRWARD AND RETURN STROKES. 


























~~ 
92 Ratio of Length of Connecting-rod to Length of Stroke. 
fog * 
End Infi- 
Cc n 
See 2 214 3 314 4 5 nite 
aos — |_| — —- | — 
Pico For. 
Ma | For.| Ret.| For.| Ret.| For.| Ret.| For.| Ret.| For.| Ret.| For.| Ret.| or 
.S) Ret. 
-O' | 10.3] 13.2) 10.5} 12.8) 10.6) 12.6] 10.7} 12.4] 10.8] 12.3] 10.9] 12.1] 11.5 
.02 | 14.6] 18.7) 14.9] 18.1] 15.1] 17.8) 15.2) 17.5] 15.3) 17.4] 15.5) 17.1] 16.3 
.03 | 17.9] 22.9) 18.2) 22.2] 18.5) 21.8] 18.71 21.5] 18.8) 21.3] 19.0) 21.0} 19.9 
-04 | 20.7) 26.5) 21.1] 25.7} 21.4) 25.2) 21.6) 24.9} 21.8) 24.6} 22.0] 24.3) 23.1 
.05 | 23.2) 29.6] 23.6] 28.7) 24.0) 28.2] 24.2) 27.8] 24.4] 27.5) 24.7] 27.2) 25.8 
.10 | 83.1] 41.9} 33.8} 40.8) 34.3] 40.1] 84 6] 89.6] 34.9] 39.2! 35.2] 38.7] 36.9 
215 | 41 | 51.5) 41.9) 50.2) 42.4) 49.3] 42.9] 48.7] 43.2] 48.3] 43.6] 47.7] 45.6 
.20 | 48 | 59.6) 48.9} 58.2] 49.6) 57.3] 50:1] 56.6) 50.4) 56.2] 50.9) 55.5) 53.1 
.25 | 54.3} 66.9) 55.4] 65.4| 56.1) 64.4) 56.6] 63.7| 57.0) 63.3] 57.6) 62.6] 60.0 
80 | 60.3] 73.5) 61.5] 72.0} 62.2) 71.0] 62.8] 70.8) 63.3] 69.8] 63.9] 69.1] 66.4 
.35 | 66.1) 79 8} 67.3) 78.3) 68.1) 77.3] 68.8] 76.6) 69 2] 76.1) 69.9) 75.3} 72.5 
.40 | 71.7] 85.8) 73.0] 84.3) 73.9) 83.3] 74.5] 82.6] 75.0) 82.0] 75.7) 81.3] 78.5 
45 | 77.2) 91.5} 78.6) 90.1] 79.6) 89.1] 80.2] 88.4} 80.7) 87.9] 81.4} 87.1] 84.3 
-50 | 82.8! 97.2! 84.3] 95.7] 85.2) 94.8] 85.9} 94.1] 86.4) 93.6] 87.1] 92.9] 90.0 
.55 | 88.5)102.8] 89.9)101.4] 90.9]100.4| 91.6] 99.8] 92.1] 99.3] 92.9] 98.6] 95.7 
.60 | 94.2}108.3} 95.7/107.0) 96.7/106.1] 97.4]105.5) 98.0)105.0} 98.7/104.3/101.5 
-65 |100.2]118.9)101.7}112. 7) 102.7}111.9}103.4/111.2/103.9}110.8)104.7)110.1)107.5 
-7O0 1106.5]119.7/108.0)118.5/109.0)117.8)109.7)117.21110.2)116.7/110.9) 116.1]113.6 
~75 1118.1(125.7)114.6]124. 6115. 6)123.9)116.3)123.4]116.7)123.0)117.4)122.4]120.0 
.80 |120.4]132  |121.8/131.1)122.7]130.4]123.4]129.9]123.8]129.6}124.5]129.1/126.9 
685 {128.5)139 $129.8]188. 1,180. 7/137 .6)1381.3)187. 1/131 .7/1386.8}132.3/1386.4}134.4 
-90 1188.1/146 9/189.2)146.2}139.9)145.7)140.4}145.4/140.8)145. 1/141 .3)144.8]143.1 
.95 1150.4/156.8)/151 .3/156.4/151 .8)156.0)152.2)155.8]152.5)155.6]152.8)155.3)154.2 
96 |153.5}159.3]154.3)158.9)154 8) 158.6] 155.1)158.4/155.4)158.21155.7|158.0}156 9 
97 (157.11162.1,157.8}161.8)158.2/161 .5)158.5)161.3}158.7/161.2/159.0)161.0]160.1 
.98 }161.3)165.4)161.9)165.1)162. 2/164 .9)162.5/164.8)162.6/164.7/162.9)164.5)163.7 
99 |166.8/169.7|167.21169.5}167. 4/169. 4/167.6|169.3/167.7;169.2/167.9/169.1|168.5 
1.00 |180 [180 {180 1180 1180 [180 l180 180 {180 {180 /180 |180 4180 





THE SLIDE-VALVE 831 


Relative Motions of Cross-head and Crank,—lf 2 = length 
of connecting-rod, & = length of crank, @ = angle of crank with centre line 
of engine, D = displacement of cross-head from the beginning of its stroke, 


3= R11 —cos6)+ L— VL? — R?2 sin? 6. 
Lap and Travel of Valve. 

































asa, | 3.1 ee (esae 13 (2s (ateg 1271 ea 
eo 5 = e358 ERS Seo ia @a 6£n2e ls a 8, 
ce = Pom eS sh | > bo FeenO [es a) 
Set ape s 2 B25 S wt et) s te 
afoe |e (oS PALE |e | oS Pace |S | es 
So & = Oo Hs 2 Sh! 2 v a2e® 19 o 
Dae > oH Has > 4 De® 4 aS 
oO ga Ra ee ee = go ose 2, % 
Exes.) § jeg [Btes.14 jes (Ets3.|8 | 4a 
So Bool faa 2 CaS) 282310 a eo | aS SSELD9 a4 4° as 
One a OW Ores KH Raw Al Ooo oS Rm eZ oo om 
2 AD Bats = Dene of | TE Osta rer ee 
2 a. | 2S |S wk. cs, 9! SS] Swi. 2| Sa | OK ee 
OL 3S SOs Foe Sk a G BOg BMW th] SD BO s 
ac sr Sia Se oe le Se a a a ae out 
20° 4830 538.70 85° .8686| 7.61 135° 1913) 3.24 
35 4769 43.22 90 .3036| 6.83 140 -1710} 3.04 
40 .4699 33.17 95 .337 6.17 145 1504} 2.86 
45 -4619 26.27 100 3214} 5.60 150 1294) 2.7 
50 4532 21.34 105 3044] 5.11 155 1082] 2.55 
55 4435 17.70 110 -2868} 4.69 160 0868} 2.42 
60 4330 14.93 115 BCOU Mae OS 165 -0653}) 2.30 
65 4217 12.77 120 .2500) 4.00 170 04386] 2.19 
v 4096 11.06 125 2309} 3.72 175 0218} 2.09 
25 3967 9.68 130 .2113] 3.46 180 .0000} 2.00 
80 3830 | 8.55 } 


PERIODS OF A DIISSION, OR CUT-OFF, FOR VARIOUS 
LAPS AND TRAVELS OF SLIDE-VALVES. 


The two following tables are from Clark on the Steam-engine. In the first 
table are given the periods of admission corresponding to travels of valve 
of from 12 in. to 2in., and laps of from 2 in. to 3 in., with 14 in. and }{ in. of 
lead. With greater leads than those tabulated, the steam would be cut off 
earlier than as shown in the table. 

The influence of a lead of 5/16 in. for travels of from 154 in. to 6 in., and 
laps of from 14 in. to 114 in., as calculated for in the second table, is exhibited 
by comparison of the periods of admission in the table, for the same lap and 
travel. The greater lead shortens the period of admission, and increases the 
range for expansive working. 


Periods of Admission, or Points of Cut-off, for Given 
Travels and Laps of Slide-valves. 





Periods of Admission, or Points of Cut-off, for the following 
Laps of Valves in inches. 








ee | | ff | | | | 











4 Glide Leas. 17 (pao as7a le? 7 | 83 | 88 | 92 | 95 
ves | Ra 2 | 44 | 63 | 71 | 79 | 84 | 90 | 94 

fee .|...... ee 93.) 50 | 61 | 71 | ¢ 86 | 91 
Oigetmares loc ...|. ... dean oy | 43 | 5% | 70 | 80 | 88 
2 eS i a F: 6 ee 33 | 62 | 70 | 81 


§32 THE STEAM-ENGINE. 


Periods of Admission, or Points of Cuteoff, for given 
Travels and Laps of Slide-valves, 


Constant lead, 5/16. 





Travel. Lap. 
Inches. % 58 34 % 1 11g 114 | 134 114 
154 19 
134 BORE | es Bere eal AG cede Se cl aiat ol Mere er ete ogee cee, Gc sates tome ee ar ree [iene 
1% 47 aL FT eS es AE LN «| Reamer Td OOP eee sills avatanceatttncarcleras aeons 
55 Be ee ee Te eS rae Bee she MMehcawsiral We aultevete ser emenl eee attatels | [eeshate ets 
214 61 42 TA pe Ws ee coe) MR OMT oc es te ease aan | er Ze 
214 65 50 BO Pe ie ke Bt es ee oc dct eae ile oe ae leet 
234 68 55 88 TB Sl, Be westivdl Cac Sp sorepoll petete casi Sateen | eames 
216 41 59 45 BT FS PR Me Suk sc ca Ge 4 ole Bete nil a ten an ieee 
256 74 63 49 36 a . 
2 %6 ig 56 43 OG Ae YE. OP Se yl kee cea Melts eee e 
2% %8 70 59 47 32 V1 Sie, ie ravers | Sadao ol rat eee 
80 73 2 50 88 ind baal be ES Nee Mo, 
3 81 74 65 55 44 30 AOU | rca PSS 
314 83 %6 68 59 48 84 Pie ee ee ER 5 
834 84 "8 71 62 51 40 29 9 
8% 85 80 3 64 53 45 84 20 sce 
354 86 81 45 66 5Y. 49 38 26 9 
334 87 82 %6 68 60 52 42 82 19 
8% 87 83 78 70 63 55 46 36 25 
4 88 84 "9 72 66 58 49 40 29 
444 89 86 81 76 70 63 56 47 S 
416 90 87 83 %9 %3 67 61 54 45 
434 92 89 85 81 %6 70 65 58 51 
93 90 87 83 %8 vo 67 62 56 
54% 94 §2 89 86 82 %8 73 68 63 
6 95 93 91 88 85 82 “i 74 69 





Diagram for Port-opening, Cut-off, and Lap.—tThe diagram ~ 
on the opposite page was published’in Power, Aug., 1893. It shows at a 
glance the relations existing between the outside lap, steam port-opening, 
and cut-off in slide valve engines. 

In order to use the diagram to find the lap, having given the cut-off and 
maximum port-opening, follow the ordinate representing the latter, taken 
on the horizontal scale, until it meets the oblique line representing the given 
cut-off. Then read off this height on the vertical lap scale. Thus, with a 
port-opening of 1144 inch and a cut-off of .50, the intersection of the two lines 
occurs on the horizontal 38, The required Jap is therefore 3 in. 

If the cut-off and lap are given, follow the horizontal representing the 
latter until it meets the oblique line representing the cut-off. Then vertically 
below this read the corresponding port-opening on the horizontal scale. 

If the lap and port-opening are given, the resulting cut-off may be ascer- 
tained by finding the point of intersection of the ordinate representing the 
port-opening with the horizontal representing the lap. The oblique line 
passing through the point of intersection will give the cut-off. 

If it is desired to take lead into account, multiply the lead in inches by the 
numbers in the following table corresponding to the cut-off, and deduct the 
result from the lap as obtained from the diagram: 





Cut-off. Multiplier. Cut-off. Multiplier. 
220 4.717 .60 1.358 
22D 8.731 625 1.288 
.30 8.048 .65 a). 222 
.00 2.717 0 1.108 
old 2.381 Bt) 1.000 
40 2.171 -80 0.904 
245 1.930 85 0.815 
.00 1.706 875 0.772 


-55 1,515 90 0.731 





THE SLIDE-VALVE. 833 


20.25 80 85 .375 40 45 .50 55 60 


beth Seti Va Neniitabe.t 











maven i yet ey a 
Me vdeshid bap aedamntiae Sete ptt ViAteeepe tes A ada 















CCC 
AAT Av vA a a A 
COMA CV Ld 
[CORA EA AV 
Rea ACA LIOR ha ona 
a A AVA a 
“COnUIn I A VL 
COME LLIL LZIZE 
CCV 
CO. 
COI VT 
COMA AAA 
SWNT VIAL 
SOMA AV TT 
POV LAA LAL 
s UIC 
EULA a 
TMM VIZ ZA 
WA AA er 
SW LOA 
a LY Oe ae aS eee 
MMI ZA 
WW ZL TOLE 
WWI Ee 
MWe ere Sora 
WYO ZOOZLE CCE Ee 
WYLLIE CEE 
WIZE CLEC 
VA Po ee 
tA i 


3 
Maximum wide Port opening in a 
DIAGRAM FOR SLIDE VALVES. 


Fic. 149, 


834 THE STEAM-ENGINE. 


e 


Piston«valve,—tThe piston-valve is a modified form of the slide-vaiva 
The lap, lead, etc., are calculated in the same manner as for the common 
slide-valve. The diameter of valve and amount of port-opening are calcu- 
lated on the basis that the most contracted portion of the steam-passagy 
between the valve and the cylinder should have an area such that the 
velocity of steam through it will not exceed 6000 ft. per minute. The area 
of the opening around the circumference of the valve should be about double 
the area of the steam-passage, since that portion of the opening that is 
opposite from the steam-passage is of little effect. 

Setting the Valves of an Engine.—The principles discussed 
above are applicable not only to the designing of valves, but alsoto adjus¢- 
ment of valves that have been improperly set; but the final adjustment uf 
the eccentric and of the length of the rod depend upon the amount of lost 
motion, temperature, etc., and can be effected only after trial. After the 
valve has been set as accurately as possible when cold, the lead and lap for 
the forward and return strokes being equalized, indicator diagrams should 
be taken and the length of the eccentric-rod adjusted, if necessary, to cor’ 
rect slight irregularities. 

To Put an Engine on its Centre.—Place the engine in a posi- 
tion where the piston will have nearly completed its outward stroke, and 
opposite some point on the cross-head, such as a corner, make a mark upon 
the guide. Against the rim of the pulley or crank-disk place a pointer and 
mark a line withitonthepulley. Then turn the engine over the centre until 
the cross-head is again in the same position on its inward stroke. This will 
bring thecrank as much below the centre as it was above it before. With the 
pointer in the same position as before make a second mark on the pulley- 
rim. Divide the distance between the marks in two and mark the middle 
point. Turn the engine until the pointer is opposite this middle point, and 
it will then be on its centre. To avoid the error that may arise from the 
looseness of crank-pin and wrist-pin bearings, the engine should be turned 
a little above the centre and then be brought up to it, so that the ecrank- pin 
ae press against the same brass that it does when the first two marks are 
made. 

Link-motion,—Link-motions, of which the Stephenson link is the 
most commonly used, are designed for two purposes: first, for reversing the 
motion of the engine, and second, for varying the point of cut-off by varying 
the travel of the valve. The Stephenson link-motion is a combination of 
two eccentrics, called forward and back eccentrics, with a link connecting 
the extremities of the eccentric-rods; so that by varying the position of 
the link the valve-rod may be put in direct connection with either eccentric, 
or may be given a movement controlled in part by one and in part by the 
other eccentric. When the link is moved by the reversing lever into a posi- 
tion such that the block to which the valve-rod is attached is at either end 
of the link, the valve receives its maximum travel, and when the link is in 
mid-gear the travel is the least and cut-off takes place early in the stroke. 

In the ordinary shifting-link with open rods, that is, not crossed, the lead 
of the valve increases as the link is moved from full to mid-gear, that is, as 
the period of steam admission is shortened. The variation of lead is equa- 
lized for the front and back strokes by curving the link to the radius of the 
eccentric-rods concavely to the axles. With crossed eccentric-rods the lead 
decreases as the link is moved from full to mid-gear. In a valve-motion 
with stationary link the lead isconstant. (For illustration see Clark’s Steam- 
engine, vol. ii. p. 22.) 

The linear advance of each eccentric is equal to that of the valve in full 
gear, that is, to lap-+ lead of the valve, when the eccentric-rods are attached 
to the link in such position as to cause the half-travel of the valve to equal 
the eccentricity of the eccentric. 

The angle between the two eccentric radii, that is, between lines drawn 
from the centre of the eccentric disks to the centre of the shaft equals 180° 
less twice the angular advance. 

Buel, in Appleton’s Cyclopedia of Mechanics, vol. ii. p. 316, discusses the 
Stephenson link as follows: “* The Stephenson link does not give a perfectly 
correct distribution of steam; the lead varies for different points of cut-off. 
The period of admission and the beginning of exhaust are not alike for both 
ends of the cylinder, and the forward motion varies from the backward. 

‘* The correctness of the distribution of steam by Stephenson’s link-motion 
depends upon conditions which, as much as the circumstances will permit, 
ought to be fulfilled, namely: 1. The link should be curved in the are of a 
circle whose radius is equal to the length of the eccentric-rod. 2. The 


THE SLIDE-VALVE. 835 


eccentric-rods ought to be long; the longer they are in proportion to the 
eccentricity the more symmetrical will the travel of the valve be on both 
sides of the centre of motion. 3. The link ought to be short. Each of its 
points describes a curve in a vertical plane, whose ordinates grow larger the 
farther the considered point is from the centre of the link; and as the hori- 
zontal motion only is transmitted to the valve, vertical oscillation will cause 
irregularities, 4. The link-hanger ought to be long. The longer it is the 
nearer will be the are in which the link swings to a straight line, and thus 
the less its vertical oscillation. If the link is suspended in its centre, the 
curves that are described by points equidistant on both sides from the centre 
are not alike, and hence results the variation between the forward and back- 
ward gear. If the link is suspended at its lower end, its lower half will have 
less vertical oscillation and the upper half more. 5. The centre from which 
the link-hanger swings changes its position as the link is lowered or raised, 
and also causes irregularities. To reduce them to the smallest amount the 
arm of the lifting-shaft should be made as long as the eccentric-rod, and the 
centre of the lifting-shaft should be placed at the height corresponding to 
the central position of the centre on which the link-hanger swings.”’ 

All these conditions can never be fulfilled in practice, and the variations 
in the lead and the period of admission can be somewhat regulated in an 
artificial way, but for one gear only. This is accomplished by giving differ- 
ent lead to the two eccentrics, which difference will be smailer the longer the 
eccentric-rods are and the shorter the link, and by suspending the link not 
exactly on its centre line but at a certain distance from it, giving what is 
called ‘‘ the offset.”’ 

For application of the Zeuner diagram to link-motion, sée Holmes on the. 
Steam-engine, p. 290. See also Clark’s Railway Machinery (1855), Clark’s 
Steam-engine, Zeuner’s and Auchincloss’s Treatises on Slide-valve Gears, 
and Halsey’s Locomotive Link Motion, (See page 859a.) 

The following rules are given by the American Machinist for laying out a 
link for an upright slide-valve engine. By the term radius of link is meant 
the radius of the link-are ab, Fig. 150, drawn through the centre of the slot; 


~Link-arg-_! 


6 





Fia. 150. 


this radius is generally made equal to the distance from the centre of shaft 
to centre of the link-block pin P when the latter stands midway of its travel. 
The distance between the centres of the eccentric-rod pins e, é, should not 
be less than 244 times, and, when space will permit, three times the th row of 
the eccentric. By the throw we mean twice the eccentricity of the eccentric. 
The slot link is generally suspended from the end next to the forward eccen- 
tric at a point in the link-are prolonged. This will give comparatively a 
small amount of slip to the link-block when the link is in forward gear; but 
this slip will be increased when the link isin backward gear, This increase 


836 THE STEAM-ENGINE, 


of slip is, however, considered of little importance, because marine engines, 
as arule, work but very little in the backward gear. When it is necessary 
that the motion shall be as efficient in backward gear as in forward gear, 
then the link should be suspended from a point midway between the two 
eccentric-rod pins; in marine engine practice this point is generally located 
on the link-are; for equal cut-offs it is better to move the point of suspen- 
sion a smal] amount towards the eccentrics. 

For obtaining the dimensions of the link in inches: Let Z denote the 
length of the valve, B the breadth, p the absolute steam-pressure per sq. 


in., and R a factor of computation used as below; then R=.01 VL XBXp. 
Breadtnof.éhe link .¢ 25 cepecacs ves nce sipuisoaiceis he 


te) Bixen.6 
Thickness ZOf the: Dar s'. scicnee ce ghs ss piesbg code lasses 1 LUI NO 
Length of sliding-block........ Sa seleelee.p eb USe bees SH) EONS 
Diameter of eccentric-rod pins ....ce.c:eccesseeee =(RX 1H 
Diameter of Suspension-rod Pin......s.seeeceeeeee- =(RX 6)+4+144 
Diameter of suspension-rod pin when overhung.. =(R X .8) +14 
Diameter of block-pin when overhung..... ied Bk s = R+% 


Diameter of block-pin when secured at both ends = (R X 8) +i% 


The length of the link, thatis, the distance from a to b, measured on a 
straight line joining the ends of the link-arc in the slot, should besuch as to 
allow the centre of the link-block pin P to be placed in a line with the eccen- 
tric-rod pins, leaving sufficient room for the slip of the block. Another type 
of link frequently used in marine engines is the double-bar link, and this 
type is again divided into two classes: one class embraces those links which 
have the eccentric-rod ends as well as the valve-spindle end between the 
bars, as Shown at B (with these links the travel of the valve is less than 
the throw of the eccentric); the other class embraces those links, shown at 
©, for which the eccentric-rods are made with fork-ends, so as to connect to 
studs on the outside of the bars, allowing the block to slide to the end of the 
jink, so that the centres of the eccentric-rod ends and the block-pin are in 
line when in full gear, making the travel of the valve equal to the throw of 
the eccentric. The dimensions of these links when the distance between 
the eccentric-rod pins is 214 to 234 times the throw of eccentrics can be 
found as follows: 


Depth OF DATR Ais s : ans cvotne eetenteeeccapes econ =(RxX 1.25) +14” 
Thickness Of Dare she fos: 26 cosas eee. sa bulles pE=ICle Cele) == 34 
Diameter of centre of sliding-block. ...... ...... = RX13 


When the distance between the eccentric-rod pins is equal to 3 or 4 times 
the throw of the eccentrics, then 


Depth"Or bars se. .c sa cc aausciiiee sings ese neeivesalisc ==) Me xaleco ata 
MHiCKNESS OL DATSs ccs accenere CCCs SC eeH Eee E HEED = (Che 0) -+ 14” 


All the other dimensions may be found by the first table. These are em- 
pirical rules, and the results may have to be slightly changed to suit given 
conditions. In marine engines the eccentric-rod ends for all classes of links 
have adjustable brasses. In locomotives the slot-link is usually employed, 
and in these the pin-holes have case-hardened bushes driven into the pin- 
holes, and have no adjustable brasses in the ends of the eccentric-rods. The 
link in Bis generally suspended by one of the eccentric-rod pins; and the 
link in C is suspended by one of the pins in the end of the link, or by one of 
the peed ed ayer pins. (See note on Locomotive Link Motion in Appendix. 

TLOTT. 
other Worms of Valve-Gear, as the Joy, Marshall, Hackworth, 
Bremme, Walschaert, Cortiss, eic., aré described in Clark’s Steam-engine, 
vol. ii. The design of the Reynolds-Corliss valve-gear is discussed by A. H. 
Eldridge in Power, Sep. 1893. See also Henthorn on the Corliss engine. 
Rules for laying down the centre lines of the Joy valve-gear are given iu 
American Machinist, Nov. 13, 1890. For Joy’s *‘ Fluid-pressure Reversing- 
valve,” see Hing’g, May 25, 1894. 


GOVERNORS, 


Pendulum or Fly-bal!l Governor.—The inclination of the arms 
of a revolving pendulum to a vertical axis is such that the height of the 
point of suspension h above the horizontal plane in which the centre of 
gravity of the balls revolve (assuming the weight of the rods’ to be small 


GOVERNORS. 837 


compared with the weight of the balls) bears to the radius r of the circle 
described by the centres of the balls the ratio 





h weight w or 
r centrifugal force wy? ~ y?” 
gr 


which ratio is independent of the weight of the balls, v being the velocity 
of the centres of the balls in feet per second. 

If T= number of revolutions of the ballsin 1 second, v = 2arT = ar, in 
which @ = the angular velocity, or 277, and 
gr? 9 0.8146 Oriole 
ot > Gat? ori = 7 feet = [2 inches, 


g being taken at 32.16. If VY = number of revs. per minute, h = 








he 


35190 
N2 





inches 


Fov revolutions per minute......... 40 45 50 60 15 
The height in inches will be..... ... 21.99 17.88 14.08 9.775 6.256 


Number of turns per minute required to cause the arms to take a given 
angle with the vertical axis: Let / = length of the arm in inches from the 
centre of suspension to the centre of gyration, and a the required angle; 


then 
/ 35190 a8 
Ree | fete ee 181.04/ rae = 181.0 4/ 4 
lcos a ¢ cosa h 


The simple governor is not isochronous; that is, it does not revolve at a 
uniform speed in all positions, the speed changing as the angle of the arms 
changes. To remedy this defect loaded governoi;s, such as Porter’s, are 
used. From the balls of a common governor whose collective weight is A 
let there be hung by a pair of links of lengths equal to the pendulum arms 
a load B capable of sliding on the spindle, having its centre of gravity in 
the axis of rotation. Then the centrifugal force is that due to A alone, and 
the effect of gravity is that due to 4 + 2B; consequently the altitude for a 
given speed is increased in the ratio (A + 2B) : A, as compared with that of 
a simple revolving pendulum, and a given absolute variation in altitude pro- 
duces a smaller proportionate variation in speed than in the common gover- 
nor. (Rankine, S, E., p. 551.) 

For the weighted governor let 1 = the length of the arm from the point of 
suspension to the centre of gravity of the ball, and let the length of the sus- 
pending-link, 7, = the length of the portion of the arm from the point of 
Suspension of the arm to the point of attachment of the link; G = the weight 
of one ball, Q = half the weight of the sliding weight, h = the height of the 
governor from the point of snspension to the plane of revolution of the 
bails, a = the angular velocity = 27T, T being the number of revolutions per 


; ES] 3216 21, 2), weet 210) , 
second ; then I a) lie I+ TG in feet, or 


a2 
iS 9 
h= aT “+P “a i in inches, N being the number of revolutions per 
minute. 

For various forms of governor ste App. Cyc]. Mech., vol. ii. 61, and Clark’s 
Steam-encgine, vol. ii. p. 65. 

Wo Change the Speed of an Engine Having a Fly-ball 
Governor.—aA slight difference in the speed of a governor changes the 
position of its weights from that required for fnll load to that required for 
no load. It is evident therefore that, whatever the speed of the engine, the 
normal speed of the governor must be that for which the governor was de- 
signed; i.e., the speed of the governor must be kept the same. Tochange the 
speed of the engine the problem is to so adjust the pulleys which drive the 
governor that the engine at its new speed shall drive it just as fast as it was 
driven at its original speed. In order to increase the engine-speed we must 
decrease the pulley upon the shaft of the engine, i.e., the driver, or increase 
that on the governor, i.e., the driven, in the proportion that the speed of the 
engine is to be increased. 











838 THE STEAM-ENGINE, 


Fly-wheet or Shaft Governors.—At the Centeunial Exhibition 
in 1876 there were shown a few steam-engines in which the governors were 
contained in the fly-wheel or band-wheel, the fly-balls or weights revolving 
around the shaft in a vertical plane with the wheel and shifting the eccen- 
tric so as automatically to vary the travel of the valve and the point of cut- 
off. This form of governor has since come into extensive use, especially for 
high-speed engines. In its usual form two weights are carried on arms the 
ends of which are pivoted to two points on the pulley near its circum- 
ference, 180° apart. Links connect these arms to the eccentric, The 
eccentric is not rigidly keyed to the shaft but is free to move trans: 
versely across it for a certain distance, having an oblong hole which allows 
of this movement. Centrifugal force causes the weights to fly towards the 
circumference of the wheel and to pull the eccentric into a position of min- 
imum eccentricity. This force is resisted by a spring attached to each arm 
which tends to pull the weights towards the shaft and shift the eccentric to 
the position of maximum eccentricity. The travel of the valve is thus 
varied, so that it tends to cut off earlier in the stroke as the engine increases 
its speed. Many modifications of this general form are in use. For discus- 
sions of this form of governor see Hartnell, Proc. Inst. M. E., 1882, p. 408; 
Trans. A.S. M. E., ix. 300; xi. 10813 xiv. 923 xv. 929; Modern’ Mechanism, 
p. 399; Whitham’s Constructive Steam Engineering; J. Begtrup, Am. Mach., 
Oct. 19 and Dec. 14, 1893, Jan. 18 and March 1, 1894. 

Calculation of Springs for Shaft-covernors. (Wilson Hart- 
nell, Proc. Inst. M. E., Aug. 1882.)—The springs for shatt-governors may be 
conveniently calculated as follows, dimensions being in inches: 


Let W = weight of the balls or weights, in pounds; 

r, and rg = the maximum and minimum radial distances of the centre 
of the balls or of the centre of gravity of the weights; 

7, and lg = the leverages, i.e., the perpendicular distances from the cen- 
tre of the weight-pin to a line in the direction of the centrifugal force. 
ey through the centre of gravity of the weights or balls at radii 
YT, aNd 15 

m, and ma = the corresponding leverages of the springs; 

C; ae C2 = HHS centrifugal forces, for 100 revolutions per minute, at 
radii 7, and 1°93 

P, and P, = the corresponding pressures on the spring; 

(It is convenient to calculate these and note them down for reference.) » 

C, and Cy = maximum and minimum centrifugal forces; 

S = mean speed (revolutions per minute) 3 

S, and S, = the maximum and minimum number of revolutions per 
minute; 

P, and P, = the pressures on the spring at the limiting number of revo, 
jutions (S, and S89); 

P, - P; = D= the difference of the maximum and minimum pressures 
on the springs; 

V = the percentage of variation from the mean speed, or the sensitive- 


ness; 
t = the travel of the spring; 
w = the initial extension of the spring; 
v = the stiffness in pounds per inch; 
w = the maximum extension = u-+ ft, 


The mean speed and sensitiveness desired aré supposed to be given. Then 


sv. sv 
Sas ber 09 | Sa Se, coges 
Oy 210.2807) XW; Cg = 0.28% rg X W; 
uy hh, ED cove ly 
Ci es ai: pi atte boat 
mu ae S_ \?, 
P= Px (3); Pye Pa x (roe ’ 


a, yee, 6 

t Uv v 
It is usual to give the spring-maker the values of Py and of vor w. To 
ensure proper space being provided, the dimensions of the spring should be 


CONDENSERS, AIR-PUMPS, ETC. 839 


calculated by the formule for strength and extension of springs, and the 
least length of the spring as compressed be determined. 
Ps+ Ps x t 
2s 12° 
With a straight centripetal line, the governor-power 


» Cs ete x Ce —"1), 


For a preliminary determination of the governor-power it may be taken 
as equal to this in all cases, although it is evident that with a curved cen- 
tripetal line it will be slightly less. The difference D must be constant for 
the same spring, however great or little its initial compression. Let the 
spring be screwed up until its minimum pressure is /’5. Then to find the 
speed Pg = P, + D, 


The governor-power = 


P, 

Ss = 1004 / —; Se = 100 P, 

The speed at which the governor would be isochronous would be 
D 


Suppose the pressure on the spring with a speed of 100 revolutions, at the 
maximum and minimum radii, was 200 lbs. and 100 lbs., respectively, then 
the pressure of the spring to suit a variation from 95 to 105 revolutions will 


ays os (ee Ee, i: Loni 
be 100 x (= = 90.2 and 200 x >) = 220.5. That is, the increase 


of resistance from the minimum to the maximum radius must be 220 — 90 = 
130 lbs. 

The extreme speeds due to such a spring, screwed up to different press- 
ures, are shown in the following table: 








Revolutions per minute, balls shut...............- 80} 90) 95) 100} 110] 126 
Pressure on springs, balls shut............. Bee Sean 64} 81] 90) 100} 121) 144 
Increase of pressure when balls open fully....... 130} 130); 130; 1380; 130; 130 
Pressure on springs, balls open fully............. 194] 211] 220] 280} 251] 274 
Revolutions per minute, balls open fully. ....... 98} 102) 105] 107) 112) 117 
Variation, per cent of mean speed ... ........... TO}RP"O | PPO ero | ened 


The speed at which the governor would become isochronous is 114. 

Any spring will give the right variation at some speed; hence in experi- 
menting with a governor the correct spring may be found from any wrong 
one by a very simple calculation. Thus, if a governor with a spring whose 
stiffness is 50 los. per inch acts best when the engine runs at 95, 90 being its 


2 
proper speed, then 50 x az) = 45 lbs. is the stiffness of spring required. 


To determine the speed at which the governor acts best, the springs may 
be screwed up until it begins to *“‘ hunt” and then slackened until the gov- 
ernor is as sensitive as is compatible with steadiness. 


CONDENSERS, AIR-PUMPS CIRCULATING= 
PUMPS, ETC. 


The Jet Condenser. (Chiefly abridged from Seaton’s Marine Engi- 
neering.»-The jet condenser is now uncommon in marine practice, being 
enerally supplanted by the surface condenser. It is commonly used where 
resh water is available for boiler feed, With the jet condensera vacuum of 24 
in. was considered fairly good, and 25 in. as much as was possible with most 
condensers; the temperature corresponding to 24 in. vacuum, or 3lbs. pressure 
absolute, is 140°. In practice the temperature in the hot-well varies from 110° 
to 120°, and occasionally as much as 130° is maintained, To find the quantity 
of injection-water per pound of steam to be condensed: Let 7, = tempera- 
ture of steam at the exhaust pressure; 7) = temperature of the cooling. 


840 THE STEAM-ENGINE, 


water; 7, = temperature of the water after condensation, or of the hot-well; 
Q = pounds of the cooling-water per lb. of steam condensed; then 


g = 1 +087 — 1 
Se eyes : 


. WH 
Another formula is: Q@ = —;,in which W is the weight of steam con- 


v 
densed, H the units of heat given up by 1 lb. of steam in condensing, and 
F& the rise in temperature of the cooling-water. 

This is applicable both to jet and to surface condensers. The allowance made 
for the injection-water of engines working in the temperate zone is usually 
27 to 80 times the weight of steam, and for the tropics 30 to 35 times; 30 
times is sufficient for ships which are occasionally in the tropics, and this is 
what was usual to allow for general traders. 

atte of injection orifice = weight of injection-water in lbs. per min. -+ 650 
to 780. 

A rough rule sometimes used is: Allow one fifteenth of a square inch for 
every cubic foot of water condensed per hour. 

Another rule: Area of injection orifice = area of piston + 250. 

The volume of the jet condenser is from one fourth to one half of that of 
the cylinder. It need not be more than one third, except for very quick- 
running engines. 

Hjector Condensers.—For ejector or injector condensers (Bulkley’s, 
* Schutte’s, etc.) the calculations for quantity of condensing-water is the same 
as for jet condensers. 

The Surface Condenser—Cooling Surface.—Peclet found that 
with cooling water of an initial temperature of 68° to 77°, one sq. ft. of copper 
plate condensed 21.5 lbs. of steam per hour, while Joule states that 100 Ibs. 
per hour can be condensed. In practice, with the compound engine, brass 
condenser-tubes, 18 B.W.G thick, 18 Ibs. of steam per sq. ft. per hour, with 
the cooling-water at an initial temperature of 0°, is considered very fair 
work when the temperature of the feed-water is to be maintained at 120°. 
It has been found that the surface in the condenser may be half the heating 
surface of the boiler, and under some circumstances considerably less than 
this. In general practice the following holds good when the temperature of 
sea-water is about 60°: 


Terminal pres.,lbs.,abs.... 380 20 15 1244 10 8 6 
Bag. ftper dl WP Nis... cadeed. B 2,50 2.25 © 2.00) oh80)- 43.600. 1:80 


For ships whose station is in the tropics the allowance should be increased 
by 20%. and for ships which occasionally visit the tropics 10% increase will 
give satisfactory results. Ifa ship is constantly employed in cold climates' 
10% less suffices 

Whitham (Steam-engine Dean p. 283, also Trans. A. 8. M. E., ix. 481) 


gives the following: S = FA in which S = condensing-surface in sq. 


ck T, 
ft.; 7, = temperature Fahr. of steam of the pressure indicated by the 
vacuum-gauge; ¢ = mean temperature of the circulating water, or the 
arithmetical mean of the initial and final temperatures; L = latent heat of 
saturated steam at temperature 7,; k = perfect conductivity of 1 sq. ft. of 
the metal used for the condensing-surface for a range of 1° F. (or 557 B.T.U. 
per hour for brass, according to Isherwood’s experiments): c = fraction de- 
noting the efficiency of the condensing-surface; W = pounds of steam con- 
densed per hour. _From experiments by Loring and Emery, on U.S8.S. Dallas, 
WL 
180(7, — t)° 
Whitham recommends this formula for designing engines having indepen- 
dent circulating pumps. When the pump is worked by the main engine the 
value of S should be increased about 102. . 
Taking 7, at 185° F., and L = 1020, COnFeaPOuainE to 25 in. yee, and z 


for summer temperatures at 75°, we have: S = 


c is found to be 0.323, and ck = 180; making the equation § = 


180(135 — 75) 180° 
For a mathematical discussion of the efficiency of surface condensers see 
a paper by T. E. Stanton in Proc. Inst. C. E., exxxvi, June 1899, p. 321. 
Condenser Tubes are generally made of solid-drawn brass tubes, and 
tested both by hydraulic pressure and steam, They are usually made of a 
composition of 68% of best selected copper and 82% of best Silesian spelter, 


CONDENSERS, AIR-PUMPS, ETO. 841 


The Admiralty, however, always specify the tubes to be made of 70% of best 
selected copper and to have 1% of tin in the composition, and test the tubes 
to a pressure of 300 lbs. per sq. in. (Seaton.) 

The diameter of the condenser tubes varies from 44 inch in small conden: 
sers, when they are very short, to 1 inch in very large condensers and long 
tubes. In the mercantile marine the tubes are, as a rule, 34 inch diameter 
externally, and 18 B.W.G. thick (0.049 inch); and 16 B.W.G. (0.065), under 
some exceptional circumstances. In the British Navy the tubes are also, 
as a rule, 34 inch diameter, and 18 to 19 B.W.G.thick, tinned on both sides; 
when the condenser is made of brass the Admiralty do not require the tubes 
to be tinned. Some of the smaller engines have tubes 5¢ inch diameter, and 
19 B.W.G. thick. The smaller the tubes, the larger is the surface which 
can be got in a certain space. 

In the merchant service the almost universal practice is to circulate the 
water through the tubes. 

Whitham says the velocity of flow through the tubes should not be less 
than 400 nor more than 700 ft. per min. 

Wube=-plates are usually made of brass. Rolled-brass tube-plates 
should be from 1.1 to 1.5 times the diameter of tubes in thickness, depending 
on the method of packing. When the packings go completely through the 
plates the latter, but when only partly through the former, is sufficient. 
Hence, for 34-inch tubes the plates are usually % to 1 inch thick with glands 
and tape-packings, and 1 to 114 inch thick with wcoden ferrules. 

The tube-plates should be secured to their seatings by brass studs and 
nuts, or brass screw-bolts; in fact there must be no wrought iron of any 
kind inside a condenser. When the tube-plates are of large area it is advis- 
able to stay them by brass-rods, to prevent them from collapsing. 

Spacing of Tubes, ete,—The holes for ferrules, glands, or india- 
rubber are usually 44 inch larger in diameter than the tubes; but when ab- 
solutely necessary the wood ferrules may be only 3/382 inch thick. 

The pitch of tubes when packed with wood ferrules is usually 14 inch 
more than the diameter of the ferrule-hole. For example, the tubes are 
generally arranged zigzag, and the number which may be fitted into a 
square foot of plate is as follows: 














Pitch of No. ina No. in a Pitch of No. ina 
Tubes. sq. ft. sq. ft. Tubes. sq. ft. 
1” 172 1 5/32// 128 14" 110 
11/16” 150 13/16” 121 19/32" 106 
14g” 137 1 7/32/7 116 1 5/16” 99 


Quantity of Cooling Water.—The quantity depends chiefly upon 
its initial temperature, which in Atlantic practice may vary from 40° in the 
winter of temperate zone to 80° in subtropical seas. To raise the tempera- 
ture to 100° in the condenser will require three times as many thermal units 
in the former case as in the latter, and therefore only one third as much 
cooling- water will be required in the former case as in the latter. 


T, = temperature of steam entering the condenser; 
ee 


a= * circulating-water entering the condenser3 
Tex i» 3 ty “* leaving the condenser3 
TT, = ss ** water condensed fram the steam; 


Q = pounds of circulating water per 1b. of steam condensed 
11144+-0.37;, — Ts 


T3.— Lo 


{It is usual to provide pumping power sufficient to supply 40 times the 
weight of steam for general traders, and as much as 50 times for ships sta- 
tioned in subtropical seas, when the engines are compound. If the cireulat- 
ing-pump is double-acting, its capacity may be 1/53 in the former and 1/42 
in the latter ease of the capacity of the low-pressure cylinder. ~ 

Air=-pump,—The air-pump in all condensers abstracts the water con- 
densed and the air originally contained in the water when it entered the 
boiler. In the case of jet-condensers it also pumps out the water of con- 
densation and the air which it contained. The size of the pumpis calculated 
from these conditions, making allowance for efficiency of the pump. 


842 THE STEAM-ENGINE. 


Ordinary sea-water contains, mechanically mixed with it, 1/20 of its vol- 
ume of air when under the atmospheric pressure. Suppose the pressure in 
the condenser to be 2 lbs. aud the atmospheric pressure 15 lbs., neglecting 
the effect of temperature, the air on entering the condenser will be expanded 
to 15/2 times its original volume; so that a cubic foot of sea-water, when it 
has entered the condenser, is represented by 19/20 of a cubic foot of water 
and 15/40 of a cubic foot of air. 

Let q be the volume of water condensed per minute, and Q the volume of 
sea- water required to condense it; and let T, be the temperature of the 
condenser, and 7, that of the sea- water. 

Then 19/20 (g++ Q) will be the volume of water to be pumped from the 
condenser per minute, 


15 T, + 461° ; 
and ae Q) XS T, + 461° the quantity of air. 


If the temperature of the condenser be taken at 120°, and that of sea- 
water at 60°, the quantity of air will then be .418(q + @Q), so that the total 
volume to be abstracted will be 


95(¢ + Q) + .418(¢ + Q) = 1.°°68(q -+ Q). 


If the average quantity of injection-water be taken at 26 times that con- 
densed, g-+ Q will equal 27q. Therefore, volume to be pumped from the 
condenser per minute = 37q, nearly. 

In surface condensation allowance must be made for the water occasion- 
ally admitted to the boilers to make up for waste, and the air contained in 
it, also for slight leak in the joints and glands, so that (he air-pump is made 
about half as large as for jet-condensation. 

The efficiency of a single-acting air-pump is generally taken at 0.5, and 
that of a double-acting pump at 0.35. When the temperatur of the sea is 
60°, and that of the (jet) condenser is 120°, @ being the volume of the cooling 
water and q the volume of the condensed water in cubic feet, and n the 
number of strokes per minute, 


The volume of the single-acting pump = 2.74 (ee = D) c 


The volume of the double-acting pump = 4( era ) ‘ 

The following table gives the ratio of capacity of cSlinder or cylinders te 
that of the air-pump; in the case of the compound engine, the low-pressure 
cylinder capacity only is taken. 











Description of Punip. Description of Engine. Ratio. 
Single-acting vertical...... Jet-condensing, expansion 1144 to2....| 6to 8 
rf Det as hl \- 21 SUTLACC hee eS 14% to2....| 8to10 
a et) cas cue Let s sf 3 to5....| 10to12 
SS pees. OUITACe °° ee 3 £0 Boel ke tole 
Me Lica oe ak Surface ‘‘ COMpPOUNTT se ee eee -..| 15 t0 18 
Double-acting horizontal..| Jet a expansion 11% to 2....| 10 to 13 
a e --| Surface ‘* os 114 to 2....}] 13 to 16 
Me et .e| Jet fe of 38 to5...| 16to 19 
te s -.| Surface ‘* s 8." 2t0\5e..a) 9 to. 24 
st ¥% ..| Surface * COMPOUNG/T HU is eae 24 to 28 





The Area through Valve-seats and past the valves should not be 
less than will admit the full quantity of water for condensation at a velocity 
not exceeding 400 ft. per minute. In practice the area is generally in 
excess of this. 


Area through foot-valves = D? x S+ 1000 square inches, 
Area through head-valves = D? x S+ 800 square inches, 
Diameter of discharge-pipe = D x /S + 35 inches. 

D= diam. of air-pump in inches, S = its speed in ft. per min. 


James Tribe (4m. Much., Oct. 8, 1891) gives the following rule for air- 


CONDENSERS, AIR-PUMPS, ETC. 843 


pumps used with jet-condensers: Volume of single-acting air-pump driven 
“y main engine = volume of low-pressure cylinder in cubic feet, multiplied 
by 3.5 and divided by the number of cubiz feet contained in one pound of 
exhaust-steam of the given density. For a double-acting air-pump the 
same rule will apply, but the volume of steam for each stroke of the pump 
will be but one half. Should the pump be driven independently of the 
engine, then the relative speed must be considered. Volume of jet-con- 
Janser = volume of air-pump X 4. Area of injection valve = vol, of air- 
v“mp in cubic inches + 520. 

Circulating=-pump.—Let Q be the quantity of cooling water in cubic 
e2t, n the number of strokes per minute, and S the length of stroke in feet, 


Capacity of circulating-pump = @ + 7 cubic feet, 








Diameter * had “ = 1385 4/ @ inches. 
nxSs 


The following table gives the ratio of capacity of steam-cylinder or cyline 
ers to that of the circulating-pump: 


Description of Pump Description of Engine. Ratio. 
Single-acting. Expansive 114 to 2 times. 13 to 16 

a oe se 8 to5 20 to 25 

vy oc Compound. 25 to 20 
Double *“ Expansive 14 to 2 times. 25 to 30 

‘ “ Se UO Oe 86 to 46 

_ oe Compound. 46 to 56 


The c:ear area through the valve-seats and past the valves should be such 
that the mean velocity of flow does not exceed 450 feet per minute. The 
flow through the pipes should not exceed 500 ft. per min. in small pipes and 
600 in large pipes. 

For Centrifugal Circulating-pumps, the velocity of flow in the inlet and 
outlet pipes should not exceed 400 ft. per min. The diameter of the fan-wheel 
is from 24% to 3 times the diam. of the pipe, and the speed at its periphery 
450 to 500 ft. per min. If W = quantity of water per minute, in American 
gallons, d = diameter of pipes in inches, # = revolutions of wheel per min., 
C= / aa diam. of fan-wheel = not less than a Breadth of blade at 


tip = ae Diam. of cylinder for driving the fan = about 2.8 //diam. of pipe, 


and its stroke = 0.28 < dian. of fan. 

Feed-pumps for Marine Engines.—With surface-condensing 
engines the amount of water to be fed by the pump is the amount condensed 
from the main engine plus what may be needed to supply auxiliary engines 
and to supply leakage and waste. Since an accident may happen to the 
surface-condenser, requiring the use of jet-condensatiou, the pumps of 
engines titted with surface-condensers must be sufficiently large to do duty 
under such circumstances. With jet-condensers and boilers using salt water 
the dense salt water in the boiler must be blown off av intervals to keep the 
density so low that deposits of salt will not be tormed. Sea-water contains 
about 1/32 of its weight of solid matter in solution. The boiler of a surface- 
concensing engine may be worked with safety when the quantity of salt is 
four times that in sea-water. If Q = net quantity of feed-water required in 
a given time to make up for what is used as steam, 7 = number of times the 
saltness of the water in the boileris to that of sea- water, then the gross feed- 


i = 12: In order to be capable of filling the boiler rapidly each 
feec-pump is made of a capacity equal to twice the gross feed-water. Two 
feec-pumps should be supplied, so that one may be kept in reserve to be 
used while the other is out of repair. If Q be the quantity of net feed-water 
in cubie feet, the Jength of stroke of feed-pump in feet, and x the num: 
ber of strokes per minute, 





water = 


550 x 


Diameter of each feed-pump plunger in inches = et 


844 THE STEAM-ENGINE, 


If W be the nwt feed-water in pounds, 


Diameter of each feed-pump plunger in inches = / ae. 


An Evaporative Surface Condenser built at the Virginia Agri 
cultural College is described by James dH. Fitts (Trans. A.S. M. E., xiv. 690). 
It consists ef two rectangular end-chambers connected by a series of hori- 
zontal rows of tubes, each row of tubes immersed in a pan of water. 
Through the spaces between the surface of the water in each pan and the 
bottom of the pan above air is drawn by means of an exhaust-fan. At the 
top of one of the end-chambers is an inlet for steam, and a horizontal dia- 
phragm about midway causes the steam to traverse the upper half of the 
tubes and back through the lower. An outlet at the bottom leads to the air- 
pump. The condenser, exclusive of connection to the exhaust-fan, occupies 
a floor space of 5/ 446” x 1’ 934””, and 4’ 1144’ high. There are 27 rows of 
tubes, 8 in some and 7 in others; 210 tubes in all. The tubes are of brass, 
No. 20 B.W.G., 34’’ external diameter and 4’ 914” in length. The cooling sur- 
face (internal) is 176.5 sq. ft. There are 27 cooling pans, each 4/ 914’’ x'1/ 934’, 
and 17/16’ deep. These pans have galvanized iron bottoms which slide 
mto horizontal grooves 14” wide and 14” deep, planed into the tube-sheets. 
The total evaporating surface is 234.8 sq.ft. Wateris fed to every third pan 
through small cocks, and overflow-pipes feed the rest. A wood casing con- 
nects one side with a 30’ Buffalo Forge Co.’s disk-wheel. This wheel is 
belted toa 3” x 4” vertical engine. The air-pump is 534’ diameter with a 
6’ stroke, is vertical and single-acting. 

The action of this condenser is as follows: The passage of air over the 
water surfaces removes the vapor as it rises and thus hastens evaporation. 
The heat necessary to produce evaporation is obtained from the steam in the 
tubes, causing the steam to condense. It was designed to condense 800 lbs. 
steam per hour and give a vacuum of 22 in., with a terminal pressure in the 
cylinder of 20 lbs. absolute. 

Results of tests show that the cooling-water required is practically equal in 
amount to the steam used by the engine. And since consumption of steam 
is reduced by the application of a condenser, its use will actually reduce the 
total quantity of water required. From a curve showing the rate of evapora- 
tion per square foot of surface in still air, and also one show .ng the rate 
when a current of air of about 2300 ft. per min. velocity is passed over its 
surface, the following approximate figures are taken: 

















Evaporation, Ibs. per Evaporation, lbs. per 
Temp. sq. ft. per hour. Temp, sq. ft. per hour. 
Still Air. Current. Still Air. Current. 
100° 0.2 mere 440° 0.8 5.0. 
110 0.25 1.6 150 1.1 6.7 
120 0.4 2.5 160 1.5 9.5 
1380 0.6 3.5 170 2.0 fee 


The Continucus Use of Condensing=water is described in a 
series ot articles in Power, Aug.—Dec., 1892. It finds its application in situa- 
tions where waterfor ondensing purposes is expensive or difficult to obtain. 

In San Francisco J. .H. Stut cools the water after it has left the hot- 
well by means of a system of pans upon the roof. These pans are shallow 
troughs of galvanized iron arranged in tiers, on a slight incline, so that the 
water flows back and forth for 1500 or 2000 ft., cooling by evaporation and 
radiation as it flows. The pens are about 5 ft. in width, and the water as it 
flows has a depth of about half an inch, the temperature being reduced from 
about 140° to 90°. The water from the hvt-well is pumped up to the highest 
point of the cooling system and allowed to flow as above described, discharg- 
ing finally into the main tank or reservoir, whence it again flows to the con- 
denser as required. As the water in the reservoir lowers from evaporation, an 
auxiliary feed from the city mains to tLe condenser is operated, thereby 
keeping the amount of water in circulation practically constant. An accu- 
mulation of oil from the engines, with dust from the surrounding streets, 
makes a cleaning necessary about once in six weeks or two months. It is 
found by comparative trials, running condensing and non-condensing, that 


CONDENSERS, AIR-PUMPS, ETC. 845 


about 50% less water is taken from the city mains when the whole apparatus 
is in use than when the engine is run non-condensing. 22 to 23 in. of vacuum 
are maintained. A better vacuum is obtained on a warm day with a brisk 
breeze blowing than on a cold day with but a slight movement of the air. 

In another plant the water from the hot-well is sprayed from a number of 
fountains, and also from a pipe extending around its border, into a large 
pore, the exposure cooling it sufficiently for the obtaining of a good vacuum 

y its continuous use. 

In the system patented by Messrs. See, of Lille, France, the water is dis- 
charged from a pipe laid inthe form of a rectangle and elevated above a 
pond through a series of special nozzles, by which it is projected into a fine 
spray. On coming into contact with the air in this state of extreme divi- 
sion the water is cooled 40° to 50°, with a loss by evaporation of only one 
tenth of its mass, and produces an excellent vacuum. <A 38000-H.P. cooler 
upon this system has been erected at Lannoy, one of 2500 H.P. at Madrid, and 
one of 1200 H.P. at Liege, as well as others at Roubaix and Tourcoing.: The 
system could be used upon a roof if ground space were limited. 

In the *‘ self-cooling’’ system of H. R. Worthington the injection-water is 
taken from a tank, and after having passed through the condenser is dis- 
charged in a heated condition to the top of a cooling tower, where it is scat- 
tered by means of distributing-pipes and trickles down through a cellular 
structure made of 6-in. terra-cotta pipes, 2 ft. long, stood on end. The 
water is cooled by a blast of air furnished by a disk fan at the bottom of the 
tower and the absorption of heat caused by a portion of the water being 
vaporized, and is led to the tank to be again started on its circuit. (Hng’g 
News, March 5, 1896.) 

In the evaporative condenser of T. Ledward & Co. of Brockley, London, 
the water trickles over the pipes of the large condenser or radiator, and by 
evaporation carries away the heat necessary to be abstracted to condense 
the steam inside. The condensing pipes are fitted with corrugations 
mounted with circular ribs, whereby the radiating or cooling surface is 
largely increased. The pipes, which are cast in sections about 76 in. long by 
314 in. bore, have a cooling surface of 26sq. ft., which is found sufficient 
under favorable conditions to permit of the condensation of 20 to 30 lbs. 
of steam per hour when producing a vacuum of 13 lbs. per sq. in, In a 
condenser of this type at Rixdorf, near Berlin, a vacuum ranging from 24 
to 26 in. of mercury was constantly maintained during the hottest weather 
of August. The initial temperature of the cooling-water used in the appara- 
tus under notice ranged from 80° to 85° F., and the temperature in the sun, 
to which the condenser was exposed, varied each day from 100° to 115° F. 
During the experiments it was found that it was possible to run one engine 
under a load of 100 horse-power and maintain the full vacuum without the 
use of any cooling-water at all on the pipes, radiation afforded by the pipes 
alone sufficing to condense the steam for this power. 

In Klein’s condensing water-cooler, the hot water coming from the con- 
denser enters at the top of a wooden structure about twenty feet in height, 
and is conveyed into a series of parallel narrow metal tanks. The water 
overflowing from these tanks is spread asa thin film over aseries of wooden 
partitions suspended vertically about 344 inches apart within the tower. 
The upper set of partitions, corresponding tothe number of metal tanks, 
reaches half-way down the tower. From there down to the well is sus- 
pended a second set of partitions placed at right angles to the first set. This 
impedes the rapidity of the downflow of the water, and also thoroughly 
mixes the water, thus affording a better cooling. A fan-blower at the base of 
the tower drives a strong current of air with a velocity of about twenty feet 
per second against the thin film of water running down over the partitions. 
It is estimated that for an effectual cooling two thousand times more air 
than water must be forced through the apparatus. With such a velocity 
the air absorbs about two per cent of aqueous vapor. The action of the 
strong air-current is twofold: first, it absorbs heat from the hot water by 
being itself warmed by radiation; and, secondly, it increases the evapora- 
tion, which process absorbs a great amount of heat. These two cooling 
effects are different during the different seasons of the year. During the 
winter months the direct cooling effect of the cold air is greater, while 
during summer the heat absorption by evaporation is the more important 
factor. Taking all the year round, the effect remains very much the same. 
The evaporation is never so great that the deficiency of water would not 
be supplied by the additional amount of water resniting from the condensed 
steam, while in véry cold winter months it may be necessary to occasionally 
rid the cistern of surplus water. It was found that the vacuum obtained by 


846 THE STEAM-ENGINE, 


this continual use of the same condensing-water varied during the year 
between 27.5 and 28.7 inches. The great saving of space is evident trom 
the fact that only the five-hundredth part of the floor-space is required as 
if cooling tanks or ponds were used. For a 100-horse-power engine the 
floor-space required is about four square yards by a height of twenty feet. 
For one horse-power 3.6 square yards cooling-surface is necessary. The 
vertical suspension of the partitions is very essential. With a ventilator 50 
inches in diameter and a tower 6 by 7 feet and 20 feet high, 10,500 gallons of 
water per hour were cooled from 104° F. to 68° F. The following record 
was made at Mannheim, Germany: Vacuum in condenser, 28.1 inches; tem- 
perature of condensing-water entering at top of tower, 104° to 108° F.; 
temperature of water leaving the cooler, 66.2° to 71.6° F. The engine was 
of the Sulzer compound type, of 120 horse-power. The amount of power 
necessary for the arrangement amounts to about three per cent of the total 
horse-power of the engine for the ventilator, and from one and ove half to 
three per cent for the lifting of the water to the top of the cooler, the total 
being four and one half to six per cent. 

A novel form of condenser has been used with considerable success in 
Germany and other parts of the Continent, The exhaust-steam from the 
engine passes through a series of brass pipes immersed in water, to which 
it gives up its heat. Between each section of tubes a number of galvanize 
disks are caused to rotate. These disks are cooled by a current of air 
supplied by a fan and pass down into the water, cooling it by abstract- 
ing the heat given out by the exhaust-steam and carrying it up where it is 
driven off by the air-current, The disks serve also to agitate the water and 
thus aid it in abstracting the heat from the steam. With 85 per cent 
vacuum the temperature of the cooling water was about 130° F., and a 
consumption of water for condensing is guaranteed to be less than a pound 
for each pound of steam-condensed. Foran engine 40 in. X 50 in., 70 revo- 
lutions per minute, 90 lbs. pressure, there is about 1150 sq. ft. of condensing- 
surface. Another condenser, 1600 sq. ft. of condensing-surface, is used for 
three engines, 32 in. X 48 in., 27 in. X 40 in., and 30 in. X 40 in., respectively. 
—The Steamship. 

The Imcrease of Power that may be obtained by adding a condenser’ 
giving a vacuum of %6 inches of mercury to 2 non-condensing engine may be 
approximated by considering it to be equivalent to.a net gain of 12 pounds 
mean effective pressure per square inch of piston area, if A = area of piston 
1245) ASay HP 
83/0002 7b0i ae 
made available by the vacuum. If the vacuum = 13.2 Ibs. per sq. in. = 27.9 
in. of mercury, then H.P. = AS -~ 2500. 

The saving of steam for a given horse-power will be represented approxi- 
mately by the shortening of the cut-off when the engine is run with the 
condenser. Clearance should be included in the calculation. To the mean 
effective pressure non-condensing, with a given actual cut-off, clearance 
considered, add 3 lbs. to obtain the approximate mean total pressure, con~ 
densing. From tables of expansion of steam find what actual cut-off will 
give this mean total pressure. The difference between this and the original 
actual cut-off, divided by the latter and by 100, will give the percentage of 
saving. | 

The following diagram (from catalogue of H. R. Worthington) shows the 
percentage of power that may be gained by attaching a condenser to a non- 
condensing engine, assuming that the vacuum is 12 lbs. per sq. in. The dia- 
gram also shows the mean pressure in the cylinder for a given initial pres- 
sure and cut-off, clearance and compression not considered. 

The pressures given in the diagram are absolute pressures above a vacuum. 

To find the mean effective pressure produced in an engine-cylinder with 90 
lbs. gauge ( = 105 lbs. absolute) pressure, cut-off at 14 stroke: find 105 in the 
left-hand or initial-pressure column, follow the horizontal line to the right 
until it intersects the oblique line that corresponds to the 14 cut-off, and read 
the mean total pressure from the row of figures directly above the point of 
intersection, which in this case is 63 lbs. From this subtract the mean abso. 
lute back pressure (say 3 lbs. for a condensing engine and 15 Ibs. for a non- 
condensing engine exhausting into the atmosphere) to obtain the mean ef- 
fective pressure, which in this case, for a non-condensing engine, gives 48 
lbs. To find the gain of power by the use of a condenser with this engine,. 
read on the lower scale the figures that correspond in position to 48 lbs. in 
the upper row, in this case 25%. As the diagram does not take into consid 
eration clearance or compression. the results are only approximate. 


in square inches, S = piston-speed in ft. per minute, then 


GAS, PETROLEUM, AND HOT-AIR ENGINES, 847 






Novonunua 
Expansions. ™) aj 












an’ Pressure in Pound 
10 / NO 











WIA 

























































































[| [}} 
go AMAT ATA L171 A 
MEGA 





“Absolute Initial 





VALLE | 


50 TI VALY 
WW NGI a 

LG 
SWAT 

Ne YY a 
LAA 

20a 


oe ne oo oe ee en ee we oe ew ew eee seo ——2- 
wee mewn eee owe recen ene & eee ee ee ec ese sees ese ces ~~ e rn eseees 


mo ot nr ne rn we sn oo ee eee 


was came eowcces cece euwcc cance owecwe — 


cemewwese ew eee ces o= 


we eroeoec coro wn 


wececcessae 
we a a oe ee ow ee re ee a ee ee oo ere pec 0g - - 


0 60 40 30 ee CON PIS) Tone Cee lO 
Per Cent of Power Gained by Vacuum. 


Fia. 151. 


Evaporators and Distillers are used with marine engines for the 
purpose of providing fresh water for the boilers or for drinking purposes. 

Weir’s Evaporator consists of a small horizontal boiler, contrived so as 
to be easily taken to pieces and cleaned. The water in it is evaporated by 
the steam from the main boilers passing through a set of tubes placed in its 
bottom. The steam generated in this boiler is admitted to the low- 
pressure valve-box, so that there is no loss of energy, and the water con- 
densed in it is returned to the main boilers. 

In Weir’s Feed-heater the feed-water before entering the boiler is heated 
up very nearly to boiling-point by means of the waste water and steam 
from the low-pressure valve-box of a compound engine. 


GAS, PETROLEUM, AND HOT-AIR ENGINES. 


Gas-engines.—For theory of the gas-engine, see paper by Dugald 
Clerk, Proc. Inst. C..E, 1882, vol. Ixix.; and Van Nostrand’s Science Series, 
No. 62. See also Wood's Thermodynamics. Three standard works on gas- 
engines are * A Practical Treatise on the *‘ Otto’ Cycle Gas-engine,” by Wm. 
Norris: ** A Text-book on Gas, Air, and Oil Engines,” by Bryan Donkin; and 
‘The Gas and Oil Engine,” by Dugald Clerk (6th edition, 1896). 

In the ordinary type of single-cylinder gas-engine (for example the Otto) 
known as a four-cycle engine one ignition of gas takes place in one end of 
the cylinder every two revolutions of the fly-wheel, or every two double 
strokes. The following sequence of operations takes place during four con- 
secutive strokes: (a) inspiration during an entire stroke; (6) compression 
during the second (return) stroke; (ce) ignition at the dead-point, and expan- 
sion during the third stroke; (d) expulsion of the burnt gas during the fourth 
(return) 8ftoke. Beau de Rochas in 1862 laid down the law that there are 


848 GAS, PETROLEUM, AND HOT-AIR ENGINES. 


four conditions necessary to realize the best results from the elastic force 
of gas: (1) The cylinders should have the greatest capacity with the smallest 
circumferential surface; (2) the speed should be as high as possible; (3) the 
cut-off should be as early as possible; (4) the initial pressure should be as 
high as possible. In modern engines it is customary for ignition to take 
place, not at the dead point, as proposed by Beau de Rochas, but somewhat 
later, when the piston has already made part of its forward stroke. At first 
sight it might be supposed that this would entail a loss of power. but experi- 
ence shows that though the area of the diagram is diminished, the power 
registered by the friction-brake is greater. Starting is also made easier by 
this method of working. (The Simplex Engine, Proc. Inst. M. E. 1889.) 

In the Otto engine the mixture of gas and air is compressed to about 3 
atmospheres. When explosion takes place the temperature suddenly rises 
to somewhere about 2900° F. (Robinson.) 

The two great sources of waste in gas-engines are: 1. The high tempera- 
ture of the rejected products of combustion; 2. Loss of heat through the 
cylinder walls to the water-jacket. As the temperature of the water-jacket 
is increased the efficiency of the engine becomes higher. 

With ordinary coal-gas the consumption may be taken at 20 cu. ft. per 
hour per I.H.P., or 24 cu. ft. per brake H.P. The consumption will vary with 
the quality of the gas. When burning Dowson producer-gas the consump- 
tion of anthracite (Welsh) coal is about 1.3 Ibs. per I.H.P. per hour for 
ordinary working. With large twin engines, 100 H.P., the consumption is 
reduced to about 1.11b. The mechanical efficiency or B.H.P. + I.H.P. in 
ordinary engines is about 85%; the friction loss is less in larger engines. 
at ane ane of the Gas-engime. (Thurston on Heat asa Form of 

nergy. 


Heat transferred into useful work.......... ae Wate trate 17% 
H: yt? _tothe jacket-water...........0..-: 52 
*. Jost.in. the, exhaust-ass . 6.53 des oe coe ee 16 
a) “© by conduction and radiation.............. 15 ag 


This represents fairly the distribution of heat in the best forms of gas- 
engine. The consumption of gas in the best engines ranges from a mini- 
mum of 18 to 20 cu. ft. per I1.H.P. per hour to a maximum exceeding in the 
smaller engines 25 cu. ft. or 830cu. ft. In small engines the consumption per 
brake horse-power is one third greater than these figures. \ 

The report of a test of a 170-H.P. Crossley (Otto) gas-engine in England, © 
1892, using producer-gas, shows a consumption of but .85 lb. of coal per H.P. 
hour, cr an absolute combined efficiency of 21.8% for the engine and pro- 
ducer. The efficiency of the engine alone is in the neighborhood of 254. 

The Taylor gas-producer is used in connection with the Otto gas-engine 
at the Otto Gas-engine Works in Philadelphia, The only loss is due to 
radiation through the walls of the producer and a small amount of heat 
carried off in the water from the scrubber. Experiments on a 100-H.P, 
engine show a consumption of 97/100 1b. of carbon per 1.H.P. per hour. This 
result is superior to any ever obtained on a steam-engine. (Iron Age, 1893.) 

Tests of the Simplex Gas-engime. (Proc. Inst. M. E. 1889.)— 
Cylinder 7% X 1534 in., speed 160 revs. per min. Trials were made with town 
gas of a heating value of 607 heat-units per cubic foot, and with Dowson 
gas, rich in CO, of about 150 heat-units per cubic foot, 





Town Gas. Dowson Gag. 
ht oo HE 
: He De 3. 1. D4, 3. 
MifectivesH;: Pawlet tweed ee ee 6.70 8.67 9.28 7.12 3.61 5.26 


Gas per H.P. per hour, cu. ft.. 21.55 20.12 20.73 88:03 114.85 97.88 
Water per H.P. per hour, lbs. 54.7 44.4 48.8 58.3 
Temp. water entering, F...... 51°) SSR o1e 48° 

ts So) GEM EI GE ch Sisvs rs 185° = 1449-1729 144° 


The gas volume is reduced to 82° F. and 80 in barometer. A 50-H.P. engine 
working 385.to 40 effective H.P. with Dowson generator consumed 51 lbs. 
English anthracite per hour, equal to 1.48 to 1.8 Ibs. per effective H.P. A 16- 
H.P. engine working 12 H.P. used 19.4 cu, ft. of gas per effective H.P. 

A 320-Hi.P. Gas-engine,— The flour-mills of M. Leblanc, at Pantin, 
France, have been provided with a 320-horse-power fuel-gas engine of the 
Simplex type. With coal-gas the machine gives 450 horse-power. There is 
one cylinder, 34,8in. diam.; the piston-stroke is 40 in.; and the speed 100 revs, 


GAS-ENGINES. 849 


per min. Special arrangements have been devised in order to keep the 
different parts of the machine at ao eg tia temperatures. The coal used 
is 0.812 lb. per indicated or 1.03 lb. per raed horse-power. The water used 
is 8 allons per brake horse-power per hour. 

Tost of aie Otto Gas-engine. (Jour. F. I., Feb. 1890, p. 115.)—En- 
gine 7 H.P. nominal; working capacity of cylinder .2594 cu. ft.; clearance 
space .1796 cu. ft. 





oF, Heat-units. Per cent. 
Temperature of gas supplied.. 62.2 | Transferred into work......... 22.54 
x *« ““ exhaust... 774.3 | Taken by jacket-water........ 49.94 
= “ enteringwater 50.4 Rice OR TIAUS Ua atelga re cin gene's aie 27,22 
ye “ exit water.... 89.2 0 
Pressure of gas, in. of water.. 3.06 Composition of the gas: 
Revolution per min., av’ge.... 161.6 By Volume. By Weight. 
Explosions missed per min., co : _. 0.50% 1.9234 
AVETAZE.....-- ss eeeeese sees 6.8 C i Fo salsa eisAeie 4.39 10.520 
Mean effective pressure, lbs. és rae anid = sis sin 3 1.00 2 ng 
SP oe ih set ei ete ieee AAI 2 eg eae ts ik Nee f 
Bees oirer: indicated....... 4.94 an asleisinie heey "Fe ues ale 
Work per explosion, foot- i AB site Ae an 51 by 9.021 
pounds ......... Leet eee cece 2204. Nett cn BLOG 99 973 
Explosions per minute......06 74. EA aah } 
Gas per I1.H.P. per hour, cu. ft, 23.4 99.96 99.995 


Test of the Clerk Gas-engime. (Proc. Inst. C. E. 1882, vol. lxix.)— 
Cylinder 6 X 12 in., 150 revs. per min.; mean available pressure, 70,1 lbs., 9 
I.H.P.; maximum pressure, 220 lbs. per sq. in. above atmosphere; pressure 
before ignition, 41 lbs. above atm.; temperature before compression, 60° F., 
after compression, 313° F.; temperature after ignition calculated from pres- 
sure, 2800° F.; gas required per I.H.P. per hour, 22 cu. ft. 

More Recent Tests of gas-engines, 1898, have given higher economical re- 
sults than those above quoted. The gas-consumption (city gas) has been as 
low as 15 cu. ft. per I.H.P. per hour, and the efficiency as high as 27% of the 
heating value of the gas. The principal improvement in practice has been 

the use of much higher compression of the working charge. 

' Combustion of the Gas in the Otto Engine.—John Imray, in 
discussiou of Mr. Clerk’s paper on Theory of the Gas-engine, says: The 
change which Mr, Otto introduced, and which rendered the engine a success, 
was that, instead of burning in the cylinder an explosive mixture of gas and 
air, he burned it in company with, and arranged in a certain way in respect 
of, a large volume of incombustible gas which was heated by it, and which 
diminished the speed of combustion. W..R. Bousfield, in the same discus- 
sion, says: In the Otto engine the charge varied from a charge which was 
an explosive mixture at the point of ignition to a charge which was merely 
an inert fluid near the piston. When ignition took place there was_n explo- 
sion close to the point of ignition that was gradually communicated through- 
out the mass of the cylinder. As the ignition got farther away from the 
primary point of ignition the rate of transmission became slower, and if the 
engine were not worked too fast the ignition should gradually catch up to 
the piston during its travel, all the combustible gas being thus consumed. 
This theory of slow combustion is, however, disputed by Mr. Clerk, who 
holds that the whole quantity of combustible gas is ignited in an instant. 

Vemperatures and Pressures developed in a Gas-engine. 
(Clerk on the Gas-engine.)—Mixtures of air and Oldham coal-gas. _‘l’emper- 
ature before explosion, 17° C. j 


: Temp. of Explo- Theoretical 
Mixture. Max. Press emp: D 
crud above Atmos., ae neue’ pene AR 
"Gada: Air. : lbs, per sq. in. rom ok Sel ve sion I a eat 
Pressure. were evolved. 
Jvol. 14 vols, 40. 806° C. 786° C, 
13 iby le 51.5 1033 1912 
phe ds poms 60. 1202 2058 
1 hl ee 61. 1220 2228 
ght p75, 66 78. 1557 2670 
i Whee fa 87. 1733 8334 
1a Gar 90. 1792 3808 
1'ts pans 91. 1812 tees 
Fos hs 8 80. 1595 Reue 
Use of Carburetted Air in Gas-engimes,—Air passed over 


850 GAS, PETROLEUM, AND HOT-AIR ENGINES. 


gasoline or volatile petroleum spirit of low sp. gr., 0.65 to 0.70, liberates 
some of the gasoline, and the air thus saturated with vapor is equal in heat- 
ing or lighting power to ordiuary coal-gas, It may therefore be used as a 
fuel for gas-engines. Since the vapor is given off at ordinary temperatures 
gasoline is very explosive and dangerous, and should be kept in an under- 
ground tank out of doors. <A defect in the use of carburetted air for gas- 
engines is that the more volatile products are given off first, leaving an oily 
residue which is often useless. Some of the substances in the oil that are 
taken up by the air are apt to form troublesome deposits and incrustations 
when burned in the engine cylinder. 

The Otto Gasoline-engine. (Hng’g News, May 4, 1893.)—It is 
claimed that where but a small gasoline-engine is used and the gasoline 
bought at retail the liquid fuel will be on a par with a steam-engine using 6 
lbs. of coal per horse-power per hour, and coal at $3.50 per ton, and will 
besides save all the handling of the solid fuel and ashes, as well as the at- 
tendance for the boilers. As very few small steam-engines consume less 
than 6 lbs. of coal per hour, this is an exceptional showing for economy. At 
8 cts. per gallon for gasoline and 1/10 gal. required per H.P. per hour, the 
vost per H.P. per hour will be 0.8 cent. ; 

Gasoline-engines are coming into extensive use (1898). In these engines 
the gasoline is pumped from an underground tank, located at some distance 
outside the engine-room, and led through carefully soldered pipes to the 
working cylinder. In the combustion chamber the gasoline is sprayed into 
a current of air, by which it is vaporized. The mixture is then compressed 
and ignited by an electric spark. At no time does the gasoline come in con-: 
tact with the air outside of the engine, nor is there any flame or burning 
gases outside of the cylinder. 

~Naphtha-engimes are in use to some extent in smal! yachts and 
launches. The naphtha is vaporized in a boiler, and the vapor is used ex- 
pansively in the engine-cylinder, as steam is used; it is then condensed and 
returned to the boiler. A portion of the naphtha vapor is used for fuel un- 
der the boiler. According to the circular of the builders, the Gas Engine 
and Power Co. of New York, a 2-H.P. engine requires from 3 to 4 quarts of 
naphtha per hour, and a 4-H.P. engine from 4 to6 quarts. The chief advan- 
tages of the naphtha-engine and boiler for launches are the saving of weight 
and the quickness of operation. A 2-H.P. engine weighs 200 lbs.,a 4-H.P. 300 
lbs. It takes only about two minutes to get under headway. (Modern 
Mechanism, p. 270.) 

Hot-air (or Caloric) Engines.—Hot-air engines are used to some 
extent, but their bulk is enormous compared with their effective power. For 
an account of the largest hot-air engine ever built (a total failure) see 
Church’s Life of Ericsson. For theoretical investigaton, see Rankine’s 
‘Steam-engine and Rontgen’s Thermodynamics. For description of con-: 
structions, see Appleton’s Cyc. of Mechanics and Modern Mechanism, and 
Babcock on Substitutes for Steam, Trans. A. S. M. E., vii., p. 698. 

West of a Hot-air Engime (Robinson),—A vertical double-cylinder 
(Caloric Engine Co.’s) 12 nominal H.P. engine gave 20.19 I.H.P. in the work- 
ing cylinder and 11.38 I.H.P. in the pump, leaving 8.81 net I.H.P.; while the 
effective brake H.P. was 5.9, giving a mechanical efficiency of 67%. Con- 
sumption of coke, 3.7 lbs. per brake H.P. per hour. Mean pressure on 
pistons 15.37 lbs. per square inch, and in pumps 15.9 lbs., the area of working 
cylinders being twice that of the pumps. The hot air supplied was about 
1160° F. and that rejected at end of stroke about 890° F. s 

The Priestman Petroleum-engine. (Jour. Frank. Inst., Feb. 
1893 )—The following is a description of the operation of the engine: Any 
ordinary high-test (usually 150° test) oil is forced under air-pressure to an 
atomizer, where the oil is met by a current of air and broken up into atoms 
and sprayed into a mixer, where it is mixed with the proper proportion of 
supplementary air and sufficiently heated by the exhaust from the cylinder 
passing around this chamber. The mixture is then drawn by suction into 
the cylinder, where it is compressed by the piston and ignited by an electric 
spark, a governor controlling the supply of oil and air proportionately to 
the work performed. The burnt products are discharged through an ex- 
haust-valve which is actuated by a cam. Part of the air supports the com- 
pustion of the oil, and the heat generated by the combustion of the oil 
expands the air that remains and the products resulting from the explosion, 
and thus develops its power from air that it takes in while running. In 

other words, the engine exerts its power by inhaling air, heating that air, 
and expelling the products of combustion when done with. In the largest 
engines only the 1/250 part of a pint of oil is used af any one time, énd in 


EFFICIENCY OF LOCOMOTIVES. 851 


the smallest sizes the fuel is prepared in correct quantities varying from 
1/7000 of a pint upward, according to whether the engine is running on light 
or full duty. The eycle of operations is the same as that of the Otto gas- 
engine. 

Trials of a 5-H.P. Priestman Petroleum-engine. (Prof. 
W.C. Unwin, Proc. Inst. C. H. 1892.)—Cylinder, 8144 < 12in., making normally 
200 revs. per min. Two oils were used, Russian and American. The more 
important results were given in the following table: 








—_— 


THalvoet Trial lt | TriallVo tral ines 
Full Full Full Half hea 
Power. | Power. Power. Power. at 


oe Day- Russo- | Russo- | Russo- | Russo- 
Oilused...-........-. ; { light. lene. lene. lene, lene. 
IS VEISOM Els P, Weterste nore ke suaerae 7.22 6.765 6. 882 Je Oa Raila 
TRE Bawa chcieias sels aces 9.369 7.408 8.332 4.70 0.889 
Mechanical efficiency... 0.824 0.91 0.87 0209 cccrer ce 
Oil used per brake H.P. 

OUT PAD. sks, each ee skese 0.842 0.946 0.088 TSS baila pregere ae 5 
Oil used per indicated 

HAS OUT lb sete ae tare 0.694 0.864 0.S1G 1.063 5.734 
Lb. of air per lb. of oil..| 33.4 31.7 43.2 21.7 10.1 
Mean explosion pressure, 

Maskper Ssqain 2.36. ce. 151.4 134.3 128.5 48.5 9.6 
Meen compression pres- 

sure, Ibs. per sq. in .. | 35.0 27.6 26.0 14.8 6.0 
Mean terminal pressure, 

LOSE DEL SGI ceonce. - 35.4 23.7 25.5 15.640 Sh Seer 


~ To compare the fuel consumption with that of a steam-engine, 1 Ib. of 
oil might be taken as equivalent to 114 lbs. of coal. Then the consumption 
in the oil-engine was equivalent, in Trials I., IV., and V., to 1.42lbs., 1.48 Ibs., 
and 1.261bs. of coal per brake horse-power per hour. From Trial IV. the 
followin, values of the expenditure of heat were obtained: 





Per cent. 
eoatul work at Drake. 25.9 meeteatt cies + steasie stn s cies aa cic estes Erica is tarsi 
Pein STIChIOIN ..2 Ca. sandiisaineas ett exicte scenes soe aeecdesosticecot a 
Heat shown or. indicator-diagram..... Se Sea shea 7 iAP ars Sari 16.12 
Rejected in jacket-water (22.02... 6... eee eee SOBOOOD HOME OSS 47.54 

a in exhaust-gases.......- afetale/eptis ein tacets aye stoininle: fe terete ator ate 26.72 

Radiation and unaccounted for. .......cccccscenccees SE Nes 9.61 

Total®’. a. .sre cometutots eee caer etetee acts sl ACCECax CIC Me LER Le 
LOCOMOTIVES. 


Hesistance of Trains. — Resistance due to Speed.—Various formule 
and tables for the resistance of trains at different speeds on a straight level 
track have been given by different writers. Among these are tne following: 

By Gecrge R. Henderson (Proc. Engrs. Club of Phila., 1886): 


R = 0.0015(1 + v2 + 650), 
in which R = resistance in lbs. per ton of 2240 lbs. and v = speed in miles per 
hour. 
Speed in miles per hour: 
5 10 15 20 25 30 35 40 45 50 55 60 
Resistance in pounds per ton of 2000 Ibs.: 
3.1 3. 4. 4.5) OceieteoO 10,2 | 12.1. 14.3 ose tye 
By D. L Barnes (Eng. Mag.), June, 1894 : 
Speed, miles per hour. .. .. ...... 50 ~=—s- 60 mv 80 90 100 
Resistance, pounds per grosston.. 12 124 135 15 17% 20 


852 - LOCOMOTIVES. 


By Engineering News, March 8. 1894: 
Resistance in lbs. per ton of 2000 Ibs. = 144v + 4. 


Speed... ... 5 10°15 20 25 30 ° 35 40 45° 50 60 70 80° 90° 100 
Resistance.. 344 4.5 534 7 814 9.5 1034 12 1314 14.5 17 19.5 22 24.5 27 


By Baidwin Locomotive Works : 
Resistance in Ibs. per ton of 2000 lbs. = 3 + u + 6, 


Speed........5 10 15-20 25 30.35 40 45 50. 55. 60 70 80.90 100 
Resistance.. 3.8 4.7 5.5 6.3 7.2 8 88 9.7 10.5 11.3 12.2 138 14.7 16.3 18 19.7 


The resistance due to speed varies with the condition of the track, the 
number of cars in a train, and other conditions. 

For tables showing that the resistance varies with the area exposed to the 
resistance and friction of the air per ton of loads, see Dashiell, Trans. A. S. 
M. #., vol. xiii. p. 371. 

P. H. Dudley (Bulletin International Ry. Congress, 1900, p. 1734) shows 
that the condition of the track is an important factor of train resistance 
which has not hitherto been taken account of. The resistance of heavy 
trains on the N. Y. Central R. R. at 20 miles an hour is only about 3% Ibs. per 
ton on smooth 80-lb. 54-in. rails. The resistance of an 80-car freight train, 
60,000 Ibs. per car, as given by indicator cards, at speeds between 15 and 25 
miles per hour is represented by the formula R = 1+ 14V, in which R = re- 
sistance in lbs. per ton and V = miles per hour. 

Resistance due to Grade.—The resistance due to a grade of 1 ft. per mile 


1 : ; 
is, per ton of 2000 Ibs., 2000 x 5280 = 0.3788 lb. per ton, or if Rg = resistance 


in Ibs, per ton due to grade and G = ft. per mile, Rg = 0.3788G. 

If the grade is expressed as a percentage of the length, the resistance is 20 
Ibs per ton for each per cent of grade. 

Resistance due to Curves.—Mr. Henderson gives the resistance due to 
curvature as 0.5 lb. per ton of 2000 lbs. per degree of the curve. (or defini- 
tion of degrees of a railroad curve see p. 53.) 

If cis the number of degrees, Re the resistance in Ibs. per ton, = 0.5c. The 
Baldwin Locomotive Works take the approximate resistance due to each 
degree of curvature as that due to a straight grade of 114 ft. per mile. This 
corresponds to Re = 0.5682c. 

Resistance due to Acceleration.—This may be calculated by means of the 
ordinary formule for acceleration, as follows: 


Let V, = velocity in ft. per second at the beginning of a mile run. 
V, = velocity at the end of the mile. 
44(V_ — V,) = average velocity during the mile. 
T = 5280 + 14(V_2 — V,) = time in seconds required to run the mile. 
w = weight of the train inlIbs. W = weight in tons. 


f = resistance in lbs. due to acceleration = 3 Cae 
Ww (Vg — V,)? SO Oou TT 
= 329 10,560 = 005882 W (T nes V;,)2. 
S = increase of speed in miles per hour 3 (V_ — V,)2 = S? x (22/15)?. 
Ra = resistance in lbs. per ton = .01265S?. 

Total Resistance.—The total resistance in Ibs. per ton of 2000 Ibs. due to 
speed, to grade, to curves, and to acceleration is the sum of the resistances 
ealculated above. Taking the Baldwin Locomotive Works’ rules for speed 
and curvature, we have 


Ri= (3 ie -) 1 0.3788G -+ 0.5682c + .0126582, 


in which R: is the resistance in lbs. per ton of 2000 lbs., » = speedin miles per 
hour, G = grade in ft. per mile. c = degrees of curvature, S = rate of in- 
crease of speed in miles per hour in a run of one mile. 

Resistance due to Friction.—In the above formula no account 
has been taken of the resistance to the friction of the working parts of the 
engine, nor to the friction of the engine and tender on curves due to the 
rigid wheel bases. No satisfactory formula can be given for these resist- 
ances Mr. Henderson takes them as being proportional to the tractive 
power, so that, if the total tractive power be F, the effective tractive is uP, 


TRACTIVE POWER OF A LOCOMOTIVE. 853 


and the -‘esistance (1 — w)P, the value of the coefficient w being probably 
about 0.3. 

The Baldwin Locomotive Works in their ‘‘ Locomotive Data’ take the 
total resistance on a straight level track at slow speeds at from 6 to 10 Ibs. 
per ton. and in a communication printed in the fourth edition (1898) of this 

ocket-book, p. 1076, say: ‘‘ We know that in some cases, for instance in 
mine construction, the frictional resistance has been shown to be as much as 
60 lbs. per ton at slow speed. The resistance should be approximated to 
suit the conditions of each individual case, and the increased resistance due 
to speed added thereto.”’ 

Holmes on the Steam-engine, p. 142, says: ‘‘ The frictional resistance 
to uniform motion of the whole train, incliding the engine and tender, is 
usually expressed by giving the direct pull in pounds necessary in order to 
propel each ton’s weight of the train along a level line at slow speed. The 
pull varies with the condition of the line, the state of the surface of the rails, 
the state of the rolling stock, and the speed. If M be the speed in miles per 
hour, and 7 the weight of the train in tons [2240 lbs.| exclusive of engine 
and tender, the resistance to uniform motion may be expressed by the 
formula 

. R= [6+ 0.8(M — 10)T]. 

If T, be the weight of the engine and tender, the corresponding resistance is 
R, = [12 + 0.3(M@ — 10)T,], 


which expression includes the friction of the mechanism of the engine. 

Holmes also says that a strong side wind by pressing the tires of the 
wheels against the rails may increase the frictional resistance of the train by 
as much as 20 per cent. 

Hauling Capacity due to Adhesion.—The limit of the hauling 
capacity of a lecomotive is the adhesion due to the weight on the driving 
wheels. Holmes gives the adhesion, in English practice, as equal to 0.15 of 
the load on the driving wheels in ordinary dry weather, but only 0,07 in 
damp weather or when the rails are greasy. In American practice it is gener- 
ally taken as from 1/4 to 1/5 of the load on the drivers. The hauling capacity 
at slow speed on a track of different grades may be calculated by the fol- 
lowing formula: 

Let J’= tons of 2000 lbs., locomotive and train, per 1000 lbs. load on 
drivers, a = the reciprocal of the coefficient of adhesion, g = the per cent 
ef grade, R = the frictional resistance in lbs. per ton. Then T= ea 0G 
From this formula the following table has been calculated ; 

Grade Per’ Cent: 0" “025 | 1 T5225, 8 8. 4 Dae O a 


Tons Hauling Capacity per 1000 lbs. Weight on Drivers. 


Hon a= 4, Bh = 67042 15.6 99:2 6.9) 524) Leb eae B 8812.9. 2145 SONI 
hie SR Bs Qt hed. 252 16 Bp Gr2 wie OA oR AB 1.9). 1.60 3.4 
Ga De eet On eel Oa: 1G St eiS uel a aie ol es. Bl) 2 2) oT 8) Ibias 


Tractive Power of a Locomotive.—Single Hxpansion. 
Let P = tractive power in lbs. 

p = average effective pressure in cylinder in Ibs. per sq. in. 

S = stroke of piston in inches. 

d = diameter of cylinders in inches. 

D = diameter of driving-wheels in inches. Then 


ie = 





4nd*pS _ d’pS 
0, ae 


The average effective pressure can be obtained from an indicator-dia- 
gram. or by calculation, when the initial pressure and ratio of expansion are 
known, together with the other properties of the valve-motion. The sub 
joined table from *‘* Auchincloss” gives the proportion of mean effective 
aap to boiler-pressure above atmosphere for various proportions of 
cut-off. 


854 LOCOMOTIVES, 


























, easy ees é Stroke, ee “| Stroke, oad 
“ut off at— pres. = 1). ut of at-- pres. = 1). Cut off at— pres. = 1) 
1 15 Bian 1G dani Who lt S62S Bales 79 
an Py 2 10 = % 55 .666 = % 82 
15 24 4 57 WV .35 
175 28 45 62 Sie 301 .89 
132 Be paeiee | p68 ba 93 
2.= 4 4 5d “12 810 = 98 

46 





These values were deduced from experiments with an English locomotive 
by Mr. Gooch. As diagrams vary so much from different causes, this table 
will only fairly represent practical cases. It is evident that the cut-off must 
be such that the boiler will be capable of supplying sufficient steam at the 
given speed. 

Compound Locomotives.—The Baldwin Locomotive Works give the fol- 
lowing formule for compound engines of the Vauclain four-cylinder type : 


T= C28 x %P , c?3S x YP 
D at Deas 

T = tractive power in lbs. tort 

C = diam. of high-pressure cylinder in ins. 

oc be 6 low 6 oe be 66 

P = boiler-pressure in Ibs. 

S = stroke of piston in ins. 

D = diam. of driving-wheels in ins. 
For a two-cylinder or cross-compound engine it is only necessary to con- 
sider the high-pressure cylinder, allowing a sufficient decrease in boiler 
pressure to compensate for the necessary back-pressure. The formula is 


C'S x %P 
sata Siciiees 


Efficiency of the Mechanism of a Locomotive.—frank C. 
Wagner (Proc, A. A. A. S., 1900, p. 140) gives an account of some dy namom- 
eter tests which indicate that in ordinary freight service the power used 
to drive the locomotive and tender and to overcome the friction of the mech- 
anism is from 10% to 35% of the total power developed in the steam-cylinder. 
In one test the weight of the Jocomotive and tender was 16% of the total 
weight of the train, while the power consumed in the locomotive and tender 
was from 30% to 33% of the indicated horse-power. 

The Size of Locomotive Cylinders is usually taken to be such 
that the engine will just overcome the adhesion of its wheels to the rails 
under favorable circumstances. 

The adhesion is taken by a committee of the Am. Ry. Master Mechanics’ 
Assn. as 0.25 of the weight on the drivers for passenger engines, 0.24 for 
freight, and 0.22 for switching engines ; and the mean effective pressure in 
the cylinder, when exerting the maximum tractive force, is taken at 0.85 of 
the boiler-pressure. 

Let W = weight on drivers in lbs.; P = tractive forcein lbs., = say 0.25W 3 
p, = boiler-pressure in lbs. per sq. in.; p = mean effective pressure, = 0 85p, ; 
a = diam. of cylinder, S = length of stroke, and D= diam. of driving- 
wheels, alliniaches. Then 


W=4P'= 


les 


4d°pS _ 4d? x 0.85p,8 


Die D . 

DW DW 
Whence d = 0.5 4/ =, = 0540 / oe 
: ps v DiS 


Von Borries’s rule for the diameter of the low-pressure cylinder of a com< 


pound locomotive is d? = , 


oe 


LOCOMOTIVES, 855 


where d = diameter of 1.p. cylinder in inches; 
D= diameter of driving-wheel in inches; 
p = mean effective pressure per sq. in., after deducting internal 
machine friction; 
h = stroke of piston in inches; 
Z = tractive force required, usually 0.14 to 0.16 of the adhesion. 


The value of p depends on the relative volume of the two cylinders, and 
from indicator experiments may be taken as follows: 


: Ratio of Cylinder pin percentage for Boiler-press 
Class of Engine. Volumes. of Boiler-pressure. _ure of 176 lbs. 
Large-tendereng’s 1:2o0r1: 2.05 42 74 
Tank-engines...... AesetOrid tees 40 71 


Horse-power of a Locomotive.—For each cylinder the horse- 
power is H.P. = pLaN ~ 33,000, in which p = mean effective pressure, LZ 
= stroke in feet, a = area of cylinder = 1447d?, N = number of single strokes 
per minute, L.N = piston speed, ft. permin. Let M = speed of train in miles 
per hour, S = length of stroke in inches, and D = diameter of driving-wheel 
in inches. Then LN = M x 88 x 28+7D. Whence for the two cylinders 
the horse-power is 


2x p x 4nd? x 1768S x M _ pd*SM 
wD x 33,000 i otoD ila 


The Size of Locomotive Boilers. (Forney’s Catechism of the 
Locomotive.)—They should be proportioned to the amount of adhesive 
weight and to the speed at which the locomotive is intended to work. Thus 
a locomotive with a great deal of weight on the driving-wheels could pull a 
heavier load, would have a greater cylinder capacity than one with little 
adhesive weight, would consume more steam, and therefore should have a 
larger boiler. 

The weight and dimensions of locomotive boilers are in nearly all cases 
determined by the limits of weight and space to which they are necessarily 
confined. It may be stated generally that within these limits a locomotive 
boiler cannot be made too large. In other words, boilers for locomotives 
should always be made as large as is possible under the conditions that de- 
termine the weight and dimensions of the locomotives. (See also Holmes on 
the Steam-engine, pp. 371 to 377 and 383 to 389, and the Report ofthe Am. Ry. 
M. M. Assn. for 1897, pp. 218 to 232.) 

Holmes gives the following from English practice : 

Evaporation, 9 to 12 Ibs. of water from and at 212°. 

Ordinary rate of combustion, 65 lbs. per sq. ft. of grate per hour. 
Ratio of grate to heating surface, 1 : 60 to 90. 

Heating surface per 1b. of coal burut per hour, 0.9 to 1.5 sq. ft. 

Qualities Essential for a Free-steaming Locomotive. 
(From a paper by A. E. Mitchell, read before the N. Y. Railroad Club ; 
Engg News, Jan, 24, 1891.)—Square feet of boiler-heating surface for bitu- 
minous coal should not be less than 4 times the square of the diameter in 
inches of a cylinder 1 inch larger than the cylinder to be used. One ‘tenth 
of this should be in the fire-box. On anthracite locomotives more heating- 
surface is required in the fire-box, on account of the larger grate-area 
required, but the heating-surface of the flues should not be materially - 
decreased. 

Wootten’s Locomotive. (Clark’s Steam-engine; see also Jour. 
Frank. Inst. 1891, and Modern Mechanism, p. 485.)—J. E. Wootten designed 
and constructed a locomotive boiler for the combustion of anthracite and 
lignite, though specially for the utilization as fuel of the waste produced in 
the mining and preparation of anthracite. The special feature of the engine 
is the fire-box, which is made of great length and breadth, extending clear 
over the wheels, giving a grate-area of from 64 to 85 sq. ft. The draught 
diffused over these large areas is so gentle as not to lift the fine pa~*icles of 
the fuel. A number of express-engines having this type of boiler are engaged 
on the fast trains between Philadelphia aud Jersey City. The fire-box shell 
is 8 ft. 8in. wide and 10 ft. 5 in. long ; the fire-box is 8914 ft., making 76 sq. 
ft. of grate-area. The grate is composed of bars and water-tubes alternately, 
‘he regular types of cast-iron shaking grates are also used. The height of 
the fre-box is only 2 ft.5in. above the grate. The grate is terminated by 
a bridge of fire-brick, beyond which a combustion-chamber, 27 in. long, 
jJeads to the flue-tubes, about 184 in number, 134 in. diam. The cylinders are 





856 LOCOMOTIVES, 


21 in. diam., w'th a stroke of 22inches. The driving-wheels, four-coupled, 
are 5 ft. 8in. diam. The engine weighs 44 tons, of which 29 tons are on driv- 
ing wheels. The heating-surface of the fire-box is 135 sq. ft., that of the 
flue-tubes is 982 sq. ft.; together, 1117 sq. ft., or 14.7 times the grate-area. 
Hauling 15 passenger-cars, weighing with passengers 360 tons, at an average 
speed of 42 miles per hour, over ruling gradients of 1 in 89, the engine con- 
sumes 62 lbs. of fuel per mile, or 3414 lbs. per sq. ft. of grate per hour. 

Grate-surface, Smokesstacks, and Exhaust-nozzles for 
Locomotives. (Am. Mach., Jan. 8, 1891.)—For grate-surface for anthra- 
cite coal: Multiply the displacement in cubic feet of one piston during a 
stroke by 8.5; the product will be the area of the grate in square feet. 

For bituminous coal: Multiply the displacement in feet of one piston 
during a stroke by 614; the product will be the grate-area in square feet for 
engines with cylinders 12 in. in diameter and upwards. For engines with 
smaller cylinders the ratio of grate-area to piston-displacement should be 714 
to 1, or even more, if the design of the engine will admit this proportion. 

The grate-areas in the following table have been found by the foregoing 
rules, and agree very closely with the average practice : 

Smoke-stacks.—The internal area of the smallest cross-section of the stack. 
should be 1/17 of the area of the grate in soft-coal-burning engines. 

A. E. Mitchell, Supt. of Motive Power of the N. Y. L. E. & W. RB. R., says 
that recent practice varies from this rule. Some roads use the same size of 
stack, 134 in. diam. at throat, for all engines up to 20 in. diam. of cylinder. 

The area of the orifices in the exhaust-nozzles depends on the quantity and 
quality of the coal burnt, size of cylinder, construction of stack, and the 
condition of the outer atmosphere, It is therefore impossible to give rules 
for computing the exact diameter of the orifices. All that can be done is to 
give arule by which an approximate diameter can be found. The exact 
diameter can only be found by trial. Our experience leads us to believe that 
the area of each orifice in a double exhaust-nozzle should be equal to 1/400 
part of the grate-surface, and for single nozzles 1/200 of the grate-surface. 
These ratios have been used in finding the diameters of the nozzles given in 
the following table. The same sizes are often used for either hard or soft 
coal-burners. 





Double Single 
: Grate-area | Grate-area : Nozzles. Nozzles. 
Size of for Anthra- | for Bitumin-| Diameter |___—_—]_ 
Qylinders, | cite Coal, in | ous Coal, in | Of Stacks, 








near ; é ot ns Diam. of | Diam. of 
os Sq. 10, ES: ft perigee Orifices, in |Orifices, in 
inches. inches. 
12 x 20 1591 1217 914 2 2 13/16 
13 x 20 1873 1432 1044 2 3 
14 x 20 2179 1666 1114 25/16 314 
15 «22 2742 2097 1214 2 9/16 8 11/16 
16 x 24 8415 2611 14 2% 4 1/16 
17'* 24 8856 2948 15 3 1/16 4 5/16 
18 « 24 4321 8304 1534 314 454 
19 x 24 4810 8675 164 37/16 | 4 13/16 
20 x 24 53837 4081 1% 854 5 1/16 


Exhaust-nozzles in Locomotive Boilers.—A committee of 
the Am. Ry. Master Mechanics’ Assn. in 1890 reported that they had, after 
two years of experiment and research, come to the conciusion that, owing 
to the great diversity in the relative proportions of cylinders and boilers, 
together with the difference in the quality of fuel, any rule which does not 
recognize each and all of these factors would be worthless. 

The committee was unable to devise any plan to determine the size of the 
exhaust-nozzle in proportion to any other part of the engine or boiler, and 
believes that the best practice is for each user of locomotives to adopt a 
nozzle that will make steam freely and fill the other desired conditions, best 
determined by an intelligent use of the indicator and a check on the fuel 
account. The conditions desirable are : That it must create draught enough 
on the fire to make steam, and at the same time impose the least possible 
amount of work on the pistons in the shape of back pressure. It should be 
large enough to produce a nearly uniform blast without lifting or tearing 


SIZE, WEIGHT, TRACTIVE POWER, ETO, 85? 


the fire, and be economical in its use of fuel. The Annual Report of the As- 
sociation for 1896 contains interesting data on this subject. 

Fire-brick Arches in Locomotive WFire-boxes.—A com- 
mittee of the Am. Ry. Master Mechanics’ Assn. in 1890 reported strongly in 
favor of the use of brick arches in locomotive fire-boxes. They say: It is 
the unanimous opinion of all who use bituminous coal and brick arch, that 
it is most efficient in consuming the various gases composing black smoke, 
and by impeding and delaying their passage through ‘the tubes, and ming- 
ling and subjecting them to the heat of the furnace, greatly lessens the 
volume ejected, and intensifies combustion, and does not in the least check 
but rather augments draught, with the consequent saving of fuel and in- 
creased steaming capacity that might be expected from such results. This 
in particular when used in connection with extension front. 

Size, Weight, Tractive Power, etc., of Different Sizes of 
Locomotives. (J. G. A. Mever. Modern Locomotive Construction. Anz. 
Mach., Aug. 8, 1885.)—The tractive power should not be more or less than 
the adhesion. Im column 3 of each table the adhesion is given, and since the 
adhesion and tractive power are expressed by the same number of pounds, 
these figures are obtained by finding the tractive power of each engine, for 
this purpose always using the small diameter of driving-wheels given in 
column 2. The weight on drivers is shown in column 4, which is obtained by 
multiplying the adhesion by 5 for all classes of engines. Column 5 gives the 
weights on the trucks, and these are based upon observations. ‘Thus, the 
weight on the truck for an eight-wheeled engine is about one half of that 
placed on the drivers. 

For Mogul engines we multiply the total weight bn drivers by the decimal 
.2, and the product will be the weight on the truck. 

For ten-wheeled engines the total weight on the drivers, multiplied by the 
decimal .32, will be equal to the weight on the truck. 

And lastly, for consolidation engines, the total weight on drivers multi- 
plied by the decimal .16, will determine the weight on the truck. 

In column 6 the total weight of each engine is given, which is obtained by 
adding the weight on the drivers to the weight on the truck. Dividing the 





EIGHT-WHEELED LOCOMOTIVES. TEN-WHEELED ENGINES. 






































































! : Ke a 
a a Saat 8 | 8 a P ee 
S S | ad rea ge S S | g/g /BSs 
a3 |= ay ee sec Te |% & | S/S legs 
am | A BE.) Bodog [ogee | a BR) BAsscter | an 
AS | a Al xa | a jek pu A Pa A | Al ag las ox 
1B | 9 re & |S ean | © Alia a | Ms |Oa¥o 
ay sag ° 3 f=} coal <2) aod m 4 d ) 3 od 3S fo Qs 
17) Oo: a ° o we Se Hs Des OS bps 
o.-| 8a iS) » ~ = ope Oo |] £3 ao) ~ 2 |B leo 
coe aa] cer a | SsSuf t¥ |.coo | @) 4 | 2 |.Agsa 
Ae | go g op of Sq |sbe = oe eee eg ©) Se |\SEpR 
Seise 315 | 3B] 5 lesuetss | sed) s) 8 | S| Se lesue 
OA 18 5 a = es & |prori oe | a a = = S Hos 
1 2 38 4. 5 6 ‘9 1 2 8 4. 5 6 v9 
in. in. .| Ibs...| Ibs.) Jbs, _| lbs. in, in. | lbs.}| lbs. | Ibs. | Ibs, 
10x20} 45-51] 4000! 20000} 10000} 30000 533 12x18] 39-43) 5981) 29907) 9570) 39477 197 
11x22] 45-51! 5324! 26620] 13310] 39930 709 8183x18| 41-45) 6677) 33387)10683| 44070 890- 
12x22) 48-54] 5940) 29700) 14850) 44550 792 14x20) 43-47) 8205] 41023|13127| 54150) 1093 
13X22| 49-57] 6828] 34140] 17070) 51210 910 §15x22! 45-50! 9900) 49500)15840) 65340! 1320 
14X24] 55-61] 7697) 38485] 19242) 57727; 1026 §16x24) 48-54/11520) 57600) 18432 76032| 1536 
15X24] 55-66] 8836) 44180) 22090) 66270] 1178 $1724) 51-56/12240| 61200/19584| 80784; 1632 
16X24| 58-66] 9533) 47665| 23832] 71497) 1271 §18x24) 51-56/13722| 68611)21955) 90566; 1829 
17 X24| 60-66] 10404) 52020] 26010} 78030) 1387 iba 54-60 14440} 72200)23104| 95304) 1925 
18X24] 61-66] 11472! 57360] 28680! 86040| 1529 | 





MoaguL ENGINES. CONSOLIDATION ENGINES. 











in. in. | Ibs. | Ibs. | Ibs. | Ibs. in. | in. | Ibs. | Ibs. | Ibs.] Ibs. 
11X16] 35-40] 4978] 24891} 4978] 29869} 663 f14x16| 36-38) 7840) 89200) 6272] 45472] 1045 
1218] 36-41] 6480} 32400] 6480] 38880) 864 91518} 36-38/10125| 50625) 8100) 58725) 1350 
13X18] 37-42} 7399] 36997| 7399] 44396] 986 20x24) 48-50|18000} 90000|14400/104400} 2400 
14X20] 39-43] 9046} 45230} 9046) 54276} 1206 fa2x 24] 50--52/20909]104544/16727|121271| 2787 
15x 22| 42-47| 10607] 53035| 10607] 63642) 1414 

16X24, 45-51) 12288] 61440) 12288] 73738) 1638 
17x 24| 49-54] 12739| 63697) 12739] 76436] 1698 
18x 24| 51-56] 13722] 68611] 13722] 82333] 1829 
19x 24! 54-60] 14440] 72200) 14440] 86640] 1925 








858 LOCOMOTIVES. 


adhesion given in column 8 by 74 gives the tons of 2000 lbs. that the engine 
is capable of hauling on a straight and level track. column 7. at slow speea. 

The weight of engines given in these tables will be found to agree gen- 
erally with the actual weights of locomotives recently built, although it 
must not be expected that these weights will agree in every case with the 
actual weights, because the different builders do not build the engines alike. 

The actual weight on trucks for eight-wheeled or ten-wheeled engines will 
not differ much from those given in the tables, because these weights depend 
greatly on the difference between the total and rigid wheel-base, and these 
are not often changed by the different builders. The proportion between 
the rigid and total wheel-base is generally the same. 

The rule for finding the tractive power is: 


; Square of dia. of t x { Mean effect. steam t x { stroke t 
piston in inches press. per sq. in. in feet 


Diameter of wheel in feet. 


Leading: American Types of Locomotive for Freight and 
Passenger Service. 


1. The eight-wheel or “‘ American ”’ passenger type, having four coupled 
driving-wheels and a four-wheeled truck in front. 

2. The ‘‘ten-wheel”’ type, for mixed traffic, having six coupled drivers and 
a leading four-wheel truck. 

3. The ‘‘ Mogul”? freight type, having six coupled driving-wheels and a 
pony or two-wheel truck in front. 

4. The ‘Consolidation’ type, for heavy freight service, having eight 
coupled driving-wheels and a pony truck in front, 

Besides these there is a great variety of types for special conditions of 
service, as four-wheel and six-wheel switching-engines, without trucks; the 
Forney type used on elevated railroads, with four coupled wheels under the 
engine and a four-wheeled rear truck carrying the water-tank and fuel; 
locomotives for local and suburban service with four coupled driving- wheels, 
with-a two-wheel truck front and rear, or a two-wheel truck front and a 
four-wheel truck rear, etc. ‘‘Decapod”’ engines for heavy freight service 
have ten ccupled driving-wheels and a two-wheel truck in front. 





= tractive power. 


‘Classification of Locomotives (Penna. R. R. Co., 1900).—Class 
A, two pairs ot drivers and no truck. Class B, three pairs of drivers and no 
truck. Class C, four pairs of drivers and no truck. Class D, two pairs of 
drivers and four-wheel truck. Class EH, two pairs of drivers, four-wheel 
truck, and trailing wheels. Class F, three pairs of driving-wheels and two- 
wheel truck. Class G, three pairs of drivers and four-wheel truck. Class H, 
four pairs of-drivers and two-wheel truck. Class A is commonly called a 
“four-wheeler”’; B, a * six-wheeler’’ ; D, an ‘‘ eight-wheeler,’’ or ‘‘ Ameri- 
can” type; E, ‘Atlantic’? type; F, ‘‘Mogul”’’; G, ‘*ten-wheeler’’; H, 
* Consolidation.” 


Steam-distribution for High-speed Locomotives, 
(C. H. Quereau, Eng’g News, March 8, 1894.) 


Balanced Valves.—Mr. Philip Wallis, in 1886, when Engineer of Tests for 
the C., B. & Q. R. R., reported that while 6 H.P. was required to work un- 
balanced valves at 40 miles per hour, for the balanced valves 4.2 H.P, only 
was necessary, 


STEAM-DISTRIELUTION FOR LOCOMOTIVES. 859 


Effect of Speed on Average Cylinder-pressure.— Assume that a locomotive 
has a train in motion, the reverse lever is placed in the running notch, and 
the track is level; by what is the maximum speed limited? The resistance 
of the train and the load increase, and the power of the locomotive de- 
creases with increasing speed till the resistance and power are equal, when 
the speed becomes uniform. The power of the engine depends on the 
average pressure in the cylinders. Even though the cut-off and boiler- 
pressure remain the same, this pressure decreases as the speed increases; 
because of the higher piston-speed and more rapid valve-travel the steam 
has a shorter time in which to enter the cylinders at the higher speed. The 
following table, from indicator-cards taken from a locomotive at varying 
speeds, shows the decrease of average pressure with increasing speed: 


Miles per hour......... Rieke biota 'e Sie 46 51 51 53 54 57 60 66 
Speed, revolutions. ........... Red © 24877) 248)) 258 263 277 a 292 ost 
Average pressure per sq. in.: 
A CLULAL ink oe anes ahi Peele bs 44.0..47,30143,0 41235042, 5 eared cos 
Caloulated ic ve ceteccclaceintie, conic 46.5 46.5 44.7 48.8 41.6 39.5 35.9 


The ‘‘average pressure calculated’’ was figured on the assumption that 
the mean effective pressure would decrease in the same ratio that the speed 
increased. The main difference lies in the higher steam-line at the lower 
speeds, and consequent higher expansion-line, showing that more steam 
entered the cylinder. The back pressure and compression-lines agree quite 
closely for all the cards, though they are slightly better for the slower 
speeds. That the difference is not greater may safely be attributed to the 
large exhaust-ports, passages, and exhaust tip, which is 5 in. diameter. 
These are matters of great importance for high speeds. . 

Boiler-pressure.—Assuming that the train resistance increases as the speed 
after about 20 miles an hour is reached, that an average of 50 lbs. per sq. 
in. is the greatest that can be realized in the cylinders of agiven engine at 40 
miles an hour, and that this pressure furnishes just sufficient power to keep 
the train at this speed, it follows that, to increase the speed to 50 miles, the 
mean effective pressure must be increased in the same proportion. To in- 
crease the capacity for speed of any locomotive its power must be increased, 
and at least by as much as the speed is to be increased. One way to acconi- 
plish this is to increase the boiler-pressure. That this is generally realized, 
isshown by the increase in boiler-pressure in the last ten years. For twenty- 
three single-expansion locomotives described in the railway journals this 
year the steam-pressures are as follows: 3, 160 lbs.; 4, 165 lbs.; 2, 170 lbs.; 
13, 180 lbs.; 1, 190 lbs. 

Valve-travez. — An increased average cylinder-pressure may also be 
obtained by increasing the valve-travel without raising the boiler-pressure, 
and better results will be obtained by increasing both. The longer travel 
gives a higher steam-pressure in the cylinders, a later exhaust-opening, 
later exhaust-closure, and a larger exhaust-opening—all necessary for high 
speeds and economy. I believe that a 20-in. port and 61%-in. (or even ‘-in.) 
travel could be successfully used for high-speed engines, and that frequently 
by so doing the cylinders could be economically reduced and the counter- 
balance lightened. Or, better still, the diameter of the drivers increased, 
securing lighter counterbalance and better steam-distribution, | 

Size of Drivers.—Economy will increase with increasing diameter of 
drivers, provided the work at average speed does not necessitate a cut-off 
longer than one fourth the stroke. The piston-speed of a locomotive with 
62-in. drivers at 55 miles per hour is the same as that of one with 68-in. 
drivers at 61 miles per hour. , ; 

Steam-ports.—The length of steam-ports ranges from 15 in. to 23 in., and 
has considerable influence on the power, speed, and economy of the loco- 
motive. In cards from similar engines the steam-line of the card from the 
engine with 23-in. ports is considerably nearer boiler-pressure than that of 
the card from the engine with 1714-in. ports. That the higher steam-line is 
due to the greater length of steam-port there is little room for doubt. The 
93-in. port produced 531 H.P. in an 181-in. cylinder at a cost of 23.5 Ibs. of 
indicated water per I.H.P. per hour. The 1714-in. port, 424 H.P., at the rate 
of 22.9 lbs. of water, in a 19-in. cylinder. am 

Allen Valves.—There is considerable difference of opinion as to the advan- 
tage of the Allen ported-valve (See Eng. News, July 6, 1893.) " 

Speed of Railway Trains,—In 1834 the average speed of trains on 
the Liverpool and Manchester Railway was twenty miles an hour; in 18388 it 


859a LOCOMOTIVES. 


was twent;-five miles an hour. But by 1840 there were engines on the Great 
Western Raifway capable of running fifty miles an hour with a train, and 
eighty miles an hour without. (Trans. A. S. M. E., vol. xiii., 363.) 

The limitation to the increase of speed of heavy locomotives seems at 
present to be the difficulty of counterbalancing the reciprocating parts. The 
unbalanced vertical component of the reciprocating parts causes the pres- 
sure of the driver on the rail to vary with every revolution. Whenever the 
speed is high, it ic of considerable magnitude, and its change in direction is 
so rapid that the resulting effect upon the rail is not inappropriately called 
a ‘‘hammer blow.”? Heavy rails have been kinked, and bridges have been 
shaken to their fall under the action of heavily balanced drivers revolving 
at high speeds. The means by which the evil is to be overcome has not yet 
been made clear. See paper by W. F. M. Goss, Trans. A. 8S. M. E.. vol. xvi. 

Engine No, 999 of the New York Central Railroad ran a mile in 32 seconds 
equal to 112 miles per hour, May 11, 1893. 





Speed in miles t __ circum. of driving-wheels in in. X no. of rev. per min. x 66 


per hour = 63,360 
= diam, of driving-wheels in in. < no. of rev. per min. X .003 
(approximate, giving result 8/10 of 1 per cent too great). 


Formule for Curves, (Baldwin Locomotive Works.) 


Approximate Formula for Radius. Approximate Formula for Swing. 
eae as Wal tig 
ree RE hae raat en . 
R = radius of min. curve in feet. W = rigid wheel base. 
P=play of driving-wheels in Tf = total “t i 
decimals of 1 ft. R = radius of curve, 
W = rigid wheel-base in feet. ; S = swing on each side of centre,.”’ © 


Performance of a High-speed Locomotive,—The Baldwin 
eompound locomotive No. 1027, on the Phila. & Atiantic City Ry., in July and 
August, 1897, made a record of which the following is a summary: 

On July 2da train was placed in service scheduled to make the run 
between the terminal cities in 1 hour. Allowing 8 minutes for ferry from 
Philadelphia to Camden, the time for the 5514 miles from the latter point to 
Atlantic City was 52 minutes, or at the rate of 64 miles per hour. Owing to 
the inability of the ferry-boats to reach Camden on time, the train always 
left late, the average detention being upwards of 2 minutes. This loss was 
invariably made up, the train arriving at Atlantic City ahead of time, 2 
minutes on an average, every day. For the 52 days the train ran, from July 
2d to August 3lst, the average time consumed on the run was 48 minutes, 
equivalent to a uniform rate of speed from start to stop of 69 miles per hour. 
On July 14th the run from Camden to Atlantic City was made in 4614 min., 
an average of 71.6 miles per hour for the total distance. On 22 days the 
train consisted of 5 cars and on 30 days it was made up of 6, the weight of 
ears being as follows: combination car, 57,200 lbs.; coaches, each, 59,200 lbs. ; 
Pullman car, 85,500 lbs. 

The general dimensions of the locomotive are as follows: cylinders, 13 and 
22 x 26in.; height of drivers, 8414 in.; total wheel-base, 26 ft. 7 in.; driving- 
wheel base, 7 ft..a in.; length of tubes, 13 ft.; diameter of boiler, 5834 in.; 
diameter of tubes, 134 in.; number of tubes, 278; length of fire-box, 113% in.; 
width of fire-box, 96 in.,; heating-surface of fire-box, 136.4 sq. ft.; heating- 
surface of tubes, 1614.9 sq. ft.; total heating-surface, 1835.1 sq. ft.; tank 
capacity, 4000 gallons; boiler-pressure, 200 Ibs. per sq, in.; total weight of 
engine and tender, 227,000 lbs.; weight on drivers (about), 78,600 Ibs, 

Locomotive Link Motion.—Mr. F. A. Halsey, in his work on 
*‘ Locomotive Link Motion,” 1898, shows that the location of the eeccentric- 
rod pins back of the link-are and the angular vibrations of the eccentric- 
rods introduce two errors in the motion which are corrected by the angular 


LOCOMOTIVE LINK MOTION. 8596 


vibration of we connecting-rod and by locating the saddle-stud back of the 
link-arec. He holds that itis probable that the opinions of the critics of the 
locomotive link motion are mistaken ones, and that it comes little short of 
all that can be desired for a locomotive valve motion. The increase of lead . 
from full to mid gear and the heavy compression at mid gear are both 
. advantages and not defects. The cylinder problem of a locomotive is en- 
tirely different from that of a stationary engine. With the latter the 
problem is to determine the size of the cylinder and the distribution of 
steam to drive economically a given load ata given speed. With locomotives 
the cylinder is made of a size which will start the heaviest train which the 
adhesion of the locomotive will permit, and the problem then is to utilize 
that cylinder to the best advantage at a greatly increased speed, but under 
a greatly reduced mean effective pressure. 
Negative lead at full gear has been used in the recent practice of some 
railroads. The advantages claimed are an increase in the power of the 
' engine at full gear, since positive lead offers resistance to the motion of the 
piston ; easier riding; reduced frequency of hot bearings; and a’slight gain 
in fueleconomy. Mr. Halsey gives the practice as to lead on several roads 
as follows, showing great diversity ; 





Full Gear Full Gear Reversing 
Forward, in. Back, in, Gear, in. 
New York, New Haven & 

ERAT CL ORGMNE Sie ie tesco oh sco ce 1/16 pos. 14 neg. 14 pos. 
Maire Central.: ya. 5222. ek: 0 LAMen wy Y le Fos...) Wake pedles 
Lilinois. Centrale ak... 1/32 pos. Bi. oe a abt, 3/16 
RAKE SROVeL eet oes eset 1/16 neg. 9/64 neg. 5/16 pos. 
Chicago Great Western..... 0 0 3/16 to 9/16 
Chicago & Northwestern.... OY LOINC anal late ate eenes cferonss siete Y4 pos. 





The link-chart of a locomotive built in 1897 by the Schenectady Locomotive 
Works for the Northern Pacifie Ry. is as follows: 











Lead, Valve Open. Cut-off. 
Forward Rearward Forward | Rearward | Forward Rearward 
Stroke, in. | Stroke, in. | Stroke, in.| Stroke, in. | Stroke, in. | Stroke, in. 
“see — 1 1% 1% 22 9/16 2256 
— ye _ {999 yt P16 1 7/16 21 21 
+ 1/32 + 1/32 1 1/16 1 1/16 19 19 
3/382 3/32 23/32 23/82 16 16 
\ \% 14 V4 13 1344 
9/64 9/64 32 36 10 10 
5/82 s. 5/32 Ss. 5/16 5/16 8 8 
5/32 5/32 A 4 6 6 
5/32 f. 5/32 f. 7/82 7/82 4 4 1/16 





Cylinders 20 ~ 26 in., driving-wheels 69 in., six coupled wheels, main rods 
'126% in., radius of link 40 in., lap 144 in., travel 6 in., Allen valve. 


DIMENSIONS OF SOME LARGE AMERICAN 
LOCOMOTIVES, 1893. 


The four locomotives described below were exhibited at the Chicago 
Exposition in 1893. The dimensions are from Engineering News, June, 1893. 
The first. or Decapod engine, has ten-coupled driving-wheels. It is one of 
the heaviest and most powerful engines ever built for freight service. The 
Philadelphia & Reading engine is a new type for passenger service, with four- 
coupled drivers, The Rhode Island engine has six drivers, with a 4-wheel 
leading truck and a 2-wheel trailing truck. These three engines have all 
compound cylinders. The fourth is a simple engine, of the standard Ameri- 
can 8 wheel type, 4 driving-wheels, and a 4-wheel truck in front. This 
engine holds the world’s record for speed (1893) for short distances, having 
run a mile in 32 seconds. 


Cylinders: 





EDC) AIN: ale selon a tate, epterats ic 16 x 28 in. 
DED MOV A see Sere cea eer cue otk Ou ag 
Distance centre to centre.| ‘ft. 5 
Piston-rod, diam..... ... 4 in. 
Connecting-rod, length... 8 7/16” 
Steam-ports.............. 2814 x 2 in. 
Exhaust-ports.... .....-. 2814 x8 ‘ 
Slide- valves, out. lap, h.p. % in 
out. lap, Lp.. be ‘ 
a ie ATVepLA OS VED. sist. tor iste kates elt 
*f in. lap, lp... ae oneRMEGY. S 
See rt max. travel. 6 in 
+t re lead, b.p..... 1/16 in. 
of ca leads lips .: 5/16 ** 
Boiler—tType.. Straight 
Diam. of barrel inside... .| 6 ft. 24% in 
Thickness of barrel- -plates 34 in. 
Height from rail to centre 
INL OMB MOT Si akiicsie ty evs Sees 8ft.0 in. 
Length of smoke-box..... Dee ivatos 
Working steam-pressure..| 180 Ibs 
Firebox—type............. Wootten 
Length inside,............ 10’ 11 9/16” 
WVAt Rese ite 228. be. 8 ft. 214 in 
Depth at front .......... Gat 
Thickness of side plates..| 5/16 in, 
** back plate. . 5/16 
Thickness of bic ag -sheet. Be 
7 e P % 46 
Graté-areat Pee... 89.6 sq. ft. 
Stay-bolts, diam., 11g in. -|pitch, ae in, 
Tubes—irauiMene eke. 
Pitch.. Riichdcad 984 | in 
Diam., ‘outside... 2 


Length betw’n tube- -plates deft; Adin: 


- Heating-surface ; 
Tubes, exterior .......... 
Fire-box da kate Oe eee 
Miscellaneous: 
Exhaust-nozzle, diam... 
Smokestack, smal’st diam. 
height from 
rail to top... <>... dese. 


2,208.8 ft. 
234.3 * 


5 in. 
fetbGns* 


13 x 24 in. 
22 x B46 


7 ft. 414 in. 


316 in. 


8 ft. 04 in. 


24x 114 in. 


24x 414 * 


% in. 
5g ee. 


(neg.) 1g in. 


None 
5 in. 


be 


eset eeeeoes- 


sisiel piers "eto 


180 lbs. 
Wootten 
9ft.6 in. 
8 ee 0g ee 
3 ee 234 6é 

5/16 in. 

b/16GS 

5/16, se 


76.8 sq. ft. 


2 1/16 in. 


114 in. 
10 ft. 0 in. 


1,262 sq. ft. 


66 


1733S 


514 in. 
1 ft. 6 in. 


15“ 614 “ |14 ft. 034 in. 


one 21 x 26 


31% in. 





860 LOCOMOTIVES. 
Baldwin. | Baldwin. N.Y.C.& 
N.Y... E,|) Phila... | Rhode Isl. | H.R, BR. 
& Locomoti’e Empire 
W.R.R. [Read R.R| Works. State 
Decapod | Express Heavy | Express, 
Freight. | Passenger.| EXPress. | No, 999. 
Running-gear: 
Driving-wheels, diam wast d4efte Qin. w|eGteG ink, (6 LeGineye 7th. 2 ia 
Truck ex TAR Ree tS eiieG TF 4 TEOMS Pie OE Bede oa 
Journals, driving-axles...| 9 x10in. | 84x12in. |8 x"834in.J9 x 1214in, 
nf truck- nese | O.  K10 el Ole x 10K (ble e110 Saige lONras 
- tender- ‘ 44x 9 *S | dex 8S [4lgx 8 * Idlgx 8 * 
W heel-base: 

MD VY LENO pods sua atcho ts B's Wed alle eee 18 ft. 10 in.] 6 ft. 10in.| 18 ft.6 in.| 8 ft. 6 in. 
Total engine.......2...2.. eb Sa B Saeed Ei Ak 29 oo OF hein Oss eo toate 
nae LgLONGEY stats theyre cies Sk 16 Skee Setts e160 Ordo OSS teeta = 

‘engine and tender...| 53 ‘* 4 ‘* | 47 *¢ 3 ** | 50 “* 684 ‘* 147 ** 81g * 
Wt. in working-order: 
On drivers. ....-+.| 170,000 Ibs.| 82,700 1bs.} 88,500 Ibs. 84,000 lbs. 
On truck-wheels........ e OQ: 47,000 se 54,500 *‘ 40,000 ** 
Engine, total.......:... 192,500 -**'*} 129,700 * 143,000 ‘* | 124,000 ‘ 
PDGUG OTS gaan niss tm esrasateirnrens HOU O mass 80,573 ** 75,000 ‘* 80,000 * 
Engine and tender, loaded| 310,000 ‘* | 210,273 ‘* | 218,000 ‘* | 204,000 ‘ 


19 x 24 in, 
“6 ft. 5in. 
33@ in 


10 ft. 3a in. 8 ft. 114 in. 


114 x 20 and 
114 x 25 
3 x 20 in, 


« (ele See cl dee ® 


144 x 18 in. 


234 x 18 * 
lin. 


Wagon top | Wagon top 


5 ft. 2 in. 


4 ft. 9 in. 


5g in. 9/16 in. 
8 ft. 11 in. |7 ft. 1114 in, 
6 ee i ve se 8 ae 
200 lbs. 190 Ibs. 
Radial stay| Buchanan 
10 ft. O in.| 9 ft. 63¢ in, 
D> 93 ee 3 oe 4% “e 
6 a3 1034 ee 6 “a 144 ae 
5/16 in 0/16 in. 
36 be 5/16 be 
34 66 38 at 
1% ee % (77 
28 sq. ft. | 30.7 sq. ft. 
4 in. 4 in. 
272 268 
234g OO AAC. AEE, 
Qa 2in 


seer ewer oes. 


ce ee ewes wees 


ee we ee ewe 


1 ft. 3in. 
15 oe 9 77 


in.| 12 ft. O in. 


1,697 sq. ft. 
93 be oe 
314 in. 

1 ft. 34 in, 

14‘ 10 


861 





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. 


DIMENSIONS OF AMERICAN LOCOMOTIVES. 


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9 FL | O9T TAI 
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G1. | = OSE & Le-<79T 
O9L | FEST 
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-SUIJBIFT eqny, 


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‘6° TPT 


seers 


£681 
G OFT 


gcT 
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G TPL 


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OSS9IT |000°661 
00096 |000'6e1 
O0S*TOL 00S" 281 
OOP*SIT |000'S8T 
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0OE‘OST |008‘OST 
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00°86  |000'STT 
000°E8 |000‘68I 
000°00E {000°SEI 
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000°30L |000°88T 
000°66 |000°¢ET 
000‘00T |009°2é1 
00S°98 |086'6eL 
OPTS  |OST 96 
00999 |e 
00°68 000‘ SBT 
000°T8 |000‘E3T 
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96 X 0G PUB ZI 
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86 x 1G PUB OT 
9% X 83 PUB OZ 
98 X 18 PUB ET 

Po X61 

9% X 0% 

98 X18 

Fo X61 

8B x & 

96 x 61 
9% x 1g pus TZ 
FSX 6G PUB OZ 
PBX GS Pu Sl 
PSX PS PUB FT 
FSX GS PUB EL 
FS X OF PUB OZ 
FBX 6G PUB 0S 

FB X 0% 

$a x HQT 

bE x BI 

Fe x BT 

£3 X61 

FE X61 

FG x AQT 

93 X 18 

£3 x 61 

FS x OT 


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862 LOCOMOTIVES. 


Dimensions of Some American Locomotives,—tThe table on 
page 861 is condensed from one given by D. L. Barnes, in his paper on 
“ Distinctive Features and Advantages of American Locomotive Practice,”’ 
Trans. A.S.C.E., 1898. The formula from which column marked ‘‘ Ratio ot 
cylinder-power to weight available for adhesion”’ is calculated as follows: 


2 x eylinder area X boiler-pressure x stroke 
Weight on drivers X diameter of driving-wheel” 


(Ratio of cylinder-power of compound engines cannot be compared with 
that of the single-expansion engines. ) 

Where: the boiler-pressure could not be determined from. the description 
of the locomotives, as given by the builders and operators of the locomotives, 
it has been assumed to be 160 lbs. per sq. in. above the atmosphere. 

For compound locomotives. the figures in the last column of ratios are 
based on the capacity of the low-pressure cylinders only, the volume of the 
high-pressure being omitted. This has been done for the purpose of com- 
parison, and because there is no accurate simple way of comparing the 
cylinder-power of single-expansion and compound locomotives. 


Dimensions of Standard Locomotives on the N. ¥. ©. & 
H. R. R. and Penna. R. R., 1882 and 1893. 


C. H. Quereau, Hng’g News, March 8, 1894. 
N.Y. GC; & ER. RB: Pennsylvania R. R. 














Through Through Through Through 
Passenger.| Freight. | Passenger. | Freight. 


1882. | 1893. | 1882. | 1893. | 1882. | 1893. | 1882. | 1893. 





Grate surface, sq. ft.... | 17.87) 27.3 | 17.87) 29.8 | 17.6. | 33.2 | 28. | 31.5 


Heating surface, sq. ft..| 1353} 1821 | 1353 | 1763 | 1057 | 1583 | 1260 | 1498 
Boiler, diam:, in. ........ 50) 58 50 58 50 57 54 60 
Driver, diam., in ....... 70| 78, 86) 64 67 62 78 50 50 
Steam-pressure, lbs.. .. T5Or 180") 150° FTES 17 "125 175 | :125 |; 140 


Cylin., diam. and stroke. |17X24|19 x 24} 17X 24|19 26] 17 x 24/183 x 24/20 24/20 24 

Valve-travel, ins ........ 5144; 546) 514) 5384; 5 54| 5 5i 

Lead at full gear, ins....}| 1/16} 1/16 | 1/16 | 1/16 | 1/16 0 Ye | 1/16 
z : 1 : 








Outside lap 2-25... 22h «- wl #1 % % 34 4 34 
Inside lap or clearance... O; 0. | 17160 |.3/3822 @ | Yel | 1/321 | 1/327 
Steam-ports, length..... 15%} 18 1514%4| 18 16 17144) 16 16, 
es ca wid thee. . 3 144) 114 1144| 114 144; 1%) 114) 156 
Type of engine...... ... Am, | Am.! Am.|Mog.! Am. | Am. 'Cons.'Cons. 





Indicated Water Consumption of Single and Compound 
Locomotive Engines at Varying Speeds. 


C. H. Quereau, Hing’g News. March 8, 1894. 





—- —~ 




















Two-cylinder Compound. Single-expansion, 
Speed Water . 
Revolu- : ; Revolu- | Miles per 
: miles per | per I.H.P. : s Water, 
tions. hour. per hour. tions. Hour, 
100.to 150 | 21 to 31 18.33 Ibs, 151 31 21.70 
150.‘ 200 | 31 ‘ 41 TBO ee 219 45 20.91 
20082 250" | 4h S 61 1 < 253 52 20.52 
250: ‘* 275; ‘5L % 56 20.4 * 307 63 20.23 
321 66 20.01 


It appears that the compound engine is the more economical at low speeds, 
the economy decreasing as the speed increases, and that the single engine 
invreases in economy, with increase of speed within ordinary limits, becom- 
ing moe economical] than the compound at speeds of more than 50 miles 

er hour. 

. The C., B. & Q. two-eylinder compound, which was about 30% less eco- 
nomical than simple engines of the same class when tested in passenger 
service, has since been shown to be 15% more economical in freight service 


~= 


ADVANTAGES OF COMPOUNDING. 863 


than the best single-expansion engine, and 29% more economical than the 
average record of 40 simple engines of the same class on the same division. 

Indicator-tests of a Locomotive at High Speed. (Locomo- 
tive Eng’g, June, 1893.)—Cards were taken by Mr. Angus Sinclair on the 
locomotive drawing the Empire State Express. 


RESULTS OF INDICATOR-DIAGRAMS. 
Card No. Revs. . Miles yup. | caraNo, Revs, . Miles. pup. 


per hour. per hour. 
1 160 37.1 648.3 4 304 70.5 7 
2 260 60.8 728 8 296 68.6 972 
3 190 44 551 9 300 69.6 1,045 
4 250 58 891 10 304 70.5 = 1,059 
5 260 60 960 11 340 "8.9 1,120 
6 298 69 983 12 310 74.9», 1,026 


The locomotive was of the eight-wheel type, built by the Schenectady 
Locomotive Works, with 19 x 24in. cylinders, 78-in. drivers, and a large 
boiler and fire-box. Details of important dimensions are as follows; 
Heating-surface of fire-box, 150.8 sq. ft.; of tubes, 1670.7 sq. ft.; of boiler, 
1821.5.sq ft. Grate area, 27.3 sq. ft. Fire-box: length, 8 ft.; width, 3 ft. 4% 
in. Tubes, 268; outside diameter, 2in. Ports: steam, 1814 in.; exhaust, 
18 < 284in. Valve-travel, 5144 in. Outside lap, 1 in.; inside lap, 1/64 in. 
Journals: driving-axle, 8144 x 1014 in.; truck-axle, 6 < 10 in. 

The train consisted of four coaches, weighing, with estimated load, 340,000 
lbs. The locomotive and tender weighed in working order 200,000 lbs,, 
making the total weight of the train about 270 tons. During the time that 
the engine was first lifting the train into speed diagram No.1 was taken. It 
shows a mean cylinder-pressure of 59 lbs. According to this, the power 
exerted on the rails to move the train is 6553 lbs., or 24 lbs. per ton. The 
speed is 37 miles an hour. When a speed of nearly 60 miles an hour was 
reached the average cylinder-pressure is 40.7 lbs., representing a total 
traction force of 4520 lbs., without making deductions for internal friction. 
If we deduct 10% for friction, it leaves 15 lbs. per ton to keep the train going 
at the speed named. Cards 6, 7, and 8 represent the work of keeping the 
train running 70 miles an hour. They were taken three miles apart, when 
the speed was almost uniform. The average cylinder-pressure for the three 
cards is 47.6 Ibs. Deducting 10% again for friction, this leaves 17.6 lbs. per 
ton as the power exerted in keeping the train up to a velocity of 70 miles. 
Throughout the trip 7 lbs. of water were evaporated per lb. of coal. The 
work of pulling the train from New York to Albany was done on a coal con- 
sumption of about 3814 lbs. per H.P. per hour. The highest power recorded 
was at the rate of 1120 H.P. 

Locomotive-testing Apparatus at the Laboratory of 
Purdue Wniversity. (W. F. M. Goss, Trans. A. S. M.E., vol. xiv. 826.)— 
The locomotive is mounted with its drivers upon supporting wheels which 
are carried by shafts turning in fixed bearings, thus allowing the engine to 
be run without changing its position asa whole. Load is supplied by four 
friction-brakes fitted to the supporting shafts and offering resistance to the 
turning of the supporting wheels. Traction is measured by a dynamgmeter 
attached to the draw-bar. The boiler is fired in the usual way, 4nd an 
exhaust-blower above the engine, but not in pipe connection with it, carries 
off all that may be given out at the stack. 

A Standard Method of Conducting Loconotive-tests is given in a report 
by a Committee of the A.S. M. E. in vol. xiv. of the Transactions, page 1312. 

Waste of Fuel in Locomotives,—in American practice economy 
of fuel is necessarily sacrificed to obtain greater economy due to heavy 
train-loads. D. L. Barnes, in Hing. Mag., June, 1894, gives a diagram showing 
the reduction of efficiency of boilers due to high rates of combustion, from 
which the following figures are taken: 


Lbs. of coal per sq. ft. of grate per hour...... 12°40  <80*) 120% F160 eng 
Per cent efficiency of boiler....... ............ 80. 1.75 <'67e 458 51 43 


A rate of 12. lbs. is given as representing stationary-boiler practice, 40 lbs. 
is English locomotive practice, 120 lbs. average American, and 200 lbs. max- 
imum American, locomotive practice. ; 

Advantages of Compounding.—Report of a Committee of the 
American Railway Master Mechanies’ Association on Compound Locomotives 
(Am. Mach., July 3, 1890) gives the following summary of the advantages 
gained by compounding: (a) It has achieved a saving in the fuel burnt 
averaging 18% at reasonable boiler-pressures, with encouraging possibilities 


864 LOCOMOTIVES. 


of further improvement in pressure and in fuel and water ecoriomy. (b) It 
has lessened the amount of water (dead weight) to be hauled, so that (c) the 
tender and its load are materially reduced in weight. (d) It has increased 
the possibilities of speed far beyond 60 miles per hour, without unduly 
straining the motion, frames, axles, or axle-boxes of the engine. (e) It has 
increased the haulage-power at full speed, or, in other words, has increased 
the continuous H.P. developed, per given weight of engine and boiler. (f) In 
some classes has increased the starting-power. (g) It has materially lessened 
the slide-valve friction per H.P. developed. (h) It has equalized or distrib- 
uted the turning force on the crank-pin, over a longer portion of its path, 
which, of course, tends to lengthen the repair life of the engine. (7) In the 
two-cylinder type it has decreased the oil consumption, and has even done 
so in the Woolf four-cylinder engine. (7) Its smoother and steadier draught 
on the fire is favorable to the combustion of all kinds of soft coal; and the 
sparks thrown being smaller and less in number, it lessens the risk to prop- 
erty from destruction by fire. (k) These advantages and economies are 
gained without having to improve the man handling the engine, less being 
left to his discretion (or careless indifference) than in the simple engine. (l) 
Valve-motion, of every locomotive type, can be used in its best working and 
most effective position. (m) A wider elasticity in locomotive design is per- 
mitted; as, if desired, side-rods can be dispensed with, or articulated engines 
of 100 tons weight, with independent trucks, used for sharp curves on moun- 
tain service, as suggested by Mallet and Brunner, 

Of 27 compound locomotives in use on the Phila. and Reading Railroad (in 
1892), 12 are in use on heavy mountain grades, and are designed to be the 
equivalent of 22 x 24 in. simple consolidations; 10 are in somewhat lighter 
service and correspond to 20 x 24 in. consolidations; 5 are in fast passenger 
service. Themonthly coal record shows: 


q Gain in Fuel 
Class of Engine, No. Economy. 
Mountalh locomotives. 's3 0.5000. eee Cesc 312 25% to 30% 
Heavy freight service. io. c..c. cc. deep cece ces 10 12% to 17% 
BAST PASSENLCH toi ccie see muttlctec a bP its A A at 5 9% to 11% 


(Report of Com. A. R. M. M. Assn. 1892.) For adescription of the various 
types of compound locomotive, with discussion of their relative merits, see 

aper by A. Von Borries, of Germany, The Development of the Compound 
Fcomative, Trans. A. S. M. E. 1893, vol. xiv., p. 1172. 

Counterbalancing Locomotives.—tThe following rules, adopted 
by different locomotive-builders, are quoted in a paper by Prof, Lanza 
(Trans. A. S. M. E., x. 302): 

A. ‘*‘ For the main drivers, place opposite the crank-pin a weight equal to 
oue half the weight of the back end of the connecting-rod plus one half the 
weight of the front end of the connecting-rod, piston, piston-rod, and cross- 
head. For balancing the coupled wheels. place a weight opposite the crank- 
pin equal to one half the parallel rod plus one half of the weights of the 
front end of the main-rod, piston, piston-rod, and cross-head. The centres 
of gravity of the above weights must be at the same distance from the 
axles ag the crank-pin.”’ 

B. The rule given by D. K. Clark: ‘‘ Find the separate revolving weights 
of crank-pin boss, coupling-rods, and connecting-rods for each wheel. also 
the reciprocating weight of the piston and appendages, and one half the 
connecting-rod, divide the reciprocating weight equally between each wheel 
and add the part so allotted to the revolving weight on each wheel: the 
sums thus obtained are the weights to be placed opposite the crank-pin, and 
at the same distance from the axis. To find the counterweight to be used 
when the distance of its centre of gravity is known, multiply the above 
weight by the length of the crank in inches and divide by the given dis- 
tance.” This rule differs from the preceding in that the same weight is 
placed in each wheel. 


sx(e-¥) 





C“W= , in which S = one half the stroke, G = distance 


from centre of wheel to centre of gravity in counterbalance, w = weight at 
crank-pin to be balanced, W = weight in counterbalance, f = coefficient of 
friction so called, = 5 in ordinary practice. The reciprocating weight is 
found by adding together the weights of the piston, piston-rod, cross-head, 
and one half of the main rod. The revolving weight for the main wheel is 
found by adding together the weights of the crank-pin hub, crank-pin, one 


PETROLEUM-BURNING LOCOMOTIVES. 865 


half of the main rod, and one half of each parallel-rod connecting to this 
wheel; to this add the reciprocating weight divided by the number of 
wheels. The revolving weight for the remainder of the wheels is found in 
the same manner as for the main wheel, except one half of the main rod is 
not added. The weight of the crank-pin hub and the counterbalance does 
not include the weight of the spokes, but of the metal inclosing them. This 
ealculation is based for one cylinder and its corresponding wheels.”’ 

D. ** Ascertain as nearly as possible the weights of crank-pin, additional 
weight of wheel boss for the same, add side rod, and main connections, 
piston-rod and head, with cross-head on one side: the sum of these multi- 
plied by the distance in inches of the centre of the crank-pin from the centre 
of the wheel, and divided by the distance from the centre of the wheel to 
the common centre of gravity of the countorweights, is taken for the total 
counterweight for that side of the locomotive which is to be divided among 
the wheels on that side.” 

E. ‘‘ Balance the wheels of the locomotive with a weight equal to the 
weights of crank-pin, crank-pin hub, main and parallel rods, brasses, etc., 
plus two thirds of the weight of the reciprocating parts (cross-head, piston 
and rod and packing). 

F. “Balance the weights of the revolving parts which are attached to 
each wheel with exactness, and divide equally two thirds of the weights of 
the reciprocating parts between all the wheels. One half of the main rod is 
computed as reciprocating, and the other as revolving weight.” 

See also articles on Counterbalancing Locomotives, in R. R. & Eng. Jour., 
March and April, 1890; Trans. A.S. M. E., vol. xvi, 305; and Trans. Am. Ry. 
Master Mechanics’ Assn., 1897. W.H. Dalby’s book {on the ‘ Balaucing of 
Engines ’’ (Longmans, Green & Co., 1902) contains a very full discussion of 
this subject. 

Maximum Safe Load for Steel Tires on Steel Rails. 
(A. 8S. M. E., vii., p. 786.)—Mr. Chanute’s experiments led to the deduction 
that 12,000 Ibs. should be the limit of load for any one driving-wheel. Mr. 
Angus Sinclair objects to Mr. Chanute’s figure of 12,000 lbs., and says that 
a locomotive tire which has a light load on it is more injurious to the rail 
than one which hasa heavy load. In English practice 8 and 10 tons are 
safely used. Mr. Oberlin Smith has used steel castings for cam-rollers 4 in. 
diam. and 3 in. face, which stood well under loads of from 10,000 to 20,000 
lbs. Mr. C. Shaler Smith proposed a formula for the rolls of a pivot-bridge 


which may be reduced to the form: Load = 1760 x face X //diam., all in 
lbs. and inches. 

See dimensions of some large American locomotives on pages 860 and 861, 
On the *‘ Decapod”’ the load on each driving-wheel is 17,000 lbs., and on 
“No. 999,’ 21.000 Ibs. 

Narrow-zgauge Railways in Manufacturing Works,— 
A tramway of 18 inches gauge, several miles in length, is in the works of 
the Lancashire and Yorkshire Railway. Curves of 13 feet radius are used. 
The locomotives used have the following dimensions (Proc. Inst. M. E., July, 
1888): The cylinders were 5 in. diameter with 6in. stroke, and 2 ft. 314 in. 
centre to centre. The wheels were 1614 in. diameter, the wheel-base 
2ft.9in.; the frame 7 ft. 414 in. long, and the extreme width of the engine 
3 feet. The boiler, of steel, 2 ft.3in. outside diameter and 2 ft. long between 
tube-plates, containing 55 tubes of 13¢ in. outside diameter; the fire-box, of 
iron and cylindrical, 2 ft. 3 in. long and 17 in. inside diameter. The heating- 
surface 10.42 sq. ft. in the fire-box and 36.12 in the tubes, total 46.54 sq. ft.; 
the grate-area, 1.78 sq. ft.; capacity of tank, 2614 gallons; working-pressure, 
170 lbs. per sq. in.; tractive power, say, 1412 lbs., or 9.22 lbs. per lb. of effec- 
tive pressure per sq. in. on the piston. Weight, when empty, 2.80 tons; 
when full and in working order, 3.19 tons. 

For description of a system of narrow-gauge railways for manufactories, 
see circular of the C. W. Hunt Co., New York. 

Light Locomotives.—for dimensions of light ocomotives used for, 
mining, etc., and for much valuable information concerning them, see cata. 
logue of H. K. Porter & Co., Pittsburgh. 

Petroleu™-burning Locomotives. (From Clark’s Steam-en- 
gine.)—The combustion of petroleum refuse in locomotives has been success 
fully practised by Mr. Thos. Urquhart, on the Grazi and Tsaritsin Railway, 
Southeast Russia. Since November, 1884, the whole stock of 143 locomotives 
under his superintendence has been fired with petroleum refuse. The oil is 
Injected from a nozzle through a tubular opening in the back of the fire-box, 
by means of a jet of steam, with an induced current of air, 





866 LOCOMOTIVES. 


A brickwork cavity or “ regenerative or accumulative com bustion-cham.- 
ber’ is formed in the fire-box, into which the combined current breaks as 
spray against the rugged brickwork slope. In this arrangement the brick- 
work is maintained at a white heat, and combustion is complete and smoke- 
less. The form, mass, and dimensions of the brickwork are the most im- 
portant elements in such a combination. LAG : 

Compressed air was tried instead of steam for injection, but no appreciable 
reduction in consumption of fuel was noticed. ; 

The heating-power of petroleum refuse is given as 19,832 heat-units, 
equivalent to the evaporation of 20.53 lbs. of water from and at 212° F., or to 
17.1 lbs. at 8144 atmospheres, or 125 lbs. per sq. in., effective pressure. The 
highest evaporative duty was 14 lbs. of water under 8}4 atmospheres per lb. 
of the fuel, or nearly 82% efficiency. 

There is no probability of any extensive use of petroleum as fuel Zor loco- 
motives in the United States, on account of the unlimited supply of coal and 
the comparatively limited supply of petroleum. Texas oil is now (1902) used 
in locomotives of the Southern Pacific Railway. 

Kireless Locomotive.—tThe priaciple of the Francq locomotive is 
that it depends for the supply of steam on its spontaneous generation from 
a body of heated water ina reservoir. As steam is generated and drawn 
off the pressure falls; but by providing a sufficiently large volume of water 
heated to a high temperature, at a pressure correspondingly high, a margin 
of surplus pressure may be secured, and means may thus be provided for 
supplying the required quantity of steam for the trip. 

The fireless locomotive designed for the service of the Metropolitan Rail- 
way of Paris has a cylindrical reservoir having segmental ends, about 5 ft. 
Vin. in diameter, 2614 ft. in length, with a capacity of about 620 cubic feet. 
Four fifths of the capacity is occupied by water, which is heated by the aid 
of a powerful jet of steam supplied from stationary boilers. The water is 
heated until equilibrium is established between the boilers and the reser- 
voir. The temperature is raised to about 390° F., corresponding to 225 lbs. 
per sq. in. The steam from the reservoir is passed through a reducing- 
valve, by which the steam is reduced to the required pressure. It is then 
passed through a tubular superheater situated within the receiver at the 
upper part, and thence through the ordinary regulator to the cylinders. 
The exhaust-steam is expanded to a low pressure, in order to obviate noise 
of escape. In certain cases the exhaust-steam is condensed in closed 
vessels, which are only in part filled with water. In the upper free space a 
pipe is placed, into which the steam is exhausted. Within this pipe another 
pipe is fixed, perforated, from which cold water is projected into the sur- 
rounding steam, so as to effect the condensation as completely as may be. 
The heated water falls on an inclined plane, and flows off without mixing 
with the cold water. The condensing water is circulated by means of a, 
centrifugal pump driven by a small three-cylinder engine. 

In working off the steam from a pressure of 225 lbs. to 67 Ibs., 580 cubic 
feet of water at 390° F {is sufficient for the traction of the trains, for working 
the circulating-pump for the condensers, for the brakes, and for electric- 
lighting of the train. At the stations the locomotive takes from 2200 to 3300 
ibs. of steam—nearly the same as the weight of steam consumed during the 
run between two consecutive charging stations. There is 210 cubic feet of 
condensing water. Taking the initial temperature at 60° F., the tempera- 
ture rises to about 180° F. after the longest runs underground. 

The locomotive has ten wheels, ona base 24 ft. long, of which six are 
coupled, 444 ft. in diameter. The extreme wheels are on radial axles. The 
cylinders are 2314 in. in diameter, with a stroke of 2314 in. 

The engine weighs, in working order, 53 tons, of which 86 tons are on the 
coupled wheels. The speed varies from 15 miles to 25 miles per hour. The 
trains weigh about 140 tons. 

Compressed-air Locomotives.—For an account of the Mekarski 
system of compressed-air :ocomotives see page 510 anie. 


SHAFTING. 867 


SHAFTING, 


(See also ToRSIONAL STRENGTH; also SHAFTS OF STEAM-ENGINES.) 


For diameters of shafts to resist torsional strains only, Molesworth gives 


3 
d= VA a in which d = diameter in inches, P = twisting force in pounds 


applied at the end of a lever-arm whose length is / in inches, K = a coeffi- 


cient whose values are, for cast iron 1500, wrought iron 1700, cast steel 3200, 
gun-bronze 460, brass 425, copper 380, tin 220, lead 170. The value given for 
east steel probably applies only to high-carbon steel, 

Thurston gives: 


3 3/f 
Pa avk. d= Leke do for iron; 
For head shafts well 125 & 
supported against 
springing (bearings close 


Ss aaa 
ask, ‘5 H.P. | for eold-rolled 
to pulleys or gears): HP. =— 3d y/ eae. S 


LR iron, 





| 
8 3 
ie @R. ,. 3/0 He 


So? is 4 == GOL. Aron. 
90 : 
‘i For eae shafting, 
angers 8 ft. apart: 5 
. BLP. = ak. d= ass ah for cold-rolled iron, 
53 BR 
aR 3 /62.5 H.P. : 
pie d= ——_—.,, for iron; 
EE toa Re , 


For ea nertussion sim- 
ply, no pulleys: 3 3/or nD 
H.P, = = ss / yc a for cold-rolled iron. 
i 9) 


HP, = horse-power transmitted, d = diameter of shaft in inches, R = rev- 
olutions per minute. 





3 7100 H.P. 


J. B. Francis gives for turned-iron shafting d = V ar 


Jones and Laughlins give the same formule as Prof. Thurston, with the 
following exceptions: For line shafting, hangers 8 ft. apart: 


aR 3/50 H.P. 
e i a —,d= Be ee tnciene 
cold-rolled iron, H.P. “0° j/ R 


For simply transmitting power and short counters: 


; 3 3 na Dp 
fined itcdt Pu ee is /* H.P., 











50 Forel 
3 3 See 
cold-rolled iron, H.P. = . in / 30 are 


They also give the following notes: Receiving and transmitting pulleys 
should always be placed as close to bearings as possible; and it is good prac- 
tice to frame short “‘ headers”? between the main tie-beams of a millsoas 
to support the main receivers, carried by the head shafts, with a bearing 
close to each side as is contemplated in the formule. Butif it is preferred, 
or necessary, for the shaft to span the full width of the “ bay ” without in- 


868 SHAFTING. 


termediate bearings, or for the pulley to be placed away from the bearings 
towards or at the middle of the bay, the size of the shaft must be largely 
increased to secure the stiffness necessary to support the load without un- 
due deflection. Shafts may not deflect more than 1/80 of an inch to each 
foot of clear length with safety. 

To find the diameter of shaft necessary to carry safely the main pulley at 
the centre of a bay: Multiply the fourth power of the diameter obtained by 
above formule by the length of the ‘‘ bay,”’ and divide this product by the 
distance from centre to centre of the bearings when the shaft is supported 
as required by the formula. The fourth root of this quotient will be the 
diameter required. 

The following table, computed by this rule, is practically correct and safe. 





tt, 

e KS S os Diameter of Shaft necessary to carry the Load at the Centre of 

Steps aca p 

Qty a a Bay, which is from Centre to Centre of Bearings 

oP ak 

ESS s| <_< 

c= ma) q 0) { 

Bae on 26ft.| 3ft. | 36ft.| 4 ft. 5 ft. 6 ft. 8 ft. 10 ft. 
in. eastay "in "in pen in in in ins 
2 26 QM4 286 2 | 286 234 | 2% 3 
216 214 254 234 2% 3 314 336 354 

314 334 344 334 414 

344 ; 344 856 334 4 414 414 434 
P Eis con ieee 41 414 AY, 434 51g 536 
CA ed bh aA rarer 416 458 4% 5 5 5Y% 
Bir ANE ES oe ae eA 51g 534 554 6 614 
BISA IN, Sacer its feces [ie Mae rete 514 534 6 614 6% 
ray ted Be NPA 8 eae i. Ce Ea 634 654 a2 | we 





As the strain upon a shaft from a load upon it is proportional to the 
product of the parts of the shaft multiplied into each other, therefore, 
should the load be applied near one end of the span or bay instead of at the 
centre, multiply the fourth power of the diameter.of the shaft required to 
earry the load at the centre of the span or bay by the product of the two 
parts of the shaft when the load is near one end, and divide this product by . 
the product of the two parts of the shaft when the load is carried at the 
centre. The fourth root of this quotient will be the diameter required. 

The shaft in a line which carries a receiving-pulley, or which carries a 
transmitting-pulley to drive another line, should always be considered a 
head-shaft, and should be of the size given by the rules for shafts carrying 
main pullevs or gears. 

Deflection of Shaftins. (Pencoyd Iron Works.)—As the deflection 
of steel and iron is practically alike under similar conditions of dimensions 
and loads, and as shafting is usually determined by its transverse stiffness 
rather than its ultimate strength, nearly the same dimensions should be 
used for steel as for iron. 

For continuous line-shafting it is considered good practice to limit the 
deflection to a maximum of 1/100 of an inch per foot of length. The weight 
of bare shafting in pounds = 2.6d?Z = W, or when as fully loaded with 
pulleys as is customary in practice, and aliowing 40 Ibs. per inch of width 
for the vertical pull of the belts, experience shows the load in pounds to be 
about 13d2?L = W. Taking the modulus of transverse elasticity at 26,000,000 
lbs., we derive from authoritative formulze the following: 


Sy me “T3 
L= WV 873d2, d= / 2 for bare shafting; 


873° 
rT 3 
L= V 175d?, d= {/ = for shafting carrying pulleys,'ete. ; 


L being the maximum distance in feet between bearings for continuous 
shafting subjected to bending stress alone, @ = diam. in inches. 

The torsional stress is inverselv proportional to the velocity of rotation, 
while the bending stress will not be reduced in the same ratio. It is there- 
fore impossible to write a formula covering the whole problem and suffi: 


‘“HORSE-POWER AT DIFFERENT SPEEDS. 869 


ciently simple for practical application, but the following rules are correet 
within the range of velocities usual in practice. 

For continuons shafting so proportioned as to deflect not more than 1/100 
of an inch per foot of length, allowance being made for the weakening 
effect of key-seats, 





bce / 50 a, A i) 720d2, for bare shafts; 


d= / ae, = WV 140d?, for shafts carrying pulleys, ete. 


d = diam. in inches, Z = length in feet, R = revs. per min. 

The following table (by J. B. Francis) gives the greatest admissible dis- 
tances between the bearings of continuous shafts subject to no transverse 
strain except from their own weight, as would be the case were the power 
given off from the shaft equal on all sides, and at an equal distance from 
the hanger-bearings. 


Distance between Distance between 
Bearings, in ft. Bearings, in ft. 

(aR Gi a a GE 

Diam. of Shaft, Wrought-iron Steel | Diam.ofShaft, Wrought-iron Steel 
in inches. Shafts, Shafts. in inches, Shafts. Shafts. 

Pe 15.46 15.89 6 22.30 22.92 

3 17.70 18.19 @ 23.48 24.13 

4 19.48 20.02 8 24.55 25.23 

5 2C.99 Aa heaig 9 25.53 26.24 


These conditions, however, do not usually obtain in the transmission of 
power by belts and pulleys, and the varying circumstances of each case 
render it impracticable to give any rule which would be of value for univer- 

' sal application. 

For example, the theoretical requirements would demand that the bear- 
ings be nearer together on those sections of shafting where most power 
is delivered from the shaft, while considerations as to the location and 
desired contiguity of the driven machines may render it impracticable to 
separate the driving-pulleys by the intervention of a hanger at the theo- 
retically required location. (Joshua Rose.) 


Horsec-power Transmitted by Turned Iron Shafting at 
Different Speeds. 


As PRIME MOVER OR HEAD SHAFT CARRYING MAIN DRIVING-PULLEY OR GEAR, 
WELL SUPPORTED BY BEARINGS. Formula: H.P. = d?R + 125. 





Number of Revolutions per Minute. 








——— | | | ———_—_ | | | | |) | | | 


insti) PaleheP sisal pr. Pa ei Po eee teebe be? SERPS EH: Ps tHe | AP: 
134 | 2.6 8.4, 4.3) 5.44 6.4) 7.5) 8.6) 9.7) 10.7; 11.8] 12.9 
2 3.8 5.1) 6.44 8 9.6} 11.2) 12.8] 14.4) 16 17.6) 19.2 
2144 | 5.4 @.0| bh O- lie LO 12 14 1 18 20 22 24 
214 | 7.51 10 12.5) 15 18 22 25 28 31 34 37 
234 | 10 13 16 20 24 28 82 36 40 44 48 





870 





SHAFTING. 


As SzeconpD Movers or LINE-SHAFTING, BEARINGS 8 FT, APART. 


Formula: H.P. = d?R -~ 90, 


Number of Revolutions per Minute. | 











apks 

= = 100 | 125} 150] 175 | 200] 225] 250] 275 {| 300] 3825) 350 

Ins. | H.P.|H.P.}] H.P.{/ H.P.} H.P. | H.P. sea! TH PORE BP: MEPS Ee. 
134 | 6 G4 8.9} 10.4, 11.9] 18.4] 14 16.4] 17.9} 19.4] 20.9 
1%) 7.387 9.1 10.9] 12.7%) 14.5) 16.3 iss 20 91.8), 2356) 2564 
o 8.9 | 11.1 13.3], 15.5) 17.7) 20 22.2] 24.4) 26.6) 28.8) 31 
214 | 10.6 } 13.2 | 15.9) 18.5) 21.2) 23.8) 26.5) 29.1) 31.8) 34.4) 37 
244 | 12.6] 15.8] 19 22 25 28 31 35 38 41 44 
236 | 15 18 22 26 29 83 387 41 44 48 52 
216) 17 21 26 80 84 89 43 47 52 56 60 
234 | 23 29 84 40 46 52 58 64 69 75 81 
3 30 Kg 45 52 60 if is) 82 90 9% | 105 
314 | 38 47 57 66 %6 §5 95 | 104 T14 §}} 123 }) 183 
314 | 47 59 71 83 95 | 107 | 119 | 131 143°) 155 | 167 
334 | 58 (ee: 88 | 102 | 117 | 182 | 146 | 162 | 176 | 190 } 205 
4 71 89 10¥ | 125 | 142 | 160 $178 | 196 | 218 | 231 | 249 

For SIMPLY TRAWSMiTTING —— 
Formula: H.P. = dR + 
43 Number of Revolutions per Minute, 

fad 

a a 100 } 125} 150} 175] 200] 283] 267 | 300] 333] 367; 400 

IMS. cietlaken |) Et. eeleet. Ps EPL HP. HP, ‘iB. P.|_BPo APs | EP 
144 | 6.7 8.4| 10 11.8); 13.5) 15 17.9; 20.8) 22.5} 24.8) 27.0 
15g | 8.6} 10.7 28 15 Viet 3 22.8) 25.8) 28.6] 31.5] 34.3 
134 | 10.7} 13.4) 16 1S 371 221.5], 2p 28 82 36 39 43 
1% | 18.2 | 16.5) 19.7 23 26.4) 31 35 39 44 48 52 
2 16 20 24 28 82 37 42 48 53 58 64 
214 | 19 24 29 83 88 44 51 57 63 70 76 
214 | 22 28 34 39 45 52 60 68 5 83 90° 
236 | 27 33 40 47 53 62 70 79 88 96 | 105 
216 | 31 39 47 54 62 "3 83 93 | 104 114 | -125 
234 | 41 52 62 73 §3 97 |} 111 $25 | 139:. |. 153. - | 167 
3 54 67 81 94 108 | 126 144 | 162 | 180 | 198 | 216 
314 | 68 86 103 120 137 160 182 205 228 250 273 
3146 } 85 107 128 ©6150 of 171 200 | 228 | 257 | 285 | 3138 | 342 


Horse-power Transmitted by Cold-rolled Iron Shafting 
at Different Speeds, 





As Prime Mover or Heap SHAFT CARRYING MAIN DRIVING-PULLEY OR 
GEAR, WELL SUPPORTED BY BEARINGS. 





Formula: H.P. = dR ~ 75. 


Number of Revolutions per Minute. 


ee | | | | YS S| | fj [| 


fe 
Ess 
=~! 60 | go | 100} 195 
Ins. | H.P.} H.P.| H.P. | H.P. 
414 |: 2:71 B16 |)..-4.5) 5.6 
194 | 4.3) 5.6| 7.1| 8.9 
2 6.4 8.5 10.7) 138 
a4} 9 (12 | 15 | 19 
aia}i12 |17 | 21 | 26 
93,116 |22 | 27 | 35 
8: 91 29 86 45 
3 27 36 45 57 
314134 |45 | 57 | 71 
334 | 42 |56 | 70 | 87 
4 51 69 85 106 
4% |73 |97 | 121 | 151 


HORSE-POWER AT vIFFERENT SPEEDS, 871 


As Sztconp Movers or LINE-SHAFTING, BEARINGS 8 FT, APART. 


Formula: H.P. = d8R + £0. 





Number of Revolutions per Minute. 








100 | 125} 150} 175 | 200} 225) 250) 275 | 3800] 825} 350 


Tast) te P. PAP.) EP: HP. | BPs Po BP.) HP. | A.B HP. |B. 


144 | 6.7} 8.4] 10.1] 11.8] 13.5) 15.2] 16.8} 18.5] 20.2] 21.9] 23.6 
154 | 8.6 | 10.7) 12.8) 15 | 17.1] 19.3} 21.5] 28.6] 25.7] 28.9] 31 
134 | 10.7 | 13.4 ; 








For SIMPLY TRANSMITTING POWER AND SHORT CoUNTERS,. 
Formula: H.P. = d3?R + 30. 








cs Number of Revolutions per Minute. 

ey Ht 3 

sas 

5S! 100! 125| 150] 175 | 200 |- 238 | 267] 300! 338] 267} 400 

“Ins. | H.P.| H.P.| H.P.| H.P.| H.P.| H.P.| H-P.| HP.| H.P.| H.P.| BP. 
14| 6.5| 8.1; 9.7} 11.3) 13\| 15.2] 17.4] 19.51 21.7] 23.91 26 
13 | 8.5 | 10.7] 12.8} 15 | 17 | .19.8| 22.7] 95.51 28:4] 81 | 34 
1421 11.2] 14° | 16.8] 19.6} 22.5] 26 | 30 | 33 | 37 | 44 | 45 
154 | 14.2 | 17.7] 21.2} 24.8] 98.4 383 | 38 | 42 | 47 | 52 | 57 








234 | 69 84 | 99 | 118 | 188 | 161 | 184 | 207 | 281 | 254 | Q77 
3 90 112 | 185 | 157 | 180 | 210 | 240 | 270 | 300 | 330 |: 360 
SPEED oF SHAFTING.—Machine shops................. 120 to 180 
Wood-working........... 2.... 200 to 300 

Cotton and woollen mills...... 800 to 400 


There are in some factories.lines 1000 ft. long, the power being applied at 
the middle. 


Hollow Shafts.—Let d be the diameter of a solid shaft, and d,d, the 
external and internal diameters of a hollow shaft of the same material, 


4 
Then the shafts will be of equal torsional strength when d3 = a haa 


14 2 
A 10-inch hollow shaft with internal diameter of 4 inches will weigh 16% less 
than a solid 10-inch shaft, butits strength will be only 2.56% less. If the hole 
were increased to 5 inches diameter the weight would be 25% less than that 
of the solid shaft, and the strength 6.257 less. 

Wable for Laying Out Shafting.—The table on the opposite page 
(from the Stevens Indicator, April, 1892) is used by Wm. Sellers & Co. to 
facilitate the laying out of shafting. 

The wood-cuts at the head of this table show the position of the hangers 
and position of couplings, either for the case of extension in both directions 
from a central head-shaft or extension in one direction from that head-shaft, 


TABLE FOR LAYING OUT SHAFTING 


872 









































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PROPORTIONS OF PULLEYS. 873 


PULLEYS. 


Proportions of Pulleys. (See also Fly-wheels, pages 820 to 823.)— 
Let #2 = number of arms, D = diameter of pulley, S = thickness of belt, f= 
thickness of rim at edge, 7’ = th ckness in middle, B = width of rim, B = 
width of belt, h = breadth of arm at hub, h, = breadth of arm at rim, e = 
thickness of arm at hub e, = thickness of arm at rim, c= amount of crown- 
jing; dimensions in inches. 


Unwin. Reuleaux. 
Bi Wwid bit Of rim. ems ccc Co OBOSERC 9/8 (8 + 0.4) 9/88 to 5/48 
t = thickness at edge of rim 07S-+.005p  § (thick. of rim.) 
= ge.of rim!,'..... WS + .005 1 1/5hto 4h 
i bt *imtddie of rim. . -.. 2t-+c ree ceeceeee 
Diy let 


For single ’ BD 
belts = .6337 Z, 
“~ = breadth of arm at hub..... 3 on 
For double BDA se 4 
belts = .798 n 


hy= bai Ribhle Yo waheeg ae Li heneeateer “eh 0.8h 

e = thickness of arm at hub. .... _ 0.4h 0.5h 

Q= oh See ee PLN cect. nie 0.4h, 0.5h, 

m= number of arms, for a } 3 BD 14(5 . ee 
single set, “14 150 2 2B 

T= lenetior hub ons. t at: 1 nobjess on Mee douhisned ane 

M= thickness of metal in hub....... © 0... 22-2. -.006 h to 34h 

Cu CrOWMING OL, PULLEY ..3.. cc ces «oe E/E Re eT cae os ae are 

anor arg of arms is really arbitrary, and may be altered if necessary. 

nwin. 


Pulleys with two or three sets of arms may be considered as two or three 
separate pulleys combined in one, except that the proportions of the arms 
should be 0.8 or 0.7 time that of single-arm pulleys. (Reuleaux.) 

EXAMPLE.— Dimensions of a pulley 60’” diam., 16’” face, for double belt 14” 
thick. 


SOMblON DY «223.4 7h atta ntee BT ed her et Wine mea eh ae ee 
AINWAN Aes ect <2 Os. (oe O0 os el Ole 00, 1.91) l0ce. Oo. 061 
— 


—\--~Y 
Reuleaux. . tes) 400.0 4e0F 225-220 1.25 16 «265 

The following proportions are given in an article in the Amer. Machinist, 
authority not stated: 

h= .0625D + .5 in., hy = .04D + 3125 in., e = .025D+ .2in., e, = .016D + 
.125 in. 

These give for the above example: h = 4.2% in., hy = 2.71 in.,e = 1.7 in, 
e€, = 1.09in. The section of the arms in all cases is taken as elliptical. 

The following solution for breadth of arm is proposed by the author: 
Assume a belt pull of 45 lbs. per inch of width of a single belt, that the 
whole strain is taken in equal proportions on one half of the arms, and that 
the arm is a beam loaded at one end and fixed at the other. We have the 


2 
formula for a beam of elliptical section P = .0982 “°*", in which P = the 


load, R = the modulus of rupture of the cast iron, b = breadth, d = depth, 
and J = length of the beam, and f = factor of safety. Assume a modulus 
of rupture of 36.000 Ibs., a factor of safety of 10, and an additional allow- 
ance for safety in taking / = 144 the diameter of the pulley instead of 44D 
less the radius of the hab. 

Take d =h, the breadth of the arm at the hub, and 6= @ = 0.4h, the 





4 45B B_ 3535 x 0.4h3 
thickness. We then have fP = 10 x er 900—— = iD whence 
3 3 /PpH 
Ke i/ pee = 6334/ 5”. which is practically the same as the value 
OIDIL 


reached by Unwin from a different set of assumptions, 


874 PULLEYS, 


Convexity of Pulleys.—Authorities differ. Morin gives a rise equal 
to 1/10 of the face; Molesworth, 1/24; others from 1 to 1/96. Scott A. 
Smith says the crown should not be over 1 inch for a 24-inch face. Pulleys 
for shifting belts should be “ straight,” that is, without crowning, 


CONE OR STEP PULLEYS. 


To find the diameters for the several steps of a pair of cone-pulleys: 

1. Crossed WBelts.—Let D and d be the diameters of two pulleys ¢on: 
nected by a crossed belt, £ = the distance between their centres, anc 8 = 
the angle either half of the belt makes with a line joining the centres of the 





pulleys: then total length of belt = (D+ dy + (D+ dae +22 cos B. 
Sao Dats 
B = angle whose sine is ene I, cos B =4/ © _— ie +L. Thelength of 


the belt is constant when D-+d is cOnstant; that is,in a yair of step- 
pulleys the belt tension will be uniform when the sum of the diameters of 
each opposite pair of steps is constant. Crossed belts are seldom used for 
cone-pulleys, on account of the friction between the rubbing parts of the 
belt. 


To design a pair of tapering speed-cones, so that the belt may fit 
equally tight in all positions ; When the belt is crossed, use a pair of equal 
and similar cones tapering opposite ways. 

2. Open Belts.—When the belt is uncrossed, use a pair of equal and 
similar conoids tapering opposite ways, and bulging in the middle, accord- 
ing to the following formula: Let ZL denote the distance between the axes 
of the conoids; #& the radius of the larger end of each; r the radius of the 
smaller end; then the radius in the middle, ro, is found as follows: 


R+r (R — r)2 
2 Ug 6.28L ° 


If D, = the diameter of equal steps of a pair of cone-pulleys, Dand d = 
the diaméters of peaee ae een steps, and LZ = distance between the 
— d)2 


Te = 





(Rankine.) ’ 


B08 AG Sim Tne Th Reb Te 
If a series of differences of radii of the steps, R — r, be assumed, then ~ 





a XE ro — ent and the radii of each may be 
computed from their half sum and half difference, as follows: 


Ride ir R-yr, ef de ut 
Re a Sa Fe Pome aes 


A. J. Frith (Trans. A. S. M. H., x. 298) shows the following application of 
Rankine’s method: If we had a set of cones to design, the extreme diame- 
ters of which, including thickness of belt, were 40’ and 10’’, and the ratio 
desired 4, 3, 2, and 1, we would make a table as follows, LZ being 100’; 


for each pair of steps z 














Trial Trial Diameters. |yvalyes of] Amount Corrected Values. 
Sum of | Ratio.) ————————————_| (D — d)? to be 
D+d. D d 12.56L | Added. D d 
50 4 40 10 .7165 .0000 40 10 
5C 3 '87.0 12.5 4975 .2190 87.7190 12.7190 
50 2 83.3383 16.666 .2212 .4953 33.8286 17.1619 
50 1 25 25 .0000 - 7165 25.7165 25.7165 


The above formule are approximate, and they do not give satisfactory 
results when the difference of diameters of opposite steps is large and when 
the axes of the pulleys are near together, giving a large belt-angle. The 
following more accurate solution of the problem is given by C. A Smith 
(Trans, A. S. M. E., x. 269) (Fig 152): 

Lay off the centre distance C or HF, and draw the circles D, and d, equal 
to the first pair of pulleys, which are always previously determined by 
known conditions. Draw HI tangent to the circles D, and d,. From B, 
midway between # and F, erect the perpendicular BG, making the length 


CONE OR STEP PULLEYS. 875 


BG = 3140. With G as a centre, draw a circle tangent to HI. Generally 
this cirele will be outside of the belt-line, as in the cut, but when C is short 
and the first pulleys D, and d, are large, it will fall on the inside of the belt- 
line. The belt-line of any other pair of pulleys must be tangent to the cir- 
ele G; hence any line, as JK or LM, drawn tangent to the circle G, will give 





Fie. 152. 


the diameters D,, d, or Dz, dz of the pulleys drawn tangent to these lines 
from the centres Hand F. 

The above method is to be used when the belt-angle A does not exceed 
18°. When it is between 18° and 30° a slight modification is made. In that 
case, in addition to the point G, locate another point m on the line BG .298 C 
above B. Draw a tangent line to the circle G, making an angle of 18° to the 
line of centres HF’, and from the point m draw an are tangent to this tan- 
gent line. All belt-lines with angles greater than 13° are tangent to this arc, 
The following is the summary of Mr. Smith’s mathematical method: 

At angle in degrees between the centre line and the belt of any pair of 
pulleys; 

a = .314 for belt-angles less than 18°, and .298 for angles between 18° 
an ee 

B° = an angle depending on the velocity ratio; 

C = the centre distance of the two pulleys; 
D, d = diameters of the larger and smaller of the pair of pulleys; 
- #° = an angle depending on BY; 
IL = the length of the belt when drawn tight around the pulleys; 
r = D ~d, or the velocity ratio (larger divided by smaller). 


— 9 ue 
fs cirnndg=s cee 5 ws (aun bartrnke tenet 





POD ag r+1° 
. é D+d 
ae ° ee ° 
(3) Sin H° = sin B (cos A a0 $ 
(4).4 = B° — EF? when sin E° is positive; = B°-+ E° when sin E? is negative; 
Ged = seen, = .3183(Z — 2C) when 4 = Oand r = 1; 
(6) D= rd; 


(7) L = 20 cos A +- .01745d[180 + ( — 1)(90 + A). 


Equation (1) is used only once for any pair of cones to obtain the constant 
cos A, by the aid of tables of sines and cosines, for use in equation (3). 


876 BELTING. 


BELTING. 


Wheory of Belts and Bands.—A pulley is driven bya belt by 
means of the friction between the surfaces in contact. Let 7’, be the tension 
on the driving side of the belt, 7’, the tension on the loose side; then S, = Ty 
— Ty, is the total friction between the band and the pulley, which is equal to 
the tractive or driving force. Let f = the coefficient of friction, 6 the ratie 
of the Jength of the are of contact to the length of the radius, « = the angle 
of the arc of contact in degrees, e = the base of the Naperian logarithms 
= 2.71828, m = the modulus of the common logarithms = 0.434295. The 
following formule are derived by calculus (Rankine’s Mach’y & Millwork, 
p. 8351; Carpenter’s Exper. Eng’g, p. 173): 


LEE, ee ree SARS ge tier dey hr y 

Te a 3 a Saal: T, T3=T; OW ree ae f9), 

T, ~ T= 7,1 —e ~/) = 7,01—10-F0) = 7,(1 — 107 MP8), 
Ty _ 4 .b0758fa. a 00758fa . se Ty 
Aaa} ; Pye X10 5 Ts = Th ooroaya" 


If the arc of contact between the band and the pulley expressed in turns 


and fractions of a turn = n, 6 = 2m; ef ® — 19% 188 "; that is, ef? is the 
natural number corresponding to the common logarithm 2.7288/1. 

The value of the coefficient of friction f depends on the state and material 
of the rubbing surfaces. For leather belts on iron pulleys, Morin found 
f = .56 when dry, .86 when wet, .28 when greasy, and .15 when oily. In calcu. 
lating the proper mean tension for a belt, the smallest value, f = .15, is 
to be taken if there is a probability of the belt becoming wet with oil. The 
experiments of Henry R. Towne and Robert Briggs, however (Jour, Frank. 
Tnst., 1868). show that such a state of lubrication is not of ordinary occur- 
rerice; and that in designing machinery we may in most cases _ safely take 
f = 0.42. Reuleaux takes f = 0.25. The following table shows the values ot 
the coefficient 2.72887, by which 7 is multiplied in the last equation, corre- 
sponding to different values of 7; also the corresponding values of various . 
ratios among the forces, when the arc of contact is half a circumference ; 


f = 0.15 0.25 0.42 0.56 
2.97288/ = 0.41 0.68 1.15 1.53 
Let @ = and n = 4, then 
T, -+- Tz = 1.608 2.188 8.758 5.821 
T; —S = 2.66 1 84 1.36 1.21 
T, + T; + 28 = 2.16 1.34 0.86 0.71 


In ordinary practice it is usual toassume 7, = S; T, = 28; 7; + 7T,+ 
S=1.5. ‘This corresponds to f = 0.22 nearly. 

For a wire rope on cast iron f may be taken as 0.15 nearly; and if the 
groove of the pulley is bottomed with gutta-percha, 0.25. (Rankine.) 

Centrifugal Tension of Belts.—When a belt or band runs at a 
high velocity, centrifugal force produces a tension in addition to that exist- 
ing when the belt is at rest or moving at a low velocity. This centrifugal 
tension diminishes the effective driving force. 

Rankine says : If an endless band, of any figure whatsoever, runs at a 
given speed, the centrifugal force produces a uniform tension at each cross- 
section of the band, equal to the weight of a piece of the band whose length 
is twice the height from which a heavy body must fall, in order to acquire 
the velocity of the band. (See Cooper on Belting, p. 101.) 


If Tc = centrifugal tension; 
V = velocity in feet per second; 
g = acceleration due to gravity = 82.23 


° 


W = weight of a piece of the belt 1 ft. long and 1 sq. in. sectional area,= 
Leather weighing 56 lbs. per cubic foot gives W = 56 + 144 = .888. 


2 2 
to = WV? _ 3887 


g 82 ? = 012 V%,. 








BELTING PRACTICE. 877 


Belting Practice. Handy Formule for Belting. — Since 
in the practical application of the above formulé the value of the coefficient 
of friction must be assumed, its actual value varying within wide limits (15% 
to 135%), and since the values of 7, and Ty also are fixed arbitrarily, it is cus- 
tomary in practice to substitute for these theoretical formulz more simple 
empirical formulee and rules, some of which are given below. 


Let d = diam. of pulley in inches; sd = circumference; 
V = velocity of belt in ft. per second; v = vel. in ft. per minute; 
a = angle of the are of contact; 
LZ = length of are of contact in feet = mda + (12 x 360); 
F' = tractive force per square inch of sectional area of belts 
w = width in inches; ¢ = thickness; 
S = tractive force per inch of width = FP’ + f3 
rpm. = revs. per minute; rps. = revs. per second = rpm. + 60. 


__ad _ad ., rpm. d X rpra., 
al tea onclenaes RATE 29.2 * 


= “< * rpm.; = .2618d x rpm. = 





= .004363d X rpm. = 


Florse-power, HP, = Se = Sf _ Sud X rpm: — oqooorassswd x rpm, 
If F = working tension per square inch = 275 lbs., and ¢ = 7/82 inch, S= 
60 lbs. nearly, then 


_ vw _ bs _ wd XK rpm. 
Hee. rene -109Vw = .000476wd x rpm. = STEMS (1) 
If F’ =: 180 Ibs. per square inch, and ¢ = 1/6 inch, S = 30 lbs., then 
_— ww i _ wd X rpm. 
H.P. = 7100 = .055Vw = .000238w~d xX rpm. = UT ea (2) 


If the working strain is 60 Ibs. per inch of width, a belt 1 inch wide travel- 
jing 550 ft. per minute will transmit 1 horse-power. If the working strain is 
30 lbs. per inch of width, a belt 1 inch wide, travelling 1100 ft. per minute, 
will transmit 1 horse-power. Numerous rules are given by different writers 
on belting which vary between these extremes. A rule commonly used is: 
linch wide travelling 1000 ft. per min. = I1.H.P. 


vw he _ wd X rpm, 
rie 06Vw = .000262wd X rpm. = —sa0 7° (3) 
This corresponds to a working strain of 33 lbs. per inch of width. 

Many writers give as safe practice for single belts in good condition a 
working tension of 45 lbs. per inch of width. This gives 


bald eho 


wd X rpm. 


HP. = = = .0818Vw = .000357wd X rpm, = “OA PE a) 


733 
For double belts of average thickness, some writers say that the trans 
mitting efficiency is to that of single belts as 10 to 7, which would give 


WV wd X rpm. 


H.P. of double belts = 53 = -1169Vw = .00051wd Xx rpm. = ——————.. (5) 


13 1960 
Other authorities, however, make the transmitting-power of double belts 
twice that of single belts, on the assumption that the thickness of a double- 
belt is twice that of a single belt. 

Rules for horse-power of belts are sometimes based on the number of 
square feet of surface of the belt which pass over the pulley in a minute, 
Sq. ft. per min. = wy +12. The above formule translated into this form 
give: q 

(1) For S = 60 lbs. per inch wide; H.P. = 46 sq. ft. per minute, 
30 bb os 66 t 92 (i) oe 


@) “ 8=i HP. = 

(yeaa 80. 6 lemme ELD. = 88.5 alee 

(4) “ §=45 * s 66 H.P. = 61 Sd “ 

G) “ Beas “ * HP = * — double belt 


878 BELTING. 


The above formule are all based on the supposition that the arc of con. 
tact is 180° For other arcs, the transmitting power is approximately pro 
portional to the ratio of the degrees of arc to 180°. 

Some rules base the horse-power on the length of the are of contact in 


: ada ee Sumy o)) NSw iy wa a 
feet. Since L = 7 agp and pes * = 33000 = 33000% 19 % TPM. X Fg» we 
obtain by substitution H.P. = Tra x LX rpm., and the five formulsz then 


take the following form for the several values of S: 


_ wh X rpm. ,., wh X rpm. ,,, wh X rpm... wL X rpm. _,., 
H.P = AT tie 25h. (1)$ 550 (2)5 500 (3); HIRST crane (4); 
ELF. (double belt) = eh x rp (5). 


None of the handy formule take into consideration the centrifugal ten- 
sion of belts at high velocities. When the velocity is over 3000 ft. per min- 
ute the effect of this tension becomes appreciable, and it should be taken 
account of asin Mr. Nagle’s formula, which is given below. 

Horse-power of a Leather Belt One Inch wide, (NaGLz.) 
Formula: H.P. = CVtw(S — .012V 2) <= 550, 


For f = .40,a = 180°, C= .715, w= 1. 








Lacep Bgtts, S = 275. RIVETED Bguts, S = 400, 


Thickness in inches = f. Thickness in inches = ¢. 








“11/7 | 1/6 }3/16| 7/32) 1/4 5/16) 1/3 .|7/82] 1/4 | 5/16} 1/3 | 3/8 | 7/16] 1/2 
= 148] .167) .187| .219] 250] .312} .3833)> 4] .219) 250) .812) .833) .875] .487] .500 


mo ef a ff Sf | | SS | LL 
— —— | —_ 


10 | .51] .59) .63) .73) .84)1.05/1.18) 15 |1.69/1.94] 2.42] 2.58) 2.91] 3.39) 3.87 


elocity in 
per sec 


t 




















15} .75| .88)1.00)1.16/1.32]1.66)1.77| 20 ]2.24/2.57) 8.21] 8.421 3.85! 4.49] 5.13 
20 |1.00)1.17)1°82)1.54/1.75/2.19/2.34] 25 |2.7918.19) 3.98] 4.25] 4.78) 5.57) 6.37 
25 |1.23/1.43)1.61]1.88/2.16/2.69/2.86] 80 |3.31/3.79] 4.74] 5.05) 5.67] 6.62] 7.58 
80 |1.47/1.'72/1.93}2.25/2.58]3.22/3.44) 35 ]3.82/4.37| 5.46) 5.83! 6.56] 7.65! 8.75 
85 |1.69/1.97/2.22/2.59/2.96|3.70/3.94| 40 |4.33/4.95} 6.19] 6.60] 7.42! 8.66] 9.90 
40 |1.90/2.22)2.49|2.90/3.32/4.15}4.44] 45 |4.85|5.49| 6.86] 7.32] 8.43] 9 70110.98 
45 |2.09/2.45)2.75/3.21/3.67/4.58/4.89) 50 15.26/6.01] 7.51] 8.02] 9.02/10.52/12.03 
50 |2.27)2.65/2.98/8.48/3.98)4.97/5.380) 55 |5.68/6.50! 8.12] 8.66] 9.74/11.36/13.00 
55 12.44/2.84/3.19/3.72/4.26/5.32|5.69] 60 |6.09/6.56! 8.70} 9.28]10.43]12.17/13.91 
60 |2.58/8.01/3.38/3.95)4.5115.64|6.02] 65 |6.45/7.87] 9.22) 9.83]11.06]/12.90/14.75 
65 }2.71/38.16/3.55/4.14)4.74/5.92/6.32] 70 16.78/7.75) 9.69)10.33]11.62/13.56/15.50 
70 |2.8118.27/3.68/4.29/4.91/6.14/6.54| 75 (7.09)8.11]10.13}10.84)12.16/14.18/16. 21 
7 |2.89)3.37/3.79\4.42)/5.05)6.31/6.73] 80 17.36/8.41]10.51/11.21)12-61}14,71/16.81 
80 |2.94/3.43/3.86)4.50/5.15)6.44/6.86) 85 |17.58/8.66/10.82)11.55/13.00]15.16/17.32 
85 |2.97/3.47/3.90)/4.55/5.20)6.50/6.93] 90 17.74/8.85/11.06]11.80)13.27/15.48/17.69 
90 |2.97/3.47/3.90/4.55]5.20/6.50/6.93/100 17.96/9.10]11.37/12.13]13.65/15.92/18 .20 
The H.P. becomes @ maximum The H.P. becomes a maximum at 
at 87.41 ft. persec, = 5245 ft. p. min./105.4 ft. per sec. = 6324 ft. per min. 
In the above table the angle of subtension, a, is taken at 180°, 
Should it be.. ........... 90°}100°}110°[120°| 130°] 140°| 150°] 160°) 170°) 180°/200¢ 
Multiply above values by | .65)| .70! .75{ .79| .83] .87| .91] .94] .97| 1 11.08 


























A. F. Nagle’s Formula (Trans. A. S. M. E., voi. ii., 1881, p. 91. 
Tables published in 1882.) 





S — .012V 2 
EP, = CV tw“ aE 
C=1- 107 -00758fa; t = thickness in inches; 
a = degrees of belt contazt; Vv = velocity in feet per second; 
Sf = coefficient of friction; S = stress upon belt per square inch, 


w = width in inches; 


— — 2 


WIDTH OF BELT FOR A GIVEN HORSE-POWER. 879 


Taking S at 275 lbs. per sq. in. for laced belts and 400 Ibs. per sq, in. for 
fapped and riveted belts, the formula becomes 
H.P. = CVtw(.50 — .0000218V 2) for laced belts; 
H.P. = CVtw(.727 — .0000218V 2) for riveted belts, 








VaLuEs oF C= 1 — 10 +84, (Nugrz.) 
Gand e 
é o§ Degrees of contact = a. 
o=a8 
© 2.2 
2} goe | 100° | 110° | 120° | 130° | 140° | 150° | 160° | 170° | 180° | 200° ~ 


ff crc | rf a | re | ee | | | 


"55 | 578 | .617 | .652 | .684 | .713 | .739 | .v63 | .785 ) .805 | .822 | 1853 
"60 | 1610 | .649 | 1684 | .715 | .744| {v9 | :792 | 1813 ( {832 | 's48 | lerz 
“85: ‘g97 | 1913 | 1927 | 1937 | ‘947 | 956 | “969 


The following table gives a comparison of the formule already given for 
the case of a belt one inch wide, with arc of contact 180°. 


Horse-power ofa Belt One Inch wid¢, Arc of Contact 180°. 
COMPARISON OF DIFFERENT FORMULA. 








fo Eis wa Form. 5| Nagle’s Form 
® ‘= | O'S |Form. 1}Form. 2)/Form. 3\lorm. 4 7 (207 as , 
eee Paap iAP, = LP. = |e Sty pie ee 
Sa) S%( SS] we | we | we | we | wy 
et So as 550 1100 1000 733 513 Laced. |Riveted 
10 600 50 | 1.09 55 -60 82 1.17 038 1.14 
20 1200 100 2.18 1.09 1.20 1.64 2.34 1.54 2.24 
30 1800 1501 38.27 1.64 1.80 2.46 8.51 2.25 3.31 
40 2400 200 } 4.36 2.18 2.40 3.27 4.68 2.90 4.33 
50 8000 |} 250 | 5.45 2.93 3.00 4.09 5.85 3.48 5.26 
60 3600 800 | 6.55 3.20 8.60 4.91 7.02 3.95 6.09 
70 4200 850 63 3.82 4.20 5.73 8.19 4.29 6.78 
80 | 4800] 400| 8.73 4.36 4.80 6.55 9.36 4.50 7.36 
90 | 5400 | 450] 9.82 4.91 5.40 7.387 } 10.53 4.55 %.W4 
100 6000 | 500 | 10.91 5.45 6.00 8.18 11.70 4.41 7.96 
110 PONE Aaa in Lene Soraun RASS nce! (bmereaciets (PaS- clonta4 hadiarkasee 4.05 7.97 
49 TOON | OO Ul), acs Searscti<s| a ntvene.dvoreball ovatprttivanerspberneremerers ares 3.49 7.95 


Width of Belt for a Given Horse-power.—The width of bell 
required for any given horse-power may be obtained by transposing tue for 
mul for borse-power so as to give the value of w. Thus: 


550H.P. 9.17 H.P. 2101 H.P. 2%5H.P. 
From formula (1), w= -——— = Ty eh Reo PEED 


1100 H.P. _ 18.33 H.P. 4202 H.P. 530 H.P. 


From formula (2), w= ee ee 


_ 1000 HP. 16.67 H.P. 3820 HP. 3s 500 H.P. 
i v ae V ~dxXrpm. L£X rpm. 


7388 H.P. 12.22 H.P. 2800 H.P. 860 H.P. 
from formula (4), w= ——~= Se ae aS 


tormula (6). w= CLEP. _ S56HLP. _ 1960 HP. 27 HP. 
From formula (5),* w= ——~——~ = ——, ~ @Xrpmw. LX rpm,’ 


* For double belts. , 


From formula (8), 





880 BELTING. 


Many authorities use formula (1) for double belts and formula (2) or (8) for 
single belts. ae 


: : c : - a 
To obtain the width by Nagle’s formuia, w = OPUS — 0127" or divide 


the given horse-power by the figure in the table corresponding to the given 
thickness of belt and velocity in feet per second. 

The formula to be used in any particular case is largely a 
matter of judgment. A single belt proportioned according to formula (1), 
if tightly stretched, and if the surface is in good condition, will transmit the 
horse- power calculated by the formula, but one so proportioned is objec- 
tionable, first. because it requires so great an initial tension that it is apt to 
stretch, slip, and require frequent restretching and relacing; and second, 
because this tension will cause an undue pressure on the pulley-shaft, and 
therefore an undue loss of power by friction. To avoid these difficulties, 
formula (2), (3), or (4,) or Mr. Nagle’s table, should be used; the lattcr espe- 
cially i cases in which the velocity exceeds 4000 ft. per min. 

Taylor’s Rules for Belting.—F.W. Taylor (Trans. A.S. M.E., 
xv. 204) describes a nine years’ experiment on belting in a machine-shop, 
giving results of tests of 42 belts running night and day. Some of these 
belts were run on cone pulleys and others on shifting, or fast-and-loose, pul- 
leys. The average net working load on the shifting belts was only 4/10 of 
that of the cone belts. 

The shifting belts varied in dimensions from 39 ft. 7 in. long, 3.5 in. wide, 
.25 in. thick, to 51 ft. 5 in. long, 6.5 in. wide, .87 in. thick. The cone belts 
varied in dimensions from 24 ft. 7 in. long, 2 in. wide, .25 in. thick, to 31 ft. 
10 in. long, 4 in. wide, .37 in. thick. : 

Belt-clamps were used having spring-balances between the two pairs C« 
clamps, so that the exact tension to which the belt was subjected was 
accurately weighed when the belt was first put on, and each time it was 
tightened. 

The tension under which each belt was spliced was carefully figured so as 
to place it under an initial strain—while the belt was at rest immediately 
after tightening—of 71 lbs. per inch of width of double belts, This is equiv- 
alent, in the case of 


Oak tanned and fulled belts, to 192 lbs. per sq. in. section; 
Oak tanned, not fulled belts, to 229 “* ‘tt S “6 
Semi-raw-hide belts, torebancet uscaeeermes &“ 
Raw-hide belts, to 284 % 86 se “ 


From the nine years’ experiment Mr. Taylor draws a number of conclu- 
sions, some of which are given in an abridged form below. 

In using belting so as to obtain the greatest economy and the most satis- 
factory results, the following rules should be observed: 


Other Types of 
Perera: Leather Belts 


: and 6- to 7-ply 
Leather Belts. Rubber Belts. 





A double belt, having an are of contact of 

180°, will give an effective pull on the face 

of a pulley per inch of width of belt of.... 35 Ibs. 30 Ibs, 

Or, a different form of same rule: 

The number of sq. ft. of double Belt passing 

around a pulley per minute required to 

transmit one horse: power is............... 80 sq. ft. 90 sq. ft. 
Or: The number of lineal feet of double- 

belting 1 in. wide passing around a pulley 

per minute required to transmit one horse- 


power is....... .. SSG Boon ee 950 ft. 1100 ft. 
Or: A double belt 6 in. wide, running 4000 to 
5000 ft. per min., will transmit............ 30 HE; Paw AB Ee 


The terms ‘‘initial tension,’’ ‘‘ effective pull,’’ etc., are thus explained by 
Mr. Taylor: When puileys upon which belts are tightened are at rest, both 
strands of the belt (the upper and lower) are under the same stress per in 
of width. By “ tension,” “initial tension,” or “ tension while at rest,” we 


TAYLOR’S RULES FOR BELTING. 881 


mean the stress per in. of width, or sq,in. of section, to which one of the 
strands of the belt is tightened, when at rest. After the belts are in motion 
and transmitting power, the stress on the slack side, or strand, of the belt 
becomes less, while that on the tight side—or the side which does the pull- 
ing—becomes greater than when the belt was at rest. By the term ‘‘ total 
load” we mean the total stress per in. of width, or sq. in. of section, on the 
tight side of belt while in motion. 

The difference between the stress on the tight side of the belt and its slack 
side, while in motion, represents the effective force or pull which is trans- 
mitted from one pulley to another. By the terms ‘‘ working load,” “ net 
working load,” or ‘*‘ effective pull,” we mean the difference in the tension 
of the tight and slack sides of the belt per in. of width, or sq. in. section, 
while in motion, or the net effective force that is transmitted from one pul- 
ley to another per in. of width or sq. in. of section. 

The discovery of Messrs. Lewis and Bancroft (Trans. A. S. M. E., vii. 749) 
that the ‘‘sum of the tension on both sides of the belt does not remain 
constant,” upsets all previous theoretical belting formule. 

The belt speed for maximum economy should be from 4000 to 4500 ft. per 
minute. 

The best distance from centre to centre of shafts is from 20 to 25 ft. 

Idler pulleys work most satisfactorily when located on the slack side of 
the belt about one quarter way from the driving-pulley. 

Belts are more durable and work more satisfactorily made narrow and 
thick, rather than wide and thin. 

It is safe and advisable to use: a double belt on a pulley 12 in. diameter or 
larger; a triple belt on a pulley 20 in. diameter or larger; a quadruple belt 
on a pulley 30 in. diameter or Jarger. 

As belts increase in width they should also be made thicker. 

The ends of the belt should be fastened together by splicing and cement- 
ing, instead of lacing, wiring, or using hooks or clamps of any kind. 

A V-splice should be used on triple and quadruple belts and when idlers 
are used, Stepped splice, coated with rubber and vulcanized in place, is best 
for rubber belts. 

For double belting the rule works well of making the splice for all belts 
up to 10 in. wide, 10 in. long; from 10 in. to 18 in. wide the splice should be 
the same width as the belt, 18 in. being the greatest length of splice required 
for double belting. 

Belts should be cleaned and greased every five to six months. 

Double leather belts will last well when repeatedly tightened under a 
strain (when at rest) of 71 lbs. per in. of width, or 240 lbs. per sq. in. section. 
They will not maintain this tension for any length of time, however. 

Belt-clamps having spring-balances between the two pairs of clamps 
should be used for weighing the tension of the belt accurately each time it 
is tightened. 

The stretch, durability, cost of maintenance, etc., of belts proportioned 
(A) according to the ordinary rules of a total load of 111 lbs. per inch of 
width corresponding to an effective pull of 65 Ibs. per inch of width, and (B) 
according to a more economical rule of a total load of 54 Ibs., corresponding 
to an effective pull of 26 Ibs. per inch of width, are found to be as follows: 

When it is impracticable to accurately weigh the tension of a belt in tight- 
ening it, it is safe to shorten a double belt one half inch for every 10 ft. of 
length for (A) and one inch for every 10 ft. for (B), if it requires tightening. 

Double leather belts, when treated with great care and run night and day 
at moderate speed, should last for 7 years (A); 18 years (B). 

The cost of all labor and materials used in the maintenance and repairs of 
double belts, added to the cost of renewals as they give out, through a term 
of years, will amount on an average per year to 37% of the original cost of 
the belts (A); 14% or less (B). 

In figuring the total expense of belting, and the manufacturing cost 
ehargeable to this account, by far the largest item is the time lost on the 
machines while belts are being relaced and repaired. 

The total stretch of leather belting exceeds 6% of the original length. 

The stretch during the first six months of the life of belts is 86% of their 
antire stretch (A)s 15% (B). ; 

A double belt will stretch 47/100 of 1% of its length before requiring to be 
tightened (A); 81/100 of 1% (B). 

The most important consideration in making up tables and rules for the 
use and care of belting is how to secure the minimum of interruptions to 
manufacture from this source. 


” 


B82 BELTING, 


The average double belt (A), when running night and day in a machine 
shop, will cause at least 26 interruptions to manufacture during its life, or 5 
interruptions per year, but with (B) interruptions to manufacture will not 
average oftener for each belt than one in sixteen months, 

The oak-tanned and fulled belts showed themselves to be superior in all 
respects except the coefficient of friction to either the oak-tanned,not fulled, 
the semi-raw-hide, or raw-hide with tanned face. 

Belts of any width can be successfully shifted backward and forward on, 
tight and loose pulleys. Belts running between 5000 and 6000 ft. per min. 
and driving 300 H.P. are now being daily shifted on tight and loose pulleys, 
to throw lines of shafting in and out of use. 

The best form of belt-shifter for wide belts is a pair of rollers twice the 
width of belt, either of which can be pressed onto the flat surface of the 
belt on its slack side close to the driven pulley, the axis of the roller making 
an angle of 75° with the centre line of the belt. 

Remarks on Mr. Taylor’s Rules, (Trans. A.S. M. E., xv., 242.) 
—The most notable feature in Mr. Taylor’s paper is the great difference be- 
sween his rules for proper proportioning of belts and those given by earlier 
writers. A very commonly used rule is, one horse-power may be transmitted 
by a single belt 1 in. wide running « ft. per min., substituting for # various 
values, according to the ideas of different engineers, ranging usually from 
550 to 1100. 

The practical mechanic of the old school is apt to swear by the figure 
600 as being thoroughly reliable, while the modern engineer is more apt. to 
use the figure 1000. Mr. Taylor, however, instead of using a figure from 556 
to 1100 for a single belt, uses 950 to 1100 for double belts. If we assume that 
a double belt is twice as strong, or will carry twice as much power, as a 
single belt, then he uses a figure at least twice as large as that used in 
modern practice, and would make the cost of belting for a given shop twice 
as large as if the belting were proportioned according to the most liberal of 
the customary rules. 

This great difference is to some extent explained by the fact that the 
problem which Mr. Taylor undertakes to solve is quite a different one from 
that which is solved by the ordinary rules with their variations. The prob- 
lem of the latter generally is, ‘‘ How wide a belt must be used, or how nar- 
row a belt may be used, to transmit a given horse-power ?”? Mr. Taylor’s 
problem is: * How wide a belt must be used so that a given horse-power. 
may be transmitted with the minimum cost for belt repairs, the longest life 
to the belt, and the smallest loss and inconvenience from stopping the 
machine while the belt is being tightened or repaired ?” 

The difference between the old practical mechanie’s rule of a 1-in,-wide 
single belt, 600 ft. per min., transmits one horse-power, and the rule com- 
monly used by engineers, in which 1000 is substituted for 600, is due to the 
belief of the engineers, not that a horse-power could not be transmitted by 
the belt proportioned by the older rule, but that such a proportion involved 
undue strain from overtightening to prevent slipping, which strain entailed 
too much journal friction, necessitated frequent tightening, and decreased 
the length of the life of the belt. 

Mr. Taylor’s rule substituting 1100 ft. per min. and doubling the belt is a 
further step, and a long one, in the same direction. Whether it will be taken 
in any case by engineers will depend upon whether they appreciate the ex: 
‘tent of the losses due to slippage of belts slackened by use under overstrain, 
and the loss of time in tightening and repairing belts, to such a degree as to 
induce them to allow the first cost of the belts to be doubled in order to 
avoid these losses. 

It should be noted that Mr. Taylor’s experiments were made on rather 
narrow belts, used for transmitting power from shafting to machinery, and 
his conclusions may not be applicable to heavy and wide belts, such as 

, engine fly-wheel belts. 


MESCELLANEOUS NOTES ON BELTING. 


Formule are useful for proportioning belts and pulleys, but they furnish 
no means of estimating how much power a particular belt may be trans- 
mitting at any given time, any more than the size of the engine is a measure 
of the load it is actually drawing, or the known strength of a horse is a 
measure of the load on the wagon. The only reliable means of determining 
the power actually transmitted is some form of dynamometer. (See Trans, 
A.S. M. E., vol. xii. p. 707.) 


MISCELLANEOUS NOTES ON BELTING. 883 


¥f we increase the thickness, the power transmitted ought to increase in 
proportion; and for double belts we should have half the width required for 
a single belt under the same conditions. With large pulleys and moderate 
velocities of belt it is probable that this holds good. With small pulleys, 
however, when a double belt is used, there is not such perfect contact 
between the pulley-face and the belt, due to the rigidity of the latter, and 
more work is necessary to bend the belt-fibres than when a thinner and 
more pliable belt is used. The centrifugal force tending to throw the belt 
from the pulley also increases with the thickness, and for these reasons the 
width of a double belt required to transmit a given horse-power when used 
with small pulleys is generally assumed not less than seven tenths the 
width of a single belt to transmit the same power. (Flather on ** Dynamom- 
eters and Measurement of Power.” 

F. W. Taylor, however, finds that great pliability is objectionable, and 
favors thick belts even for small pulleys: The power consumed in bending 
the belt around the pulley he considers inappreciable. According to Ran- 
kine’s formula for centrifugal tension, this tension is proportional to the 
sectional area of the belt, and hence it does not increase with increase of 
thickness when the width is decreased in the same proportion, the sectional 
area remaining constant. 

Scott A. Smith (Trans. A. S. M. E., x. 765) says: The best belts are made 
from all oak-tanned leather, and curried with the use of cod oil and tallow, 
all to be of superior quality. Such belts have continued in use thirty to 
forty years when used as simple driving-belts, driving a proper amount of 
power, and having had suitable care. The flesh side should not be run to 
the pulley-face, for the reason that the wear from contact with the pulley 
should come on the grain side, as that surface of the belt is much weaker 
in its tensile strength than the flesh side; also as the grain is hard it is more 
enduring for the wear of attrition; further, if the grain is actually worn off, 
then the belt may not suffer in its integrity from a ready tendency of the 
hard grain side to crack. ; 

The most intimate contact of a belt with a pulley comes, first, in the 
smoothness of a pulley-face, including freedom from ridges and hollows left 
by turning-tools; second, in the smoothness of the surface and evenness in 
the texture or body of a belt; third,in having the crown of the driving and re- 
ceiving pulleys exactly alike,—as nearly so as is practicablein a commercial 
sense; fourth, in having the crown of pulleys not over 14” for a 24’’ face, that 
is to say, that the pulley is not to be over 14” largerin diameter in its centre; 
fifth, in having the crown other than two planes meeting at the centre; 
sixth, the use of any material on or in a belt, in addition to those necessarily 
used in the currying process, to keep them pliable or increase their tractive 
quality, should wholly depend upon the exigencies arising in the use of 
belts; non-use is safer than over-use; seventh, with reference to the lacing 
of belts, it seems to be a good practice to cut the ends to a convex shape by 
using a former, so that there may be a nearly uniform stress on the lacing 
through the centre as compared with the edges. Fora belt 10’ wide, the 
centre of each end should recede 1/10”. 

Lacing of Belts.—In punching a belt for lacing, use an oval punch, 
the longer diameter of the punch being parallel with the sides of the belt. 
Punch two rows of holes in each end, placed zigzag. Ina 3-in. belt there 
should be four holes in each end—two in each row. In a 6-inch belt, seven 
holes—four in the row nearest the end, A 10-inch telt should have nine 
holes. The edge of the holes should not come nearer than 34 of an inch from 
the sides, nor % of an inch from the ends of the belt. The second row should 
be at least 134 inches from the end. On wide belts these distances should 
be even a little greater, 

Begin to lace in the centre of the belt and take care to keep the ends 
exactly in line, and to lace both sides with equal tightness. The lacing 
should not be crossed on the side of the belt that runs next the pulley. In 
taking up belts, observe the same rules as putting on new ones. 

Setting a Belt on Quarter-twist.—A belt must run squarely on to 
the pulley, Tio connect witha belt two horizontal shafts at right angles 
with each other, say an engine-shaft near the floor with a line attached to 
the ceiling, will require a quarter-turn, First, ascertain the central point 
on the face of each pulley at the extremity of the horizontal diameter where 
the belt will leave the pulley, and then set that point on the driven pulley 

lumb over the corresponding point on the driver. This will cause the belt 

run squarely on to each pulley, and it will leave at an angie greater or 
Jess, according to the size of the pulleys and their distance from each other, 


884 BELTING. 


In quarter-twist belts, in order that the belt may remain on the pulleys, 
the central plane on each pulley must pass through the point of delivery of 
the other pulley. This arrangement does not admit of reversed motion. 

To find the Length of Belt required for two given 
Pulleys.—When the length cannot be measured directly by a tape-line, 
the following approximate rule may be used: Add the diameter of the twa 
pulleys together, divide the sum by 2, and multiply the quotient by 314, and 
add the product to twice the distance between the centres of the shafts. 
(See accurate formula below.) 

To find the Angle of the Arc of Contact of a Belt.—Divide 
the difference between the radii of the two pulleys in inches by the distance 
between their centres, also in inches, and in a table of natural sines find the 
angle most nearly corresponding with the quotient. Multiply this angle by 
2, and add the product to 180° for the angle of contact with the larger 
pulley, or subtract it from 180° for the smaller pulley. 

Or, let R = radius of larger pulley, r = radius of smaller; 

JL = distance between centres of the pulleys; 
@ = angle whose sine is (R — r) + L. 
Arc of contact with smaller pulley = 180° — 2a3 
ee “ ‘“* larger pulley = 180° + 2a. 

To find the Length of Belt in Contact with the Pulley,— 

For the larger pulley, multiply the angle a, found as above, by .0349, to the 


Prous add 3.1416, and multiply the sum by the radius of the pulley. Or 
ength of belt in contact with the pulley 


= radius X (a -++ .0349a) = radius x n(4 +5). 


For the smaller pulley, length = radius x (7 —.0349a)= radius x (1 =~ 5 


The above rules refer to Open Belts. The accurate formula for length 
of an open belt is, 


Length =: 7R(1 +o) ae mr(1 ne a) + 2L cosa 


= Rim + .0349a) + r(7 — .0349a) + 2L cos a, 


in which R = radius of larger pulley, r = radius of smaller pulley, 
L = distance between centres of pulleys, and a = angle whose sine ig 


(R—r)+L;cosa= YL? —(R—1r)?+L. 
For Crossed Belts the formula is 


Length of belt = mR(1 am Fr) re mr(1 4 FY) 4+ 2L cos B, 


—(R-+r) x Gr + .03498) + 2L cos B, 
in which 8 = angle whose sine is (R +r) + L; cosB = VL? —(R+7)?+ L. 


Yo find the Length of Belt when Closely Rolled.—The sum 
of the diameter of the roll, and of the eye in inches, x the number of turns 
made by the belt and by .1309, = length of the belt in feet 

To find the Approximate Weight of Belts —Multiply the 
length of belt, in feet, by the width in inches, and divide the product by 12 
for single. and 8 for double belt. ; 

Relations of the Size and Speeds of Driving and Driven 
Pulleys.—tThe driving pulley is called the driver, D, and the driven pulley 
the driven, d._ If the number of teeth in gears is used instead of diameter, in 
these calculations, number of teeth must be substituted wherever diameter 
eccurs. #& = revs. per min. of driver, x = revs. per min. of driven. 


D=dr+R; 

Viam., of driver = diam. of driven x revs. of driven ~ revs. of driver. 
d= DR+r;3 

Diam. of driven = diam. of driver x revs. of driver ~ revs. of driven. 
R= dri Dz 


Revs. of driver = revs, of driven x diam. of driven + diam. of driver. 


MISCELLANEOUS NOTES ON BELTING. . 88d 


r= DR+dad; 
Revs. of driven = revs. of driver < diam. of driver + diam. of driven. 


Evils of Tight Belts. (Jones and Laughlins,)—Clamps with powerful 
screws are often used to put on belts with extreme tightness, and with most 
injurious strain upon the leather. They should be very judiciously used for 
horizontal belts, which should be allowed sufficient slackness to move with a 
loose undulating vibration on the returning side, as a test that they have no 
more strain imposed than is necessary simply to transmit the power. 

On this subject a New England cotton-mill engineer of large experience, 
says: I believe that three quarters of the trouble experienced in broken pul- 
leys, hot boxes, etc., can be traced to the fault of tight belts. The enormous 
and useless pressure thus put upon pulleys must in time break them, if they 
are made in any reasonable proportions, besides wearing out the whole out- 
fit, and causing heating and consequent destruction of the bearings. Below 
are some figures showing the power it takes in average modern mills with 
first-class shafting, to drive the shafting alone : 


Shafting Alone. Shafting Alone. 
Whole teres ee 
Mill, Load 
H.P,. Horse- |Per cent Horse- | Per cent 
ek power. jof whole. power. jof whole, . 
1 199 51 25.6 72.6 22.7 
2 472 1D s§ 23.6 84.8 36.1 
3 486 134 27.5 262.9 39.2 
4 677 190 28.1 182 26 








These may be taken as a fair showing of the power that is required in 
many of our best mills to drive shafting. It is unreasonable to think that all 
that power is consumed by a legitimate amount of friction of bearings 
and belts. I know of no cause for such a loss of power but tight belts. These, 
when there are hundreds or thousands in a mill, easily multiply the friction 
on the bearings, and would account for the figures. 

Sag of Belts.—In the location of shafts that are to be connected with 
each other by belts, care should be taken to secure a proper distance one 
from the other. This distance should be such as to allow of a gentle sag to 
the belt when in motion. : 

A general rule may be stated thus: Where narrow belts are to be run over 
small pulleys 15 feet is a good average, the belt having a sag of 114 to 2 inches. 

For larger belts, working on larger pulleys, a distance of 20 to 25 feet does 
well, with a sag of 21% to 4 inches. 

For main belts working on very large pulleys, the distance should be 25 to 
30 feet, the belts working well with a sag of 4 to 5 inches. 

If too great a distance is attempted,the belt will have an unsteady flapping 
motion, which will destroy both the belt and machinery. 

Arrangement of Belts and Pulleys.—If possible to avoid it, con< 
nected shafts should never be placed one directly over the other, as in such 
case the belt must be kept very tight to do the work. For this purpose belts 
should be carefully selected of well-stretched leather. 

It is desirable that the angle of the belt with the floor should not exceed 
45°. It is also desirable to locate the shafting and machinery so that belts 
should run off from each shaft in opposite directions, as this arrangement 
will relieve the bearings from the friction that would result when the belts all 
pull one way on the shaft. 

In arranging the belts leading from the main line of shafting to the 
counters, those pulling in an opposite direction should be placed as near 
each other as practicable, while those pulling in the same direction should be 
separated. This can often be accomplished by changing the relative posi- 
tions of the pulleys on the counters. By this proceduré much of the friction 
on the journals may be avoided. 

If possible, machinery should be so placed that the direction of the belt 
motion shall be from the top of the driving to the top of the driven puiley, 
when the sag will increase the are of contact. ‘ 

The pulley should be a little wider than the belt required for the work. 


886. BELTING. 


The motion of driving should run with and not against the Japs of the belts, 

Tightening or guide pulleys should be applied to the slack side of belts and 
near the smaller pulley. 

Jones & Laughlins, in their Useful Information, say: The diameter of the 
pulleys should be as large as can be admitted, provided they will not pro- 
duce a speed of more than 4750 feet of belt motion per minute. 

They also say: It is better to gear a mill with small pulleys and run them 
at a high velocity, than with large pulleys and to run them slower. A mill 
thus geared costs less and has amuch neater appearance than with large 
heavy pulleys. 

M.- Arthur Achard (Proce. Inst. M. E., Jan. 1881, p. 62) says: When the belt 
is wide a partial vacuum is formed between the belt and the pulley at 4 
high velocity. The pressure is the> greater than that computed from the 
tensions in the belt, and the resistance to slipping is greater. This has the 
advantage of permitting a greater power to be transmitted by a given belt, 
and of diminishing the strain on the shafting, 

On the other hand, some writers claim that the belt entraps air between 
itself and the pulley, which tends to diminish the friction, and reduce the 
tractive force. On this theory some manufacturers perforate the belt with 
numerous holes to let the air escape. 

Care of Belts.—Leather belts should be well protected against water, 
loose steam, and all other moisture, with which they should not come in con- 
tact. But where such conditions prevail fairly good results are obtained by 
using a special dressing prepared for the purpose of water-proofing leather, 
though a positive water-proofing material has not yet been discovered. ~ 
’ Belts made of coarse, loose-fibred leather will do better service in dry and 
_ warm places, but if damp or moist conditions exist then the very finest and 

firmest leather should be used. (Fayerweather & Ladew.) 
| Do not allow oil to drip upon the belts. It destroys the life of the leather. 

Leather belting cannot safely stand above 11C° of heat. 

Strength of Belting.—The ultimate tensile strength of belting does 
not generally enter as a factor in calculations of power transmission. 

The strength of the solid leather in belts is from 2000 to 5000 lbs. per square 
inch; at the lacings, even if well put together, only about 1000 to 1500. If 
riveted, the joint should have half the strength of the solid belt. The work- 
ing strain on the driving side is generally taken at not over one third of the 
strength of the lacing, or from one eighth to one sixteenth of the strength 
of the solid belt. Dr. Hartig found that the tension in practice varied from 
80 to 532 lbs. per square inch, averaging 273 lbs. i 

Adhesion Independent of Diameter. (Schultz Belting Co.)— 
1. The adhesion of the belt to the pulley is the same—the are or number of 
degrees of contact, aggregate tension or weight being the same—without 
reference to width of belt or diameter of pulley. 

2. A belt will slip just as readily on a pulley four feet in diameter as it will 
on a pulley two feet in diameter, provided the conditions of the faces of the 
pulleys, the are of contact, the tension, and the number of feet the belt 
travels per minute are the same in both cases. 

3. To obtain a greater amount of power from belts the pulleys may be 
covered with leather; this will allow the belts to run very slack and give 254 
more durability. 

Endless Belts,—If the belts are to be endless, they should be put on 
and drawn together by “‘ belt clamps ’’ made for the purpose. If the belt is 
made endless at the belt factory, it should never be run on to the pulleys, lest 
the irregular strain spring the belt. Lift out one shaft, place the belt on the 
pulleys, and foree the shaft back into place. 

Belt Data,.—A fly-wheel at the Amoskeag Mfg. Co., Manchester, N. H., 
30 feet diameter, 110 inches face, running 61 revs. per min., carried two heavy 
double-leather belts 40 inches wide each, and one 24inches wide. The engine 
indicated 1950 H.P., of which probably 1850 H.P. was transmitted by the 
belts. The belts were considered to be heavily loaded, but not overtaxed. 

(30 X 3.14 « 104 X 61) + 1850 = 323 ft. per min. for 1 H.P. per inch of width. 

Samuel Webber (Am. Mach., Feb, 22, 1894) reports a case of a belt 30 
inches wide, 3g inch thick, running for six years at a velocity of 3900 feet per 
minute, on to a pulley 5 feet diameter, and transmitting 556 H.P. This gives 
a velocity of 210 feet per minute for 1 H.P. per inch of width. By Mr. Nagle’s 
table of riveted belts this belt would be designed for 332 H.P. By Mr. Taylor's 
rule it would be used to transmit only 123 H.P. 

The above may be taken asexamples of what a beltmay be made to do, but 
they should not be used as precedents in designing. Itis not stated how much 
power was lost by the journal friction due te over-tightening of these belts. 


TOOTHED-WHEEL GEARING. 887 


Belt Drossings.—We advise that no belt dressing should be used ex: 
cept when the belt becomes dry and husky, and in such instances we recom- 
mend the use of a dressing. Where this is not used beef tallow at blood- 
warm temperature should be applied and then dried in either by artificial 
heat or the sun. The addition of beeswax to the tallow will be of some ser- 
vice if the belts are used in wet or damp places. Our experience convinces 
y el resin should never be used on leather belting. (Fayerweather & 

adew. 

Belts should not be soaked in water before oiling,.and penetrating oils 
should but seldom be used, except occasionally when a belt gets very dry’ 
and husky from neglect. It may then be moistened a little, andjhave neat’s- 
foot oil applied. Frequent applications of such oils to a new belt render the 
leather soft and flabby, thus causing it to stretch, and making it liable to. 
rup out of line. A composition of tallow and oil, with a little resin or bees- 
wax, is better to use. Prepared castor-oil dressing is good, and may be 
applied with a brush or rag while the belt is running. (Alexander Bros.) 

Cement for Cloth or Leather. (Molesworth.)—16 parts gutta- 
percha, 4 india-rubber, 2 pitch, 1 shellac, 2 linseed-oil, cut small, melted to- 
gether and well mixed. 

Rubber Belting.—The advantages claimed for rubber belting are 
ee uniformity in width and thickness; it will endure a great degree of 

eat and cold without injury; it is also specially adapted for use in damp or 
wet places, or where exposed to the action of steam; it is very durable, and 
has great tensile strength, and when adjusted for service it has the most per- 
fect hold on the pulleys, hence is less liable to slip than leather. 

Never use animal oil or grease on rubber belts, as it will greatly injure and 
soon destroy them. 

Rubber belts will be improved, and their durability increased, by putting 
on with a painter’s brush, and letting it dry, a composition made of equal 
parts of red lead, black lead, French yellow, and litharge, mixed with boiled 

inseed-oil and japan enough to make it dry quickly. The effect of this will 

be to produce a finely polished surface. If, from dust or other cause, the 
beit should slip, it should be lightly moistened on the side next the pulley 
with boiled linseed-oil. (From circulars of manufacturers.) 

The best conditions are large pulleys and high speeds, low tension and re- 
duced width of belt. 4000 ft. per min. is not an excessive speed on proper 
sized pulleys. 

H.P. of a4-ply rubber belt = (length of are of contact on smaller pulley 
in ft. x width of belt in ins. x revs. per min.) + 325. For a 5-ply belt mul- 
tiply by 114, for a 6-ply by 134, fora 7-ply by 2, for an 8-ply by 244. When 
the proper weight of duck is used a 3- or 4-ply rubber belt is equal to asingle 
leather belt and a 5- or 6-ply rubber to a double leather belt. When the 
are of contact is 180°, H.P. of a 4-ply belt = width in ins, x velocity in ft. 
per min, + 650, (Boston Belting Co.) 


GEARING. 


TOOTHED-WHEEL GEARING, 


Pitch, Pitch-circle, etc.—If two cylinders with parallel axes are 
ressed together and one of them is rotated onits axis, it will drive the other 
by means of the friction between the surfaces. The cylinders may be con- 
sidered as a pair of spur-wheels with an infinite number of very small teeth. 
If actual teeth are formed upon the cylinders, making alternate elevations 
and depressions in the cylindrical surfaces, the distance between the axes 
remaining the same, we have a pair of gear-wheels which will drive one an- 
other by pressure upon the faces of the teeth, if the teeth are properly 
shaped. In making the teeth the cylindrical surface may entirely disap- 
pear, but the position it occupied may still be considered as a cylindrical 
surface, which is called the ‘ pitch-surface,’’ and its trace on the end of the 
wheel, or on a plane cutting the wheel at right angles to its axis, is called 
the ‘‘ pitch-eircle ”’ or “‘ pitch-line,’’ The diameter of this circle is called the 
pitch-diameter, and the distance from the face of one tooth to the corre- 
sponding face of the next tooth on the same wheel, measured on an arc of 
ike pitch-circle, is called the *‘ pitch of the tooth,” or the cireular pitch. 
If two wheels having teeth of the same pitch are geared together so that 
their pitch-circles touch, it is a property of the pitch-circles that their diam- 
eters are proportional to the number of teeth in the wheels, and vice versa; 


888 . GEARING. 


thus, if one wheel is twice the diameter (measured on the pitch-circle) of the 
other, it has twice as many teeth. If the teeth are properly shaped the 
linear velocity of the two wheels are equal, and the angular velocities, or 
speeds of rotation, are inversely proportional to the number of teeth and to 
the diameter. Thus the wheel that has twice as many teeth as the other 
will revolve just half as many times in a minute. 

The ‘ pitch,” or distance measured on an arc of the pitch-circle from the 
face of one tooth to the face of the next, consists of two parts—the ‘‘ thick- 
ness’? of the tooth and the ‘“‘space’’ between it and the next tooth. The 
space is larger than the thickness by a small amount ecailed the ‘* back- 
lash,’ which is allowed for imperfections of workmanship. In finely cut 
gears the backlash may be almost nothing. 

The length of a tooth in the direc- 
tion of the radius of the wheel is 
called the ‘‘depth,” and this is di- 
vided into two parts: First, the 
* addendum,” the height of the tooth 
above the pitch line; second, the 
**dedendum,’’ the depth below the 
pitch line, which is an amount equal 
to the addendum of the mating gear. 
The depth of the space is usually 
given a little “‘clearance”’ to allow 
for inaccuracies of workmanship, 
especially in cast gears. 

Referring to Fig. 153, pl, pl are the 
pitch-lines, al the addendum-line, rl 

Fic. 153 the root-line or dedendum-line, cl 
: ot the clearance-line, and b the back- 
lash. The addendum and dedendum are usually made equal to each other. 





Wictrnetrcil ttc xk Rita ass Ob OCU ies ts ole Bateman 
rametra’ pire’ = diam. of pitch-circle in inches — Circular pitch’ 
Circular itch' — (iam. _X 8.1416 elivg bs Sab Gps) Mii 

pie. = "No. of teeth ~ diametral pitch’ 
diam. 


Some writers use the term diametral pitch to mean No. of teeth ~ 


3 1416 , but the first definition is the more common and the more. 


convenient. A wheel of 12 in. diam, at the pitch-circle, with 48 teeth is 48/12 
= 4 diametral pitch, or simply 4 pitch, The circular pitch of the same 


2 X%3.1416 8.1416 ie) 
: dip CASI = . 7854, or 7 = .7854 in. 


Relation of Diametral to Circular Pitch. 


wheel is 




















siete Circular Mele Circular | Circular bee Circular hes 
SO ee UCGEn fot PON AWE Pixechagcecro | Prantalel Fly sttpariy oy Reet te oie 2 Gos oe) 
5| 3.142 in 11 286 in 3 1.047 15/16 3.351 
1% 2.094 12 262 244 1.257 % 3.590 
Q 1.571 14 224 ry 1.571 13/16 3.867 
214 1.396 16 196 1% 1.676 4.189 
216 1.257 18 45 134 1.7 11/16 4.57 
234 1.142 20 157 15g 1.933 5 D024 
3 1.047 22 143 144 2.094 | 9/16 5.585 
344 898 24 131 1 7/16 2.185 6.283 
JL 785 26 121 134 2.285 [/16 7.181 
5 628 28 112 1 5/16 2.394 3 8.378 
6 524 30 105 114 2.0138 5/16 10.053 
% 449 32 098 1 3/16 2.646 A 12.566 
8 093 36 087 1% 2.793 3/16 16.755 
9 049 40 07 1 1/16 2.957 ig 25.133 
10 314 4; 48 .065 a 3.142 1/16 50.266 
; , Tt. diain. X 3.1416 ‘ cire. pitch « No. of teeth 
Since circular pitch = Saesrtecth diam, = “ay 8 1416 Ge 


which always brings out the diameter as a number with an inconvenient 


TOOTHED-WHEEL GEARING. | 889 


fraction if the pitch is in even inches or simple fractions of an inch. By the 
diametral-pitch system this inconvenience is avoided. The diameter may 
be in even inches or convenient fractions, and the number of teeth is usually 
an even multiple of the number of inches in the diameter. 


Diameter of Pitch-line of Wheels from 10 to 100 Teeth 
of 1 in. Circular Pitch. 














27.056 [100 | 31.831 





For diameter of wheels of any other pitch than 1 in., multiply the figures 
in the table by the pitch. Given the diameter and the pitch, to find the num- 
ber of teeth. Divide the diameter by the pitch, look in the table under 
diameter for the figure nearest to the quotient, and the number of teeth will 
be found opposite. 


Proportions of Teeth. Circular Pitch = 1. 
yi 2. 3. 4. 5. Ge 














Depth of tooth above pitch-line...| .35 380 e 387 .83 | .30 .30 

‘* below pitch-line.. 40 .40 .48 eee ea .35 
Working depth of tooth...... Babeae Sth. .60 Att POG mea ar Ae 
Total depth of tooth ...........-- £05 70 ESOS meni 70. | .65 
@learance at_coot ey ...cekie ret. once .05 10 .07 eRe te ae Afi 
Thickness of tooth.........escoe. «456 BAG 47 .45 | .475 | .485- 
Width of space. 4. sissies sc. 54 .55 53 SOD | i O2Os | eeple 
Backlash k.iys;.\..neceniecet en eas eo 10 06 -10 | .05 .08 
Thickness of rim..............--- sees Gisici 47 pA a ee 65 
SRE SPIES LT PR LE IE DEI EEA ES 

fhe 8. 9. 10.* 

Depth of tooth above pitch-line. ..|.25 to .33 80 3818 1+P 

‘¢ below pitch-line. ..|.85 to .42 |.85-+-.08/” .869 =|1.157+P 
Working depth of tooth........... oe 637 2+P 
Mota) depthor tootlken.t.ts =. <0 6 to .75 .65-+ .08/ .687 |2.157+P 
Clearance at root..... SAPO ARGHATO! losce re ot al ieee Piacies oc .04 to .05 | .157--P 
Thickness of tooth... ..... .-....|.48 to .485] .48—.03/” | 48 to .5 | ae 
Width of space .....ssssseseeeses 52 to .515|.52+-.03” |.52 to 54/52, 75 *° 
Backlash PS aS aace othe Oo ee a .04 tc 08 |.04+-.06/7 1.0 to .04 |0to06+P 











* In terms of diametral pitch. 


AUTHORITIES.—1, Sir Wm. Fairbairn. 2, 3. Clark, R. T. D.; ‘“‘used by en- 
gineers in good practice.’ 4. Molesworth. 5, 6. Coleman Sellers: 5 for 
cast, 6 for cut wheels. 7,8. Unwin. 9, 10. Leading American manufacturers 
of cut gears. 

The Chordal Pitch (erroneously called “true pitch”’ by some 
authors) is the length of a straight line or chord drawn from centre to 
centre of two adjacent teeth. The term is now but little used. 


890 GEARING. 


: ‘ : 180° 

Chordal pitch = diam. of pitch-circle x sine of Naot death: Chorda\ 
pitch of a wheel of 10 in. pitch diameter and 10 teeth, 10 x sin 18° = 3.0902 
in. Circular pitch of same wheel = 3 1416. Chordal pitch is used with chain 
or sprocket wheels, to conform <o the pitch of the chain. 


Formule for Determining the Dimensions of Smail Gears. 
(Brown & Sharpe Mfg. Co.) 


F = diametral pitch, or the number of teeth to one inch of diameter of 
pitch-circle; 





D’ = diameter of pitch circle...... mb ae Poor Cok. 








D = whole diameter ........... Magee Po Sead .| Larger 

N = number of teeth .....-...... ce ee Wheel. 

Ve velocity).c.: cnc: aes Browsers eke apes ae dices wlane' se These wheels 
kt RR eee) be er run 

d’ = diameter of pitch-circle....... ... ..+.... together, 

dad = whole diameter............. ee a8 seiae one Smaller 

7 = number of teeth £.hicess pes vc ccs de hece ote Wheel. 

Diss VOIOCILY ..26 a sls ve s’o08 scsi e's Si baiees Meee aoe: 








a = distance between the centres of the two wheels; 
b = number of teeth in both wheels; 
t = thickness of tooth or cutter on pitch-circle; 
s = addendum; 
D’’= working depth of tooth; 
f = amount added to depth of tooth for rounding the corners and for 


clearance; 
D’'+ f = whole depth of tooth; 
w = 3.1416. 


P’= circular pitch, or the distance from the centre of one tooth to the 
centre of the next measured on the pitch-circle. 


Formule for a single wheel: 























~N+2 pet x N Pe oda ettean ate a 
a ile Napa tO) Spa ee ee a ee aes 
— Na poy, N = PD’; a. ie D 
na re aes N = PpD-2; °~ Ww * Woe! 
pe, _N+2, . 1 7 
Kb Nese Mitac aaa page els 
P= rd D=D'+ t= P =r 
Formule for a pair of wheels: 
aa Pe EDT _ 2a(N 4 2) 
b = 2aP3 a = D=— 3 
nv , PD'V an 
N=-73 Ui eres a= TS, 
a NK Pap od ake 
r= © 9 — n ry edhe Ee Fo 
bv, Re. Di +d’, 
N= 549 Be 3 or eee 
bv , _ 2av ,. 2aV 
n= Ve aS ae 


The following proportions of gear- wheels are recommended by Prof. Cole 
man Sellers, (Stevens Indicator, April, 1892.) 


TOOTHED-WHEEL GEARING. 891 


Proportions of Gear-wheels. 

















Inside of Pitch-line. Width of Space. 
3 
2a i | 
© | Circular Beate tee eee For Cut For Cast | For Cut 
ES Pitel ae. Spurs. Spurs or | Bevels or 
og A itch, PX.3 | or for Cast Pp ? 
= Spurs PX .35 Bevels. Spurs. 
pra PX 525 fox sd 
iY 07 .100 -088 -131 128 
12 .2618 079 105 092 137 134 
10 31416 094 126 Aly! 165 16 
364 113 150 131 197 19] 
8 3927 118 157 13% 206 2 
7 447 134 179 157 235 228 
15 20le Ait 263 255 
5236 157 .209 183 27 267 
9/16 169 225 197 295 287 
5 188 225 .219 328 319 
5 2832 188 feos ee 33 32 
3 225, 3 263 394 383 
4 7854 236 314 275 412 -401 
% 263 385 807 459 -446 
3 4 .35 525 51 
3 | 1.0472 314 419 364 255 034 
1 338 45 394 591 574 
234] 1.1424 343 457 -40 583 
375 438 656 . 638 
214) 1.25664 377 503 44 66 .641 
134 413 50 481 122 701 
11 45 6 525 “785 765 
2 | 1.5708 47 628 55 825 801 
134 525 ve 613 919 .893 
6 8 atl 1.05 1.02 
114| 2.0944 -628 838 (33 ies 1.068 
214 675 9 .788 1.161 1,148 
2% 75 1.0 87 1.313 1255 
234 825 1.1 .963 1.444 1.403 
3 ao 1.2 1.05 1.575 1.53 
1 | 3.1416 942 1,257 1.1 1.649 1.602 
314 975 1.3 1.138 1.706 1 657 
316 1.05 1.4 1.225 1.838 1.785 


—, 


Thickness of rim below root = depth of tooth. 


Width of Teeth.—The width of the faces of teeth is generally made 
from 2 to 3 tines the circular pitch — from 6.28 to 9.42 divided by the diam- 
etral pitch. There is no standard rule for width. 

The following sizes are given in a stock list of cut gears in ‘‘ Grant’s 
Gears: ”’ 


Diameter pitch..... 3 4 6 8 12 16 
Face, inches......i¢+ 8and4 24% 138and2 144 and1% 34and1 Wand % 


The Walker Company give: 


Circular pitch,in.. 4% % 4% % D116 2 thee Oy eee 
Facey it» cere TAS ioe scum eee ta dt G7 726. 19) Te) 1b 20 


Rules for Calculating the Speed of Gears and Pulleys.— 
The relations of the size and speed of driving and driven gear wheels are 
the same as those of belt pulleys. In calculating for gears, multiply or 
divide by the diameter of the pitch-circle or by the number of teeth, as 
may be required. In calculating for pulleys, multiply or divide by their 
diameter in inches. ; 

If D = diam. of driving wheel, d = diam. of driven, & = revolutions per 
minute of driver, 7 = revs. per min. of driven. 

R=rd+D; r= khD+-d: D=dr--R} d= DR+ ?. 
If N = number of teeth of driver and » = number of teeth of driven, 
Noeur+TRk; n=NR+7; Ra=rn+sN; r= kRN+7. 


892 GEARING. 


To find the number of revolutions of the last wheel at the end of a train 
of spur-wheels, all of which are in a line and mesh into one another, when 
the revolutions of the first wheel and the number of teeth or the diameter 
of the first and last are given: Multiply the revolutions of the first wheel by 
its number of teeth or its diameter, and divide the product by the number 
of teeth or the diameter of the last wheel. 

To find the number of teeth in each wheel for a train of spur-wheels, 
each to have a given velocity: Multiply the number of revolutions of the 
driving-wheel by its number of teeth, and divide the product by the number 
of revolutions each wheel is to make. 

To find the number of revolutions of the last wheel in a train of wheels 
and pinions, when the revolutions of the first or driver, and the diameter, 
the teeth, or the circumference of all the drivers and pinions are given: 
Multiply the diameter, the circumference, or the number of teeth of all the 
driving-wheels together, and this continued product by the number of revo- 
lutions of the first wheel, and divide this product by the continued product 
of the diameter, the circumference, or the number of teeth of all the driven 
wheels, and the quotient will be the number of revolutions of the last wheel. 

EXAMPLE.—1. A train of wheels consists of four wheels each 12 in. diameter 
of pitch-circle, and three pinions 4, 4, and 3 in, diameter. The large wheels 
are the drivers, and the first makes 36 revs. per min. Required the speed 
of the last wheel. 


86 X 12 X 12 K 12 
4x4x3 

2. What is the speed of the first large wheel if the pinions are the drivers, 
the 3-in. pinion being the first driver and making 36 revs. per min.? 

86x 38x4x4 

125412 <2 

Milling Cutters for Interchangeable Gears.—The Pratt & 

Whitney Co. make a series of cutters for cutting epicycloidal teeth. The 

number of cutters to cut from a pinion of 12 teeth toa rack is 24 for each 

pitch coarser than 10. The Brown & Sharpe Mfg. Co. make a similar series, 


and also a series for involute teeth, in which eight cutters are made for 
each pitch, as follows: 


= 1296 rpm. 


=I1rpm. Ans. 


INO Meet Jove 1. 2. 3. 4. 5. 6. rf 8. 
Will cut from 135 55 35 26 21 1% 14 12 
to Rack = 134 54 34 25 20 16 13 


FORMS OF THE TEETH. 


In order that the teeth of wheels and pinions may run together smoothly 
and with a constant relative velocity, it is necessary that their working 
faces shall be formed of certain curves called odontoids. The essential 
property of these curves is that when two teeth are in contact the common 
normal to the tooth curves at their point of contact must pass through the 
pitch-point, or point of contact of the two pitch-circles. Two such curves 
are in common use—the cyloid and the involute. 

Whe Cycloidal Tooth.—In Fig. 154 let PL and pl be the pitch-circles 
of two gear-wheels; GC and gc are two equal generating-circles, whose radii 
should be taken as not greater than one half of -the radius of the smaller 
pitch-circle. If the circle gc be rolled to the left on the larger pitch-circle 
PL, the point O will describe an epicycloid, oefgh. If the other generating- 
circle GC be rolled to the right on PJ, the point O will describe a hypocy- 
cloid oabcd. These two curves, which are tangent at O, form the two parts 
of a tooth curve for a gear whose pitch-circle is PL. The upper part oh is 
called the face and the lower part od is called the flank, If the same circles 
be rolled on the other pitch-circle pl, they will describe the curve for a tooth 
of the gear pl, which will work properly with the tooth on PL. 

The cycloidal curves may be drawn without actually rolling the generat- 
ing-circle, as follows: On the line PL, from O, step off and mark equal dis- 
tances, as 1,2, 3, 4, etc. From 1, 2, 3, etc., draw radial lines toward the centre 
of PL, and from 6, 7, 8, etc., draw radial lines from the same centre, but be- 
yond PL. With the radius of the generating-circle, and with centres suc- 
cessively placed on these radial lines, draw arcs of circles tangent to PL at 
123,678, etc. With the dividers set to one of the equal divisions, as Q,, 


FORMS OF THE TEETH. 893 


step off 1a and 6e; step off two such divisions on the circle from 2 to b, and 
from 7 to f; three such divisions from 3 toc, and from 8 to g; and so on, thus 
locating the several points abcdH and efgk, and through these points draw 
the tooth curves. 

The curves for the mating tooth on the other wheel may be found in like 
manner by drawing ares of the generating-circle tangent at equidistant 
points on the pitch-cirele pl. 

The tooth curve of the face oh is limited by the addendum-line r or 7, 






ve q \ sae = 
: 8 a PS ‘ 
2 Z| 


EN 
FS 
EN 
] 
Z| 
7 
/ 
av 


Fig. 154. 


and that of the flank oH by the root curve R or R,. Rand r represent the 
root and addendum curves for a large number of small teeth, and &,r the 
like curves for a small number of large teeth. The form or appearance of 
the tooth therefore varies according to the number of teeth, while the pitch. 
circle and the generating-circle may remain the same. 

In the cycloidal system, in order that a set of wheels of different diam- 
eters but equal pitches shall all correctly work together, it is necessary that 
the generating-circle used for the teeth of all the wheels shall be the same, 
and it should have a diameter not greater than half the diameter of the pitch- 
line of the smallest wheel of the set. The customary standard size of the 
generating-circle of the cycloidal system is one having a diameter equal to 
the radius of the pitch-circle of a wheel having 12 teeth. (Some gear- 
makers adopt 15 teeth.) This circle gives a radial flank to the teeth of a 
wheel having 12 teeth. A pinion of 10 or even a smaller number of teeth 
can be made, but in that case the flanks will be undercut, and the tooth will 
not be as strong asa tooth with radial flanks. If in any case the describing 
circle be half the size of the pitch-circle, the flanks will be radial; if it be 
less, they will spread out toward tthe root of the tooth, giving a stronger 
form; but if greater, the flanks will curve in toward each other, whereby the 
teeth become weaker and difficult to make. { 

In some cases cycloidal teeth for a pair of gears are made with the gener- 
ating-circle of each gear, having a radius equal to half the radius of its pitch- 
circle. In this case each of the gears will have radial flanks. This method 
makes a smooth working gear, but a disadvantage is that the wheels are 
not interchangeable with other wheels of the same pitch but different num- 
bers of teeth, 


- 


894 GEARING. 


The race in the cycloidal system is equivalent to a wheel with an infinite 
number of teeth. ‘he pitch is equal to the circular pitch of the mating 
gear. Both faces and flanks are cycloids formed by rolling the generating- 
circle of the mating gear-wheel on each side of the straight pitch-line of 
the rack. 


i) 


prs Cc 

8 “WY b 3 

2 a 2 
3 cece SiN ie : 
4 HX rd 
ia] hn aan i; \ alates seeps 5 
P ‘ --7 - i tem ~~ F 
gan “~R 
G 
Fia. 155, 


Another method of drawing the cycloidal curves is shown in Fig. 155. It 
is known as the method of tangent ares. The generating-circles, as before, 
are drawn with equal radii, the length of the radius being less‘than half the 
radius of pl, the smaller pitch-circle. Equal divisions 1, 2, 3, 4, ete., are 
marked off on the pitch circles and divisions of the same length stepped off 
on one of the generating-circles, as oabc, etc. From the points 1, 2, 3,4, 5 on 
the line po, with radii successively equal to the chord distances oa, ob, oc, 
od, oe, draw the five small ares F#’. A line drawn through the outer edges of 
these small-arcs, tangent to them all, will be the hypocycloidal curve for the 
flank of a tooth below the pitch-line pl. From the points 1, 2, 3, etc., on the 
line ol, with radii as before, draw the small ares G. A line tangent to these 
arcs will be the epicycloid for the face of the same tooth for which the flank 
curve has already been drawn. In the same way, from centres on the line 
Po, and oL, with the same radii, the tangent arcs H and.K may be drawn, 
which will give the tooth for the gear whose pitch-circle is PL. 

If the generating-circle had a radius just one half of thc radius of pl, the 
bypocycloid # --ld be a straight line, and the flank of the tooth would 
have been radial. . 

Khe Involute Tooth.—In drawing the involute tooth curve, the 
angle of obliquity, or the angle which a common tangent to the teeth, when 
they are in contact at the pitch-point, makv. with a line joining the centres 
of the wheels, is first arbitrarily determined. Itis customary to take it at 15°, 
The pitch-lines pl and PL being drawn in contact at O, the line of obliquity 
AB is drawn through Onormal to a common tancent to the tooth curves, or 
at the given angle of obliquity to a common tangent to the pitch-circles.. In 


FORMS OF THE TEETH, 895 


the cut the angle is' 20°. From the centres of the pitch-circles draw circles c 
and d tangent to the line AB. These circles are called base-lines or base- 
circles, froin which the involutes #’ and K are drawn. By laying off conven- 
ient distances, 0, 1, 2,3, which should each be less than 1/10 of the diameter 
of the base-circle, small ares can be drawn with successively increasing 
radii, which will form the involute. The involute extends from the points # 


IN.\. 4 
\ 





Fia. 156. 


and K down to their respective base-circles, where a tangent to the invo- 
lute becomes a radius of the circle, and the remainders of the tooth curves, 
as G and H, are radial straight lines. 

In the involute system the customary standard form of tooth is one 
having an angle of obliquity of 15° (Brown and Sharpe use 1414°), an adden- 
dum of about one third the circular pitch, and a clearance of about one 
eighth of the addendum. Im this system the smallest gear of a set has 12 
teeth, this being the smallest number of teeth that will gear together when 
made with this angle of obliquity. In gears with less than 30 teeth the 
points of the teeth must be slightly rounded over to avoid interference (see 
Grant’s Teeth of Gears). All involute teeth of the same pitch and with the 
same angle of obliquity work smoothly together. The rack to gear with an 
involute-toothed wheel has straight faces on its teeth, which make an angle 
with the middle line of the tooth equal to the angle of obliquity, or in the 
standard form the faces are inclined at an angle of 30° with each other. 

To draw the teeth of a rack which is to gear with an involute wheel (Fig. 
157).—Let AB be the pitch-line of the rack and AJ=J/’/=the pitch. Through 





Wie. 157. 


the pitch-point 7draw HF'at the given angle of obliquity, Draw AH and 
I’F perpendicular to HF. Through Hand F draw lines EGG’ and FH par- 
allel to the pitch-line. HGG’ will be the addendum-line and HF the flank- 
line. From J draw IK perpendicular to AB equal to the greatest addendum 
in the set of wheels of the given pitch and obliquity plus an allowance for 
clearance equal to “of the addendum. Through K, parallel to AB, draw 
the clearance-line. The fronts of the teeth are planes perpendicular to HF, 
and the backs are planes inclined at the same angle to AB in the contrary 
direction. The outer half of the working face 4H may be slightly curved. 
Mr. Grant makes it a circular are drawn from a centre on the pitch-line 


896 GEARING. 


with a radius = 2.. inches divided by the diametral pitch, or .67 in. x cir 
cular pitch. : 

To Draw an Angle of 15° without using a Protractor.—From C,on the 

line AC, with radius AC, draw 
B an are AB, and from <A, with 
the same radius, cut the are at 
B. Bisect the arc BA by draw- 
ing small ares at D from A and B 
as centres, with the same radius, 
which must be greater than one 
half of AB. Join DC, cutting BA 
at H#. The angle ECA is 30°. Bi- 
sect the arc AE in like manner, 
and the angle F'CA will be 15°, 

A property of involute-toothed 
wheels is that the distance between 
the axes of a pair of gears may be 

fe} altered to a considerable extent 

A without interfering with their ac- 

Fig. 158 tion. The backlash is therefore 

: is variable at will, and may be ad- 

justed by moving the wheels farther from or nearer to each other, and may 

thus be adjusted so as to be no greater than is necessary to prevent jam- 
ming of the teeth. 

The relative merits of cycloidal and involute-shaped teeth are still a sub- 
ject of dispute, but there is an increasing tendency to adopt the involute 
tooth for all purposes. 

Clark (R. T. D., p. 784) says: Involute teeth have the disadvantage of 
being too much inclined to the radial line, by which an undue pressure is 
exerted on the bearings. 

Unwin (Elements of Machine Design, 8th ed., p. 265) says: The obliquity 
of action is ordinarily alleged as a serious objection to involute wheels. Its 
importance has perhaps been overrated. 

George B. Grant (Am. Mach., Dec. 26, 1885) says: 

1. The work done by the friction of an involute tooth is always less than 
the same work for any possible epicycloidal tooth. 

2. With respect to work done by friction, a change of the base from a 
gear of 12 teeth to one of 15 teeth makes an improvement for the epicycloid 
of less than one half of one per cent. 

3. For the 12-tooth system the involute has an advantage of 11/5 per 
cent, and for the 15-tooth system an advantage of 34 per cent. 

4, That a maximum improvement of about one per cent can be accom- 
plished by the adoption vf any possible non-interchangeable radial flank ~ 
tooth in preference to the 12-tooth interchangeable system. 

5. That for gears of very few teeth the involute has a decided advantage. 

6. That the common opinion among millwrights and the mechanical pub. 
lic in general in favor of the epicycloid is a prejudice that is founded on 
long-continued custom, and not on an intimate knowledge of the properties 
of that curve. 

Wilfred Lewis (Proc. Engrs. Club of Phila., vol. x., 1893) says a strong 
reaction in favor of the involute system is in progress, and he believes thas 
an involute tooth of 221¢° obliquity will finally supplant all other forms. 

Approximation by Circular Ares,—Having found the form of 
the actual tooth-curve on the drawing-board, circular ares may be found by 
trial which will give approximations to the true curves. and these may be 










H 
‘ f centres_ >> ___for /Rvot 
int, 8) S 7B AA 











ee ira 





/ 
Notes 


—— eee \ I 


“ 


Fie. 159, 


FORMS OF THE TEETH. 897 


used In completing the drawing and the pattern of the gear-wneels. The 
root of the curve is connected to the clearance by a fillet, which should be 
as large aspossible to give increased strength to the tooth, provided it is not 
large enough to cause interference. 

Molesworth gives the following method of construction by circular ares: 

From the radial line at the edge of the tooth on the pitch-line, lay off the 
line HK at an angle of 75° with the radial line; on this line will be the cen- 
tres of the root AB and the point HF. The lines struck from these centres 
are shown in thick lines. Circles drawn through centres thus found will 
give the lines in which the remaining centres will be. The radius DA for 
striking the root AB is = pitch + the thickness of the tooth. The radius 
CE for striking the point of the tooth HF’ = the pitch. 

George B. Grant says: It is sometimes attempted to construct the curve 
by some handy method or empirical rule, but such methods are generally 
worthless. 

Stepped Gears.--Two gears of the same pitch and diameter mounted 
side by side on the same shaft will act as a single gear. If one gear is keyed 
on the shaft so that the teeth of the two wheels are not in line, but the 
teeth of one wheel slightly in advance of the other, the two gears form a 
stepped gear. If mated witha similar stepped gear on a parallel shaft the 
number of teeth in contact will be twice as great as in an ordinary gear, 
which will increase the strength of the gear and its smoothness of action. 

Twisted Teeth.—If a great number of very thin gears were placed 
together, one slightly in advance of the other, they would still act asa 
stepped gear. Continuing the subdivision until the = 
thickness of each separate gear is infinitesimal, the 
tkces Gt the teeth instead of being in steps take the 
form of a spiral or twisted surface, and we have a 
twisted gear. The twist may take any shape, and if it is 
in one direction for half the width of the gear and in the 
opposite direction for the other half, we have what is 
known as the herring-bone or double helical tooth. The 
obliquity of the twisted tooth if twisted in one direction 
causes an end thrust on the shaft, but if the herring- 
bone twist is used, the opposite obliquities neutralize 
each other. This form of tooth is much used in heavy 
rolling-mill practice, where great strength and resistance 
to shocks are necessary. They are frequently made of “ 
steel castings (Fig. 160). The angle of the tooth with a es 
line parallel to the axis of the gear is usually 30°. Fic. 160. 

Spiral Gears.—If a twisted gear has a uniform twist it becomes a 
spiral gear. The line in which the pitch-surface intersects the face of the 
tooth is part of a helix drawn on the pitch-surface. A spiral wheel may be 
made with only one helical tooth wrapped around the eylinder several 
times, in which it becomes a screw or worm. If it has two or three teeth 
so wrapped, it is a double- or triple-threaded screw or worm, A spiral-gear 
meshing into a rack is used to drive the table of some forms of planing- 
machine. : ’ 

Worm-gearing.—When the axes of two spiral gears are at rignt . 
angles, and a wheel of one, two, or three threads works with a larger wheel 
of many threads, it becomes a worm-gear, or endless screw, the smaller 









\ 


Ss 





Fra. 161, 


wheel or driver being called the worm, and the larger, or driven wheel, the 
worm-wheel. With this arrangement a high velocity ratio may be obtained 
with a single pair of wheels. For a one-threaded wheel the velocity ratio ig 


898 GEARING. 


the number of teeth :n the worm-wheel. The worm and wheel are com- 
monly so constructed that the worm will drive the wheel, but the wheel will 
not drive the worm. 

To find the diameter of a worm-wheel at the throat, number of teeth and 
pitch of the worm being given: Add 2 to the number of teeth, multiply the 
sum by 0.3188, and by the pitch of the worm in inches, 

To find the number of teeth, diameter at throat and pitch of worm being 
given: Divide 3.1416 times the diameter by the pitch, and subtract 2 from 
the quotient, 

In Fig. 161 ab is the diam. of the pitch-circle, cd is the diam. at the throat, 

EXAMPLE.— Pitch of worm 14 in., number of teeth 70, required the diam. 
- at the throat. (70-+ 2) X .3188 X .25 ='5.73 in. 

Weeth of Bevel=-wheels, (Rankine’s Machinery and Millwork.)— | 
The teeth of a bevel-wheel have acting surfaces of the conical kind, gen- 
erated by the motion of a line traversing the apex of the conical pitch- 
surface, while a point in it is carried round the traces of the teeth upon a 
spherical surface described about that apex. 

The operations of drawing the traces of the teeth of bevel-wheels exactly, 
whether by involutes or by rolling curves, are in every respect analogous to 
those for drawing the traces of the teeth of spur-wheels; except that in the 
case of bevel- wheels all those operations are to be performed on the surface 
of a sphere described about the apex, instead of on a plane, substituting 
poles for centres and great circles for straight lines. 

In consideration of the practical difficulty, especially in the case of large 
wheels, of obtaining an accurate spherical surface, and of drawing upon it 
when obtained, the following approximate method, proposed originally by 
Tredgold, is generally used: 

Let O, Fig. 162, be the common apex of the pitch-cones, OBJ, OB’T, of a 
pair of bevel-wheels; OC, OC’, the axes of those cones; OJ their line of con- 
B tact. Perpendicular to OJ draw 
AIA’, cutting the axes in A, A’; 

make the outer rims of the patterns 

and of the wheels portions of the 

cones ABI, A’B’T, of which the nar- 

A Yow zones occupied by the teeth will 

be sufficiently near for practical pur- 

| poses to a spherical surface described 

| about O. Asthe cones ABI, A’B’l | 

| cut the pitch-cones at right angles in 

the outer pitch-circles IB, 1B’, they 

D may be called the normal cones. To 

find the traces of the teeth upon the 

normal cones, draw on a flat surface 

circular ares, ID, ID’, with the radii 

N’ D AI, A'I; those ares will be the de- 

Fia. 162. velopments of arcs of the pitch- 

circles JB, IB’ when the conical sur- 

faces ABI, A’B’Tare spread out flat. Describe the traces of teeth for the 

developed arcs as for a pair of: spur-wheels, then wrap the developed ares 

on the normal cones, so as to make them coincide with the pitch-circles, and 
trace the teeth on the conical surfaces. 

For formule and instructions for designing bevel-gears, and for much other 
valuable information on the subject of gearing, see ‘‘ Practical Treatise on 
Gearing,” and ** Formulas in Gearing,’’ published by Brown & Sharpe Mf’g 
Co.; and *‘Teeth of Gears,” by George B. Grant, Lexington, Mass. The 
student may also consult Rankine’s Machinery and Millwork, Reuleaux’s 
Constructor, and Unwin’s Elements of Machine Design. See also article on 
Gearing, by C. W. MacCord in App, Cye. Mech., vol. ii. 

Annular and Differential Gearing. (S. W. Balch., Am. Mach., 
Aug. 24, 1893.)—In internal gears the sum of the diameters of the describing 
circles for faces and flanks should not exceed the difference in the pitch 
diameters of the pinion and its internal gear, The sum may be equal to this 
difference or it may be less; if it is equal, the faces of the teeth of each 
wheel will drive the faces as well as the flanks of the teeth of the other 
wheel. The teeth will therefore make contact with each other at two points 
at the same time. 

Cycloidal tooth-curves for interchangeable gears are formed with describ- 
ing circles of about 5¢ the pitch diameter of the smallest gear of the series. 
To admit two such circles between the pitch-circles of the pinion and internai 






B. 


EFFICIENCY OF GEARING. 899 


gear the number of teeth in the internal gear should exceed the number in 
the pinion by 12 or more, if the teeth are of the customary proportions and 
curvature used in interchangeable gearing. 

Very often a less difference is desirable, and the teeth may be modified in 
several ways to make this possible. 

First. The tooth curves resulting from smaller describing circles may be 
employed. These will give teeth which are more rounding and varrower at 
their tops, and therefore not as desirable as the regular forms. 

Second. The tips of the teeth may be rounded until they clear, Thisisa 
cut-and-try method which aims at modifying the teeth to such outlines as 
smaller describing circles would give. 

Third. One of the describing circles may be omitted and one only used, 
which may be equal to the difference between the pitch-circles. This will 
permit the meshing of gears differing by six teeth. It will usually prove 
preredions to put wheels in inside gears that differ jby much less than 12 
teeth. 

If a regular diametral pitch and standard tooth forms are determined on, 
the diameter to which the internal] gear-blank is to be bored is caleulated by 
subtracting 2 from the number of teeth, and dividing the remainder by the 
diametral pitch. 

The tooth outlines are the match of a spur-gear of the same number of 
teeth and diametral pitch, so that the spur gear will fit the internal gear as 
a punch fits its die, except that the teeth of each should fail to bottom in 
the tooth spaces of the other by the customary clearance of one tenth the 
thickness of the tooth. 

Internal gearing is particularly valuable when employed in differential 
action. This is a mechanical movement in which one of the wheels is 
mounted on a crank so that its centre can move in a circle about the centre 
of the other wheel. Means are added to the device which restrain the wheel 
on the crank from turning over and confine it to the revolution of the crank. 

The ratio of the number of teeth in the revolving wheel compared with 
the difference between the two will represent the ratio between the revolv- 
ing wheel and the crank-shaft by which the other is carried. The advan- 
tage in accomplishing the change of speed with such an arrangement, as 
compared with ordinary spur-gearing, lies in the almost entire absence of 
friction and consequent wear of the teeth. 

But for the limitation that the difference between the wheels must not be 
too small, the possible ratio of speed might be increased almost indefinitely, 
and one pair of differential gears made to do the service of a whole train of 
wheels. If the problem is properly worked out with bevel-gears this limita- 
tion may be completely set aside, and external and internal bevel-gears, 
lie ig by but a single tooth if need be, made to mesh perfectly with each 
other. 

Differential bevel-gears have been used with advantage in mowing-ma- 
chines. A description of their construction and operation is given by Mr. 
Balch in the article from which the above extracts are taken. 


EFFICIENCY OF GEARING, 


An extensive series of experiments on the efficiency of gearing, chiefly 
worm and spiral gearing, is described by Wilfred Lewis in Trans. A. S. M. E., 
vii. 273. The average results are shown in a diagram, from which the fol- 
lowing approximate average figures are taken : 


EFFICIENCY OF SPUR, SPIRAL, AND WoRM GEARING. 





Velocity at Pitch line in feet per min, 





Gearing. Pitch. as 
3 10 40 100 200 
DU ls PINTO. occas fies sei .90 935 19 .98 985 
Syollez Why a) FINK) shee Gee SIA See 45° 81 87 .93 955 965 
ee bd gis e's'>= corer ate 30 of 815 89 93 945 
a SOR Aa'sns sae es enacted 20 67 te 845 .90 92 
os Seal via sin dyisvat 7a 15 61 70 805 87 90 
Spiral pinion or worm..... 10 51 615 74 82 86 
eS se ob Vi 


saaeie OMG hs 134 | 143 60 70 765 








900 GEARING, 


The experiments showed the advantage of spur-gearing over all other 
kinds in both durability and efficiency. The variation from the mean resuits 
rarely exceeded 5% in either direction, so long as no cutting occurred, but 
the variatiun became much greater and very irregular as soon as cutting 
began. The loss of power varies with the speed, the pressure, the tempera- 
ture, and the condition of the surfaces. The excessive friction of worm and 
spiral gearing is largely due to thee nd thrust on the collars of the shaft. 
This may be considerably reduced by roller-bearings for the collars. 

When two worms with opposite spirals run in two spiral worm-gears that 
also work with each other, and the pressure on one gear is opposite that on 
the other, there is no thrust on the shaft. Even with light loads a worm 
will begin to heat and cut if run at too high a speed, the limit for safe work- 
ing being a velocity of the rubbing surfaces of 200 to 300 ft. per minute, the 
former being preferable where the gearing has to work continuously. The 
wheel teeth will keep cool, as they form part of a casting having a large 
radiating surface; but the worm itself is so small that its heat is dissipated 
slowly. Whenever the heat generated increases faster than it can be con- 
ducted and radiated away, the cutting of the worm may be expected to be- 
gin. A low efficiency for a worm-gear means more than the loss of power, 
since the power which is lost reappears as heat and may cause the rapid 
destruction of the worm. 

Unwin (Elements of Machine Design, p. 294) says: The efficiency is greater 
the less the radius of the worm. Generally the radius of the worm = 1.5 to 
3 times the pitch of the thread of the worm or the circular pitch of the 
worm-wheel. For a one-threaded worm the efficiency is only 2/5 to 4; 
for a two-threaded worm, 4/7 to 2/5; for a three-threaded worm, % to 4. 
Since so much work is wasted in friction it is not surprising that the wear 
is excessive. The following table gives the calculated efficiencies of worm- 
wheels of 1, 2, 3, and 4 threads and ratios of radius of worm to pitch of teeth 
of from 1 to 6, assuming a coefficient of friction of 0.15: 





Radius of Worm -- Pitch. 








No. of 
TTLNY ead S| sammie 
1 igen lie | 13{ 2 | 2% | Sin |edit 
1 50 af lee. 40 36 | .33 | .28] .25] .20| .14 
2 "67 62 | 157 BB 1) 508 | 244 12 a0 leet selene 
3 5 7 67 63-3 (060) 1 bse boreal eee 
4 307) {org NE og 70 nbY oh 368. | Ste lat attest 





STRENGTH OF GEAR-TEETH. 


The strength of gear-teeth and the horse-power that may be transmitted 
by them depend upon so many variable and uncertain factors that it is not 
surprising that the formulas and rules given by different writers show a 
wide variation. In 1879 John H. Cooper (Jour. Frank. Inst., July, 1879) 
found that there were then in existence about 48 well-established rules for 
horse-power and working strength, differing from each other in extreme 
cases about 500%. In 1886 Prof. Wm. Harkness (Proc. A. A. A.S, 1886), 
from an examination of the bibliography of the subject, beginning in 1796, 
found that according to the constants and formulee used by various authors 
there were differences of 15 to 1 in the power which could be transmitted 
by a given pair of geared wheels. The various elements which enter into 
the constitution of a formula to represent the working strength of a toothed 
wheel are the following: 1. The strength of the metal, usually cast iron, which 
is an extremely variable quantity. 2. The shape of the tooth, and espec- 
ially the relation of its thickness at the root or point of ieast strength to the 
pitch and to the length. 3. The point at which the toad ig taken to be ap- 
plied, assumed by some authors to be at the pitch-line, by others at the 
extreme end, along the whole face, and by still others at a single outer 
corner. 4. The consideration of whether che total load is at any time re- 
ceived by a single tooth or whether it is divided between two teeth. 5. The 
influence of velocity in causing a tendency to break the teeth by shock. 6. 
The factor of safety assumed to cover all the uncertainties of the other ele 
ments of the problem. 


STRENGTH OF GEAR-TEETH. 901 


Prof. Harkness, as a result of his investigation, found that all the formule 
on the subject might be expressed in one of three forms, viz.: 


Horse-power = CVp/f, or CVp?, or CVp?f/; 


in which Cis a coefficient, V = velocity of pitch-line in feet per second, p = 
pitch in inches, and f = face of tooth in inches. 

From an examination of precedents he proposed the following formula 
for cast-iron wheels: 


0.910V pf 
H.P.= 740.657" 


He found that the teeth of chronometer and watch movements were sub- 
ject to stresses four times as great as those which any engineer would dare 
to use in like proportion upon cast-iron wheels of large size. 

It appears that all of the earlier rules for the strength of teeth neglected 
the consideration of the variations in their form; the breaking strength, as 
said by Mr. Cooper, being based upon the thickness of the teeth at the pitch- 
line or circle, as if the thickness at the root of the tooth were the same in 
all cases as it is at the pitch-line. 

Wilfred Lewis (Proc. Eng’rs Club, Phila., Jan. 1893; Am. Mach., June 22, 
1893) seems to have been the first to use the form of the tooth in the con- 
struction of a working formula and table. He assumes that in well-con- 
structed machinery the load can be more properly taken as well distribured 
across the tooth than as concentrated in one corner, but that it cannot be 
safely taken as concentrated at a maximum distance from the root less 
than the extreme end of the tooth. He assumes that the whole load is 
taken upon one tooth, and considers the tooth as a beam loaded at one end, 
and from a series of drawings of teeth of the involute, cycloidal, and radial 
flank systems, determines the point of weakest cross-section of each, and 
the ratio of the thickness at that section to the pitch. He thereby obtains 
the general formula, 

W = spfy; 


in which W is the load transmitted by the teeth, in pounds; s is the safe 
working stress of the material, taken at 8000 lbs. for cast iron, when the 
working speed is 100 ft. or less per minute; p = pitch; f = face, in inches; 
y = a tactor depending on the form of the tooth, whose value for different 
cases is given in the following table: 


























Factor for Strength, y. Factor for Strength, y. 
tes i Involute { Involut tr othe Invol Invol 
Teeth. } Involute | Involute . eeth. | Involute | Involute : 
20° Obli- | 15° and | Radial 20° Obli- | 15° and | Radial 
quity. |Cycloidal 1 quity. |Cycloidal 7 
42 ~«| ~~ ~.078 067 052 27 111. | .100 064 
13 083 070 053 30 114 102 065 
14 088 072 054 34 118 104 066 
15 092 075 055 388 122 107 067 
16 094 077 056 43 126 110 068 
ilgy 096 -980 057 50 730 112 069 
18 098 083 058 60 134 114 70 
19 100 087 059 5 138 116 071 
20 102 090 060 100 142 118 072 
21 104 092 061 150 146 120 073 
23 106 094 062 300 150 122 074 
25 108 097 063 Rack 154 cleat 075 
SAFE WORKING STRESS, s, FOR DIFFERENT SPEEDS. 
Speed of Teeth in 100 or] . 
Pe snerteninute. less, | 200 | 3800 | 600 } 990 | 1200 } 1800 | 2400 
Cast iron....... Bey Ss) 8000] 6000! 4800! 4000] 3000 ; 2400 | 2000 | 1700 


Steel} ieee ees 20000} 15000! 12000! 10000] 7500 | 6000 | 5000 j 4300 


‘902 GEARING. 


The values of s in the above table are given by Mr. Lewis tentatively, in 
the absence of sufficient data upon which to base more definite values, but 
they have been found to give satisfactory results in practice. 

Mr. Lewis gives the following example to illustrate the use of the tables; 
Let it be required to find the working strength of a 12-toothed pinion of 1- 
inch pitch, 214-inch face, driving a wheel of 60 teeth at 100 feet or less per 
minute, and let the teeth be of the 20-degree involute 
form. Inthe formula W = spfy we have for a cast-iron 
pinion s = 8000, pf = 2.5, and y =.078; and multiplying these 
values together, we have W = 1560 pounds. For the wheel 
we have y = .134 and W = 2680 pounds. 

The cast-iron pinion is, therefore, the measure of 
strength; but if a steel pinion be substituted we have > 
s = 20,000 and W = 3900 pounds, in which combination 
the wheel is the weaker, and it therefore becomes the 
measure of strength. 

For bevel-wheels Mr. Lewis gives the following, rcfer- 
ring to Fig. 168: D=Jarge diameter of bevel; d= 
small diameter of bevel; » = pitch at large diameter; 
nm = actual number of teeth; f = face of beve., WN = for- 
mative nuniber of teeth = n *% secant a, or the number 
corresponding to radius R; y = factor depending upon 
shape of teeth and formative number NV; W = working load on teeth. 


Ww Di-d , aAyW. We ad 
= spfy 3D(D —d)? or, more simply, = sPfys 





which gives almost identical results when d is not less than 3% D, as is the 
case in good practice. 

In Am, Mach., June 22, 1893, Mr. Lewis gives the following formule for 
the working strength of the three systems of gearing, which agree very 
closely with those obtained by use of the table: 


For involute, 20° obliquity, W = spf (154 ¥ 2R 3 
bs ( 684 

For involute 15°, and cyc‘oidal, W = spf, .124 — iy ag 

For radial flank system, W= spf (078 i sa ; 


in which the factor within the parenthesis corresponds to y in the general 
formula, For the horse-power transmitted, Mr. Lewis’s general formula 
W=spfyt = ae may take the form H.P. = Pa 
velocity in feet per minute; or since v=dz X rpm. + 12 = .2618d xX rpm.,in 
which d = diameter in inches and rpm. = revolutions per minute, 


» In which v = 


HP. = Wv_ __ spfy Xd X rpm. 
te 3,000 |. 126,050 





= .000007938dspfy X rpm. 
) 

It must be borne in mind, however, that in the case of machines which 
consume power intermittently, such as punching and shearing machines. 
the gearing should be designed with reference to the maximum load W, 
which can be brought upon the teeth at any time, and not upon the average 
horse-power transmitted. P 

Comparison of the Hiarkness and Lewis Formulas.— 
Take an average case in which the safe working strength of the material, 
s = 6000, v = 200 ft. per min., and y = .100, the value in Mr. Lewis’s table 
for an involute tooth of 15° obliquity, or a cycloidal tooth, the number of 
teeth in the wheel being 27. 


_ spfyv _ 6000pfv x .100 piv _ ang 
HP. = 35000! 38,000 By Oe 
if Vis taken in feet per pong a 
Prof. Harkness gives H.P.= teh call 


———-—-, If the V in the denominato 
W1-+ 0.657 


STRENGTH OF GEAR-TEETH. - 903 


be taken at 20b _ o = 314 feet per second, 1+ 0.6BY & V 8.167 = 1.78, 
-and H.P. = "ot = .571pfV, or about 52% of the result given by Mr. Lewis’s 


formula. This is probably as close an agreement as can be expected, since 
Prof. Harkness derived his formula from an investigation of ancient prece- 
dents and rule-of-thumb practice, largely with common cast gears, while 
Mr. Lewis’s formula was derived from considerations of modern practice 
with machine-moulded and cut gears. 

Mr. Lewis takes into consideration the reduction in working strength of a 
tooth due to increase in velocity by the figures in his table of the values of 
the safe working stress s for different speeds. Prof. Harkness gives expres- 
sion to the same reduction by means of the denominator of his formula, 


71+ 0.65V. The decrease in strength as computed by this formula is 
somewhat less than that given in Mr. Lewis’s table, and as the figures given 
in the table are not based on accurate data, a mean between the values given 
by the formula and the table is probably as near to the true value as may 
be obtained from our present knowledge. The following table gives the 
values for different speeds according to Mr. Lewis’s table and Prof. Hark- 
ness’s formula, taking for a basis’ a working stress s, for cast-iron 8000, and 
for steel 20,000 lbs. at speeds of 100 ft. per minute and less: 





# = speed of teeth, ft. per min.. | 100 | 200 | 300 | 600 | 900 | 1200) 1800 | 2400 
ran © ft. per sec.. | 124] 8344| 5 | 10 | 15 | 20 | 80 | 40 


——— | — — oe | | ee | | — —__——_ 


tafe stress s, arene Lewis... ree 6000 4800 4000; 3000) 2400} 2000) 1700 








Relative do., s + 8000..... Ati ee : a76)| 86 |S lp oro ce Wit eee leetes 
= 1+ V1+0.65V............. |.6930] 5621] .4850) .8650) .8050) .2672| .2208] .1924 

Relative val. ¢-- .698.........6.. 1 -811| .700) .526] .439} .885}) .3818) .27 

Si = 8000: X (C’-= .698)... ie eo eee 8000) 6488} 5600) 4208) 3512] 8080) 2544) 2216 


Mean of s and s;, cast-iron = sg. | 8000} 6200) 5200} 4100} 3300; 2700) 2800} 2000 
Eee swig ts “ha for steel = sg. |20000)15500/13000)10300} 8100} 6800) 5700} 4900 
Safe stress for steel, Lewis...... 20000) 15000/12000) 100001 7500| 6000) 5000}: 4300 





Comparing the two formule for the case of s = 8000, corresponding to a 
speed of 100 ft. per min., we have 


Harkness: H.P. = 1+ 71-+4-0.65V X .910Vpf = .695 x .91 x 1% pf = 1.051 pf? 
Lewis: He spfge _ Biuy, oOo x Teel = 24.24pfy, 


in which y varies according to the shape and number of the teeth. 


For radial-flank gear with 12 teeth y == .0525 24.24pfy = 1.260pf s 
For 20° involute, 19 teeth, or 15° inv., 27 teeth y = .100; 24.24pfy = 2.424pf; 
For 20° involute, 300 teeth Y = 150; 24.24pf/y = 3.636pf. 


Thus the weakest-shaped tooth, according to Mr. Lewis, will transmit 20 
per cent more horse-power than is given by Prof. Harkness’s formula, in 
which the shape of the tooth is not considered, and the average-shaped 
tooth, according to Mr. Lewis, will transmit more than double the horse. 
power given by Prof. Harkness’s formula. 

Comparison of Other Formulz.—Mr. Cooper, in summing up 
his examination, selected an old English rule, which Mr. Lewis considers as 
a passably correct expression of good general averages, viz. : X = 2000pf, 
X = breaking load of tooth in pounds, p = pitch, f = face. If a factor of 
safety of 10 be taken, this would give for safe working load W = 200pf. 

George B. Grant, in his Teeth of Gears, page 33, takes the breaking load 
at 3500pf, and, with a factor of safety of 10, gives W = 350pf. 

Nystrom’s Pocket-Book, 20th ed., 1891, says : ‘‘ The strength and durability 
of cast-iron teeth require that they shall transmit a force of 80 lbs, per inch 
of pitch and per inch breadth of face.’’ This is equivalent to W = 80pf, or 
only 40% of that given by the English rule. 

F, A. Halsey (Clark’s Pocket Book) gives a table calculated from the 
formula H.P. = pfd X rpm. + 850. © 

Jones & Laughlins give H.P. = pfd x rpm. + 550. 


These formule transformed give W= 128pf and W = 218pf, respectively, 


504. . GEARING. 


Unwin, on the assumption that the load acts on the corners of the teetn, 


derives a formula p = K  W, in which K is a coefficient derived from ex- 
isting wheels, its values being: for slowly moving gearing not subject to- 
much vibration or shock K = .04; in ordinary mill-gearing, running at 
greater speed and subject to considerable vibration, K = .05; and in wheels 
subjected to excessive vibration and shock, and in mortise gearing, K = .06. 
Reduced to the form W = Cpf, assuming that f = 2p, these values of K give 
W = 262pf, 200pf, and 139pf, respectively. ! 

Unwin also gives the following formula, based on the assumption that the 


pressure is distributed along the edge of the tooth: p= K, {/ A VW, 


where K, = about .0707 for iron wheels and .0848 for mortise wheels when 
the breadth of face is not less than twice the pitch. For the case of f = 2p 
and the given values of K, this reduces to W = 200pf and W = 139pf, 


respectively. 
12p2f Vdn 
1 


Box, in his Treatise on Mill Gearing, gives H.P. = , in which » 


= number of revolutions per minute. This formula differs from the more 
modern formule in making the H.P. vary as p?f, instead of as pf, and in 
this respect it is no doubt incorrect. 


Making the H.P. vary as /dn or as Vv, instead of directly as v, makes 
the velocity a factor of the working strength as in the Harkness and Lewis 
formule, the relative strength varying as or as Vo which for different 
velocities is as follows : 


Speed of teeth in ft. per min.,v = 100 200 300 600 900 1200 1800 2400 
Relative strength = 1 .707 .574 .408 .833 .289 .236 .204 


Showing a somewhat more rapid reduction than is given by Mr. Lewis. 
For the purpose of comparing different formule they may in general be 
reduced to either of the following forms : 


H.P. = Cpfv, H.P. = C,pfd X rpm., W = cpf, 


in which p = pitch, f = face, d = diameter, all in inches ; v = velocity in 
feet per minute, rpm. revolutions per minute, and C, C, and c coefficients. 
The formule for transformation are as follows: 


We | WxXdxXrpm., 
33000 ~ 126,050 f 


33,000H.P. 126,050 H.P. _ PG SS biel EN de (ona 
Y= v ~ ad Xrpm. phetiends His hs Cv C,d@Xrpm. ec 


HP 


CO, = .2618C; c= 33,000C; C=3.82C,,= c = 126,0500,. 


c e 
83,000” 
In the Lewis formula C varies with the form of the tooth and with the 


speed. and is equal to sy + 33,000, in which y and s are the values taken from 
the table, and c = sy. 


910 
In the Harkness formula C varies with the speed and is equa tOVi+0.6577 
(V being in feet per second), = —201? _ 
; Vi+ Ol1v. 


In the Box formula C varies with the pitch and also with the velocity, 


and equals Pe Xen == 02345 P.. o= 33,0000 = 774 ao 


v v 
For v = 100 ft. per min. C= ‘7.4p ; for v = 600 ft. per minute c =381.6p. 
In the other formule considered C, C, , and c are constants. Reducing 
the several] formule to the form W = cpf, we have the following: 


FRICTIONAL GEARING. 905 


COMPARISON OF DIFFERENT FoRY. LA FOR STRENGTH OF GEAR-TEETH. 


Safe working pressure per inch pitch and per inch of face, or value of c in 
formula W = cpf: : 


v7=100ft. v= 600 ft. 


per min. per min. 
Lewis: Weak form of tooth, radial flank, 12 teeth... c= 416 208 
Medium tooth, inv. 15°, or cycloid, 27 teeth.. c= 800 400 
Strong form of tooth, inv. 2U°, 3Uu teeth...... e = 1200 600 
Harkness: Average tooth.............. niger Spans cay (hts Byte 184 
Box: Tooth of 1 inch pitch......2..... coopers conde Paine’: Ca acrt. 31.6 
ae come cca.cs TU CHES PILGM arrfreatin «6: SPL e ae eet Ch— moos 95 


Various, in which c is independent of form and speed: Old Englisn 
rule, c = 200; Grant, c = 350; Nystrom, c = 80; Halsey, c = 128; Jones & 
Laughlins, c = 218; Unwin, c = 262, 200, or 139, according to speed, shock, 
and vibration. 

The value given by Nystrom and those given by Box for teeth of small 
pitch are so much smaller than those given by the other authorities that they 
may be rejected as having an entirely unnecessary surplus of strength. The 
values given by Mr. Lewis seem to rest on the most logical basis, the form of 
the te2th as well as the velocity being considered; and since they are said to 
have proven satisfactory in an extended machine practice, they may be con- 
sidered reliable for gears that are so well made that the pressure bears 
along the face of the teeth instead of upon the corners. For rough ordi- 
nary work the old English rule W = 200pf is probably as good as any, ex- 
cept that the figure 200 may be too high for weak forms of tooth and for 
high speeds. 


The formula W = 200pf is equivalent to H.P, = 227 X TPM _ PIU oy 


630 165’ 
H.P. = .00158738pfd & rpm. = .006063pfv. 
Maximum Speed of Gearing.—A. Towler, Hng’g, April 19, 1889, 
Pp. 888, gives the maximum speeds at which it was possible under favorable 
conditions to run toothed gearing safely as follows: 


Ordinary cast-iron wheels....... ES cvatipedmeate tes ese 
Helical < sf $6) AE te ate B oiheje obits ois s male optic eltelerca aesles 2400 
Mortise £6 We is eee eeeeeeee eee sees Se SGeeeseeeveeeteeeee 2400 
Ordinary cast-steel wheels vias. etuss.csssuores ses Vasticte seseeeees 2000 
elica i ss Ooms + rata at ree noe wpa ra toe PR ASRS EEO SEE LORNA 8000 
Special cast-iron machine-cut wheels............... seeceses ee 3000 


Prof. Coleman Sellers (Stevens Indicator, April, 1892) recommends that 
gearing be not run over 1200ft. per minute, to avoid great noise. The 
Walker Company, Cleveland, O., say that 2200 ft. per min. for iron gears and 
8000 ft. for wood and iron (mortise gears) are excessive, and should be 
avoided if possible. The Corliss engine at the Philadelphia Exhibition (1876) 
had a fly-wheel 30 ft. in diameter running 35 rpm. geared into a pinion 12 ft. 
diam. The speed of the pitch-line was 3300 ft. per min. 

A Heavy Machine-cut Spur-gear was made in 1891 by the 
Walker Company, Cleveland, O., for a diamond mine in South Africa, with 
dimensions as follows: Number of teeth, 192; piten aiameter, 30’ 6.66’; face, 
30’; pitch, 6’; bore, 27’; diameter of hub, 9’ 2’; weight of hub, 15 tons; and 
total weight of gear, 6634 tons. The rim was made in 12 segments, the joints 
of the segments being fastened with two bolts each. The spokes were bolted 
to the middle of the segments and to the hub with four bolts in each end. 

Frictional Gearing.—In frictional gearing the wheels are toothless, 
and one wheel drives the other by means of the friction between the two 
surfaces which are pressed together. They may be used where the power 
to be transmitted is not very great; when the speed is so high that toothed 
wheels would be noisy; when the shafts require to be frequently put inte 
and out of gear or to have their relative direction of motion reversed; or. 
when it is desired to change the velocity-ratio while the machinery is in mo- 
Hon, as in the case of disk friction-wheels for changing the feed in inachine 
tools. 

Let P = the normal pressure in pounds at the line of contact by which 
two wheels are pressed together, 7 = tangential resistance of the driven 
wheel at the line of contact, f = the coefficient of friction, V = the velocity 
of the pitch-surface in feet per second, and H.P. = horse-power3; then 
T may be equal to or Jess than fP; H.P. = TV -- 550. The value of f for 


s 


906 HOISTING, 


metal on meta: usay be taken at .15 to .20; for wood on metal, .25 to .30; and 
for wood on compressed paper, .20. The tangential driving force T may be 
as high as 80 lbs. per inch width of face of the driving surface, but this is ac- 
companied by great pressure and friction on the journal-bearings. 

In frictional grooved gearing circumferential wedge-shaped grooves are 
cut in the faces of two wheels in contact. If P = the force pressing the 
wheels together, and N = the normal pressure on all the grooves, P = N 
(sin a + f cos a), in which 2a = the inclination of the sides of the grooves, 
and the maximum tangential available force T = fN. The inclination of the 
sides of the grooves to a plane at right: angles to the axis is usually 30°. . 

Frictional Grooved Gearing.—A set of friction-gears for trans- 
mitting 150 H.P. is on a steam-dredge described in Proc. Inst. M. E., July, 
1888. Two grooved pinions of 54 in. diam., with 9 grooves of 134 in. piteh and 
angle of 40° cut on their face, are geared into two wheels of 12714 in diam. 
similarly grooved. The wheels can be thrown in and out of gear by levers 
operating eccentric bushes on the large wheel-shaft. The circumferential 
speed of the wheels is about 500 ft. per min. Allowing for engine-friction, 
if half the power is transmitted through each set of gears the tangential 
force at the rims is about 3960 lbs., requiring, if the angle is 40° and the co- 
efficient of friction 0.18, a pressure of 7524 lbs. between the wheels and 
pinion to prevent slipping. ¢ 

The wear of the wheels proving excessive, the gears were replaced by spur- 
gear wheels and brake-wheels with steel brake-bands, which arrangement 
has proven more durable than the grooved wheels. Mr. Daniel Adamson 
states that if the frictional wheels had been run at a higher speed the results 
would have been better, and says they should run at least 30 ft. per second. 


HOISTING AND CON /EYING. 


Approximate Weight and Strength of Cordage. (Boston 
and Lockport Block Co,)—See also pages 339 to 345, 








Weightof| Strength 


Pte Sas Weicht of} St t 
Size in | Size in 100 ft. 5 rength 

















. Size in | Size in , 

Circum-| Diam- Manila ee Sasa ircum- Diant. cna Sey eee 
ference.} eter. in inva: a lbs: ference. | eter. ea Ibs.’ in ae 

ire inch. oh. Rae inenan Ribak op 
‘ 36 13 4,000 434 1 9/16 eh 22,500 
214 34 6 5,000 5 15g 80 25,000 
216 13/16 20 6,250 514 134 97 80,250 
me | BR | aed g, | See 
, 2 133 42,250 
3144 11/16 33 10,500 vd 214 153 49,000 
3 14 38 12,250 wy 2 184 56,250 
Bek 1G Ce RRS UR ES gt Lue ge 236 | 721950 
t 2% 236 72,250 
414 | 13 58 18,062 9 3 262 81,000 
416 1% 65 20,250 








Working Strength of Blocks, (B. & L. Block Co.) 
Regular Mortise-blocks Single and Wide Mortise and Extra Heavy 


Double, or Two Double Iron- Single and. Double, or Two Double, 
strapped Blocks, will hoist about— Tnppretsaphed Blocks, will hoist 
about— 
inch, lbs. inch, Ibs. 
ly 250 8 2,000 
6 350 10 6, 
v¢ 600 12 12,000 
8 1,200 14 24,000 
9 « 2,000 16 36,000 
10 4,000 18 50,000 
12 10,000 20 90,000 
14 16,000 


_ Where a double and triple block are used together, a certain extra propor- 
tioned amount of weight can be safely hoisted, as larger hooks are used. 


PROPORTIONS OF HOOKS. 907 


Comparative Efficiency in Chain-blocks both in 
Hoisting and Lowering. 


(Tests by Prof. R. H. Thurston, Hoisting, March, 1892.) 























Work oF HoIstinc. WoRK OF LOWERING, 

Load of 2000 Ibs. Load of 2000 lbs., lowered % ft. in each case, 
of Pe B E Exclusive of Factor of Time. hate of 
} S eS ES4) Wh Sealed (MIST coaaael saan asi, Lib he 
= Or. oO - € +2 5S} : 2 a) . 
faa) om =p | fas] » =| s Ss . c . 
meee ee colo 2 | Saabuee ie cls lees 
© |/52/85 | eal a] a= | eas | ved ass) = | Fe 
i io ol Epos ere qa re ov ona Dros 5 oo 
ZB }oh|shle°| 8 | Sa | eee less less) 5 | 33 
8 4 @ | <3 Ci) aa Sa o- |eSol g ce 
Shien ke ° es > sO [AG o |S & a 
Zz IE < Rett ca ° m 

1 | 20.50] 79.50] 1.00 } 32.50) 8.00] 227. | 1,816 | 1.00] 0.75 | 1.000 
2 68.00} 32.00] .40 | 62.448 14.00 436. 6,104 3.33] 1.20 .186 
3 69.00} 31.00] .39 | 30 O08 92.30 196. 18,090 | 10.00) 1.50 | .050 
4 71.20] 28.80) .386 | 28.008 92.60 168. 15,556 8.60] 2.50 035 
5 73.96] 26.04, .33 | 48.0 73.30 17.5 1,282 0.71) 2.80 .880 
6 75.66) 24.84) .31 | 53.0 56.60 370. 20,942 | 11.60} 1.80 .036 
jG 77.00) 23.00) .29 | 44.308 55.00 310. 17,050 9.40) 2.75 029 
8 81.03) 18.97] .24 | 61.0 48.50 426. 20,000 | 11.60! 3.75 018 





No, 1 was Weston’s triplex block; No.3, Weston’s differential; No. 4, 
Weston’s imported. The others were from different makers, whose names 
are not given. All the blocks were of one-ton capacity. 

Proportions of Hooks.—The following formule are given by 
Henry R. Towne, in his l'reatise on Cranes, as a result of an extensive 
experimental and mathematical investi- itnek 
gation. They apply to hooks of capaci- i 5 
ties from 250 lbs. to 20,000 lbs. Each size il 
of hook is made from some commercial 
size of round iron. The basis in each 
ease is, therefore, the size of iron of 
which the hook is to be made, indicated 
by Ainthe diagram. The dimension D 
is arbitrarily assumed. The other di- 
mensions, as given by the formule, are 
those which, while preserving a proper 
bearing-face on the interior of the hook 
for the ropes or chains which may be 
passed through it, give the greatest re- 
sistance to spreading and to ultimate 
rupture, which the amount of material 
in the original bar admits of. The sym- 
bol A is used to indicate the nominal ca- 
pacity of the hook in tons of ~000 lbs. 
The formule which determine the lines 
of the other parts of the hooks of the 
several sizes are as follows, the measure- 
ments being all expressed in inches: Fic. 164. 





* 
\ 
i 


s 


D=.56 A+1.25 G =.75D. H = 1.08A L=1.05A4 
E = .644 + 1.60 O = 3268 A+ .66 Sih eB BV M= .50A 
Fo = 33 A+ .85 Q = .64 A+ 1.60 Jaw AL IN 85 Be eakG 


The dimensions A are necessarily based upon the ordinary merchant sizes 
of round iron, The sizes which it has been found best to select are the 
following: 

Capacity of hook: 

¥% y& 1 144 2 Gets — 5 6 8 10 tons. 

Dimension A: 


5% 11/16 34 11/16 1% 1% 134 2 2% 26 2% 3% in, 


908 HOISTING. 


Experiment has shown that hooks made according to the above formul@ 
will give way first by opening of the jaw, which, however, will not occur 
except witha load much in excess of the nominal capacity of the hook. 
This yielding of the hook when overloaded becomes a source of safety, as it 
constitutes a signal of danger which cannot easily be overlooked, and which 
must proceed to a considerable length before rupture will occur and the 
load be dropped. 


POWER OF HOISTING-ENGINES. 


WHorse-power required to raise a Load at a Given 


ne miss in lt 3 f 
Speed. —H.P. = Gross vor. x speed in ft. per min. To this add 


25% to 50% for friction, contingencies, ete. The gross weight includes the 
weight of cage, rope, etc. In ashaft with two cages balancing each other 
use the net load + weight of one rope, instead of the gross weight. 

To find the load which a given pair of engines will start.—Let A = area 
of cylinder in square inches, or total area of both cylinders, if there are two; 
P = mean effective pressure in cylinder in Ibs. per sq. in.; S = stroke of 
cylinder in inches; C = circumference of hoisting-drum in inches; LZ = load 
lifted by hoisting-rope in lbs.; #’= friction, expressed as a diminution of 


theload. Then Z = vt Blake 


Anexample in Coll’y Engr., July, 1891, is a pair of hoisting-engines 24” < 
40’, drum 12 ft. diam., average steam-pressure in cylinder = 59.5 lbs.; A = 
904.8; P= 59.5; S = 40; C= 452.4. Theoretical load, not allowing for friction, 
AP2S—~— C= 9589 lbs. The actual load that could just be lifted on trial was 7988 
lbs., making friction loss F’ = 1601 lbs., or 20-++ per cent of the actual load 
lifted, or 1624% of the theoretical load. 

The above rule takes no account of the resistance due to inertia of the 
load, but for all ordinary cases in which the acceleration of speed of the 
cage is moderate, it is covered by the allowance for friction, etc. The re. 
sistance due to inertia is equal to the force required to give the load the 
velocity acquired in a given time, or, as shown in Mechanics, equal to the 





product of the mass by the acceleration, or R = on in which R& = resist- 


ance in lbs. due to inertia; W = weight of load in lbs.; V = maximum veloc- 
ity in fot per second; 7' = time in seconds taken to acquire the velocity V3; 

= 32:16, 

Effect of Slack Rope upon Strain in Hoisting.—aA series of 
tests with a dynamometer are published by the Trenton Iron Co., which 
show that a dangerous extra strain may be caused by a few inches of slack 
rope In one case the cage and full tubs weighed 11,800 lbs.; the strain when 
the load was lifted gently was 11,525 Ibs.; with 3 in. of slack chain it was 
19.025 lbs , with 6 in. slack 25,750 lbs., and with 9 in. slack 27,950 lbs. 

Limit of Depth for Hoisting.—Taking the weight of a cast-steel 
hoisting-rope of 14 inches diameter at 2 lbs. per running foot, and its break- 
ing strength at 84,000 lbs., it should, theoretically, sustain itself until 42,000 
feet long before breaking from its own weight. But taking the usual factor 
of safety of 7, then the safe working length of such a rope would be only 
6000 feet. If a weight of 3 tons is now hung to the rope, which is equivalent 
to that of a cage of moderate capacity with its loaded cars, the maximum 
length at which such a rope could be used, with the factor of safety of 7, is 
3000 feet, or 

2x +6000 = HO, +. a = 3000 feet. 


This limit may be greatly increased by using special steel rope of higher 
strength, by using a smaller factor of safety, and by using taper ropes, 
(See paner bv H. A. Wheeler, Trans. A. I. M. E., xix. 107.) 

Large Hoisting Records,—At a colliery in North Derbyshire dur- 
ing the first week in June, 1890, 6309 tons were raised from a depth of 509 
yards, the time of winding being from 7 a.m. to 3.30 p.m. 

At two other Derbyshire pits, 170 and 140 yards in depth, the speed of 
winding and changing has been brought to such perfection that tubs are 
drawn and changed three times in One minute. (Proc. Inst. M. E., 1890.) 


POWER Ot HOISTING-ENGINES. 909 


At the Nottingham Colliery near Wilkesbarre, Pa., in Oct. 1891, 70,152 tons 
were shipped in 24.15 days, the average hoist per day being 1318 mine ears. 

The depth of hoist was 470 feet, and all coal came from one opening. The 
engines were fast motion, 22 X 48 inches, conical drums 4 feet 1 inch long. 7 
feet diameter at small end and 9 feet at Jarge end. (Hng’g News, Nov. 1891.) 

Pneumatic Hoisting. (H.A. Wheeler, Trans. A. I. M. E., xix. 107.)— 
A pneumatic hoist was installed in 1876 at Epinac, France, consisting of two 
continuous air-tight iron cylinders extending from the bottom to the top of 
the shaft. Within the cylinder moved a piston from which was hung the 
cage. It was operated by exhausting the air from above the piston, the 
lower side being open to the atmosphere. Its use was discontinued on ac- 
count of the failure of the mine. Mr. Wheeler gives a description of the sys- 
tem, but criticises it as not being equal on the whole to hoisting by steel ropes. 

Pneumatic hoisting-cylinders using compressed air have beer used at 
blast-furnaces, the weighted piston counterbalancing the weight of the cage, 
and the two being connected by a wire rope: passing over a pulley-sheave 
above the top of the cylinder. In the more modern furnaces steam-engine 
hoists are generally used. 

Counterbalancing of Winding-engines. (H.W. Hughes, Co- 
lumbia Coll. Qly.)—Engines running unbalanced are subject to enormous 
variations in the load; for Jet W = weight of cage and empty tubs, say 6270 
lbs.; c = weight of coal, say 4480 lbs.; r = weight of hoisting rope, say 6000 
Ibs.; +’ = weight of counterbalance rope hanging down pit, say 6000 lbs. The 
weight to be lifted will be: 


If weight of rope is unbalanced. If weight of rope is balanced. 
At beginning of lift: 
W-+c+r-— Wor 10,480 lbs. W+e+r-—(W-+7r'), 
At middle of lift: 


or 
7 Lf HG 108 al ELEN ope 
W+e+t -~(w + sor 4480 Ibs. Wee e+ > ace ec lata tt 


at end of lift: 
W+e—(W-+r) or minus 1520 Ibs. W+etr—(W+n, J 


That counterbalancing materially affects the size of winding-engines is 
shown by a formula given by Mr. Robert Wilson, which is based on the fact 
that the greatest work a winding-engine has to do is to get a given mass into 
a certain velocity uniformly accelerated from rest, and to raise a load the 
distance passed over during the time this velocity is being obtained. 


Let W = the weight to be set in motion: one cage, coal, number of empty 
tubs on cage, one winding rope from pit head-gear to bottom, 
and one rope from banking level to bottom. 

v = greatest velocity attained, uniformly accelerated from rest; 

g = gravity = 82.2; 

t = time in seconds during which v is obtained; 

ZL = unbalanced load on engine; 

R = ratio of diameter of drum and crank circles; 

P = average pressure of steam in cylinders; 

N = number of cylinders; 

S = space passed over by crank-pin during time ¢; 

C= %, constant to reduce angular space passed through by crank, to 
the distance passed through by the piston during the time ¢; 

A= area of one cylinder, without margin for friction. To this an ad- 
dition for friction, etc., of engine is to be made, varying from 16 
to 30% of A. 


Ist. Where load is balanced, 
Wv?.- vt 
A 2g y+ 9) le 


PNSC. 
2d. Where load is unbalanced: 
The formula {is the same, with the addition of another term to allow for 
the variation in the lengths of the ascending and descending ropes. In this 
ease i Cae ‘b ; ; 


910 HOISTING. 


= reduced iength of rope in ¢ attached to ascending cages 
increased length of rope in ¢ attached to descending cages 
w = weight of rope per foot in pounds. Then 


a= [(t) + 1(9)- 


ee 


PNSC. 


Applying the above formula when designing new engines, Mr. Wilson 
found that 30 inches diameter of cylinders would produce equal results,wnen 
balanced, to those of the 36-inch cylinder in use, the latter being unbal. 
anced. 

Counterbalancing may be employed in the following methods : 

(a) Tapering Rope.—At the initial stage the tapering rope enables us to - 
wind from greater depths than is possible with ropes of uniform section, 
The thickness of such a rope at any point should only be such as to safely 
bear the load on it at that point. 

With tapering ropes we obtain a smaller difference between the initial and 
final load, but the difference is still considerable, and for perfect equaliza- 
sion of the load we must rely on some other resource. The theory of taper 
ropes is to obtain a rope of uniform strength, thinner at the cage end where 
the weight is least, and thicker at the drum end where it is greatest. 

(b) The Counterpoise System consists of a heavy chain working up and 
down a staple pit, the motion being obtained by means of a Special small 
drum placed on the same axis as the winding drum, It is so arranged that 
the chain hangs in full length down the staple pit at the commencement of 
the winding; in the centre of the run the whole of the chain rests on the 
bottom of the pit, and, finally, at the end of the winding the counterpoise 
has been rewound upon the small drum, and is in the same condition as it 
was at the commencement. 

(c) Loaded-wagon System.— A plan, formerly much employed, was to 
have a loaded wagon running on a short incline in place of this heavy chain; 
the rope actuating this wagon being connected in the same manner as the 
above to a subsidiary drum. The incline was constructed steep at the com- 
rmencement, the inclination gradually decreasing to nothing. At the begin- 
ning of a wind the wagon was at the top of the incline, and during a portion 
of the run gradually passed down it till, at the meet of cages, no pull was 
exerted on the engine—the wagon by this time being at the bottom. In the 
latter part of the wind the resistance was all against the engine, owing to ~ 
- its having to pull the wagon up the incline, and this resistance increased 
ee: notping at the meet of cages to its greatest quantity at the conclusion 
of the lift. 

(da) The Endless-rope System is preferable to all others, if there is suffi- 
cient sump room and the shaft is free from tubes, cross timbers, and other 
impediments. It consists in placing beneath the cages a tail rope, similar 
in diameter to the winding rope, and, after conveying this down the pit, it is 
attached beneath the other cage. 

(e) Flat Ropes Coiling on Reels. —This means of winding allows of a cer- 
tain equalization, for the radius of the coil of lascending rope continues to 
increase, while that of the descending one continues to diminish. Conse- 

uently, as the resistance decreases in the ascending load the leverage 
ncreases, and as the power increases in the other, the leverage diminishes. 
The variation in the leverage is a constant quantity, and is equal to the 
thickness of the rope where it is wound on the drum. 

By the above means a remarkable uniformity in the load may be ob- 
tained, the only objection being the use of flat ropes, which weigh heavier 
and only last about two thirds the time of round ones. 

(f) Conical Drums.—Results analogous to the preceding may be obtained 
by using round ropes coiling on conical drums, which may either be smooth, 
with the successive coils lying side by side, or they may be provided with a 
spiral groove. The objection to these forms is, that perfect equalization is 
not obtained with the conical drums unless the sides are very steep, and con- 
sequently there is great risk of the rope slipping ; to obviate this, scroll 
drums were proposed. They are, however, very expensive, and the lateral 
displacement of the winding rope from the centre line of pulley becomes 
very great, owing to their necessary large width. 

(g) The Koepe System of Winding.—An iron pulley with a single circular 
groove takes the place of the ordinary drum. The winding rope passeg 
from one cage, over its head-gear pulley, round the drum, and, after passe 


~ 
0 
Lud 


CRANES. 911 


ing over the other head-gear pulley, is connected with the second cage. The 
winding rope thus encircles about half the periphery of the drum in the 
same manner as a driving-belt on an ordinary pulley. There is a balance 
rope beneath the cages, passing round a pulley in the sump; the arrange- 
ment may be likened to an endless rope, the two cages being simply points 
of attachment. 


CRANES. 


Classification of Cranes. (Henry R. Towne, Trans. A.S. M.E., iv. 
288. Revised in Hoisting, published by The Yale & Towne Mfg. Co.) 

A Hoistis a machine for raising and lowering weights. A Crane is a 
hoist with the added capacity of moving the load in a horizontal or lateral 

irection. 

Cranes are divided into two classes, as to their motions, viz., Rotary and 
&ectilinear, and into four groups, as to their source of motive power, viz.: 

Hand.—When operated by manual power. 

Power.—When driven by power derived from line shafting. 

Steam, Electric, Hydraulic, or Pneumatic.—When driven by an engine or 
motor attached to the crane, and operated by steam, electricity, water, or 
air transmitted to the crane from a fixed source of supply. } 

Locomotive.—When the crane is provided with its own boiler or other 
generator of power, and is self-propelling ; usually being capable of both 
rotary and rectilinear motions. — 

. Rotary and Rectilinear Cranes are thus subdivided : 


RoTARY CRANES. 


(1) Swing-cranes.—Having rotation, but no trolley motion. 

(2) Jib-cranes.—Having rotation, and a trolley travelling on the jib. 

(8) Column-cranes.—Identical with the jib-cranes, but rotating around a 
fixed column (which usually supports a floor above). 

(4) Pillar-cranes.—Having rotation only; the pillar or column being sup- 
ported entirely from the foundation. 

(5) Pillar Jib-cranes.—Ideutical with the last, except in having a jib and 
trolley motion. 3 

(6) Derrick-cranes.—ldentical with jib-cranes, except that the head of the 
are is held in position by guy-rods, instead of by attachment to a roof or 
ceiling. 

(7) Walking-cranes.—Consisting of a pillar or jib-crane mounted on wheels 
and arranged to travel longitudinally upon one or more,rails. 

(8) Locomotive-cranes.—Consisting of a pillar crane mounted on a truck, 
and provided with a steam-engine capable of propelling and rotating the 
crane, and of hoisting and lowering the load. | 


RECTILINEAR CRANES. 


(9) Bridge-cranes.—Having a fixed bridge spanning an opening, and a 
trolley moving across the bridge. 

(10) Tram-cranes.—Consisting of a truck, or short bridge, travelling lon- 
gitudinally on overhead rails, and without trolley motion. 

(11) Travelling-cranes.—Consisting of a bridge moving longitudinally on 
overhead tracks, and a trolley moving transversely on the bridge. 

(12) Gantries.—Consisting of an overhead bridge, carried at each end by a 
trestle travelling on longitudinal tracks on the ground, and having a trolley 
moving transversely on the bridge. 

(13) Rotary Bridge-cranes.—Combining rotary and rectilinear movements 
and consisting of a bridge pivoted at cne end to a central pier or post, 
and supported at the other end on a circular track ; provided with a trolley 
moving transversely on the bridge. ‘ 

For descriptions of these several forms of cranes see Towne’s ‘ Treatise 
on Cranes.” 

Stresses in Cranes.—See Stresses in Framed Structures, p. 440, ante, 

Position of the Inclined Brace in a Jib-crane,—The most 
economical arrangement is that in which the inclined brace intersects the 
jib at a distance from the mast equal to four fifths the effective radius of 
the crane. (Hoisting.) : 

A Large Travelling-crane, designed and built by the Morgan 
Engineering Co., Alliance, O.. for the 12-inch-gun shop at the Washington 
Navy Yard, is described in American Machinist, June 12, 1890. Capacity, 
150 net tons; distance between centres of inside rails, 59 ft. 6 in.; maximum 
cross travel, 44 ft. 2 in.; effective lift, 40 ft.; four speeds for main hoist, 1, 2, 


912 HOISTING, 


4, and 8ft. per min.; loads for these speeds, 150, 72, 3745, and 1834 tonev<" pec- 
tively; traversing speeds of trolley on bridge, 25 and 50 ft. per minute; 
speeds of bridge on main track, 30 and 60 ft. per minute. Square shafts are 
employed for driving. 

A 150-ton Pillar-crane was erected in 1893 on Finnieston Quay, 
Glasgow. The jib is formed of two steel tubes, each 39 in. diam. and 90 ft. 
long. The radius of sweep for heavy lifts is 65 ft. The jib and its load are 
counterbalanced by a balance-box weighted with 100 tons of iron and steel 
punchings. Ina test a 130-ton load was lifted at the rate of 4 ft. per minute, 
and a complete revolution made with this load in 5 minutes. Hng’g News, 
July 20, 1893. 

Compressed-air Travelling-cranes.—Compressed-air overhead 
travelling-cranes have been built by the Lane & Bodley Co., of Cincinnati. 
They are of 20 tons nominal capacity, each about 50 ft. span and 400 ft. length 
of travel, and are of the triple-motor type, a pair of simple reversing-engines 
being used for each of the necessary operations, the pair of engines for the 
bridge and the pair for the trolley travel being each 5-inch bore by 7-inch 
stroke, while the pair for hoisting is 7-inch bore by 9-inch stroke. Air is 
furnished by a compressor having steam and air cylinders each 10-in. diam. 
and 12-in. stroke, which with a boiler-pressure of about 80 pounds gives an air- 
pressure when required of somewhat over 100 pounds, The air-compressor 
is allowed to run continuously without a governor, the speed being regulated 
by the resistance of the air in a receiver. From a pipe extending from the 
receiver along one of the supporting trusses communication is continuously 
maintained with an auxiliary receiver on each traveller by means of a one- 
‘ inch hose, the object of the auxiliary receiver being to provide a supply of 
air near the engines for immediate demands and independent of the hose 
connection, which may thus be of small dimension. Some of the advantages 
said to be possessed by this type of crane are: simplicity; absence of all mov- 
ing parts, excepting those required for a particular motion when that motion 
is in use; no danger from fire, leakage, electric shocks, or freezing; ease of 
repair; variable speeds and reversal without gearing; almost entire absence 
of noise; and moderate cost. 

Quay-cranes,.—An illustrated description of several varieties of sta- 
tionary and travelling cranes, with results of experiments, is given in a 
paper on Quay-cranes in the Port of Hamburg by Chas. Nehls, Trans. A. S. 
C. E., Chicago Meeting, 1893. 

Hydraulic Cranes, Accumulators, ete.—See Hydraulic Press. 
ure Transmission, page 616, ante. 

Electric Cranes.—Travelling-cranes driven by electric motos have 
largely supplanted cranes driven by square shafts or flying-ropes. Each of 
the three motions, viz., longitudinal, traversing and hoisting, is usually ac- 
complished by a separate motor carried upon the crane, 


COAL-“HANDLING MACHINERY, 


The following notes and tables are supplied by the Link-Belt Engineer- 
ing Co. of Philadelphia, Pa.: 

In large boiler-houses coal is usually delivered from hopper-ears into 
a track-hopper, about 10 feet wide, and 12 to 16 feet long. A feeder 
set under the track-hopper feeds the coal at a regular rate to a crusher, 
which reduces it to a size suitable for stokers. 

After crushing, the coal is elevated or conveyed to overhead storage-bins, 
Overhead storage is preferred for several reasons: 

1. ‘fo avoid expensive wheeling of coal in case of a breakdown of the 
coal-handling machinery. F 

2. To avoid running the coal-handling machinery continuously. 

3. Coal kept under cover indoors will not freeze in winter and clog the 
supply-spouts to the boilers. 

4. It is often cheaper to store overhead than to use valuable ground- 
space adjacent to the boiler-house. 

5. As distinguished from vault or outside hopper storage, it is cheaper 


tq build steel bins and supports than masonry pits, 


COAL-HANDLING MACHINERY. 912a 


Weight of Overhead Bins.—Steel bins of approximately rectangu- 
lar cross-section, say 1010 feet, will weigh, exclusive of supports, about 
one-sixth as much as the contained coal. Larger bins, with sloping bottoms, 
may weigh one-eighth as much as the contained coal. Bag bottom bins of 
the Berquist type will weigh about one-twelfth as much as the contained 
coal, not including posts, and about one-ninth as much, including posts. 

Supply-pipes from Bins.—The supply-pipes from overhead bins 
to the boiler-room fioor, or to the stoker-hoppers, should not be less than 
12 inches in diameter. They should be fitted at the top with a flanged 
casting and a cut-off gate, to permit removal of the pipe when the boilers 
are to be cleaned or repaired. 

Types of Coal Elevators.—Coal elevators consist of buckets of 
various shapes attached to one or more strands of link-belting or chain, 
or to rubber belting. The buckets may either be attached continuously 
or at intervals. The various types are as follows: 

Continuous bucket elevators consist usually of one strand of chain and 
two sprocket-wheels with buckets attached continuously to the chain. 
Each bucket after passing the head -wheel acts as a chute to direct the 
flow from the next bucket. This type of elevator will handle the larger 
sizes of coal. It runs at slow speeds, usually from 90 to 175 feet per min- 
ute, and has a maximum capacity of about 120 tons per hour. 

Centrifugal discharge elevators consist usually of a single strand of chain, 
with the buckets attached thereto at intervals. They are used to handle 
the smaller sizes of coal in small quantities. They run at high speeds, 
usually 34 to 40 revolutions of the head wheel per minute, and have a 
SADA, up to 40 tons per hour. 

erfect discharge elevators consist of two strands of chain, with buckets 
at intervals between them. A pair of idlers set under the head wheels 
cause the buckets to be completely inverted, and to make a clean delivery 
into the chutes at the elevator head. This type of elevator is useful in 
handling material which tends to cling to the buckets. It runs at slow 
speeds, usually less than 150 feet per minute. The capacity depends on 
the size of the buckets. 

Combined Elevators and Conveyors are of the following types: 

Gravity discharge elevators, consisting of two strand, of chain, with spaced 
V-shaped buckets fastened between them. After 7 assing the head wheels 
the buckets act as conveyor-flights and convey ‘he coal in a trough to 
any desired point. This is the cheapest type ‘sf combined elevator and 
conveyor, and is economical of power. A mf chine carrying 100 tons of 
coal per hour, in buckets 20 inches wide, 10 in~;hes deep, and 24 inches long, 
spaced 3 feet apart, requires 5 H.P. when loacied and 1144 H.P. when empty 
for each 100 feet of horizontal run, and % H.P. for each foot of vertical lift. 

Rigid bucket-carriers consist of two strands of chain with a special bucket 
rigidly fastened between them. ‘The buckets overlap and are so shaped 
that they will carry coal around three sides of a rectangle. The coal is 
carried to any desired point and is discharged by completely inverting 
the bucket over a turn-wheel. 

Pivoted bucket-carriers consist of two strands of long pitch steel chain to 
which are attached, in a pivotal manner, large malleable iron or steel buckets 
so arranged that their adjacent lips are close together or overlap. Over- 
lapping buckets require special devices for changing the lap at the corner 
turns, Carriers in which the buckets do not overlap should be fitted with 
auxiliary pans or buckets, arranged in sucha manner as to catch the spill 
which falls between the lips at the loading point, and so shaped as to return 
the spillto the buckets at the corner turns. Pivoted bucket carriers will 
carry coal around four sides of a rectangle, the buckets being dumped on 
the horizontal run by striking acam suitably placed. Carriers of this type 
are economical of power, but are costly and of relatively low capacity. 

Coal Conveyors.—Coal conveyors are of four general types, viz., 
scraper or flight, bucket, screw, and belt conveyors. : 

The flight conveyor consists of a trough of any desired cross-section and 
a single or double strand of chain carrying scrapers or flights of approxi- 
mately the same shape as the trough. The flights push the coal ahead 
of them in the trough to any desired point, where it is discharged through 
openings in the bottom of the trough. ; ay ; 

For short, low-capacity conveyors, malleable link hook-joint chains 
are used. For heavier service, malleable pin-joint chains, steel link chains, 


9126 COAL-HANDLING MACHINERY. 


or monobar, aré required _ For the fei service, two strands of steel 
link chain, usually with rollers, are use 

Flight conveyors are of three types: ” plain scraper, suspended flight, 
and roller flight 

In the plain scraper conveyor, the flight is suspended from the chain 
and drags along the bottom of the trough. It is of low first cost and is 
useful where noise of operation is not objectionable. It has a maximum 
capacity of about 30 tons per hour, and requires more power than either 
of the other two types of flight conveyors. 

Suspended flight conveyors use one or two strands of chain. The flights 
are attached to cross-bars having wearing-shoes at each end. These wear- 
ing-shoes slide on angle-iron tracks on each side of the conveyor trough. The 
flights do not touch the trough at any point. This type of conveyor is 
used where quietness of operation is a consideration. It is of higher first 
cost than the plain scraper conveyor, but requires one-fourth less power 
for operation. It is economical up to a capacity of about 80 tons per hour. 

The roller flight conveyor is similar to the suspended flight, except that 
the wearing-shoes are replaced by rollers. It is highest in first cost of 
all the flight conveyors, but has the advantages of low power consump- 
tion (one-half that of the scraper), low stress in chain, long life of chain, 
trough, and flights, and noiseless operation. It has an economical maxi- 
mum capacity of about 120 tons per hour. 

The following formula gives approximately the horse-power at the head 
wheel required to operate flight conveyors: 

H.P.=(ATL+BWS) +1000. 

T=tons of coal per hour; =length of conveyor in feet, centre to 
centre; W=weight of chain, flights, and shoes (both runs) in pounds; 
S=speed in feet per minute; A and B constants depending on angle of 
incline from horizontal. - See example below. 


Values of A and B. 




















Angle, Angle, Angle, 
Deg. A B Deg. 2 Z Deg. A 3 
0 .343 .O1 10 .50 OL 30 279°= 4008. 009 
2 .378 .O1 14 257 .O1 34 . 84 .008 
4 .40 .O1 18 .63 .009 38 .88 008 
6 44 :O1 a2 .69 .009 42 92 .007 
8 47 .O1 ee 74 909 46 95 .007 














~ For suspended flight conveyors take B as 0.8, and for roller flights as 0.6 , 
of the values given in the table. 


Weight of Chain in Pounds per Foot. 









































LINK-BELTING. MOoNOBAR. 
Biren gS tae Pitch of Flights, Inches. 
Chain et Aee Chain 
oO No.* 
125) Se eet | 36 Leds 24: 36 48 54 v2 
78) OVA OBIS 2612: 2 6121359) eee BIGIA "Sui cesta loko wie ei len keer 
Be] Sisto tera ee5lt 618|... 7] MBeOh ant 2 8h ct & 2a Mla ges 
Bh SA, ZS 27a 2.6 RUS PERO aioe bate 535 1 oe 575 tae ee 
108.} 4.6] 4.44.3 1 4.2 SOA) eae EAS ae Ada. AM ANG 
108 | 4.9 4.74.4 mann LOLS.) 2. ER Se LOM eee 10), 4) oe 
TO SSG) be 24s 1024)... Tee. SFG OT itea 8.8 
TA | 3). 66016 Oe imomm e224). el Fa ae Ties LanOAl. to. Lass 
POD 7 77 ae OO)... < lt og ista lekes, On 1158) eet ae 11.34 
TOA BG) 848.97) Sa 424). . . | oe 2ZONS he Fe LOB 2F 38 19.4 











“* In monobar the first one or two figures in the number of the chain 
denote the diameter of the chain in eighths of an inch. The last two fig- 
ures denote the pitch in inches. 


COAL-HANDLING MACHINERY. 912c¢ 








Pin CHAINS. ROLLER CHAINS. 
BG: ee Pitch of Flights, Inches. 
No. ee ee No. 
12eP LS rieCsniEnso ope med: 2 36 
MUTI OL OL OlOee nH coset LEZ. 7 Gow. 2h) Ook 
iAOME GEO) 626l6s4 In G.oi| 2113)99).51 8.8) 8.01 7.5 
825 | 9.6) 9.3/9.1 | 8.9|]] 1130)10.5| 9.5}; 9.0] 7.8 

















Weight of Fiights with Wearing-shoes and Bolts. 


——a 


Suspended Flights. 





: Malleable 
Size, Inches. Steel re 
Size. Weight, Lbs. 

4x10 BoD 4.3 6x14 12.3% 
4x12 3.9 4.7 8x19 15.55 
5x10 Ay} Dad 10 x 24 OSE, 
5 X12 4.6 Diaks 10 x 30 29.37 
5X15 D8 5.9 10 x 36 Some 
6x18 8.1 9.2 10x42 34.97 
8X18 10.1 1 es 
8 X 20 11.0 13.4 
8X 24 12.6 14.4 
10 X 24 52 17.4 





ExaMpPLe. — Required the H.P. for a monobar conveyor 200 ft. centre 
to centre, carrying 100 tons of coal per hour, up a 10° incline at a speed 
of 100 feet per minute. Conveyor has No. 818 chain and 8 X19 suspended 
flights, spaced 18 inches apart. t 


.5 X 100 x 200 + .008(400 X 5.7 + 267 XK 15.55) K 100 
ee = 
1000 
The following table shows the conveying capacities of various sizes of 


flights at 100 feet per minute in tons of 2000 lbs. per hour. The values 
are true for continuous feed only. 





=15.15. 
































Horizontal Conveyors. Inclined Conveyors. 
ae P d 10° 20° 30° 
oO ‘ ; : ounds 
Flight.) Pieht | Fight | exert | Coal || Flights | Flights | Flights 
16” 18” 24/7 per Every Every Every 
: , Flight Qa DAGS 24” 
Tons. Tons. Tons. Tons. Tons. Tons. 
6xX14!l 69.75 62 46.5 31 40.5 Sine 2250 
SSC 1 O Caer ee 130 97.5 65 78 62 52 
10 X24 See eho chalk. slats 172.6 115 150 120 90 
LOSGS0 Weer holes de los 220 147 184 146 116 
OSC SG enreameneee ciel) Ses oh see: = he 268 179 225 Las 142 








Bucket Conveyors.—Rigid bucket-carriers are used to convey 
large quantities of coal over a considerable distance when there is no 
intermediate point of discharge. These conveyors are made with two 
strands of steel roller chain. They are built to carry as much as 10 tons 
of coal per minute. 


912d WIRE-ROPE HAULAGE. 
a 


Screw Conveyors.—Screw conveyors consist of a helical steel 
flight, either in one piece or in sections, mounted on a pipe or shaft, and 
running in a steel or wooden trough. These conveyors are made from 4 to 
18 inches in diameter, and in sections 8 to 12 feet long. The speed ranges 
from 20 to 60 revolutions per minute and the capacity from 10 to 30 tons 
of coal per hour. It is not advisable to use this type of conveyor for coal, 
as it will only handle the smaller sizes and the flights are very easily dam- 
aged by any foreign substance of unusual size or shape. 

Belt Conveyors.—Rubber or cotton belt conveyors are used for 
handling coal, grain, sand, or other finely divided material. They com- 
bine a high carrying capacity with low power consumption, but are rela: 
tively high in first cost. 

In some cases the belt is flat, the material being fed to the belt at it 
centre in a narrow stream. In.the majority of cases, however, the beh; 
is troughed by means of idler pulleys set at an angle from the_horizonta| 
and placed at intervals along the length of the belt. Rubber belts are 
very often made more flexible for deep troughing by removing some of 
the layers of cotton from the belt and substituting therefor an extra thick- 
ness of rubber. 

Belt conveyors may be used for elevating materials up to about 23° 
incline. On greater inclines the material slides back on the belt and spills. 
With many substances it is important to feed the belt steadily if the con- 
veyor stands at or near the limiting angle. If the flow is interrupted 
the material may slide back on the belt. 

Belt conveyors are run at any speed from 200 to 800 feet per minute, 
and are made in widths varying from 12 inches to 60 inches. 


Capacity of Belt Conveyors im Tons of Coal per Hour. 

















Bodth Velocity of Belt, Feet per Minute. 

0 

Belt, 

Ins. 300 350 400 450 500 550 600 
1 De Aah gt) 36 40.5 45 49.5 54 
14 BOE 42.8 49 owe 61.3 67.4 73.6 
16 48 56 64 2 80 88 96 
18 60.7 70.8 81 91.2 101 Tikit 135 
20 (hs) 87.5 100 Arlee teed 125 USvew 150 
24 108 126 144 162 180 198 216 
30 168.7 197 225 255 281 307 338 
36 243 283 324 365 405 446 486 














For materials other than coal, the figures in the above table should 
be multiplied by the coefficients given in the table below: 














Material. Coefficient. Material. Coefficient. 
FAcinesnCclatat Diewe rete stein s); 0.86 Eh date Rese Bese 1.4 
Cem emteeientan ideie shci. c- 1276 Dana etaekt. sce ac eee arene 1.8 
Clay Henn as oe Memeene ns ay.cc tte! 1.26 ptens Cerushed))> sieeiear 2.0 
COKE TAA Rene tenes fisicues 0.60 





Carrying-bands or Belts, used for the purpose of sorting coal and 
removing impurities, are sometimes made of an endless length of woven 
wire, or of two or three endless chains, carrying steel plates varying in width 
from 6 inches to 14 inches. (Proce. Inst. M. E., July, 1890. 

Grain-elevators.—American Grain-elevators are described in a 
paper by E. Lee Heidenreich, read at the International Engineering Con- 
gress at Chicago (Trans. A. 8S. C. E., 1893). See also Trans, A. S. M. E., vii, 
660. 

WIRE-ROPE HAULAGE. 
Methods for transporting coal and other products by means of wire rope, 
though varying from each other in detail, may be grouped in five classes; 
The Self-acting or Gravity Inclined Plane. 
Il. The Simple Engine-plane. 


WIRE-ROPE HAULAGE. 913 


Il. The Tail-rope System. 
IV. The Endless-rope System 
V. The Cable Tramway. 


The following brief description of these systems is abridged from a 

amphlet on Wire-rope Haulage, by Wm. Hildenbrand, C.E., published by 
Sahin A. Roebling’s Sons Co., Trenton, N. J. 

I. The Self-acting Inclined Plane.—The motive power for the 
self-acting inclined plane is gravity; consequently this mode of transport- 
ing coal finds application only in places where the coal is conveyed from a 
higher to a lower point and where the plane has sufficient grade for the 
loaded descending cars to raise the empty cars to an upper level. - 

At the head of the plane there is a drum, which is generally constructed 
of wood, having a diameter of seven to ten feet. Itis placed high enough 
to allow men and cars to pass under it. Loaded cars coming from the pit 
are either singly or in sets of two or three switched on the track of the 
plane, and their speed in descending is regulated by a brake on the drum. 

Supporting rollers, to prevent the rope dragging on the ground, are 
generally of wood, 5 to 6 inches in diameter and 18 to 24 inches long, with 
34- to %-inch iron axles. The distance between the rollers varies from 15 to 
30 feet, steeper planes requiring less rollers than those with easy grades. 
Considering only the reduction of friction and what is best for the preserva- 
tion of rope, a general rule may be given to use rollers of the greatest 
possible diameter, and to place them as close as economy will permit. 

The smallest angle of inclination at which a plane can be made self-acting 
will be when the motive and resisting forces balance each other. The 
motive forces are the weights of the loaded car and of the descending rope. 
The resisting forces consist of the weight of the empty car and ascending 
rope, of the rolling and axle friction of the cars, and of the axle friction of 
the supporting rollers. The friction of the drum, stiffness of rope, and 
resistance of air may be neglected. A general rule cannot be given, because 
a change in the length of the plane or in the weight of the cars changes the 
proportion of the forces; also, because the coefficient of friction, depending 
on the condition of the road, construction of the cars, etc., isa very uncer- 
tain factor. 

For working a plane with a 5¢-inch steel rope and lowering from one to 
four pit cars weighing empty 1400 lbs. and loaded 4000 lbs., the rise in 100 
feet necessary to make the plane self-acting will be from about 5 to 10 feet, 
decreasing as the number of cars increase, and increasing as the length of 
plane increases. 

A gravity inclined plane should be slightly concave, steeper at the top 
than at the bottom. The maximum deflection of the curve should be at an 
inclination of 45 degrees, and diminish for smaller as well as for steeper 
inclinations. 

Ki. The Simple Engine-plane.—tThe name ‘“ Engine-plane”’ is 
given to a plane on which a load is raised or lowered by means. of a single 
wire rope and stationary steam-engine. It is a cheap and simple method of 
conveying coal underground, and therefore is applied wherever circum- 
stances permit it. 

Under ordinary conditions such as prevail in the Pennsylvania mine 
region, a train of twenty-five to thirty loaded cars will descend, with reason- 
able velocity, a straight plane 5000 feet long’ on a grade of 134 feet in 109, 
while it would appear that 214 feet in 100 is necessary for the same number 
of empty cars. For roads longer than 5000 feet, or when containing sharp 
curves, the grade should be correspondingly larger. 

Kit. Whe Tail-rope System.-——Of all methods for conveying coal 
underground by wire rope, the tail-rope system has found the most applica- 
tion. It can be applied under almost any condition. The road may be 
straight er curved, level or undulating, in one coutinuous line or with side 
branches. In general principle a tail-rope plane is the same as an engine- 
plane worked in both directions with two ropes. One rope, called the ‘‘ main 
rope,” serves for drawing the set of full cars outward; the other, called 
the ‘‘ tail-rope,’’ is necessary to take back the empty set, which on a level 
or undulating road cannot return by gravity. The two drums may be 
located at the opposite ends of the road, and driven by separate engines, 
but more frequently they are on the same shaft at one end of the plane, 
In the first case each rope would require the length of Mee) eek but in the 
second case the tail rope must be twice as long. being led from the drum 
around 9 sheave at the other end of the plane and back again to its starting- 


914 _ HOISTING. 


point. When the main rope draws 4a set of full cars out, the tail-rope drum 
runs loose on the shaft, and the rope, being attached to the rear ear, un- 
winds itself steadily. Going in, the reverse takes place. Each drum is 
provided with a brake to check the speed of the train on a down grade and 
prevent its overrunning the forward rope. As a rule, the tail rope is 
strained less than the main rope, but in cases of heavy grades dipping out- 
ward it is possible that the strain in the former may become as large, or 
even larger, than in the latter, and in the selection of the sizes reference 
should be had to this circumstance. 

IV. The Endless-rope System,—tThe principal features of this 
system are as follows: 

1, The rope, as the name indicates, is endless. - 

2. Motion is given to the rope by a single wheel or drum, and friction is 
obtained either by a grip-wheel or by passing the rope several times around 
the wheel. 

8. The rope must be kept constantly tight, the tension to be produced by 
artificial means. It is done in placing either the return-wheel or an extra 
tension wheel on a carriage and connecting it with a weight hanging over a 
pulley, or attaching it to a fixed post by a screw which occasionally can be 
shortened. 

4. The cars are attached to the rope by a grip or clutch, which can take 
hold at any place and let go again, starting and stopping the train at will, 
without stopping the engine or the motion of the rope. 

5. On a single-track road the rope works forward and backward, but on a 
double track it is possible to run it always in the same direction, the full 
cars going on one track and the empty cars on the other. 

This method of conveying coal, as a rule, has not found as general an in- 
troduction as the tail-rope system, probably because its efficacy is not so 
apparent and the opposing difficulties require greater mechanical skill and 
more complicated appliances. Its advantages are, first, that it requires 
one third less rope than the tail-rope system. This advantage, however, 
is partially counterbalanced by the circumstance that the extra tension in 
the rope requires a heavier size to move the same load than when a main 
and tail rope are used. The second and principal advantage is that it is 
possible to start and stop trains at will without signalling to the engineer. 
On the other hand, it is more difficult to work curves with the endless sys- 
tem, and still more so to work different branches, and the constant stretch 


of the rope under tension or its elongation under changes of temperature . 


frequently causes the rope to slip on the wheel, in spite of every attention, 
causing delay in the transportation and injury to the rope. 

V. Wire-rope Tramways.—tThe methods of conveying products on 
a suspended rope tramway find especial application in places where a mine 
is located on one side of a river or deep ravine and the loading station on 
the other. A wire rope suspended between the two stations forms the track 
on which material in properly constructed ‘‘carriages”’’ or ‘‘ buggies” is 
transported. It saves the construction of a bridge or trestlework, and is 
practical for a distance of 2000 feet without an intermediate support. 

There are two distinct classes of rope tramways: 

1. The rope is stationary, forming the track on which a bucket holding 
the material moves forward and backward, pwlied by a smaller endless 
wire rope. 3 

2. The rope is movable, forming itself an endless line, which serves at 
the same time as supporting track and as pulling rope. 

Of these two the first method has found more general application, and is 
especially adapted for long spans, steep inclinations, and heavy loads. The 
second method is used for long distances, divided into short spans, and is 
only applicable for light loads which are to be delivered at regular intervals. 

For detailed descriptions of the several systems of wire-rope transporta- 
tion, see circulars of John A. Roebling’s Sons Co., The Trenton Iron Co., and 
other wire-rope manufacturers. See also paper on Two-rope Haulage 
Systems, by R. Van A. Norris, Trans. A. S. M. E., xii. 626. 

In the Bleichert System of wire-rope tramways, in which the track rope is 
stationary, loads of 1000 pounds each and upward are carried. While the 
average spans on @ level are from 150 to 200 feet, in crossing rivers, ravines, 
etc., spans up to 1500 feet are frequently adopted. In a tramway on this 
system at Granite, Montana, the total length of the line is 9750 feet, with a 
fall of 1225 feet. The descending loads, amounting to a constant weight of 
about 11 tons, eed over 14 horse-power, which is sufficient to haul the 
empty buckets as well as about 50 tons of supplies per day up the line, anc 


SUSPENSION CABLEWAYS OR CABLE HOISTS. 915 


also to run the ore crusher and elevator. It is capable of delivering 250 
tons of material in 10 hours. 


Suspension Cableways or Cable Hoist-conveyors, 
(Trenton Iron Co.) 


In quarrying, rock-cutting, stripping, piling, dam-building, and many 
other operations where it is necessary to hoist and convey large individual 
loads economically, it frequently happens that the application of a system 
of derricks is impracticable, by reason of the limited area of their efficiency 
and the room which they occupy. 

To meet such conditions cable hoist-conveyors are adapted, as they can be 
operated in clear spans up to 1500 feet, and in lifting individual loads up to 
15 tons. Two types are made—one in which the hoisting and conveying are 
done by separate running ropes, and the other applicable only to inclines, 
in which the carriage descends by gravity, and but one running rope is re- 
quired. The moving of the carriage in the former is effected by means of 
an endless rope, and these are commonly known as ‘‘ endless-rope ”’ hoist- 
conveyors to distinguish them from the latter, which are termed ‘‘ inclined " 
hoist-conveyors. 

The general arrangement of the eadless-rope hoist-conveyors consists of a 
main cable passing over towers, A frames or masts, as may be most conve- 
nient, and anchored firmly to the ground at each end, the requisite tension 
in the cable being maintained by a turnbuckle at one anchorage. 

Upon this cable travels the carriage, which is moved back and forth over 
the line by means of the endless rope. The hoisting is done by a separate 
rope, both ropes being operated by an engine specially designed for the 
purpose, which may be located at either end of the line, and is constructed 
in such a way that the hoisting-rope is coiled up or paid out automatically 
as the carriage is moved in aud out. Loads may be picked up or discharged 
at any point along the line. Where sufficient inclination can be obtained in 
the main cable for the carriage to descend by gravity, and the loading and 
unloading is done at fixed points, the endless rope can be dispensed with. 
The carriage, which is similar in construction to the carriage used in the 
endless-rope cableways, is arrested in its descent by a stop-block, which 
may be clamped to the main cable at any desired point, the speed of the 
descending carriage being under control of a brake on the engine-drum. 


Stress in Hoisting=ropes on Inclined Planes, 
(Trenton Iron Co.) 





3 | 5B go tess i Bg a i S og 
5:3| us |s83)sc28| 38 |ssoieca| «8 | 283 
be atln. OS > Bue Looe Ese sles es 
ges | ue | e823] 2s8| ue | 223) ees| we | 282 
a5 | 23 |ggs|= 2| <3 |eas|*"3 | 42 | G25 

ft: Ls ft. 

5 Prt 140 55 28° 49/ 1003 110 47° 44’ 1516 
10 5° 43/ 240 60 30° 58’ 1067 120 50° 12’ alsyes} 
15 8° 32/ 336 65 3B° 02/ 1128 130 p2e26" 1620 


20 11° 10’ 432 70 35° 00’) 1185 140 | 54° 28’; 1663 
25 14° 03’ 527 75 86° 53’ | 1288 - 150 | 56° 19’| 1699 
30 16° 42’ 613 80 38° 40’ | 1287 160 | 58° 00’| 1730 
35 1920187 700 85 40° 22’; 1332 70 | 59° 33’) 1758 
40 21° 49/ 782 90 42° 00’} 1875 180 | 60° 57’ 782 
45 24° 14’ 860 95 43° 32/| 1415 190 | 62°15’) 1804 
50 26° 34’ 933 100 45° 00’ | 1450 200 | 68° 27’ | 1822 


’ The above table is based on an allowance of 40 Ibs. per ton for rolling fric- 
tion, but an additional allowance must be made for stress due to the weight 
of the rope proportional to the length of the plane. A factor of safety of 5 
to 7 should be taken. ’ 

In hoisting the slack-rope should be taken up gently before beginning the 
lift, otherwise a severe extra strain will be brought on the rope. 

A Double-suspension Cableway, carrying loads of 15 tons, erected near 
Williamsport, Pa., by the Trenton Iron Co., is described by E. G. Spilsbury 
in Trans. A.I. M, E. xx. 766. The span is 733 feet, crossing the Susquehanna 
River. Two steel cables, each 2in. diam., are used. On these cables runsa 
carriage supported on four wheels and moved by an endless cable 1 inch in 
diam. The load consists of a cage carrying « railroad-car loaded with lum- 


916 HOISTING. 


ber, the latter weighing about 12 tons. The power is furnished by a 50-H.P, 
engine, and the trip across the river is made in about three minutes. _ 

A hoisting cableway on the endless-rope system, erected by the Lidger- 
wood Mfg. Co., at the Austin Dam, Texas, had a single span 1350 ft. in 
Jength, with main cable 214 in. diam., and hoisting-rope 134 in.diam. Loads 
of 7 to 8 tons were handled at a speed of 600 to 800 ft. per minute. 

Another, of still longer span, 1650 ft., was erected by the same company at 
Holyoke, Mass., for use in the construction of a dam, The main cable is 
the Elliott or locked wire cable, having a smooth exterior. In the construc- 
tion of the Chicago Drainage Canal twenty cableways, of 700 ft. span and 8 
tons capacity, were used, the towers travelling on rails. 

Tension required to Prevent Slipping of Rope on Drum, 
(Trenton Iron Co.)—The amount of artificial tension to be applied in an-> 
endless rope to prevent slipping on the driving-drum depends on the char- 
acter of the drum, the condition of the rope and number of laps which it 
makes. If and S represer.t respectively the tensions in the taut and slack 
lines of the rope; W, the necessary weight to be applied to the tail-sheave; 
R, the resistance of the cars and rope, allowing for friction; n, the number 
of half-laps of the rope on the driving-drum; and /, the coefficient of fric- 
tion, the following relations must exist to prevent slipping: 


T=Sefx™ W=T+S, and R=T-S; 
efn™ + 4 
efn™ — 1 


fn which e = 2.71828, the base of the Naperian system of logarithms. 
The following are some of the values of f: 


from which we obtain — W= : 


Dry. Wet. Greasy. 


Wire-rope on a grooved iron drum....... .120 .085 070 
Wire-rope on wood-filled sheaves........  .235 170 140 
.Wire-rope on rubber and leather filling.. .495 -400 205 
The importance of keeping the rope dry is evident from these figures. 
efnT 1 4 


The values of the coefficient : corresponding to the above values 


ef[nt pu 


of f, for one up to six half-laps of the rope on the driving-drum or sheaves, 
are as follows: 


2. = Number of Half-laps on Driving-wheel. 


fie |. > paw Soe ers eee 
1 2 3 4 5 6 

-070 9.1380 4.623 8.14 2.418 1.999 1.729 
.085 7.536 3.833 2.629 2.047 1.714 1.505 
120 5.3845 2.007 1.953 1.570 1.3858 1.282 
140 4.623 2.418 1.729 1.416 1.249 1.154 
170 3.833 2.047 1.505 1.268 1.149 1.085 
205 3.212 1.762 1.338 1.165 1.083 1.043 
235, 2.831 1.592 1.245 1.110 1.051 1.024 
-400 1.795 shea lp 1.047 1.013 1.004 1.001 
495, 1.538 1.093 SLOSS) 1.004 NEA) ie (Oaprricnesae 


When the rope is at rest the tension is distributed equally on the two lines 
of the rope, but when running there will be a difference in the tensions of 
the taut and slack lines equal to the resistance, and the values of 7 and $ 
may be readily computed from the foregoing formule. 

TWaper Ropes of Uniform Tensile Strength.—tThe true form 
of rope is not a regular taper but follows a logarithmic curve, the girth 
rapidly increasing toward the upper end. Mr. Chas. D. West gives the fol- 
lowing formula, based on a breaking strain of 80,000 Ibs, per sq.in. of the 
rope, core included, and a factor of safety of 10: log G = #/3680 + log q, in 
which #' = length in fathoms, and Gand g the girth in inches at any two 
sections F fathoms apart. The girth g is first calculated for a safe strain 
of 8000 lbs. per sq. in., and then G is obtained by the formula. For @ 
mathematical investigation see The Engineer, April, 1880, p. 267, thks 


TRANSMISSION OF POWER BY WIRE ROPE. 917 


TRANSMISSION OF POWER BY WIRE ROPE. 


The foliowing notes have been furnished to the author by Mr. Wm Hewitt, 
Vice-President of the Trenton Iron Co. (See also circulars of the Trenton 
Iron Co. and of the John A. Roebling’s Sons Co., Trenton, N. J: ‘ Trans- 
mission of Power by Wire Ropes,’’ by A. W. Stahl, Van Nostrand’s Science 
Series, No. 28; and Reuleaux’s Constructor.) \ 

The force transmitted should not exceed the difference between the 
elastic limit of the wires and the bending stress as determined by the fol- 
lowing tables, taking the elastic limit of tempered steel, such as is used in 
the best rope, at 57,000 lbs. per sq. in., and that of Swedish iron at half this, 
or 28,500 lbs. (The el. lim. of fine steel wires may be higher than 57,000 Ibs.) 


Elastic Limit of Wire Ropes. 





7-Wire Rope. Diam. of Aggregate Elastic Limit. | Elastic Limit. 








Wires. Area of Wires. Steel. | Iron. 
diam., in. ins. sq. in. Ibs. lbs, 
14 028 .025862 1,474 (37 
5/16 035 .040109 2.303 1,152 
36 042 .058189 3.317 1,659 
7/16 049 079201 4.514 2,257 
4% 055 .099785 5,688 2,844 
9/16 -0625 . 128855 7,845 3,672 
54 07 161635 9.213 4.607 
11/16 076 190532 10,869 5,430 
34 .083 227246 12.953 6,477 
% 097 310373 17,691 8,846 
1 111 -406430 28,167 11,583 
19-Wire Rope. 
4 017 .025876 
5/16 : 021 .039485 
3% .024 051573 The elastic limit of 19-wire 
7/16 .029 -075299 rope may be taken the same 
1% .033 097504 as for 7-wire rope since the 
9/16 0375 2125909 ultimate strength of the 
d% 042 157941 wires is 7 to 10 per cent 
11/16 .046 . 189453 greater. 
34 .050 223839 
¥% 058 .301198 
1 067 -401925 





The working tension may be greater, therefore, as the bending stress is 
less; but since the tension in the slack portion of the rope cannot be less 
than a certain proportion of the tension in the taut portion, to avoid 
slipping, a ratio exists between the diameter 
of sheave and the wires composing the rope, 


corresponding to a maximum safe working Section 
tension. This ratio depends upon the num- of Rim, , 
ber of laps that the rope makes about the 

sheaves, and the kind of filling in the rims. or 

the character of the material upon which the Section 
rope tracks. of Arm. 


The sheaves (Fig. 165) are usually of 
cast iron, and are made as light as possible 
consistent with the requisite strength. Vari- 
ous materials have been used for filling the : 
bottom of the groove, such as tarred oakum. 
jute yarn, hard wood, India-rubber, and 
leather. The filling which gives the best 
satisfaction, however, in ordinary transmis- 
sions consists of segments of leather and m 
blocks of India-rubber soaked in tar and Fie. 165. 
packed alternately in the groove. Where the working tension is very 





-- -6-Ft: Diama-—<-- -34-/—> 


918 TRANSMISSION OF POWER BY WIRE ROPE. 


great, however, the wood filling is to be preferred, as in the case of long-dis- 
tarce transmissions where the rope makes several laps about the sheaves, 
and is run at a comparatively slow speed. 


The Bending Stress is determined by the formula 


Ka 


eS 2.06(R + d) + C’ 


k = bending stress in Ibs.; H = modulus of elasticity = 28,500,000; a = ag- 
gregate area of wires, sq. ins. ; ; & = radius of bend; d = diam. of wires, ins. 


For ‘%-wirerope d = 1/9 diam. of rope; C = 27.54. 
mo Sosatgey Fe) wee Aten 0 Say Bama 
From this formula the tables below have been calculated. 


Bending Stresses, 7-wire Rope. 








Diam. Rope 
V4 810} 545) 411) 330] 275] - 236) 207; 184) . 166) 151 
9/32 1,095| 7388} 556) 447] 3873; 321} 281} 250) 225) 205 
5/16 1,569 | 1,060}. 800] 642] 537) 461; 404) 3859) 324) 294 
8 2,692 | 1,822] 1,377] 1,106] 925] 794} 696) 620] 558} 508 
7/16 4,243 | 2,878) 2,178] 1,751] 1,465) 1,259} 1,104) 982] 885} 806 
6 5,962 | 4,053] 3,070| 2,470] 2,067) 1,777) 1,558) 1,387] 1,250) 1,138 
9/16 8,701 | 5,915] 4,486] 3,613] 3,025] 2,601] 2,282] 2,082] 1,831] 1,667 
Dine | scree. 8,267] 6,278) 5,060} 4,288] 3,646] 3,199] 2,849] 2,569] 2,339 
LEG ie bow tees 10,535] 8,008] 6,459] 5,412] 4,657) 4,087] 3,641} 38,283} 3,059 
SA Tamme Setare, sis 13, 655 10, 392] 8,388] 7,032] 6,053] 5,314] 4,735] 4,270) 3,888 
Hm acticig 21,585 16, 465 13, 309 }11,168] 9,620) 8,449] 7,532 6,795 6,189 
HL Maal 's: cr ofe rates |iessco eters 247492 19, "24 16, 651/14, 354 /12,613]11,249/10,151) 9,249 
HG Geen | eiclovel’ 2) cleseetoKe 34,721 281144 23/661 20,411 17, 986 16, 011/14, "453 13,172 
DAE Ve beieatorlacs bacaligangan 38,472 |32,374|27,945 24,582 21,942 19°814 18,062 
Pgs OS ae ee Mateo pote eal BE ied 42, 962/37, 110|32,661 |29, 164 | 26,344 | 24,02 
Tiwi clas ep sabe emuhelabae ox a- betes s'< 55,595] 48,054 | 42,314 |37,799/34,155) 31,151 © 





Bending Stresses, 19-Wire Rope. 





Diam. Rope 
4 965| 495} 3388; 250} 200; 167| 144; 126| 112| 101 
5/16 1,774] 920) 621] 468} 376; 314) 270; 236) 210) 189 
8 2,620 | 1,366) 924) 698) 561) 469) 403) 353) 314) 283 


9/16 oe 5,089} 3,468} 2,630} 2,118) 1,773] 1,525) 1,838} 1,191) 1,074 
OO mre ae eetes 7,095| 4,847] 3,680} 2,967) 2,485) 2,137) 1,876] 1,671) 1,506 

11/16 pee 9,257| 6,201] 4,518] 3,886] 3,257] 2,802) 2,459) 2,191} 1,976 
elontnre 11,807} 8,101) 6,165] 4,977) 4,173] 3,591) 38,153) 2,809] 2,534 

% eteratets 18, 183 12; 528} 9,556| 7,724] 6,481) 5,583] 4,886) 4,871) 3,943 

ei P Valse z%, 612)19,113/14,614]11,830) 9,987] 8,566) 7,528] 6,714] 6,059 
TUG py 1 siete tore Nermreterers 26, 566 20, 807 |16,500 13, 872 11, 966 10, 523] 9,387] 8,474 
DLA a0) erare ever oemeper 35,683 27, 400 22,239 18, 713 16, 153 14, 209} 12, 68211 452 
NG) een aliases od os D4 48,109 37,028 80,096 25, 350/21, 397 19, 272 1%, 209| 15.545 
ST al podrtsol|o4 32.0 61,288 [47,229 38, 436 32) 403 28, 008 24) 662) 22, "080 19,906 
0 Aas Sen areal Mar S° Ooo cores 59.094 48, 152 40, 629 35, 140 30, 957 27, 664 | 25, °005 
1b 7 a osisasdiion oc silocdeus 74,565 60, 844 49, 919 44, 476 39,208 35,048 131, 689 
HA SER NES orion llaoucdd 90,325 |73,795 62) 379 54, 022/47, 639 | 42,606 38, 534 
SN Sp llevelcvele'« [15/0 cig ae HERMES ino) s/o 88, 409 |74, 795 64,814/57,183 51,160 46,285 
EAM |: lsha te rata |love) occ oral ReReMeRs foley e\s,0 |. </>» ocovo' | @hevenatehe 92, 203/81, 42 72,908 |66,002 








SMR Thy t«scente stich oo UNM t.-.ul »« «chevy» RRO Ded 99,951 190,540 


TRANSMISSION OF POWER BY WIRE ROPE. G19 


Horse-Power Transmitted. —The general formula for the amount 
of power capable of being transinitted is as follows: 


H.P. = [cd? — .000006 (w + g, + gq)]v; 


in which d = diameter of the rope in inches, v = velocity of the rope in feet 
per second, w = weight of the rope, g; = weight of the terminal sheaves 
and shafts, gg = weight of the intermediate sheaves and shafts (all in lbs.), 
and c = a constant depending on the material of the rope, the filling in the 
grooves of the sheaves, and the number of laps about the sheaves or drums, 
a single lap meaning a half-lap at each end. The values of c for one up to 
six laps for steel rope are given in the following table: 





Number of Laps about Sheaves or Drums. 





c = for steel rope on 


2 3 4 5 6 
TRO71 Fe seeded oe. ayein ays sacoite Sb ave 5.61 8.81 10.62 11.65 12.16 12.56 
EWOOGs caret ale tts acute oi stesetouiely fo sere 0200 9.93 11.51 12.26 12.66 12.83 
Ruther and leather........ 9.29 11.95 12.70 12.91 12.97 13.00 


The values of c for iron rope are one half the above. 

When more than three laps are made, the character of the surface in 
contact is immaterial as far as slippage is concerned. 

From the above formula we have the general rule, that the actual horse- 
power capable of being transmitted by any wire rope approximately equals 
c times the square of the diameter of the rope in inches, less sia millionths 
the entire weight of all the moving parts, multiplied by the speed of therope, 
in feet per second. 

Instead of grooved drums or a number of sheaves, about which the rope 
makes two or more laps, it is sometimes found more desirable, iid anaes 
where space is limited, to use grip-pulleys. The rim is fitted with a con- 
tinuous series of steel jaws, which bite the rope in contact by reason of the 
pressure of the same against them, but as soon as relieved of this pressure 
they open readily, offering no resistance to the egress of the rope. 

In the ordinary or * flying *” transmission of power, where the rope makes 
a single lap about sheaves lined with rubber and leather or wood, the ratio 
between the diameter of the sheaves and the wires of the rope, correspond- 
ing to amaximum safe working tension, is: For 7-wire rope, steel, 76.9; iron, 
157.8. ee) 12-wire rope, steel, 59.3; iron, 122.6. For 19-wire rope, steel, 44.5; 
iron, 93.1. 


Diameters of Minimum Sheaves in Inches, Corresponding 
toa Maximum Safe Working Tension, 




















Diameter Steel. Iron. 
of Rope. 
In. 7-Wire. | 12-Wire. | 19-Wire. | %-Wire. | 12-Wire. | 19-Wire. 
4 19 15 11 39 31 28 
5/16 24 19 14 49 38 29 
6 29 29 17 59 46 35 
7/16 34 26 19 69 54 41 
38 30 29 79 61 47 
9/16 43 3 25 89 69 52 
64 48 37 98 99 7 58 
11/16 53 41 31 109 84 64 
Y 58 44 34 119 92 20 
Vi 67 52 39 138 107 81 
1 7 59 45 158 123 93 


Assuming the sheaves to be of equal diameter, and of the sizes in the 
above table, the horse-power that may be transmitted by a steel rope making 
a single lap on wood-fulled sheaves is given in the table on the next page, 





920 TRANSMISSION OF POWER BY WIRE ROPE. 


The transmission of greater horse-powers than 250 is impracticable with 
filled sheaves, as the tension would be so great that the filling would 
quickly cut out, and the adhesion on a metallic surface would be insufficient 
where the rope makes but a single lap. In this case it becomes necessary 
to use the Reuleaux method, in whicb the rope is given more than one lap, 
as referred to below, under the caption ‘t Long-distance Transmissions.”’ 


Horse-power Transmitted by a Steel Rope on Wood-filled 














Sheaves, 
Dinmoter Velocity of Rope in Feet per Second. ome 
of Rope. 
ja 10 | 20| 30| 40 | 50 | 60! zo | 80] 90 | 100 
A 4 8 13 17 21 25 28 32 37 40 
5/16 7 13 20 26 83 40 44 51 57 62 
3 10 19 28 38 ve 56 64 93 80 89 
7/16 13 26 88 51 63 95 88 99 109 121 
V% 17 34 51 va 83 99 115 1380 144 159 
9/16 22 43 65 86 106 128 147 167 184 | 2038 
5 27 5S fi: 104 130 | 155 179 | 2038 225 247 
11/16 32 63 95 126 15% 186 | 217 245 
4, 38 76 103 150 186 | 223 
% 52 104 156 } 206 
1 68 135 | 202 


The horse-power that may be transmitted by iron ropes is one half of the 
above. 

This table gives the amount of horse-power transmitted by wire ropes 
under maximum safe working tensions. In using wood-lined sheaves, there- 
fore, it is well to make some allowance for the stretching of the rope, and 
to advocate somewhat heavier equipments than the above table would give; 
that is, if it is desired to transmit 20 horse-power, for instance, to put in a 
plant that would transmit 25 to 30 horse-power, thus avoiding the necessity 
of having to take up a comparatively small amount of stretch. On rubber 
and leather filling, however, the amount of power capable of being trans- 
mitted is 40 per cent greater than for wood, so that this filling is generally © 
used, and in this case no allowance need be made for stretch. as such 
sheaves will likely transmit the power given by the table, under all possible 
deflections of the rope. 

Under ordinary conditions, ropes of seven wires to the strand, laid about 
a hemp core, are best adapted to the transmission of power, but conditions 
often occur where 12- or 19-wire rope is to be preferred, as stated below. 

Defiections of the Rope.—tThe tension of the rope is measured by 
the amount of sag or deflectiun at the centre of the span, and the deflection 
corresponding to the maximum safe working tension is determined by the 
following formule, in which S represents the span in feet: 


Steel Rope. Iron Rope. 

Def. of still rope at centre, in feet.... h =.00004S2 h =.00008S2 

es driving ‘“ C pe eet == 00002582 hy = .00005S2 

ss slack . te ew... Ag=.0000875S2 hgo=.000175S2 

Limits of Span.—On spans of less than sixty feet, it is impossible to 
splice the rope to such a degree of nicety as to give exactly the required de- 
flection, and as the rope is further subject to a certain amount of stretch, it 
becomes necessary in such cases to apply mechanical means for producing 
the proper tension, in order to avoid frequent splicing, which is very objec- 
tionable ; but care should always be exercised in using such tightening 
devices that they do not become the means, in unskilled hands, of over- 
straining the rope. The rope also is more sensitive to every irregularity in 
the sheaves and the fluctuations in the amount of power transmitted, and 
is apt to sway to such an extent beyond the narrow limits of the required 
deflections as to cause a jerking motion, which is very injurious. For this 
keason on very short spans it is found desirable to use a considerably 
heavier rope than that actually required to transmit the power: or in 
other words, instead of a 7-wire rope corresponding to the conditions of 
maximum tension, it is better to use a 19-wire rope of the same size wires, 
and to run this under a tension considerably below the maximum. In this 
way is obtained the advantages of increased weight and less stretch, without 


TRANSMISSION OF POWER BY WIRE ROPE. 921 


having to use larger sheaves, while the wear will be greater in proportion to 
the increased surface. 

In determining the maximum limit of span, the contour of the ground 
and the available height of the terminal sheaves must be taken into cone 
sideration, It is customary to transmit the power through the lower portion 
of the rope, as in this case the greatest deflection in this portion occurs 
when the rope is at rest. When running, the lower portion rises and the 
upper portion sinks, thus enabling obstructions to be avoided which other- 
wise would have to be removed, or make it necessary to erect very high 
towers. The maximum limit of span in this case is determined by the max- 
imum deflection that may be given to the upper portion of the rope when 
running, which for sheaves of 10 ft. diameter is about 600 feet. 

Much greater spans than this, however, are practicable where the contour 
of the ground is such that the upper portion of the rope may be the driver, 
and there is nothing to interfere with the proper deflection of the under 
portion. Some very long transmissions of power have been effected in this 
way without an intervening support, one at Lockport, N. Y., having a clear 
span of 1700 feet. 

Long-distance Transmissions.—When the distance exceeds the 
jimit for a clear span, intermediate supporting sheaves are used, with plain 
grooves (not filled), the spacing and size of which will be governed by the 
contour of the ground and the special conditionsinvolved. Thesize of these 
sheaves will depend on the angle of the bend, gauged by the tangents to the 
curves of the rope at the points of inflection. If the curvature due to this 
angle and the working tension, regardless of the size of the sheaves, as deter- 
mined by the table on the next page, is less than that of the mininum 
sheave (see table p. 919) the intermediate sheaves should not be smaller 
than such minimum sheave, but if the curvature is greater, smaller inter- 
mediate sheaves may be used. 

In very long transmissions of power, requiring numerous intermediate 
supports, it is found impracticable to run the rope at the high speeds main- 
tained in “‘ flying transmissions.’> The rope therefore is run under a higher 
working tension, made practicable by wrapping it several times about 
grooved terminal drums, with a lap about a sheave on a take-up or counter- 
weighted carriage, which preserves a constant tension in the slack portion. 

Inclined Transmissions,—When the terminal sheaves are not on 
the same elevation, the tension at the upper sheave will be greater than that 
at the lower, but this difference is so slight, in most cases, that it may be 
ignored. The span to be considered is the horizontal distance between the 
sheaves, and the principles governing the limits of span will hold good in 
this case, so that for very steep inclinations it becomes necessary to resort 
to tightening devices for maintaining the requisite tension in the rope. The 
limiting case of inclined transmissions occurs when one wheel is directly 
above the other. The rope in this case produces no tension whatever on 
the lower wheel, while the upper is subject only to the weight of the rope, 
which is usually so insignificant that it may be neglected altogether, and 
on vertical transmissions, therefore, mechanical tension is an absolute ne- 
cessity. 

Bending Curvature of Wire Ropes.—tThe curvature due to 
any bend in a wire rope is dependent on the tension, and is not always the 
same as the sheave in contact, but may be greater, which explains how it is 
that large ropes are frequently run around comparatively small sheaves 
without detriment, since it is possible to place these so close that the bend- 
ing angle on each will be such that the resulting curvature will not over- 
strain the wires. This curvature may be ascertained from the formula 
and table on the next page, which give the theoretical radii of curvature in 
inches for various sizes of ropes and different angles for one pound tension 
intherope. Dividing these figures by the actual tension in pounds, gives 
the radius of curvature assumed by the rope in cases where this exceedsthe | 
curvature of the sheave. The rigidity of the rope or internal friction of 
the wires and core has not been taken into account in these figures, but the 
effect of this is insignificant, and it is on the safe side to ignore it. By the 
‘angle of bend’”’ is meant the angie between the tangents to the curves of 
the rope at the points of inflection. When the rope is straight the angle is 
180°. For angles less than 160° the radius of curvature in most cases will be 
less than that corresponding to the safe working tension, and the proper 
size of sheave to use in such cases will be governed by the table headed 
“Diameters of Minimum Sheaves Corresponding to a Maximum Safe 
Working Tension ’” on page 919, 


922 ROPE-DRIVING. 


Radius of Curvature of Wire Ropes in Inches for 
l-lb. Tension. 


Formula: R = Hé4n + 5.25t cos 4%; in which R = radius of curvatures 
£ = modulus of elasticity = 28,500,000; 6 = diameter of wires; n = no, 
of wires ; @ = angle of bend; t = working stress (ibs. and ins.). 


Divide by stress in pounds to obtain radius in inches. 











Diam. ° ~o ° ° ° =po 
of wire! 160 168 170 172 174 176 178° 
gf % 4,226 5,623 8,421 10,949 14,593 21,884 43,762 
‘) | 5g} 11,090} 14,753 22,095 26,731 35,628 58,429 106,841 
PA} 34] 22,274 | 29,633 45,412 54,417 72,530 108,767 217,50 
O+4 %| 43,1841 57,451 86,040 102,688 186,869 205,251 410,44C 
E | 1 71,816 | 95,541 143,085 175,182 233,492 350,150 700,193 
~ | 1146| 112,763 | 150,016 224,667 280,607 374,010 560,872 | 1,121,574 
S (14 | 169,135 | 225,012 336, 982 427,689 570,050 854,858 | 1,709,456 
of } 12,914| 17,179 20,127 31,125 41,485 62,212 124,405 
= 56] 29,762 | 39,594 59,297 75,988 101,282 151,884 803,723 
| 34] 62,813 | 82,899 124,151 157,54 210,018 314,948 629,800 
© % | 116,289 | 154,641 231,593 291,917 389,085 583,479 | 1,164,099 
= |1 199,323 | 265,173 897,129 497,998 663,767 995,390 | 1,990,478 
EB | 116 | 320.556 | 426,459 | 638,674 | 797/697 | 1,063,217 | 1,594,422 | 3'188)359 
tm (114 | 504,402 | 671,041 | 1,004,965 | 1,215,817 | 1,620,513 | 2,430,151 | 4,859,561 





ROPE-DRIVING. 


The transmission of power by cotton or manila ropes is a competitor with 
pearing and leather belting when the amount of power is large, or the dis- 
tance between the power and the work is comparatively great. The follow- 
ing is condensed from a paper by C. W. Hunt, Trans. A.S. M. E., xii. 230: 

But few accurate data are available, on account of the long period re- 
quired in each experiment, a rope lasting from three to six years. Installa- 
tions which have been successful, as well as those in which the wear of the 
rope was destructive, indicate that 200 lbs. on a rope one inch in diameter 
is a safe and economicab working strain When the strain is materially 
Increased, the wear is rapid. 

In the following equations 


C =circumference of rope in inches; g=gravity; 


D=sag of the rope in inches; H = horse-power; , 
F=centrifugal force in pounds; L=distance between pulleys in feet; 
P=pounds per foot of rope; w=working strain in pounds; 


R=force in pounds doing useful work; 

S=strain in pounds on the rope at the pulley; 

T =tension in pounds of driving side of the rope; 
#=tension in pounds on slack side of the rope; 
v=velocity of the rope in feet per second; 

W =ultimate breaking strain in pounds. 


W =720C2; P= .032C2; w= 20C2, 


This makes the normal working strain equal to 1/36 of the breaking 
strength, and about 1/25 of the strength at the splice. The actual strains 
are ordinarily much greater, owing to the vibrations in running, as well as 
from imperfectly adjusted tension mechanism. 

For this investigation we assume that the strain on the driving side of a 
rope is equal to 200 Ibs. on a rope one inch in diameter, and an equivalent 
strain for other sizes, and that the rope is in motion at various velocities of 
from 10 to 144 ft. per second. 

The centrifugal force of the rope in running over the pulley will reduce 


ROPH-DRIVING. 923 


the amotint of force available for the transmission of power. The centrifu- 
gal force F = Pv? + g. 

At a speed of about 80 ft. per second, the centrifugal force increases faster 
than the power from increased velocity of the rope, and at about 140 ft. per 
second equals the assumed allowable tension of the rope. Computing this 
force at various speeds and then subtracting it from the assumed maximum 
tension, we have the force available for the transmission of power. The 
whole of this force cannot be used, because a certain amount of tension on 
the slack side of the rope is needed to give adhesion to the pulley. What 
tension should be given to the rope for this purpose is uncertain, as there 
are no experiments which give accurate data. It is known from considerable 
experience that when the rope runs in a groove whose sides are inclined 
toward each other at an angle of 45° there is sufficient adhesion when the 
ratio of the tensions T+ t = 2. 

For the present purpose, 7’ can be divided into three parts: 1. Tension 
doing useful work; 2. Tension from centrifugal force; 3. Tension to balance 
the strain for adhesion. 

The tension ¢ can be divided into two parts: 1. Tension for adhesion; 
2. Tension from centrifugal force. 

It is evident, however, that the tension required to do a given work should 
not be materially exceeded during the life of the rope. 

There are two methods of putting ropes on the pulleys; one in which the 
ropes are single and spliced on, being made very taut at first, and less so as 
the rope lengthens, stretching until it slips, when it is respliced. The other 
method is to wind a single rope over the pulley as many turns as needed to 
obtain the necessary horse-power and put a tension pulley to give the neces- 
sary adhesion and also take up the wear. The tension ¢ required to trans- 
mit the normal horse-power for the ordinary speeds and sizes of rope is com- 
puted by formula (1), below. The total tension T on the driving side of the 
rope is assumed to be the same at all speeds. The centrifugal force, as well 
as an amount equal to the tension for adhesion on the slack side of the rope, 
must be taken from the total tension 7’ to ascertain the amount of force 
available for the transmission of power. 

It is assumed that the tension on the slack side necessary for giving 
adhesion is equal to one half the force doing useful work on the driving side 
of the rope; hence the force for useful work is R = Mr ; and the ten- 


sion on the slack side to give the required adhesion is 4(7 — F'). Hence 
t = ee) —- F. o- 0 eo 8 8 ee © wipe (1) 


The sum of the tensions T'and t¢ is not the same at different speeds, as the 
equation (1) indicates. 

AS F' varies as the square of the velocity, there is, with an increasing 
speed of the rope, a decreasing useful force, and an increasing total tension, 
t, on the slack side. 

With these assumptions of allowable strains the horse-power will be 


Transmission ropes are usually from 1 to 134 inches in diameter. A com- 
putation of the horse-power for four sizes at various speeds and under 
ordinary conditions, based on a maximum strain equivalent to 200 lbs. for a 
rope one inch in diameter, is given in Fig. 166. The horse-power of other 
sizes is readily obtained from these. The maximum power is transmitted, 
under the assumed conditions, at a speed of about 80 feet per second. 

The wear of the rope is both internal and external; the internal is caused 
by the movement of the fibres on each other, under pressure in bending 
over the sheaves, and the external is caused by the slipping and the wedg- 
ing in the grooves of the pulley. Both of these causes of wear are, within 
the limits of ordinary practice, assumed to be directly proportional to the 
speed. Hence, if we assume the coefficient of the wear to be k, the wear 
will be kv, in which the wear increases directly as the velocity, but the 
horse-power that can be transmitted, as equation (2) shows, will not vary at 
the same rate. 

The rope is supposed to have the strain 7 constant at all speeds on the 
driving side, and in direct provortion to the area of the cross-section; hence 


924 ROPE-DRIVING. 


the catenary of the driving side is not affected by the speed or by the diam- 
eter of the rope. 

The deflection of the rope between the pulleys on the slack side varies 
with each change of the load or change of the speed, as the tension equatica 
(1) indicates. 

The deflection of the rope is computed for the assumed value of T and ¢ 




































42 Ri Aaa ea ea REN Es. 42 
BN cis Te 

~ PO es aS EH a PT 

Horse Power of manilla| | 7| || 1 1/}N/L/|II1{[{ {IS 

36] rope at various speeds.| WET TTT TTT XT TT ryt 1138 
Ne Os A Hs A A 

a a A 8 SD 

PR a Ws Dd EC = 

pS 

ial | PEPE et 

Wed NSO 

ENN TE hap 

Dis kvas ERENCE 

Bg in CE 

a ENA 

ss DRE Civ ay 

Bacecuveas 

S a Ss Nh 

8 ope NA 

4 ee A 

3 SET WT 
ee Pe 
0 10 20 30 40. 50 70 380 90 100 110 120 130 140 


Velocity of Driving Rope in feet per second. 
Fig. 166. 


2 
by the parabolic formula S = a + PD,S being the assumed strain T on 


the driving side, and t, calculated by equation (1), on the slack side. The 
tension ¢ varies with the speed. 


Horse-power of Transmission Rope at Various Speeds. 
Computed from formula (2), given above. 


[ 

















ac) : : non 
2 Speed of the Rope in feet per minute, 2a 
=| = ri 3 ex q' 
| 1500 | 2000 | 2500 | 8000 | 3500{ 4000] 4500, 5000) 6000| 7000] 8000 Bsa c 
| 1.45) 1.9| 2.3 | 2.7] 8 | 8.2| 3.4) 3.4) 3.1] 2.2! 0 | 20 
54] 2.3] 8.2} 3.6 4.2 | 4.6] 5.0) 5.3) 5.3) 4.9) 3.4) 0 24 
34] 3.8 | 4.3] 5.2 Tota rt eariac) “iardl earl “cee eee 30 
| 94 .5)1,,.5.9)) 97.0 8.2} 9.1] 9.8} 10.8) 10.8) 9.3) 6.9] 0 36 
1 B.S acer) 69.2 \ 1027} 11.9) 12.8) 13:6) 138.7) 12-5). 8.81500 2 
14 9.2 | 12.1 | 14.3 | 16.8 | 18.6] 20.0} 21.2) 21.4) 19.5) 13.8] 0 54 
144 | 13.1 | 17.4 | 20.7 | 238.1 | 26.8) 28.8) 80.6! 30.8) 28.2) 19.8) 0 60 
134 | 18 23.7 | 28.2 | 82.8 | 86.4] 39.2] 41.5] 41.8) 37.4] 27.6) 0 42 
2 93.2 ' 30.8 | 86.8 | 42.8 | 47.6! 51.2] 54.4] 54 8] 50 | 35.2] 0 84 











The following notes are from the circular of the C. W. Hunt Co., New 
York: 

For a temporary installation, when the rope is not to be long in use, it 
might be advisable to increase the work to double that given in the table. 

For convenience in estimating the necessary clearance on the driving and 
on the slack sides, we insert a table showing the sag of the rope at different 
speeds when transmitting the horse-power given in the preceding table, 
When at rest the sag is not the same as when running, being greater on the 
driving ard less on the slack sides of the rope. The sag of the driving side 
when transmitting the normal horse-power is the same no matter what size 
of rope is used or what the speed’driven at, because the assumption is that 
the strain on the rope shall be the same at all speeds when transmitting the 


SAG OF THE ROPE BETWEEN PULLEYS. 925 


assumed horse-power, but on the slack side the strains, and consequently 
the sag, vary with the speed of the rope and also with the horse-power. 
The table gives the sag for three speeds. If the actual sag is less than given 
in the table, the rope is strained more than the work requires. 

This table is only approximate, and is exact only when the rope is running 
at its normal speed, transmitting its full load and strained to the assumed 
amount. All of these conditions are varying in actual work, and the table 
must be used as a guide ouly. 


Sag of the Rope between Pulleys. 


= 


Distance | Driving Side. Slack Side of Rope. 
between 


Pulleys Mars Wit Lk hk BAe 
in feet. All Speeds. 80 ft. per sec. | 60 ft. per sec. | 40 ft. per sec. 














40 Ofeet 4inches| Ofeet Vinches} Ofeet 9inches} 0 feet 11 inches 
60 0 66 10 46 1 66 5 66 1 66 8 ee it 6e 11 o6 
80 1 66 5 6é 9 66 4 66 9 66 10 6 38 66 3 66 
100 9 66 0 oe 3 66 8 66 4 66 5 66 5 66 9 66 
120 2 66 11 (T7 5 66 3 ee 6 “ 3 66 i oe 4 sé 
140 3 66 10 6 f¢ ce 23 6é 8 66 9 6b 9 6 9 66 
160 5 66 1 66 9 ce 8 66 11 66 3 C6 14 66 0 66 


The size of the pulleys has an important effect on the wear of the rope— 
the larger the sheaves, the less the fibres of the rope slide on each other, and 
consequently there is less internal wear of the rope. The pulleys should not 
be less than forty times the diameter of the rope for economical wear, and 
as much larger as it is possible to make them. This rule applies also to the 
idle and tension pulleys as well as to the main driving-pulley. 

The angle of the sides of the grooves in which the rope runs varies, with 
different engineers, from 45° to 60°. It is very important that the sides of 
these grooves should be carefully polished, as the fibres of the rope rubbing 
on the metal as it comes from the lathe tools will gradually break fibre by 
fibre, and so give the rope a short life. It is also necessary to carefully avoid 
all sand or blow holes, as they will cut the rope out with surprising rapidity. 

Much depends also upon the arrangement of the rope on the pulleys, es- 
pecially where a tension weight is used. Experience shows that the 
increased wear on the rope from bending the rope first in one direction and 
then in the other is similar to that of wire rope. At mines where two cages 
are used, one being hoisted and one lowered by the same engine doing the 
same work, the wire ropes, cut from the same coil, are usually arranged so 
that one rope is bent continuously in one direction and the other rope is bent 
first in one direction and-then in the other, in winding on the drum of the 
engine. The rope having the opposite bends wears much more rapidly than 
the other, lasting about three quarters as long as its mate. This difference 
in wear shows in manila rope, both in transmission of power and in coal- 
hoisting. The pulleys should be arranged, as far as possible, to bend the 
rope in one direction. 

TENSION ON THE SLACK PART OF THE ROPE. 


Speed of {Diameter of the Rope and Pounds Tension on the Slack Rope. 
Rope, in feet peo IS 


























per second. \% 5 34 % 1 14 1% 134 9 
20 10 27 40 54 Yi} 110 162 216 283, 
30 14 29 42 56 74 Es) 170 226 296 
40 15 31 45, 60 7 123 181 240 815 
50 16 33 49 65 85 132 195 259 339 
60 18 36 53 71 93 145 214 285 373 
vi 19 39 59 i 101 158 236 310 406 
80 2 43 64 85 111 173 255 340 445 





90 24 48 7 93 | 122 190 279 B72 487 





926 ROPE-DRIVING. 


For large amounts of power it is common to use a number of ropes lying 
side by side in grooves, each spliced separately. For lighter drives some 
engineers use one rope wrapped as many times around the pulleys as is 
necessary to get the horse-power required, with a tension pulley to take up 
the slack as the rope wears when first put in use. The weight put upon this 
tension pulley should be carefully adjusted, as the overstraining of the rope 
from this cause is one of the most common errors in rope driving. We 
therefore give a table showing the proper strain on the rope for the various 
sizes, from which the tension weight to transmit the horse-power in the 
tables is easily deduced. This strain can be still further reduced if the 
horse-power transmitted is usually less than the nominal work which the 
rope was proportioned to do, or if the angle of groove in the pulleys is 
acute. 


DIAMETER OF PULLEYS AND WEIGHT OF ROPE. 


Diameter of /|Smallest Diameter|Length of Rope to} Approximate 





Rope, of Pulleys, in allow for Splicing,|Weight, in lbs. per 
in inches. inches. in feet. foot of rope. 

6 20 6 12 
og 24 6 218 
34 30 {f 224 
1 42 9 249 
14% 54. 10 -60 
‘14% 60 12 .83 
134 [2 13 1.10 
2 84 14 1.40 


With a given velocity of the driving-rope, the weight of rope required for 
transmitting a given horse-power is the same, no matter what size rope is 
adopted. The smaller rope will require more parts, but the weight will be 
the same. 

Miscellaneous Notes on Rope-driving.—W. H. Booth commu- 
nicates to the Amer. Machinist the following data from English practice with 
cotton ropes. The calculated figures are based on a total allowable tension 
on a 134-inch rope of 600 lbs., and an initial tension of 1/10 the total allowed 
stress, which corresponds fairly with practice. 

Diameter Of rope.........2.: -eesceee 14” 136” 116” 1864 1347 176" 2 
Weight per foot, Ibs................ 2 0 Ait fee ite Cop aE ds a es 
Centrifugal tension = V2 divided by 6 53 = 44 38s 83 ley gas 

o for V = 80 ft. persec., Ibs. 100 121 145 70 193° 228 256 
Total tension allowable..... eherd slate 300 360 4380 500 600 75 %80 
PMTALLEMSION ce cele s saeias se aw eee 30 = 336 43 50 ~=—s«60 fee fi 
Net working tension at 80 ft.velocity 170 203 242 280 3847 380 446 
Horse-power perrope “ a 24 


The most usual practice in Lancashire is summed up roughly in the fol- 
lowing figures: 134-inch cotton ropes at 5000 ft. per minute velocity = 50 H.P. 
per rope. The most common sizes of rope now used are 134 and 15g in. The 
maximum horse-power for a given rope is obtained at about 80 to 83 feet 
per second, Above that speed the power is reduced by centrifugal tension. 
At a speed of 2500 ft. per minute four ropes will do about the same work as 
three at 5000 ft. per min. 

Cotton ropes do not require much lubrication in the sense that it is re- 
quired by ropes made of the rough fibre of manila hemp. Merely a slight 
surface dressing is all that is required. For small ropes, common in spin- 
ning machinery, from % to 34 inch diameter, it is the custom to prevent the 
fiuffing of the ropes on the surface by a light application of a mixture of 
black-lead and molasses,—but only enough should be used to lay the fibres, — 
put upon one of the pulleys in a series of light dabs. 

Reuleaux’s Constructor gives as the “‘ specific capacity ’? of hemp rope in 
actual practice, that is, the horse-power transmitted per square inch of 
cross-section for each foot of linear velocity per minute, .004 to .002, the 
cross-section being taken as that due to the full outside diameter of the 
rope. For a 134-in. rope, with a cross-section of 2.405sq. in., at a velocity of 
5000 ft. per min,, this gives a horse-power of from 24 to 48, as against 41.8 
by Mr. Hunt’s table and 49 by Mr. Booth’s. 


MISCELLANEOUS NOTES ON ROPE-DRIVING 927 


Reuleaux gives formule for calculating sources of ‘loss in hemp-rope 
transmission due to (1) journal friction, (2) stiffness of ropes, and (8) creep 
of ropes. The constants in these formule are, however, uncertain from 
lack of experimental data. He calculates an average case giving loss of 
power due to journal friction = 4%, to stiffness 7.8%, and to creep 5%, or 16.8%- 
in all, and says this is not to be considered higher than the actual loss. 

Spencer Miller, in a paper entitled ‘* A Problem in Continuous Rope-driv- 
ing’ (Trans. A. S. C. E., 1897), reviews the difficulties which occur in rope- 
driving, with a continuous rope froma large to a small pulley. He adopts 
the angle of 45° as a minimum angle to use on the smaller pulley, and 
recommends that the larger pulley be grooved with a wider angle to a degree 
such that the resistance to slipping is equal in both wheels. By doing this 
the effect of the tension weight is felt equally throughout all the slack 
strands of the rope-drive, hence the tight ropes pull equally. It is shown 
that when the wheels are grooved alike the strains in the various ropes may 
differ greatly, and to such a degree that danger is introduced, for while one- 
half the tension weight should represent the maximum strain on the slack 
rope, it is demonstrated in the paper that the actual maximum strain may 
be even four or six times as great. ° 

In a drive such as is recommended, with a wide angle in the large sheave 
with the larger arc of contact, the conditions governing the ropes are the 
same as if the wheels were of the same diameter; and where the wheels are 
of the same diameter, with a proper tension weight, the ropes pull alike. It 
is claimed that by widening the angle of the large sheave not only is there 
no power lost, but there is actually a great gain in power transmitted. An 
example is given in which it is shown that in that instance the power trans- 
mitted is nearly doubled. Mr. Miller refers to a 250-horse-power drive which 
has been running ten years, the large pulley being grooved 60° and the 
smaller 45°, This drive was designed to use a 1144-in. manila rope, but the 
grooves were made deep enough so that a %-in. rope would not bottom. In 
order to determine the value of the drive a common %-in. rope was put in 
at first,and lasted six years, working under a factor of safety of only 14. 
He recommends, however, the employment in continuous rope-driving of a 
factor of safety of not less than 20. 

The Walker Company adopts a curved form of groove instead of one with 
straight sides inclined to each other at 45°. The curves are concave to the 
rope. The rope rests on the sides of the groove in driving and driven pul- 
leys. In idler pulleys the rope rests on the bottom of the groove, which is 
semicircular. The Walker Company also uses a ‘differential’? drum for 
heavy rope-drives, in which the grooves are contained each in a separate 
ring which is free to slide on the turned surface of the drum in case one rope 
pulls more than another. 

A heavy rope-drive on the separate, or’English, rope system is described 
and illustrated in Power, April, 1892. It is in use at the India Mill at Darwen, 
England. This mill was originally driven by gears, but did not prove success- 
ful, and rope-driving was resorted to. The 85,000 spindles and preparation 
are driven by a 2000-horse-power tandem compound engine, with cylinders 
23 and 44 inches in diameter and %2-inch stroke, running at 54 revolutions 
per minute. The fly-wheel is 380 feet in diameter, weighs 65 tons, and is 
arranged with 30 grooves for 134-inch ropes. These ropes lead off to receiv- 
ing-pulleys upon the several floors, so that each floor receives its power direct 
from the fly-wheel. The speed of the ropes is 5089 feet per minute, and five 
7-foot receivers are used, the number of ropes upon each being proportioned 
to the amount of power required upon the several floors. Lambeth cotton 
ropes are used. (For much other information on this subject see ‘‘ Rope 
Driving,” by J. J. Flather, John Wiley & Sons, 1895.) 


928 FRICTION AND LUBRICATION. 


FRICTION AND LUBRICATION. 


Friction is defined by Rankine as that force which acts between two 
bodies at their surface of contact so as to resist their sliding on each other, 
and which depends on the force with which*the bodies are pressed together. 

Coefficient of Friction.—The ratio of the force required to slide a 
body along a horizontal plane surface to the weight of the body is called the 
coefficient of friction. It is equivalent to the tangent of the angle of repose, 
which is the angle of inclination to the horizontal of an inclined plane on 
which the body will just overcome its tendency to slide. The angle is usually © 
denoted by 6, and the coefficient by f. f = tan @. ? 

Friction of Hest and of Motion.—tThe force required to start @ 
body sliding is called the friction of cest, and the force required to continue 
its sliding after having started is called the friction of motion. 

Rolling Friction is the force required to roll a cylindrical or spheri- 
cal body on a plane or on a curved surface. It depends on the nature of the 
surfaces and on the force with which they are pressed together, but is 
essentially different from ordinary, or sliding, friction. 

Friction of Solids.—Rennie’s experiments (1829) on friction of solids, 
usually unlubricated and dry, led to the following conclusions: 

1, The laws of sliding friction: differ with the character of the bodies 
rubbing together. 

2. The friction of fibrous material is increased by increased extent of 
surface and by time of contact, and is diminished by pressure and speed. — 

,} 3. With wood, metal, and stones, within the limit of abrasion, friction 
aries only with the pressure, and is independent of the extent of surface, 
ime of contact and velocity. 

4. The limit of abrasion is determined by the hardness of the softer of the 

two rubbing parts. 

5. Friction is greatest with soft and least with hard materials. 

_ 6. The friction of lubricated surfaces is determined by the nature of the 

‘lubricant rather than by that of the solids themselves. 


Friction of Rest. (Rennie.) 


Pc aah, Values of f. 
bs. Le se as ae A ED Seo eo See ae 
per square |Wrought iron on| Wrought on Steel on Brass on 
inch, Wrought Iron. Cast Iron. . Cast Iron. Cast Iron. 
187 25 28 380 23 
224 27 29 33 22 
336 31 33 35 21 
448 38 30 35 21 
560 41 ot 36 23 
67 Abraded .38 .40 223 
484 Lasts | Abraded Abraded .23 


Law of Unlubricated Friction.—<A. M. Wellington, Eng’g News, 
April 7, 1888, states that the most important and the best determined of all 
the laws of unlubricated friction may be thus expressed: 

The coefficient of unlubricated friction decreases materially with velocity, 
is very much greater at minute velocities of 0 +, falls very rapidly with 
minute increases of such velocities, and continues to fall much less rapidly 
with higher velocities up to a certain varying point, following closely the 
laws which obtain with lubricated friction. 

Friction of Steel Tires Sliding on Steel Rails, (Westing: 
house & Galton.) 


Speed, miles per hour.......... 10 1584925 4) 288 eae 45! 550 
Coefficient of friction.......... 0.110 .087 .080 .051 .04% .040 
Adhesion, lbs, per ton (2240 lbs.) 246 195 179 428 114 90 


FRICTION. §29 


Rolling Friction is a consequence of the irregularities of form and 
the roughness of surface of bodies rolling one over the other. Its laws 
are not yet definitely established in consequence of the uncertainty which 
exists in experiment as to how much of the resistance is due to roughness of 
surface, how much to original and permanent irregularity of form, and how 
much to distortion under the load. (Thurston.) 

Coefficients of Rolling Friction.—If R= resistance applied at 
the circumference of the wheel; W = total weight, r = radius of the wheel, 
and f=a coefficient, R= fW-+-r. f is very variable. Coulomb gives .06 
for wood, .005 for metal, where W is in pounds and r in feet. Tredgold 
made the value of f for iron on iron .002. 

For wagons on soft soil Morin found f = .065, and on hard smooth roads 

02 


4 im Committee of the Society of Arts (Clark, R. T. D.) reported a loaded 
omnibus to exhibit a resistance on various loads as below: 


Pavement Speed per hour. Coefficient. Resistance. 
GEATILCG aps wisest s ciersicl cycle 2.87 miles. 007 17.41 per ton, 
ABDUAIU Si cs nectch stislewe bee's Bebo Rate 0121 OTA a 
WioOGekaem apiece tas oes cin 3.34 ° 0185 41.60 ‘ 
Macadam, gravelled..... S45 .0199 44rd 8 arcane’ 

‘s granite, new.. Ghai ok .0451 101.09 oe 


Thurston gives the value of f for ordinary railroads, .003, well-laid railroad 
track, .002; best possible railroad track, .001. 

The few experiments that have been made upon the coefficients of rolling 
friction, apart from axle friction, are too incomplete to serve as a basis for 
practical rules. (Trautwine). 

Laws of Fluid Friction,—For all fluids, whether liquid or gaseous, 
the resistance is (1) independen* of the pressure between the masses in 
contact; (2) directly proportional to the area of rubbing-surface; (8) pro- 
portional to the square of the relative velocity at moderate and high speeds, 
and to the velocity nearly at low speeds; (4) independent of the nature of 
the surfaces of the solid against which the stream may flow, but dependent 
to some extent upon their degree of roughness; (5) proportional to the den- 
sity of the fluid, and related in some way to its viscosity. (Thurston.) 

The Friction of Lubricated Surfaces approximates to that of solid fric- 
tes journal is run dry, and to that of fluid friction as it is flooded 
with oil. 


Angles of Repose and Coefficients of Friction of Build- 
ing Materials, (From Ranukine’s Applied Mechanics.) 

















i 
9. = tan 6. aie 
f tan &° 
Dry masonry and brickwork.. 381° to 35° 6 to .7 1.67 to 1.4 
Masonry and brickwork with 
GAM MOLtAI sass seals ae 86142 74 1.35 
Timber On StONC...cecc.ceecees a3 about .4 2.5 
TRONLON StONG,, face enesee tees: 85° to 16342. .7 to .8 1.43 to 3.3 
Timber On ulm DEM epee esis eisrciers- 2616° to 11144? -5 to .2 2to5 
< HS IMEtAISs astiderss:s cies 381° to 111%? -6 to .2 1.67 to5 
Metals on metals ... ........- 14° to 814° 20 to .15 4 to 6.67 
Masonry on dry clay.......... 279 25 1.96 
€ ‘* moist clay........ 1814° 33 3. 
Manrthon ECarthie soc oscemece cs. 14° to 45° .25 to 1.0 4tol 
“aes “dryesand, ‘clay, 
and mixed earth..... . ..... 21° to 37° « .88 to .75 | 2.63 to 1.88 
Earth on earth, damp clay.... 45° 1.0 1 
66 eer” SSL WEL CLAY niga as F7O us ool 3.23 


+ ae shingle and 
PVAVEL ON. side ch wise <cal Mlacdeae ek | 89° to 48° } .81 1.23 to 0.9 


Friction of Motion.—The following is a table of the angle of repose 
6, the coefficient of friction f = tan @, and its reciprocal, 1+ f, for the ma- 
terials of mechanism—condensed from the taples of General Morin (18381), 
and other sources, as given by Rankine; 


og 


930 FRICTION AND LUBRICATION. 


an 











No. Surfaces. 6, He i+f. 
1 | Wood on wood, dry..... 14° to 26149 .25 to. .5 4to2 
2 aa ** soaped..| 114° to 2° -2 to .04 5 to 25 
8 |Metals on oak, dry ...... 2614° to 31° 5 to .6 2 to 1.67 
4 ry Pee TLV big ayers 1314° to 14° 24 to .26 4.17 to 8.85 
5 #¢ sat) SOBDY: +1. 114° 2 iS 
6 SP elm, dry ..... 11149 to 14° .2 to .25 5 to 4 
” |Hemp on oak, dry....... 28° +53 1.89 
8 Sere USES ob WAL Fades 5 1814° .33 3 
9 |Leather on oak...... ... 15° to 1914° «et tO sao 3.7 to 2.86 
10 . ‘“* metals, dry.. 29149 .56 1.79 
11 ey ee os wet.. 20° 36 2.78 
12 Mi “ “* greasy 13° 223 4.35 
13 “ BS ss oily). 814° 15 6.67 
14 |Metals on metals, dry... 816° to 11° Plo tome 6.67 to 5 
15 se iy - wet... 164° “Bt 3.33 
16 |Smooth surfaces, occa- 
sionally greased....... 4° to 4%? -07 to .08 14.3 to 12.5 
1% |Smooth surfaces, con- 
tinuously greased..... 38° 05 20 
18 |Smooth surfaces, best 
MESULUS Silos 2 cement o- 134° to 2° 203, to! .0386). fees faicas 


19 |Bronze on lignum vite, 
constantly wet......... dy Ob: P| ee Thy devonas fae ens eas 


Coefficients of Friction of Journals, (Morin.) 





Lubrication. 








Material. Unguent, Was eas he 
Intermittent. | Continuous. 
Cast iron on cast iron. sa Al SoA so i OF i 08 OS OTe 
: Oil, lard, tallow. .07 to .08 .03 to .054 
Cast iron on bronze...... ; Gictiousaha watt 16 
Cast iron on lignum-vitee../Oil, lard. = = |... eee eee. .09 
Uh hake ahaha { Oil, lard, tallow. .07 to .08 | .03 to .054, 
Iron on lignum Vitee..... Ue itreied er 
Bronze on bronze........ ; als -oil. i 


Prof. Thurston says concerning the above figures that much better results 
are probably obtained in good practice with ordinary machinery. Those 
here given are so greatly modified by‘variations of speed, pressure, and tem- 
perature, that they cannot be taken as correct for general purposes. 

Average Coefficients of Friction. Journal of cast iron in bronze 
bearing; velocity 720 feet per minute; temperature 70° F.; intermittent 
feed through an oil-hole. (Thurston on Friction and Lost Work.) 


Pressures, pounds per square inch. 
Oils. 





Sperm, lard, neat’s-foot,ete.|.159 to .250].138 to .192].086 to .141] .077 to .144 
Olive, cotton-seed, rape, etc.|.160 ‘* .283].107 ** .245].101 ‘* .168] .079 ** .131 
Cod and menhaden.. ......|.248 ‘* .278].124 ** .167|.097 ‘* .102] .081 ‘* .122 
Mineral lubricating-oils. ...|.154 ‘ .261].145 ‘* .283].086 ‘* .178! .094 ‘* .222 


With fine steel journals running in bronze bearings and continuous Iubri- 
cation, coefficients far below those above given are obtained. Thus with 
sperm-oil the coefficient with 50 lbs. per square inch pressure was .0034; with 
200 Ibs., .0051; with 300 lbs.. .0057, 


FRICTION. 931 


for very low pressures, as in spindles, the coefficients are much higher. 
Thus Mr, Woodbuzy found, at a temperature of 100° and a velocity of 600 
feet per minute, 


Pressures, lbs. per sq. in,..... 1 2 3 4 5 
CoeMeienn ay. cde ane So ie eee ee BE ener? 


These hig.. coefficients, however, and the great decrease in the coefficient 
at increased pressures are limited as a practical matter only to the smaller 
pressures which exist especially in spinning machinery, where the pressure 
is solight and the film of oil so thick that the viscosity of the oil is an import- 
ant part of the total frictional resistance. 

Experiments on Friction of a Journal Lubricated by an 
Oil-bath (reported by the Committee on Friction, Proc. Inst. M. E., 
Nov. 1883) show that the absolute friction, that is, the absolute tangential 
force per square inch of bearing, required to resist the tendency of the brass 
to go road with the journal, is nearly a constant under all loads, within or- 
dinary working limits. Most certainly it does not increase in direct propor: 
tion to the load, as it should do according to the ordinary theory of solid 
friction. The results of these experiments seem to show that the friction of 
a perfectly lubricated journal follows the laws of liquid friction much more 
closely than those of solid friction. They show that under these circum- 
stances the friction is nearly independent of the pressure per square inch, 
and that it increases with the velocity, though at a rate not nearly so rapid 
as the square of the velocity. ay 

The experiments on friction at different temperatures indicate a great 
diminution in th® friction as the temperature rises. Thus in the case of 
lard-oil, taking ¢ speed of 450 revolutions per minute, the coefficient of fric- 
tion at a temperature of 120° is only one third of what it was at a tempera- 
ture of 60. 

The journal was of steel, 4 inches diameter and 6 inches long, and a gun- 
metal brass, embracing somewhat less than half the circumference of the 
journal, rested on its upper side, on which the load was applied. When the 
bottom of the journal was immersed in oil, and the oil therefore carried 
under the brass by rotation of the journal, the greatest load carried with 
rape-oil was 573 lbs. per square inch, and with mineral oil 625 lbs. 

In experiments with ordinary lubrication, the oil being fed in at the cen- 
tre of the top of the brass, and a distributing groove being cut in the brass 
parallel to the axis of the journal, the bearing would not run cool with only 
100 lbs. per square inch, the oil being pressed out from the bearing-surface 
and through the oil-hole, instead of being carried in by it. On introducing 
the oil at the sides through two parallel grooves, the lubrication appeared 
to be satisfactory, but the bearing seized with 380 lbs. per square inch. 

When the oil was introduced through two oil-holes, one near each end of 
the brass, and each connected with a curved groove, the brass refused to 
fone its oil or run cool, and seized with a load of only 200 Ibs. per square 
inch. 

With an oil-pad under the journal feeding rape-oil, the bearing fairly car- 
ried 551 lbs. Mr. Tower’s conclusion from these experiments is that the 
friction depends on the quantity and uniformity of distribution of the oil, 
and may be anything between the oil-bath results and seizing, according to 
the perfection or imperfection of the lubrication. The lubrication may be 
very small, giving a coefficient of 1/100; but it appeared as though it could 
not be diminished and the friction increased much beyond this point with- 
out imminent risk of heating and seizing. The oil-bath probably represents 
the most perfect lubrication possible, and the limit beyond which friction 
cannot be reduced by lubrication; and the experiments show that with speeds 
of from 100 to 200 feet per minute, by properly proportioning the bearing- 
surface to the load, it is possible to reduce the coefficient of friction toas low 
as 1/1000. A coefficient of 1/1500 is easily attainable, and probably is fre- 
quently attained, in ordinary engine-bearings in which the direction of the 

. force is rapidly alternating and the oil given an opportunity to get between 
the surfaces, while the duration of the force in one direction is not sufficient 
to allow time for the oil film to be squeezed out. 

Observations on the behavior of the apparatus gave reason to believe that 
with perfect lubrication the speed of minimum friction was from 100 to 150 
feet per minute, and that this speed of minimum friction tends to be higher 
with an increase of load, and also with less perfect lubrication. By the 
speed of minimum friction is meant that speed in approaching which from 
rest the friction diminishes, and above whlch the friction increases. 


932 FRICTION AND LUBRICATION. 


Coefiicients of Friction of Journal with Oil-bath,—Ab. 
stract of results of Tower’s experiments on friction (Proc. Inst. M. ., Nov. 
1683). Journal, 4 in. diam., 6 in. long; temperature, 90° F. 


Nominal Load, in pounds per square inch. 
Lubricant in Bath. 


625 | 520 | 415 | 310 | 205 | 153 } 100 


Coefficients of Friction. 
Lard-oil : 














yp papl eye nel bb nAeeritacr Dowie | vetspleet .0009 | .0012 | .0014} .0020} .0027) .0042 

Zig 8 Va Scuba sitievote lest, tereratevarecsiels laste ete .0017} .0021 |.0029} .0042} .0052] .009 
Mineral grease : 

il oy iil, Pure Oda Gao nace am cuor ts .001 .0014 | .0016 | .0022} .0034] .0038) .0076 

ATO Bos se ereirsinte vara scolelaierie scent 002 .0022] .0027].004 | .0066] .0083} .0151 
Sperm-oil : 

15d GPE WU esis as cere sei sieiesisis |e a vee SOlzed | 20015 (2001 1 0016 UGlamOUs 

2 hp ee a las dtinealsleccis cast mae lins merch a .0021 | .0019| .0027| 0087} .0064 
Rape-oil : (573 Ib.) 

AD Pat Ger OL TMIN oie cere tise eecore ce .001 -001 |.0009| .0008} .0014' .002 |.004 

ABO RS Me SAU nos oS lute abe aree acre eal spetcehere ate -0015} .0016}| .0016) .0024 .004 |.007 
Mineral-oil : 

bod pete DOL MIN se 9:5; sua co17.8, 5/010 5) =hye'5 -0613 | .0012}.0012) .0014|.0021)..... .004 

aii. Sooke ace ska src oecate caer: Svat [cenatee vee -0018] .002 | .0024).0035}..... 007 - 
Rape-oilfed by syphon lubricator: 

TO ata DOL ING se rccies 6 Nommcnieents (tic ers cate lance cl elaeer: .0056].0098].. ..).0125 

Bie ha ee Bea cave tie tatceus Se Netess cies] Sse cease tera czomare ocel| ees .0068} .0077|..... -0152 
Rape-oil, pad under journal: 

DS TehGs POV WU ricci ge cisyerc Crere tele esns| cherries ete reulinne ace cick arererene .0099}.0105)..... .0099 

34) Ppaciisie aus taigcties Gi einl aeieniee lee smell eee .00991.0078 ..... 0133 


Comparative friction of different lubricants under same circumstances, 
temperature 90°, oil-bath: 


MS PCEMISOI! eianis secs s,a30 0 100 per cent. TGA ce sss cisisicisie ie ee eos 135 per cent. 
Ra perOlle aia see cic e L0G os Oliye-Oll lc cc..4-,.15 40% - 185 S 
ME CTAL OME... ocesrcie <5, 0 129 oe Mineral grease....... Baliré “s 


Coefficients of Friction of Motion and of Rest of a 
Journal.—aA cast-iron journal in steel boxes, tested by Prof. Thurston at 
a speed of rubbing of 150 feet per minute, with lard and with sperm oil, 
gave the following: 


Pressures per sq. in., Ibs..... 50 100 250 500 750 1000 

Coeff, with sperm........<.. 5. .013 -008 -005 .004 -0043 -009 
ee SSMMILAT serie esis se «ss 00 02 -0137 ~=.0085 .0053 0066 .0128 
The coefficients at starting were: 

VP IUMESDORIN cu scinesece sess ee 07 135 .14 sale, 185 18 

Wirtian RG Preis tess so... 07 lt 11 .10 12 212 


The coefficient at a speed of 150 feet per minute decreases with increase 
of pressure until 500 lbs. per sq. in. is reached; above this it increases. The 
coefficient at rest or at starting increases with the pressure throughout the 
range of the tests. 

Walue of Anti-friction MWetals, (Denton.)—The various white 
metals available for lining brasses do not afford coefficients of friction 
lower than can be obtained with bare brass, but they are less liable to 
‘* overheating,’’ because of the superiority of such material over bronze in 
ability to permit of abrasion or crushing, without excessive increase of 
friction. 

Thurston (Friction aud Lost Work) says that gun-bronze, Babbitt, and 
other soft white alloys have substantially the same friction; in other words, 
the friction is determined by the nature of the unguent and not by that of 
the rubbing-surfaces, when the latter are in good order. The soft metals 
run at higher temperatures than the bronze. This, however, does not nec- 
essarily indicate a serious defect, but simply deficient conductivity. The 
value of the white alloys for bearings lies mainly in their ready reduction 
to a smooth surface after any local or general injury by alteration of either 
suriace or form. 


MORIN’S LAWS OF FRICTION, 933 


Cast-iron for Bearings. (Joshua Rose.)—Cast iron appears to be ar 
exception to the general rule, that the harder the metal the greater the 
resistance to wear, because cast iron is softer in its texture and easier to 
cut with steel tools than steel or wrought iron, but in some situations it is 
far more durable than hardened steel; thus when surrounded by steam it 
will wear better than will any other metal. Thus, for instance, experience 
has demonstrated that piston-rings of cast iron will wear smoother, better, 
and equally as long as those of steel, and longer than those of either 
wrought iron or brass, whether the cylinder in which it works be composed 
of brass, steel, wrought iron, or cast iron; the latter being the more note- 
worthy, since two surfaces of the same metal do not, as a rule, wear or 
work well together. So also slide-valves of brass are not found to wear so 
long or so smoothly as those of cast iron, let the metal of which the seating 
is composed be whatever it may; while, on the other hand, a cast iron slide- 
valve will wear longer of itself and cause less wear to its seat, if the latter 
is of east iron, than if of steel, wrought iron, or brass. 

Friction of Metals under Steam-pressure.—tThe friction of 
brass upon iron under steam-pressure is double that of iron upon iron. 
(G. H. Babcock, Trans, A. S. M. E., i. 151.) 

Morin’s *“*Laws of Friction.°?—1. The friction between two bodies 
is directly proportioned to the pressure; i.e., the coefficient is constant for 
ali pressures. 

2. The coefficient and amount of friction, pressure being the same, is in- 
dependent of the areas in contact. 

8 The coefficient of friction is independent of velocity, although static 
friction (friction of rest) is greater than the friction of motion. 

Eng’g News, April 7, 1888, comments on these ‘‘laws”’ as follows : From 
1831 till about 1876 there was no attempt worth speaking of to enlarge our 
knowledge of the laws of friction, which during all that period was assumed 
to be complete, although it was really worse than nothing, since it was for 
the most part wholly false. In the year first mentioned Morin began a Sse- 
ries of experiments which extended over two or three years, and which 
resulted in the enunciation of these three ‘‘ fundamental laws of friction,” 
no one of which is even approximately true. 

For fifty years these laws were accepted as axiomatic, and were quoted as 
such without question in every scientific work published during that whole 
period. Now that they are so thoroughly discredited it has been attempted 
to explain away their defects on the ground that they cover only a very lim- 
ited range of pressures, areas, velocities, etc., and that Morin himself only 
announced them as true within the range of his conditions. It is now clearly 
established that there are no limits or conditions within which any one of 
them even approximates to exactitude, and that there are many conditions 
under which they lead to the wildest kind of error, while many of the con- 
stants were as inaccurate as the laws. For example. in Morin’s ** Table of 
Coefficients of Moving Friction of Smooth Plane Surfaces, perfectly lubri- 
cated,’’ which may be found in hundreds of text-books now in use. the coeffi- 
cient of wrought iron on brass is given as .075 to .108, which would make the 
rolling friction of railway trains 15 to 20 lbs. per ton instead of the 3 to 6 lbs. 
which it actually is. 

General Morin, in a letter to the Secretary of the Institution of Mechanical 
Engineers, dated March 15, 1879, writes as follows concerningihis experiments 
on friction made more than forty years before: ‘‘ The results furnished by my 
experiments as to the relations between pressure, surface, and speed on the 
one hand, and sliding friction on the other, have always been regarded by 
myself, not as mathematical laws, but as close approximations to the truth, 
within the limits of the data of the experiments themselves. The same holds. 
in my opinion, for many other laws of practical mechanics, such as those of 
rolling resistance, fluid resistance, etc.”’ 

Prof. J. E. Denton (Stevens Indicator, July, 1890) says: It has been gen- 
erally assumed that friction between lubricated surfaces follows the simple 
law that the amount of the friction is some fixed fraction of the pressure be- 
tween the surfaces, such fraction being independent of the intensity of the 
pressure per square inch and the velocity of rubbing, between certain limits 
of practice. and that the fixed fraction referred to is represented by the co- 
efficients of friction given by the experiments of Morin or obtained from ex- 
perimental data which represent conditions of practical lubrication, such as 
those given in Webber’s Manual of Power. 

By the experiments of Thurston, Woodbury, Tower, etc., however, it 
appears that the friction between lubricated metallic surfaces, such as ma- 


934 FRICTION AND LUBRICATION. 


= 


chine bearings, is not directly proportional to the pressure, is not indepen- 
dent of the speed, and that the coefficients of Morin and Webber are about 
tenfold too great for modern journals. 

Prof. Denton offers an explanation of this apparent contradiction of au- 
thorities by skowing, with laboratory testing-machine data, that Morin’s 
laws hold for bearings lubricated by a restricted feed of lubricant, such as 
is afforded by the oil-cups common to machinery; whereas the modern ex- 
periments have been made with a surplus feed or superabundance of lubri- 
cant, such as is provided only in railroad-car journals, and a few special 
cases of practice. 

That the low coefficients of friction obtained under the latter conditions 
are realized in the case of car-journals, is proved by the fact that the tem- 
perature of car-boxes remains at 100° at high velocities; and experiment shows 
that this temperature is consistent only with a coefficient of friction ofa 
fraction of one per cent. Deductions from experiments on train resistance 
also indicate the same low degree of friction. But these low co-efficients do 
not account for the internal friction of steam-engines as well as do the co 
efficients of Morin and Webber. 

In American Machinist, Oct. 23, 1890, Prof. Denton says: Morin’s measure- 
ment of friction of lubricated journals did not extend to light pressures. 
They apply only to the conditions of general shafting and engine work. 

He clearly understood that there was a frictional resistance, due solely to 
the viscosity of the oil, and that therefore, for very light pressures, the laws 
which he enunciated did not prevail. 

He applied his dynamometers to ordinary shaft-journals without special 
preparation of the rubbing-surfaces, and without resorting to artificial 
methods of supplying the oil. 

Later experimenters have with few exceptions devoted themselves exclu- 
sively to the measurement of resistance practically due to viscosity alone. 
They have eliminated the resistance to which Morin confined his measure- 
ments, namely, the friction due to such contact of the rubbing-surfaces as 

revail with a very thin film of lubricant between comparatively rough sur- 
aces. 

Prof, Denton also says (Trans. A.S. M. E., x. 518): “ I do not believe there 
is a particle of proof in any investigation of friction ever made, that Morin’s 
laws do not hold for ordinary practical oil-cups or restricted rates of feed.”’ 

Laws of Friction of well-lubricated Journals,.—Jobn 
Goodman (Trans. Inst. C. E. 1886, Hng’g News, Apr. 7 and 14, 1888), review- 
ing the results obtained from the testing-machines of Thurston, Tower, and 
Stroudley, arrives at the following laws: 


Laws OF FRICTION: WELL-LUBRICATED SURFACES. 
(Oil-bath.) 

1. The coefficient of friction with the surfaces efficiently lubricated is from 
1/6 to 1/10 that for dry or scantily lubricated surfaces. 

2. The coefficient of friction for moderate pressures and speeds varies ap- 
proximately inversely as the normal pressure; the frictional resistance va- 
ries as the area in contact, the normal pressure remaining constant. 

3. At very low journal speeds the coefficient of friction is abnormally 
high; but as the speed of sliding increases from about 10 to 100 ft. per min., 
the friction diminishes, and again rises when that speed is exceeded, varying 
approximately as the square root of the speed. 

4. The coefficient of friction varies approximately inversely as the temper- 
ature, within certain limits, namely, just before abrasion takes place. 

The evidence upon which these jaws are based is taken from various mod- 
ern experiments. That relating to Law 1 is derived from the ‘‘ First Report 
on Friction Experiments,” by Mr. Beauchamp Tower. 








2. Coefficient of Comparative 
Method of Lubrication. Driotoa: Wreati sia 
WUEDAL as slocc:s ce.o.0 cote meateniriocine sce es .001389 1.00 
Siphon lubricator..... AOA: o 2002 00500uE .0098 7.06 
Padiundéer journal °... ... ce aeemineee so. .0090 6.48 


With a load of 293 Ibs. per sq. in. and a journal speed of 314 ft. per min. 
Mr. Tower found the coefficient of friction to be .0016 with an oil-bath, and 


LAWS OF FRICTION. 935 


.0097, or six times as much, with a pad. The very low coefficients ob- 
tained by Mr. Tower will be accounted for by Law 2, as he found that the 
ae aoa resistance per square inch under varying loads is nearly constant, 
as below: 


Load in lbs, per sq. in..... 529 468 415 363 310 258 205 158 100 
Frictional resist. persq.in. .416 .514 .498 .472 .464 .488 .43 .458 .45 


The frictional resistance per square inch is the product of the coefficient 
of friction into the load per square inch on horizontal sections of the brass. 
Hence, if this product be a constant, the one factor must vary inversely as 
the other, or a high load will give a low coefficient, and vice versa. 

For ordinary lubrication, the coefficient is more constant under varying 
loads; the frictional resistance then varies directly as the load, as shown by 
Mr. Tower in Table VIII of his report (Proc. Inst. M. E. 1883). 

With respect to Law 3, A. M. Wellington (Trans. A. 8S. C. E. 1884), in ex- 
periments on journals revolving at very low velocities, found that the friction 
was then very great, and nearly constant under varying conditions of the 
lubrication, load, and temperature. But as the speed increased the friction 
fell slowly and regularly, and again returned to the original amount when 
eee was reduced to the same rate. This is shown in the following 
table: 

Speed, feet per minute: 

0+ 2.16 3.38 4.86 8.82 21.42 35.37 58.01 89.28 106.02 
Coefficient of friction: 

-H18 8=6©.094 «=6.070 = .069 S055 Sts«w 4 .040 035 .030 .026 


It was also found by Prof. Kimball that when the journal velocity was in- 
creased from 6 to 110 ft. per minute, the friction was reduced 70%; in another 
case the friction was reduced 67% when the velocity was increased from 1 to 
100 ft. per minute; but after that point was reached the coefficient varied 
approximately with the square root of the velocity. 

The following results were obtained by Mr. Tower: 


Feet per minute...| 209 | 262 | ata | 6a | 419 | azz | Nominal Load 











per sq. in. 
Coeff. of friction..| .0010} .0012) .0013} .0014| .0015| .0017 520 Ibs. 
a ‘S -0013} .0014} .0015} .0017} .0018} .002 468 ‘* 
. . .0014! .0015} .0017! .0019} .00211 .0024 415.4%? 


The variation of friction with temperature is approximately in the inverse 
ratio, Law 4. Take, for example, Mr. Tower’s results, at 262 ft. per minute: 




















Temp. F. 110° 100° 90° g0° 70° 60° 
Guserved.:...' .004°” [)).0051 006 | .0073 “0092 0119 
Galeulated.....| 100451 | 100518 | ‘oosos | 00733 | .00964 | “o1a52 


This law does not hold good for pad or siphon lubrication, as then the co- 
efficient of friction diminishes more rapidly for given increments of tem- 
perature, but on a gradually decreasing scale, until the normal temperature 
has been reached; this normal temperature increases directly as the load - 
per sq in. This is shown in the following table taken from Mr. Stroudley’s 
experiments with a pad of rape oil: 


Ausinel es Maer ear TORS TOS SIT SSs 1209 |) 1252 «|, 130°.) 135%.) 140en ene 














Coefficient... i751. 022 | .0180; .0160} .0140} .0125) .0115| .0110] .0106| .0102 
Decrease of coeff..!...... -0040° .0020} 0020} .0015} .0010! .0005] .0004! .0002 




















In the Galton-Westinghouse experiments it was found that with velocities 
below 100 ft. per min., and with low pressures, the frictional resistance 
varied directly as the normal pressure; but when a velocity of 100 ft. per 
min. was exceeded, the coefficient of friction greatly diminished; from the 
same experiments Prof. Kennedy found that the coefficient of friction for 
high pressures was sensibly less than for low. 

Allowable Pressures on Bearing-surfaces, (Proc. Inst. M.E., 
May, 1888.)—The Committee on Friction experimented with a steel ring of 


936 FRICTION AND LUBRICATION. 


rectangular section, pressed between two cast-iron disks, the annular bear: 
ing-surfaces of which were covered with gun-metal, and were 12 in. inside 
diameter and 14 in. outside. The two disks were rotated together, and the 
steel ring was prevented from rotating by means of a lever, the holding 
force of which was measured. When oiled through grooves cut in each face 
of the ring and tested at from 50 to 130 revs. per min., it- was found that a 
pressure of 75 lbs. per sq. in. of bearing-surface was as much as it would 
bear safely at the highest speed without seizing, although it carried 90 lbs. 
per sq. in. ‘at the lowest speed. The coefficient of friction is also much 
higher than for a cylindrical bearing, and the friction follows the law of the 
friction of solids much more nearly than that of liquids. This is doubtless 
due to the much less perfect lubrication applicable to this form of bearing 
compared with a cylindrical one. The coefficient of friction appears to be 
about the same with the same load at all speeds, or, in other words, to be 
independent of the speed; but it seems to diminish somewhat as the load is 
increased, and may be stated approximately as 1/20 at 15 lbs. per sq. in., 
diminishing to 1/30 at 75 lbs. per sq. in. 

The high coefficients of friction are explained by the difficulty of lubricat~- 
ing a collar-bearing. It is similar to the slide-block of an engine, which can 
carry only about one tenth the load per sq. in. that can be carried by tke 
crank-pins. 

In experiments on cylindrical journals it has been shown that when a 
cylindrical journal was lubricated from the side on which the pressure bore, 
100 lbs. per sq. in. was the limit of pressure that it would carry; but when it 
came to be lubricated on the lower side and was allowed to drag the oil in 
with it, 600 lbs. per sq. in. was reached with impunity; and if the 600 lbs. per 
sq. in., which was reckoned upon the full diameter of the bearing, came to 
be reckoned on the sixth part of the circle that was taking the greater pro- 
portion of the load, it followed that the pressure upon that part of the circle 
amounted to about 1200 lbs. per sq. in. 

In connection with these experiments Mr. Wicksteed states that in drill- 
ing-machines the pressure on the collars is frequently as high as 336 Ibs. per 
sq. in., but the speed of rubbing in this case is lower than it was in any of 
the experiments of the Research Committee. In machines working very 
slowly and intermittently, as in testing-machines, very much higher pres- 
sures are admissible. 

Mr. Adamson mentions the case of a heavy upright shaft carried upor a 
small footstep-bearing, where a weight of at least 20 tons was carried on a 
shaft of 5 in. diameter, or, say, 20 sq. in. area, giving a pressure of 1 ton per 
sq. in. The speed was 190 to 200 revs. per min. It was necessary to force the 
oil under the bearing by means of a pump. For heavy horizontal shafts, 
such as a fly-wheel shaft, carrying 100 tons on two journals, his practice for 


getting oil into the bearings was to flatten the journal along one side , 


throughout its whole length to the extent of about an eighth of an inch in 
width for each inchin diameter up to 8in. diameter; above that size rather 
less flat in proportion to the diameter. At first sight it appeared alarming 
to get a continuous fiat place coming round in every revolution of a heavily 
loaded shaft; yet it carried the oil effectually into the bearing, which ran 
Hven bette® in consequence than a truly cylindrical journal without a flat 
side. 

In thrust-bearings on torpedo-boats Mr. Thornycroft allows a pressure of 
never more than 50 Ibs. per sq. in. 

Prof. Thurston (Friction and Lost Work, p. 240) says 7000 to 9000 lbs. 
pressure per square inch is reached on the slow-working and rarely-moved 
pivots of swing bridges. 

Mr. Tower says (Proc. Inst. M. E., Jan. 1884): In eccentric-pins of punch- 
ing and shearing-machines very high pressures are sometimes used without 
seizing. In addition to the alternation in the direction, the pressure is ap- 
pao for only a very short space of time in these machines, so that the oil 

as no time to be squeezed out. 

In the discussion on Mr. Tower’s paper (Proc. Inst. M. E. 1885) it was 
stated that it is well known from practical experience that with a constant 
load on an ordinary journal it is difficult and almost impossible to have more 
than 200 ibs. per square inch, otherwise the bearing would get hot and the 
oil go out of it; but when the motion was reciprocating, so that the load was 
alternately relieved from the journal, as with crank-pins and similar jour- 
a a much higher loads might beapplivd than even 700 or 800 lbs, per square 

Cc * 


FRICTION OF CAR-JOURNAL BRASSES. 937 


Mr. Goodman (Proce. Inst. C. E. 1886) found that the total frictional re- 
sistance is materially reduced by diminishing the width of the brass. 

The lubrication is most. efficient in reducing the friction when the brass 
subtends an angle of from 120° to 60°. The film is probably at its best be- 
tween the angles 80° and 110°. 

In the case of a brass of a railway axle-bearing where an oil-groove is cut 
along its crown and an oil-hole is drilled through the top of the brass into it, 
the wear is invariably on the off side, which is probably due to the oi] escap- 
ing as soon as it reaches the crown of the brass, and so leaving the off side 
almost dry, where the wear consequently ensues. 

In railway axles the brass wears always on the forward side. Thesame ob- 
servation has been made in marine-engine journals, which always wear in 
exactly the reverse way to what they might be expected. Mr. Stroudley 
thinks this peculiarity is due to a film of lubricant being drawn in from the un- 
der side of the journal to the aft part of the brass, which effectually lubri- 
cates and prevents wear on that side; and that when the lubricant reaches 
the forward side of the brass it is so attenuated down to a wedge shape that 
there is insufficient lubrication, and greater wear consequently follows. 

Prof. J. E. Denton (Am. Mach., Oct. 30, 1890) says: Regarding the pres- 
sure to which oil is subjected in railroad car-service, it is probably more severe 
than in any other class of practice. Car brasses, when used bare, are so im- 
perfectly fitted to the journal, that during the early stages of their use the 
area of bearing may be but about onesquare inch. In this case the pressure 
per square inch is upwards of 6000 Ibs. But at the slowest speeds of freight 
service the wear of a brass is so rapid that, within about thirty minutes the 
area is either increased to about three inches, and is thereby able to relieve 
the oil so that the latter can successfully prevent overheating of the journal, 
or else overheating takes place with any oil. and measures of relief must be 
taken which eliminate the question of differences of lubricating power 
among the different lubricants available. A brass which has been run about 
fifty miles under 5000 lbs. load may have extended the area of bearing-surface 
to about three square inches. The pressure is then about 1700 lbs. per square 
inch. It may be assumed that this is an average minimum area for car-ser- 
vice where no violent and unmanageable overheating has occurred during the 
use of a brass for a short time. This area will very slowly increase with any 
lubricant. 

C. J. Field (Power, Feb. 1893) says: One of the most vital points of an en- 
gine for electrical service is that of main bearings. They should have a sur- 
face velocity of not exceeding 350 feet per minute, with a mean bearing- 

ressure per square inch of projected area of journal of not more than 80 
bs. This is considerably within the safe limit of cool performance and easy 
operation. If the bearings are designed in this way, it would admit the use 
of grease on all the main wearing-surface, which in a large type of engines 
for this class of work we think advisable. 

Oil=-pressure in a Bearing.—Mr: Beauchamp Tower (Proc. Inst. 
M. E., Jan. 1885) made experiments with a brass bearing 4 inches diameter 
by 6 inches long, to determine the pressure of the oil between the brass and 
the journal. The bearing was half immersed in oil, and had a total load of 
8008 lbs. upon it. The journal rotated 150 revolutions per minute. Tbe 
pressure of the oil was determined by drilling small holes in the bearing at 
different points and connecting them by tubes to a Bourdon gauge. It was 
found that the pressure varied from 310 to 625 lbs. per square inch, the great- 
est pressure being a little to the ‘‘ off side of the centre line of the top of 
the bearing, in the direction of motion of the journal. The sum of the up- 
ward force exerted by these pressures for the whole lubricated area was 
nearly equal to the total pressure on the bearing. The speed was reduced 
from 150 to 20 revolutions, but the oil-pressure remained the same, showing 
that the brass was as completely oil-borne at the lower speed as at the 
higher. The following was the observed friction at the lower speed: 


Nominal load, lbs. per square inch... 443 333 211 89 
Coefficient of friction........... ;-+-. .00182 .00168 .00247 .0044 


The nominal load per square inch is the total load divided by the product of 
the diameter and length of the journal. At the same low speed of 20 revo- 
lutions per minute it was increased to 676 lbs. per square inch without any 
signs of heating or seizing. 

Friction of Car-journal Brasses. (J. E. Denton, Trans. A. 8. M. 
E., xii. 405.)—A new brass dressed with an emery-wheel, loaded with 5000 lbs., 
may have an actual bearing-surface on the journal, as sbown by the polish 


938 FRICTION AND LUBRICATION. 


of a portion of the surface, of only 1 square inch. With this pressure of 5000 
Ibs. per square inch, the coefficient of friction may be 6%, and the brass may 
be overheated, scarred and cut but, on the contrary, it may wear down evenly 
to a smooth bearing, giving a highly polished area of contact of 3 square 
inches, or more, inside of two hours of running, gradually decreasing the 
pressure per square inch of contact, and a coefficient of friction of less than 
0.5%. A reciprocating motion in the direction of the axis is of importance 
in reducing the friction. With such polished surfaces any oil will lubricate, 
and the coefficient of friction then depends on the viscosity of the oil. With 
a pressure of 1000 lbs. per square inch, revolutions from 170 to 320 per minute, 
and temperatures of 75° to 113° F. with both sperm and parraffine oils, a co- 
cast of as low as 0.11% has been obtained, the oil being fed continuously 

y a pad. 

Experiments on Overheating of Bearings.—Hot Boxes, 
(Denton.)—Tests with car brasses loaded from 1100 to 4500 lbs. per square 
inch gave 7 cases of overheating out of 82 trials. The tests show how purely 
a matter of chance is the overheating, as a brass which ran hot at 5000 lbs. 
load on one day would run cool on a later date at the same or higher pres- 
sure. The explanation of this apparently arbitrary difference of behavior is 
that the accidental variations of the smoothness of the surfaces, almost in- 
finitesimal in their magnitude, cause variations of friction which are always 
tending to produce overheating, and it is solely a matter of chance when 
these tendencies preponderate over the lubricating influence of the oil, 
There is no appreciable advantage shown by sperm-oil, when there is no ten- 
dency to overheat—that is, paraffine can lubricate under the highest pres- 
sures which occur, as well as sperm, when the surfaces are within the condi- 
tions affording the minimum coefficients of friction. 

Sperm and other oils of high heat-resisting qualities, like vegetable oil and 
etroleum cylinder stocks, only differ from the more volatile lubricants, 
ike paraffine, in their ability to reduce the chances of the continual acci- 

dental infinitesimal abrasion producing overheating. 

The effect of emery or other gritty substance in reducing overheating of a 
bearing is thus explained: 

The effect of the emery upon the surfaces of the bearings is to cover the 
latter with a series of parallel grooves, and apparently after such grooves 
are made the presence of the emery does not practically increase the friction 
over the amount of the latter when pure oil only is between the surfaces. 
The infinite number of grooves constitute a very perfect means of insuring 
a uniform oil supply at every point of the bearings. As long as grooves in 
the journal match with those in the brasses the friction appears to amount 
to only about 10% to 15% of the pressure. But if a smooth journal is placed 
between a set of brasses which are grooved, and pressure be applied, the 


journal crushes the grooves and becomes brazed or coated with brass, and . 


then the coefficient of friction becomes upward of 40%. If then emery is 
applied, the friction is made very much less by its presence, because the 
grooves are made to match each other, and a uniform oil supply prevails at 
every point of the bearings, whereas before the application of the emery 
many spots of the latter receive no oil between them. 


Moment of Friction and Work of Friction of Sliding= 
surfaces, etc. 


Moment of Fric- Energy lost by Friction 


tion, inch-lbs. in ft.-lbs. per min. 

PIAL SUPLACES Memes eet es ose. sce econ IWS 
Shafts and journals............ 144fWd .2618f Wan 
Hiab plvotsie. ec. es ee retiels ..-. %fWr 349fWrn 

rks 9 pita eae ~ 3 — 733 
Collar-bearing............ Rhee: 24 fW ie 3497 W Say 2 3 
Conieal pivot... ... .o.ehemabinws: 24 fWr cosee a -349f Win cosec a 
Conical journal: s.* 5. reacts = 24fWr sec a -349f Win sec a 
Truncated-cone pivot 26h Wt 849 oo eee 

runc PIVOL. .... 0.005. 8 rene 3849 ysina 

Hemispherical pivot............ fWr .5236f Win 


Tractrix, or Schiele’s “ anti- 
LFICUCDAMDIVOE 6. c.u ecu ee as ove SWr 5236f Wrn 


Bat J 


PIVOT-BEARINGS, 939 


In the above f= coefficient of friction; 
W = weight on journal or pivot in pounds; 
r = radius, d = diameter, in inches; 
space in feet through which sliding takes places 
outer radius, 7°, = inner radius; 
number of revolutions per minute}; 
the half-angle of the cone, ie., the angle of the slope 
with the axis. é 


eso Hh 


tt tl Ul 


To obtain the horse-power, divide the quantities in the last column by 


33,000. Horse-power absorbed by friction of a shaft = ae. 2 

The formula for energy lost by shafts and journals is approximately true 
for loosely fitted bearings. Prof. Thurston shows that the correct formula 
varies according to the character of fit of the bearing; thus for loosely 
fitted journals, if U = the energy lost, 





ee Ee ae inch-pounds = epee LO Be foot-lbs. 
vi+f? VIET 


For perfectly fitted journals U = 2.54fmr Wn inch-lbs. = .3325fWdn, ft.-Ibs, 
For a bearing in which the journal is so grasped as to give a uniform 


pressure throughout, U = fr2v Wn inch-lbs. = .4112 fWdn, ft.-lbs, 
Resistance of railway trains and wagons due to friction of trains: 
Ff X 2240 


Pull on draw-bar = pounds per gross ton, 


in which R is the ratio of the radius of the wheel to the radius of journal. 

A cylindrical journal, perfectly fitted into a bearing, and carrying a total 
Joad, distributes the pressure due to this load unequally on the bearing, the 
maximum pressure being at the extremity of the vertical radius, while at 
the extremities of the horizontal diameter the pressure is zero. At any 
point of the bearing-surface at the extremity of a radius which makes an 
angle @ with the vertical radius the normal pressure is proportional to cos @. 
If p = normal pressure on a unit of surface, w = total load on a unit of 
length of the journal, and ry = radius of journal, 


Pa _ weosé 
W COS 6 = 1.57 rp, Pe Ban) : 
PIVOT-BEARINGS. 


The Schiele Curve.—W. H. Harrison, in a letter to the Am. Machin- 
ist, 1891, says the Schiele curve is not as good a form for a bearing as the 
segment of a sphere. He says: A mill-stone weighing a ton frequently 
bears its whole weight upon the flat end of a hard-steel pivot 114’ diameter, 
Dr one square inch area of bearing; but to carry a weight of 3000 lbs. he 
advises an end bearing about 4 inches diameter, made in the form of a seg- 
ment of a sphere about 14 inch in height. The die or fixed bearing should 
be dished to fit the pivot. This form gives a chance for the bearing to 
adjust itself, which it does not have when made fiat, or when made with the 
Schiele curve. If aside bearing is necessary it can be arranged farther up 
the shaft. The pivot and die should be of steel, hardened; cross-gutterg 
should be in the die to allow oil to flow, and a central oil-hole should be 
made in the shaft. 

The advantage claimed for the Schiele bearing is that the pressure is uni- 
formly distributed over-its surface, and that it therefore wears uniformly. 
' Wilfred Lewis (Am. Mach., April 19, 1894) says that its merits as a thrust- 
bearing have been vastly overestimated; that the term ‘“ anti-friction”’ 
epplied to it is a misnomer, since its friction is greater than that of a flat 
step or collar of the same diameter. He advises that flat thrust-bearings 
should always be annular in form, having an inside diameter one half of 
the external diameter. 

Friction of a Flat Pivot-bearing.—The Research Committee 
on Friction (Proc. Inst. M. . 1891) experimented on a step-bearing, flat- 
ended, 3 in. diam., the oil being forced into the bearing through a hole in 
its centre and distributed through two radial grooves, insuring thorough 
lubrication. The step was of steel and the bearing of manganese-bronze, 


940 FRICTION AND LUBRICATION, 


At revolutions per min........... 50 128 194 290 353 
The coefficient of friction varied .0181 .0053 .0051 .0044 9053 
between Jand .0221.  .0113. = 0102. «.0178 ~—-.0167 


With a white-metal bearing at 128 revolutions the coefficient of friction 
was a little larger than with the manganese-bronze. At the higher speeds 
the coefficient of friction was less, owing to the more perfect lubrication, as 
sbown by the more rapid circulation of the oil. At 128 revolutions the 
bronze bearing heated and seized on one occasion with a load of 260 pounds 
and on another occasion with 300 pounds per square inch. The white-metal 
bearing under similar conditions heated and seized with a load of 240 
pounds per square inch. The steel footstep on manganese-bronze was after- 
wards tried, lubricating with three and with four radial grooves; but the 
friction was from one and a half times to twice as great as with only the two 
grooves. (See also Allowable Pressures, page 936.) 

Mercury-bath Pivot.—A nearly frictionless step-bearing may be 
obtained by floating the bearing with its superincumbent weight upon mer- 
eury. Such an apparatus is used in the lighthouses of La Heve, Havre. It 
is thus described in Hng’‘g, July .4, 1893, p. 41: 

The optical apparatus, weighing about 1 ton, rests on a circular cast-iron 
table. which is supported by a vertical shaft of wrought iron 2.36 in, 
diameter. 

This is kept in position at the top by a bronze ring and outer iron support, 
and at the bottom in the same way, while it rotates on a removable steel 
piyot resting in a steel socket, which is fitted to the base of the support. To 
the vertical shaft there is rigidly fixed a floating cast-iron ring 17.1 in. diam- 
eter and 11.8 in. in depth, which is plunged into and rotates in a mercury 
bath contained in a fixed outer drum or tank, the clearance between the 
vertical surfaces of the drum and ring being only 0.2 in., so as to reduce as 
much as possible the volume of mercury (about 220 lbs.), while the horizon- 
tal clearance at the bottom is 0.4 in. 


BALL-BEARINGS, FRICTION ROLLERS, ETC. 


A. H. Tyler (Eng’g, Oct. 20, 1898, p. 483), after experiments and com- 
parison with experiments of others arrives at the following conclusions: 

That each ball must have two points of contact only. 

The balls and race must be of glass hardness, and of absolute truth. 

The balls should be of the largest possible diameter which the space at 
disposal will admit of. 

Any one ball should be capable of carrying the total load upon the bearing. 

Two rows of balls are always sufficient. 

: A ball-bearing requires no oil, and has no tendency to heat unless over- 
oaded. 

Until the crushing strength of the balls is being neared, the frictional re- 
sistance is proportional to the load. 

The frictional resistance is inversely proportional to the diameter of the 
balls, but in what exact proportion Mr. Tyler is unable to say. Probably it 
varies with the square. 

The resistance is independent of the number of balls and of the speed. 

No rubbing action will take place between the balls, and devices to guard 
against it are unnecessary, and usually injurious. 

The above will show that the ball-bearing is most suitable for high speeds 
and light loads. On the spindles of wood-carving machines some make as 
much as 30,000 revolutions per minute. They run perfectly cool, and never 
have any oil upon them. For heavy loads the balls should not be less than 
two thirds the diameter of the shaft, and are better if made equal to it. 

Ball-bearings have not been found satisfactory for thrust-blocks, for 
the reason apparently that the tables crowd together. Better results have 
been obtained from coned rollers. A combined system of rollers and balls 
is described in Hng’a, Oct. 6, 1895, p. 429. 

Friction-rollers. —If a journal instead of revolving on ordinary 
bearings be supported on friction-rollers the force required to make the jour- 
nal revolve will be reduced in nearly the same proportion that the diameter 
of the axles of the rollers is less than the diameter of the rollers themselves. 
In experiments by A. M. Wellington with a journal 3% in. diam. supported 
on rollers 8 in. diam., whose axles were 134 in. diam., the friction in starting 
from rest was 4 the friction of an ordinary 3\%-in. bearing, but at a car 
speed of 10 miles per hour it was 14 that of the ordinary bearing. The ratio 
of the diam. of the axle to diam, of roller was 134:8, or as 1 to 4.6, 


FRICTION OF STEAM-ENGINES. 941 


Bearings for Very High Rotative Speeds. (Proc. Inst. M. E., 
Oct. 1888, p. 48%.)—In the Parsons steam-turbine, which has a speed of as 
high as 18,000 1ev. per min., as it is impossible to secure absolute accuracy 
of balance, the bearings are of special construction so as to allow of a certain 
very small amount of lateral freedom. For this purpose the bearing is sur- 
roundel by two sets of steel washers 1/16 inch thick and of different diam- 
eters, the larger fitting close in the casing and about 1/32 inch clear of the 
bearing, and the smaller fitting close on the bearing and about 1/32 inch 
clear of the casing. These are arranged alternately, and are pressed 
together by a spiral spring. Consequently any lateral movement of the 
bearing causes them to slide mutually against one another, and by their 
friction to check or damp any vibrations that may be set up in the spindle. 
The tendency of the spindle is then to rotate about its axis of mass, or prin- 
cipal axis as it is called; and the bearings are thereby relieved from exces- 
sive pressure, and the machine from undue vibration. The finding of the 
centre of gyration, or rather allowing the turbine itself to find its cwn 
centre of gyration, is a well-known device in other branches of mechanics: 
as in the instance of the centrifugal hydro-extractor, where a mass very 
much out of balance is allowed to find its own centre of gyration; the faster 
it ran the more steadily did it revolve and the less was the vibration. An- 
other ilustratior is to be found in the spindles of spinning machinery, 
which run at about 10,000 or 11,000 revolutions per minute: they are made 
of hardened and tempered steel, and although of very small dimensions, the 
outside diameter of the largest portion or driving whorl being perhaps not 
more than 114 in., itis found impracticable to run them at that speed in 
what might be called a hard-and-fast bearing. They are therefore run with 
some elastic substance surrounding the bearing, such as steel springs, hemp, 
or cork. Any elastic substance is sufficient to absorb the vibration, and 
permit of absolutely steady running. 


FRICTION OF STEAM-ENGINES. 


Distribution of the Friction of Engines.—Prof. Thurston in 
his *‘ Friction and Lost Work,” gives the followiug: 


ile 2: 3. 
Main bearings........ Ande FO0N GasocP 47.0 35.4 35.0 
eIStCOUPAT Ger OU ee cnteee). «hier hin ae eee ee 82.9 25.0 21.0 
@rrevnke= OM anes a citeasieavosie's tos teictels BAAR 6.8 5.1 t 13.0 
Cross-head and wrist-pin........... 5.4 4.1 i 
Walve and Tod). ceases poteras gjss ate : 2.5 26.4 | 22.0 
HeCENLLIG SEPADs.. «els ects sere eieteioierelaisie 5.3 4.0) i 
PinksanareCCentriCe ssn tes emesis ; sisters aye 9.01 
OUR L Were sntatiets Mstisivists sia) cisistsrecls Se os SSS. 
100.0 100.0 100.0 


No. 1, Straight-line, 6” x 12’”, balanced valve; No. 2, Straight-line, 6” x 12’, 
unbalanced valve; No.3, 7” x 10’’, Lansing traction locomotive valve-gear. 

Prof. Thurston’s tests on a number of different styles of engines indicate 
that the friction of any engine is practically constant under all loads. 
(Trans. A. S. M. E., viii. 86; ix. 74.) 

In a Straight-line engine, 8’’ x 14’’, I.H.P. from 7.41 to 57.54, the friction H. 
P, varied irregularly between 1.97 and 4,02, the variation being independent 
of the load. With 50 H.P. on the brake the I.H.P. was only 52.6, the friction 
being only 2.6 H.P., or about 57, 

In a compound condensing-engine, tested from 0 to 102.6 brake H.P., gave 
1.H.P. from 14.92 to 117.8 H.P., the friction H.P. varying only from 14.92 te 
17.42. At the maximum load the friction was 15.2 H.P., or 12.9%. 

The friction increases with increase of the boiler-pressure from 30 to 7 
lbs., and then becomes constant. The friction generally increases with in- 
crease of speed, but there are exceptions to this rule. 

Prof. Denton (Stevens Indicator, July, 1890), comparing the calculated 
friction of a number of engines with the friction as determined by measure- 
ment, finds that in one case, a 75-ton ammonia ice-machine, the friction of 
the compressor, 1714 H.P., is accounted for by a coefficient of friction of 744% 
on all the external bearings, allowing 6% of the entire friction of the machine 
for the friction of pistons, stuffing-boxes, and valves. In the case of the 
Pawtucket pumping-engine, estimating the friction of the external bearings 
with a coefficient of friction of 6% and that of the pistons, valves, and stuff - 
ing-boxes as in the case of the ice-machine, we have the total friction 
distributed as follows: 


942 FRICTION AND LUBRICATION. 


Horse- Per cent 
power. of Whole, 


Crank-pins and effect of piston-thrust on main shaft.. 0.71 11.4 
Weight of fly-wheel and main shaft........ Fehecteniet ae 1.95 32.4 
StCAM-VAlVESH. cscs wes eel ey aha eee ees Bice Ect cate 0.23 3.7 
HeCOnEhiGsiwe was Mi descsies aoulaleuts wots dilsles's dicta Sane tke PHOLOE 1.2 
PISCONS #..c didielsleldascisictats voldy ag stcte seth sie eye ve teers Apel aaa! 0.43 7.2 
Stuffing-boxes, six altogether ....... ac kuatecaersges ceed 0.72 11.3 
ALIE- PUI Dinas sicis clas asia s o vinials Cale bigots Paleteisie S clea ste cheese 2.10 82.8 

Total friction of engine with load....... .... 6.21 100.0 


Total friction per cent.of indicated power ... 4.27 


The friction of this engine, though very low in proportion to the indicated 
power, is satisfactorily accounted for by Morin’s law used with a coefficient ~ 
of friction of 5%. In both cases the main items of friction are those due to 
the weight of the fly-wheel and main shaft and to the piston-thrust on 
crank-pins and main-shaft bearings. In the ice-machine the latter items 
are the larger owing to the extra crank-pin to work the pumps, while 
in the Pawtucket engine the former preponderates, as the crank-thrusts are 
partly absorbed by the pump-pistons, and only the surplus effect acts on 
the crank-shaft. 

Prof. Denton describes in Trans. A. S. M. E., x. 392, an apparatus by 
which he measured the friction of a piston packing-ring. When the parts 
of the piston were thoroughly devoid of lubricant, the coefficient of friction 
was found to be about 714%; with an oil-feed of one drop in two minutes the 
coefficient was about 5%; with one drop per minute it was about 3%. These 
rates of feed gave unsatisfactory lubrication, the piston groaning at the 
ends of the stroke when run slowly, and the flow of oil left upon the surfaces 
was found by analysis to contain about 50% of iron. A feed of two drops per 
minute reduced the coefficient of friction to about 1%, and gave practically 
perfect lubrication, the oil retaining its natural color and purity. 


LUBRICATION. 


Measurement of the Durability of Lubricants, (J. E. Den. 
ton, Trans. A.S. M. E., xi. 1013.)—Practical differences of durability of lubri- 
cants depend not on any differences of inherent ability to resist being ‘‘ worn 
out’’ by rubbing, but upon the rate at which they flow through and away 
from the bearing-surfaces. The conditions which control this flow are so 
delicate in their influence that all attempts thus far made to measure dura- 
bility of lubricants may be said to have failed to make distinctions of lubri- 
cating value having any practical significance. In some kinds of service the 
limit to the consumption of oil depends upon the extent to which dust or other 
refuse becomes mixed with it, as in railroad-car lubrication and in the case 
of agricultural machinery. The economy of one oil over another, so far as 
the quality used is concerned—that is, so far as durability is concerned—is 
simply proportional to the rate at which it can insinuate itself into and flow 
out of minute orifices or cracks. Oils will differ in their ability to do this, 
first, in proportion to their viscosity, and, second, in proportion to the ca- 
pillary properties which they may possess by virtue of the particular ingre- 
dients used in their composition. Where the thickness of film between rub- 
hing-surfaces must be so great that large amounts of oil pass through 
ibearings in a given time, and the surroundings are such as to permit oil to 
be fed at high temperatures or applied by a method not requiring a perfect 
fluidity, it is probable that the least amount of oil will be used when the vis- 
cosity is as great as in the petroleum cylinder stocks. When, however, the 
oil must flow freely at ordinary temperatures and the feed of oil is 
restricted, as in the case of crank-pin bearings, it is not practicable to feed 
such heavy oils in a satisfactory manner. Oils of less viscosity or of a 
fluidity approximating to lard-oil must then be used. 

Relative Value of Lubricants. (J. E.Denton, Am. Mach., Oct. 30, 
1890.)—The three elements which determine the value of a lubricant are the 
cost due to consumption of lubricants, the cost spent for coal to overcome 
the frictional resistance caused by use of the lubricant, and the cost due to 
the metallic wear on the journal and the brasses. 

Whe Qualifications of a Good Lubricant, as laid down by 
W. H. Bailey, in Proc. Inst. C. E., vol. xlv., p. 372, are: 1/ Sufficient body to 
keep the surfaces free from contact under maximum pressure. 2, The 


‘LUBRICATION. 943 


greatest possible fluidity consistent with the foregoing condition. 3. ‘fhe 
lowest possible coefficient of friction, which in bath lubrication would be for 
fluid friction approximately. 4. The greatest capacity for storing and car- 
rying away heat, 5, A high temperature of decomposition. 6. Power to 
resist oxidation or the action of the atmosphere, 7. Freedom from corrosive 
ac .of on the metals upon which used. 


Amount of Oil needed to Run an Engine,—The Vacuum Oil 
Co. in 1892, in response to an inquiry as to cost of oil torun a 1000-H.P. 
Corliss engine, wrote: The cost of running two engines of equal size of the 
same make is not always the same. Therefore while we could furnish 
figures showing what it is costing some of our customers having Corliss 
engines o2 1000 H.P., we could only give a general idea, which in itself 
might be considerably out of the way as to the probable cost of ecylinder- 
and engine-oils per year for a particular engine. Such an engine ought to 
run readily on less than 8 drops of 600 W oil per minute. If 3000 drops are 
figured to the quart, and 8 drops used per minute, it would take about 
two and one half barrels (52.5 gallons) of 600 W cylinder-oil, at 65 cents per 
gallon, or about $85 for cylinder-oil per year, running 6 days a week and 10 
hours aday. Engine-oil would be even more difficult to guess at what the 
cost would be, because it would depend upon the number of cups required 
on the engine, which varies somewhat according to the style of the engine. 
It would doubtless be safe, however, to calculate at the outside that not 
more than twice as much engine-oil would be required as of cylinder-oil. 

The Vacuum Oil Co. in 1892 published the following results of practice 


with ‘‘ 600 W ”’ cylinder-oil: 
f ; 20 and 33 X 48; 83 revs. per min.; 1 drop of oil 
Corliss compound engine, } per min. to 1 drop in two minutes. E 


et Finie OX: ai... 20, 838, and 46 x 48; 1 drop every 2 minutes. 


6e 20 and 36 X 36; 143 revs. per min.: 2 drops of oil 
Porter-Allen per min., reduced afterwards to 1 drop per min. 
Ball es 15 X 25 X 16; 240 revs. per min.; 1 drop every 4 


minutes. 


Results of tests on ocean-steamers communicated to the author by Prof. 
Denton in 1892 gave: for 1200-H.P. marine engine, 5 to 6 English gallons (6 to 
7.2 U.S. gals.) of engine-oil per 24 hours for external lubrication; and for a 
1500-H.P. marine engine, triple expansion, running 75 revs. per min., 6 to 7 
English gals. per 24 hours. The cylinder-cil consumption is exceedingly 
variable,—from 1 to 4 gals. per day on different engines, including cylinder- 
oil used to swab the piston-rods. 

Quantity of Oil ased on a Locomotive Crank=-pin.—Prof. 
Denton, Trans. A.S. M. E., xi. 1020, says: A very economical case of practical 
oil-consumption is when a locomotive main crank-pin consumes about six 
cubic inches of oil in a thousand miles of service. This is equivalent to a 
consumption of one milligram to seventy square inches of surface rubbed 
over. 

The Examination of Lubricating-oils. (Prof. Thos. B. Still- 
man, Stevens Indicator, July, 1890.)—The generally accepted conditions of 
a good lubricant are as follows: 

1. ‘‘ Body” enough to prevent the surfaces, to which it is applied, from 
“coming in contact with each other. (Viscosity.) 

2. Freedom from corrosive acid, either of mineral or animal origin. 

3. As fluid as possible consistent with ‘‘ body.”’ 

4, A minimum coefficient of friction. 

5. High “flash” and burning points. 

6. Freedom from all materials liable to produce oxidation or “* gumming.”? 

The examinations to be made to verify the above are both chemical and 
mechanical, and are usually arranged in the following order : 

1. Identification of the oil, whether a simple mineral oil, or animal oil, or 
a mixture, 2. Density. 3. Viscosity. 4. Flash-point. 5. Burning-point. 
6. Acidity. 7%. Coefficient of friction. 8. Cold test. 

Detailed directions for making all of the above tests are given in Prof. 
Stillman’s Article. Seealso Stillinan’s Engineering Chemistry, p. 366. 
Notes on Specifications fer Petroleum Lubricants, (C. 
M. Everest, Vice-Pres. Vacuum Oil Co., Proc. Engineering Congress, Chicago 
- World’s Fair, 1893.)—The specific gravity was the first standard established 
for determining quality of lubricating oils, but it has long since been dis- 
carded as a conclusive test of lubricating quality. However, as the specific 
gravity of a particular petroleum oil increases the visccsity also increases. 


944 FRICTION AND LUBRICATION, 


The object of the fire test of a lubricant, as well as its flash test, is the pre- 
vention of danger from fire through the use of an oil that will evolve in- 
fiammable vapors. The lowest fire test permissible is 300°, which gives a 
liberal factor of safety under ordinary conditions. 

The cold test of an oil, i.e., the temperature at which the oil will congeal, 
should be well below the temperature at which it is used; otherwise the co- 
efficient of friction would be correspondingly increased. 

Viscosity, or fluidity, of an oil is usually expressed in seconds of time in 
which a given quantity of oil will flow through a certain orifice at the tem- 
perature stated, comparison sometimes being made with water, sometimes 
with sperm-oil, and again with rape seed oil. It seems evident that within 
limits the lower the viscosity of an oil (without a too near approach to metal- 
lic contact of the rubbing surfaces) the lower will be the coefficient of fric- 
tion. But we consider that each bearing in a mill or factory would probably © 
require an oil of different viscosity from any other bearing in tbe mill, in 
order to give its lowest coefficient of friction. and that slight variations in the 
condition of a particular bearing would change the requirements of that 
bearing; and further, that when nearing the ‘ danger point ’’ the question of 
viscosity alone probably does not govern. 

The requirement of the New England Manufacturers’ Association, that 
an oil shall not lose over 5% of its volume when heated to 140° Fahr. for 12 
hours, is to prevent losses by evaporation, with the resultant effects. 

The precipitation test gives no indication of the quality of the oil itself, as 
the free carbon in improperly manufactured oils can be easily removed. 

It is doubtful whether oil buyers who require certain given standards of 
laboratory tests are better served than those who do not. Some of the 
standards are so faulty that to pass them an oil manufacturer must supply 
oil he knows to be faulty; and the requirements of the best standards can 
generally be met by products that will give inferior results in actual service. 

Penna, R. KR. Specifications for Petroleum Products, 
1900.—Five different grades of petroleum products will be used, 

The materials desired under this specification are the products of the 
distillation and refining of petroleum unmixed with any other sub- 
stances. 

150° Fire-test Oil.—This grade of oil will not be accepted if sample (1) is 
not ‘‘ water-white’’ in color; (2) flashes below 130° Fahrenheit; (8) burns 
below 151° Fahrenheit; (4) is cloudy or shipment has cloudy barrels when 
received, from the presence of glue or suspended matter; (5) hecomes 
opaque or shows cloud when the sample has been 10 minutes at a tempera- ~ 
ture of 0° Fahrenheit. 

800° Fire-test Oil.—This grade of oil will not be accepted if sample (1) is 
not ‘‘ water-white”’ in color; (2). flashes below 249° Fahrenheit; (3) burns 
below 298° Fahrenheit; (4) is cloudy or shipment has cloudy barrels when 
received, from the presence of glue or suspended matter; (5) becomes 
opaque or shows cloud when the sample has been 10 minutes at a tempera- 
ture of 32° Fahrenheit; (6) shows precipitation when some of the sample is 
heated to 450° F. The precipitation test is made by having about two fluid 
ounces of the oil in a six-ounce beaker, with a thermometer suspended in 
the oil, and then heating slowly until the thermometer shows the required 
temperature. The oil changes color, but must show no precipitation. 

Paraffine and Neutral Oils.—These grades of oil will not be accepted if 
the sample from shipment (1) is so dark in color that printing with long- 
primer type cannot be read with ordinary daylight through a layer of the 
oil 4 inch thick; (2) flashes below 298° F.; (3) has a gravity at 60° F., below 24° 
or above 35° Baumé; (4) from October Ist to May Ist has acold test above 
10° F., and from May 1st to October 1st has a cold test above 32° F. 

The color test is made by having a layer of the oil of the prescribed thick- 
ness in a proper glass vessel, and then putting the printing on one side of the 
vessel and reading it through the layer of oil with the back of the observer 
toward the source of light. 

Well Oil.—This grade of oil will not be accepted if the sample from 
shipment (1) flashes, from May Ist to October 1st, below 298° F., or, 
from October 1st to May Ist, below 249° F.; (2) has a gravity at 60° F., 
below 28° or above 31° Baumé; (3) from October 1st to May 1st has 
a cold test above 10° F., and from May 1st to October ist has 
a cold test above 32° F.; (4) shows any precipitation when 5 cubic 
centimetres are mixed with 95 c. c. of gasoline. The precipitation test 
is to exclude tarry and suspended matter. It is made by putting 95 c.c. of 
88° B gasoline, which must not be above 80° F. in temperature, into a 100 ¢. ¢. 


SOLID LUBRICANTS. 945 
graduate, then auding the prescribed amount of oil and shaking thoroughly. 
Allow to stand ten minutes. With satisfactory oil no separated or precips 
itated material can be seen. 

500° Fire-test Oil.—This grade of oil will not be accepted if sampie from 
shipment (1) flashes below 494° F.; (2) shows precipitation with gasoline 
when tested as described for well oil. 

Printed directions for determining flashing and burning tests and for 
making cold tests and taking gravity are furnished by the railroad com- 
pany. 

- Penna. R.R. Specifications for Lubricating Oils (1894). 
(In force 1902.) 


























Constituent Oils. Parts by volume. 
EX EY Ae LAT Gis OM ote ei ctoye theo better sientxe a diane S9a lero erp eteays cave MsiS tote Lets hte: lias, oe Se eace ere tosea aie 
ESShLAUN O ot ALGO ll te ai crarastesters ate,.cl shell the ch siliosc ote 1 1 1 1 i| 1 
HU oMIPeLOSUIOM weakest oer te btae «cise alee Spe ieee th 1 1 2 u il 2 4 
Paraffine oil.....-. Ha AP eet ae Be A Cia 4 Ok lene: 
SV WIIG Goileve, arate oeits' apshert ap isl net s/% eiiayel nua tiaras Deselbca tesla toreceulterbersil er chavar| ag. 4 2 1 
Wseditorge 3 2s AU AE BaiGa tn CauleG gui iL g (ton tue, 





A, freight cars; engine oil on shifting-engines; miscellaneous greasing in 
foundries, ete. £&, cylinder lubricant on marine equipment and on station- 
ary engines. C, engine oil; allengine machinery; engine and tender truck 
boxes; shafting and machine tools; bolt cutting; general lubrication except 
cars. D, passenger-car lubrication. /, cylinder lubricant for locomotives. 
C,, D,, for use in Dec., Jan., and Feb.; C,, D,, in March, April, May, Sept., 
Oct., and Nov.; C3, D3. in June, July, and August. Weights per gallon, 4, 
faa bse eb Ce DE, 1.0 10s. 

Soda Mixture for Machine Tools. (Penna. R. R. 1894.)—Dissolve 
5 Ibs. of common sal-soda in 40 gallons of water and stir thoroughly. When 
needed for use mix a gallon of this sclution with about a pint of engine oil. 
Used for the cutting parts of machine tools instead of oil. 


SOLID LUBRICANTS, 


Graphite in a condition of powder and used as a solid lubricant, so 
called, to distinguish it from a liquid lubricant, has been found to do well 
where the latter has failed. 

Rennie, in 1829, says: ‘‘Graphite lessened friction in all cases where it 
was used.’”’ General Morin, at a later date, concluded from experiments 
that it could be used with advantage under heavy pressures; and Prof. 
Thurston found it well adapted for use under both light and heavy pressures 
when mixed with certain oils. It is especially valuable to prevent abrasion 
and cutting under heavy loads and at low velocities. 

Soapstone, also called tale and steatite, in the form of powder and 
mixed with oil or fat, is sometimes used as a lubricant. Graphite or soup- 
stone, mixed with soap, is used on surfaces of wood working against either 
iron or wood. 

Metalimne is a solid compound, usually containing graphite, made in the 
form of small cylinders which are fitted permanently into holes drilled in 
the surface of the bearing. The bearing thus fitted runs without any other 
lubrication, (North American Metaline Co., Long Island City, N. Y.) 


946 THE FOUNDRY. 


THE FOUNDRY. 


CUPOLA PRACTICE. 


The following notes, with the accompanying table, are taken from an 
article by Simpson Bolland in American Machinist, June 30, 1892. The table 
shows heights, depth of bottom, quantity of fuel on bed, proportion of fuel 
and iron in charges, diameter of main blast-pipes, number of tuyeres, blast- - 
pressure, sizes of blowers and power of engines, and melting capacity per 
hour, of cupolas from 24 inches to 84 inches in diameter. 

Capacity of Cupola.—The accompanying table will be of service in deter- 
mining the capacity of cupola needed for the production of a given quantity 
of iron in a specified time. 

First, ascertain the amount of iron which is likely to be needed at each 
east, and the length of time which can be devoted profitably to its disposal; 
and supposing that two hours is all that can be spared for that purpose, and 
that ten tons is the amount which must be melted, find in the column, Melt- 
ing Capacity per hour in Pounds, the nearest figure to five tons per hour, 
which is found to be 10,760 pounds per hour, opposite to which in the column 
Diameter of Cupolas, Inside Lining, will be found 48 inches ; this will be the 
size of cupola required to furnish ten tons of molten iron in two hours. 

Or suppose that the heats were likely to average 6 tons, with an occasional 
increase up to ten, then it might not be thought wise to incur the extra ex- 
pense consequent on working a 48-inch cupola, in which case, by following 
the directions given, it will be found that a 40-inch cupola would answer the 
purpose for 6 tons, but would require an additional hour’s time for melting 
whenever the 10-ton heat came along. 

The quotations in the table are not supposed to be all that can be melted 
in the hour by some of the very best cupolas, but are simply the amounts 
which a common cupola under ordinary circumstances may be expected to 
melt in the time specified. 

Height of Cupola.—By height of cupola is meant the distance from the 
base to the bottom side of the charging door. 

Depth of Bottom of Cupola.—Depth of bottom is the distance from the 
sand-bed, after it has been formed at the bottom of the cupola, up to the 
under side of the tuyeres. 

All the amounts for fuel are based upon a bottom of 10 inches deep, and 
any departure from this depth must be met by a corresponding change in 
the quantity of fuel used on the bed; more in proportion as the depth is 
increased, and less when it is made shallower. 

Amount of Fuei Required on the Bed.—The column “‘ Amount of Fuel re- 
quired on Bed, in Pounds” is based on the supposition that the cupola is a 
straight one all through, and that the bottom is 10 inches deep. If the bot- 
meee more, as in those of the Colliau type, then additional fuel will be 
needed. 

The amounts being given in pounds, answer for both coal and coke, for, 
should coal be used, it would reach about 15 inches above the tuyeres ; the 
same weight of coke would bring it up to about 22 inches above the tuyeres, 
which is a reliable amount to stock with. 

First Charge of ron.—The amounts given in this column of the table are 
safe figures to work upon in every instance, yet it will always be in order, 
after proving the ability of the bed to carry the load quoted, to make a slow 
and gradual increase of the load until it is fully demonstrated just how much 
burden the bed will carry. 

Succeeding Charges of Fuel and Ivon.—In the columns relating to succeed- 
ing charges of fuel and iron, it will be seen that the highest proportions are 
not favored, for the simple reason that successful melting with any greater 
proportion of iron to fuel is not the rule, but, rather, the exception. When- 
ever we see that iron has been melted in prime condition in the proportion 
of 12 pounds of iron to one of fuel, we may reasonably expect that the talent, 
material, and cupola have all been up to the highest degree of excellence. 

Diameter of Main Blast-pipe.—The table gives the diameters of main 
blast-pipes for all cupolas from 24 to 84 inches diameter. The sizes given 
opposite each cupola are of sufficient area for all lengths up to 100 feet. 





947 


CUPOLA PRACTICE. 























































































































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948 THE FOUNDRY. 


Tuyeres for Cupola.—Two columns are devoted tothe number and sizes of 
tuyeres requisite for the successful working of each cupola; one gives the 
number of pipes 6 inches diameter, and the other gives the number and 
dimensions of rectangular tuyeres which are their equivalent in area. 

From these two columns any other arrangement or disposition of tuyeres 
Oy be made, which shall answer in their totality te the areas given in the 
table. ; 

Cupolas as large as 84 inches in diameter are now (1906) built without, 
boshes. The most recent development with this size cupola is to place a 
centre tuyere in the bottom discharging air vertically upwards. 

On no consideration must the tuyere area be reduced; thus, an 84-inch 
cupola must have tuyere area equal to 31 pipes 6 inches diameter, or 16 flat 
tuyeres 16 inches by 13% inches. ; 

If it is found that the given number of flat tuyeres exceed in circumference 
that of the diminished part of the cupola, they can be shortened, allowing 
the decreased length to be added to the depth, or they may be built in on 
end; by so doing, we arrive at a modified form of the Blakeney cupola. 

Another important point in this connection is to arrange the tuyeres in 
such a manner as will concentrate the fire at the melting-point into the 
smallest possible compass, so that the metal in fusion will have less space 
to traverse while exposed to the oxidizing influence of the blast. 

To accomplish this, recourse has been had to the placing of additional 
rows of tuyeres in some instan es—the ‘‘Stewart rapid cupola’’ having 
three rows, and the “ Colliau cupola furnace’? having two rows, of tuyeres. 

Blast-pressure.—Experiments show that about 30,000 cubic feet of air are 
consumed in melting a ton of iron, which would weigh about 2400 pounds, 
or more than both iron and fuel. When the proper quantity of air is sup- 
plied, the combustion of the fuelis perfect, and carbonic-acid gas is the 
result. When the supply of air is insufficient, the combustion is imperfect, 
and carbonic-oxide gas is the result. The amount of heat evolved in these 
two cases is as 15 to 414, showing a loss of over two thirds of the heat by im- 
perfect combustion. ; 

It isnot always true that we obtain the most rapkl melting when we are 
forcing into the cupola the largest quantity of air. Some time is required 
to elevate the temperature of the air supplied to the point that it will enter 
into combustion. If more air than this is supplied, it rapidly absorbs heat, 
reduces the temperature, and retards combustion, and the fire in the cupola 
may be extinguished with too much blast. os 

Slag in Cupolas.—A certain amount of slag is necessary to protect the 
molten iron which has fallen to the bottom from the action of the blast; if 
it was not there, the iron would suffer from decarbonization. 

When slag from any cause forms in too great abundance, it should be led 
away by inserting a hole a little below the tuyeres, through which it'will 
find its way as the iron rises in the bottom. 

In the event of clean iron and fuel, slag seldom forms to any appreciable 
extent in small heats ; this renders any preparation for its withdrawal un- 
necessary, but when the cupola is to be taxed to its utmost capacity it is 
then incumbent on the melter to flux the charges all through the heat, car- 
rying it away in the manner directed. 

The best flux for this purpose is the chips from a white marble yard, 
About 6 pounds to the ton of iron will give good results when all is clean. 
Fluor-spar is now largely used as a flux. 

When fuel is bad, or iron is dirty, or both together, it becomes imperative 
that the slag be kept running all the time. 

Fuel for Cupolas.—The best fuel for melting iron is coke, because it re- 
quires less blast, makes hotter iron, and melts faster than coal. When coal 
must be used, care should be exercised in its selection. All anthracites 
which are bright, black. hard. and free from slate, will melt iron admirably. 
The size of the coal used affects the melting to an appreciable extent, and, 
for the best results, small eupolas should be charged with the size called 
“egg,”’ a still larger grade for medium-sized cupolas, and what is called 
“jump ”’ will answer for all large cupolas, when care is taken to pack it 
carefully on the charges. 

Charging a Cupola.—Chas. A. Smith (Am. Mach., Feb. 12, 1891) gives 
the following: A 28-in. cupola should have from 300 to 400 pounds of coke 
on bottom bed; a 36-in. cupola, 700 to 800 pounds; a 48-in. cupola, 1500 Ibs. ; 
and a 60-in. cupola should have one ton of fuel on bottom bed. To every 
pound of fuel on the bed, three, and sometimes four pounds of metal can be 
added with safety, if the cupola has proper blast; in after-charges, to every 


CUPOLA PRACTICE. 949 


poms of fuel add 8 to 10 pounds of metal; any well-constructed cupola will 
stand ten. 

F. P. Wolcott (Am. Mach., Mar. 5, 1891) gives the following as the practice 
of the Colwell Iron-works, Carteret, N. J.: ‘‘ We melt daily from twenty to 
forty tons of iron, with an average of 11.2 pounds of iron to one of fuel. In 
a 36-in. cupola seven to nine pounds is good melting, but in a cupola that 
lines up 48 to 60 inches, anything less than nine pounds shows a defect in 
arrangement of tuyeres or strength of blast, or in charging up.”’ 

‘The Moulder’s Text-book,”’ by Thos. D. West, gives forty-six reports in 
tabular form of cupola practice in thirty States, reaching from Maine to 
Oregon. 

Cupola Charges in Stove-foundries,. (Iron Age, April 14, 1892.) 
No two cupolas are charged exactly the same. The amount of fuel on the 
bed or between the charges differs, while varying amounts of iron are used 
in the charges. Below will be found charging-lists from some of the prom- 
inent stove-foundries in the country : 


Ibs. Ibs. 
A—Bed of fuel, coke.......... 1,500 } Four next charges of coke, 
First charge of iron ...... 5,000 CACIWBR Fes ee Woe ace ee eee 150 
All other charges of iron.. 1,000 Six next charges of coke, each 120 
First and second charges Nineteen next charges of coke, 
Of coke, each’ ......:...26 200 CACM errce tse ae ee oe ee 100 


Thus’for a melt of 18 tons there would be 5120 lbs. of coke used, giving a 
ratio of 7 to 1. Increase the amount of iron melted to 24 tons, and a ratio of 
8 pounds of iron to 1 of coal is obtained. 


Ibs. Ibs. 
W--Bed of fuel, coke.......... 1,600 | Second and third charges of 
First charge of iron....... 1,800 1B KS) Dp copa ae tap pale Gent ee 328 130 
First charge of fuel..-.... 150 All other charges of fuel, each 100 
All other charges of iron, 
(CEG pec, Ceo ODA pee -. 1,000 


For an 18-ton melt 5060 Ibs. of coke would be necessary, giving a ratio of 
7.1 Ibs. of iron to 1 pound of coke. 


lbs. 


©—Bed of fuel, coke........... 1,600 All other charges of iron...... 2.000 
First charge of iron...... . 4,000 All other charges of coke...... 150 
First and second charges 

OF. COKG 223955. <-sas04 38 - 200 | 
In a melt of 18 tons 4100 lbs. of coke would be used, or a ratio of 8.5 to 1. 
Ibs. Ibs. 

D—Bed of fuel, coke. ........ 1,800 All charges of coke, each...... 200 

First charge of iron....... 5,600 All other charges of iron....... 2,900 


In a melt of 18 tons, 3900 Ibs. of fuel would be used, giving a ratio of 9.4 
pounds of iron to 1 of coke. Very high, indeed, for stove-plate. 


Ibs. lbs. 
E-—Bed of fuel, coal .......... 1,900 All other charges of iron, each 2,000 
First charge of iron....... 5,000 All other charges of coal, each 175 


First charge of coal........ 200 


In a melt of 18 tons 4700 lbs. of coal would be used, giving a ratio of 7.7 
lbs. of iron to 1 lb. of coal. 

These are sufficient to demonstrate the varying practices existing among 
different stove-foundries. In all these places the iron was proper for stove- 
plate purposes, and apparently there was little or no difference in the kind 
of work in the sand at the different foundries. 

Results of Increased Driving. (Erie City Iron-works, 1891.)— 
May—Dec. 1890: 60-in. cupola, 100 tons clean castings a week, melting 8 tons 
per hour; iron per pound of fuel, 744 lbs.; per cent weight of good castings to 
iron charged, 7534. Jan.-May, 1891: Increased rate of melting to 1114 tons per 
hour; iron per lb. fuel, 914; per cent weight of good castings, 75; one week, 
1314 tous per hour, 10.3 lbs. iron per Ib. fuel; per cent weight of good cast- 
ings, 75.3. The increase was made by putting in an additional row of tuyeres 
and using stronger blast, 14 ounces. Coke was used as fuel. (W. O. Webber, 
Trans. A. 8. M. E, xii. 1045.) 


950 | : THE FOUNDRY. 


Buffalo Steel Pressure-blowers. Speeds and Capacities 
as applied to Cupolas, 





























. : (2) ; go j}2 

ap eee s 1% S Sos] 8 |Sei8 |sBs 
6 |% (2g a 1¢3.| 844) eee] 2 | se ledeless 
ra i a 85 2 Aes CEs oon 9 |48 mele Sa 
Steg ign) 2 1 35S) Sea Sea, 2 | Beisel ees 
6 | BM 1s08] © | SHR | cRalsdag © | Se lomalgda 
Gin ete Aol A | m ==) oO ao |n le 6) 

a | 4 | 20 | 8 | 4732 | 1545| 6669 9 |'5030] 1637] 717 
5 | 6 | 2 | 8 | 4209 | 2321 7731 10 | 4726] 2600| ser 
6 gs | 30 | 8 | 3660 | 3093} 9519 10 | 4108] 3671] 1067 
y | 14 | 35 | 8 | 3244 | 4218] 14869 10 | 3642| 4777! 1668 
gs | 18 | 40 | 8 | 2948 | 5425| 21999 i0 | 3310] 6099| 2469 
9 | 26 | 45 | 10 | 2785 | 7818| 32039 12 | 3260] 8598] 3523 
10 | 36 | 55 | 10 | 2195 | 11295] 49389 12 | 2413 | 12378) 5431 
11 | 45 | 65 | 12 | 1952 | 16955] ‘707 14 | 2116 | 18357] 8353 
1144] 55 | 72 | 12 | 1647 | 22607] 102769 14 | 1797 | 25176] 11144 
1 °| 7 | 84 | 12 | 1625 | 25936 | 11744 14 | 1775 | 28019! 12736 


In the table are given two different speeds and pressures for each size of 
blower, and the quantity of iron that may be melted, per hour, with each. 
In all cases it is recommended to use the lowest pressure of blast that will do 
the work. Run up to the speed given for that pressure, and regulate quan- 
tity of air by the blast-gate. The tuyere area should be at least one ninth 
of the area of cupola in square inches, with not less than four tuyeres at 
equal distances around cupola, so as to equalize the blast throughout. Va- 
riations in temperature affect the working of cupolas materially, hot 
weather requiring increase in volume of air. 

(For tables of the Sturtevant blower see pages 519 and 520.) 

Loss in Melting Iron in Cupolas.—G. O. Vair, Am. Mach., 
March 5, 1891, gives a record of a 45-in. Colliau cupola as follows: 


Ratio of fuel to iron, 1 to 7.42. 





GOOG Castings. saictsedéde ot ndbesias lees caees 21,314 lbs. 
New SCrap..... .ecscee. hsazeeh Ra tcieats ee B 05a 
Malling ce iwale tis. se cieters tie do maticle eRe EEE 200 *% 
Loss 7Ofmetal se. cits dusts soeb ens sae cate aeolian 
Anrountumelted I Sse e ek eee ee 26,000 Ibs. 


Loss of metal, 5.69%. _ Ratio of loss, 1 to 17.55, 


Use of Softeners in Foundry Practice. (W. Graham, fon Age, 
June 27, 1889.)—In the foundry the problem is to have the right proportions 
of combined and graphitic carbon in the resulting casting; this is done by 
getting the proper proportion of silicon. The variations in the proportions 
of silicon afford a reliable and inexpensive means of producing a cast iron 
of any required mechanical character which is possible with the material 
employed. In this way, by mixing suitable irons in the right proportions, 
a required grade of casting can be made more cheaply than by using irons 
in which the necessary proportions are already found. 

If a strong machine casting were required, it would be necessary to keep 
the phosphorus, sulphur, and manganese within certain limits. Professor 
Turner found that cast iron which possessed the maximum of the desired 
qualities contained, graphite, 2.59%; silicon, 1.42%; phosphorus, 0.39%; sul- 
phur, 0.06%; manganese, 0.587. 

A strong casting could not be made if there was much increase in the 
amount of phosphorus, sulphur, or manganese. Irons of the above percent- 
ages of phosphorus, sulphur, and manganese would be most suitable for this 
purpose, but they could be of different grades, having different percentages 
of silicon, combined and graphitic carbon. Thus hard irons, mottled and 
white irons, and even steel scrap, all containing low percentages of silicon 
and high percentages of combined carbon, could be employed if an iron 
having a large amount of silicon were mixed with them in sufficient amount. 
This would bring the silicon to the proper proportion and would cause the 
combined carbon to be forced into the graphitic state, aud the resulting 


SHRINKAGE OF CASTINGS. 951 


casting would be su’ é. High-silicon irons used in this way ure valled “ soft- 
eners.”’ 
The following are typical analyses of softeners: 





Ferro-silicon. Softeners, American. = hea gor 1, 


Foreign.| American. | “&!!- |qiope| Belle- | Eg- | Colt- 











ston. fonte.|linton| ness. 
Silicone... -- 10.55 19.80] 12.08 10.34 6.67 | 5.89 |} 3to6| 2.15 | 2.59 
Combined C..) 1.84 |0.69} 0.06 0.07 ete O-SON Ee Osea) COST ee oe 
Graphitie C..] 0.52 }1.12] 1.52 1.92 2500) 2.008) eo Sel Galas ans 
Manganese..} 3.86 |1.95) 0.7 0.52 Roe. 1.00 | 0.53 | 2.80 70 
Phosphorus..| 0.04 |0.21) 0.48 0.45 0.50 1.10 | 0.35 | 0.62 | 0.85 
Sulphur ..... 0.03 |0.04| Trace | Trace | Trace | 0.02 | 0.03 | 0.03 | 0.01 





(For other analyses, see pages 371 to 373.) 


Ferro-silicons contain a low percentage of total carbon and a high per- 
centage of combined carbon. Carbon is the most important constituent of 
cast iron, and there should be about 3.4% total carbon present. By adding 
ferro-silicon which contains only 2% of carbon the amount of carbon in the 
resulting mixture is lessened. 

Mr. Keep found that more silicon is lost during the remelting of pig of 
over 10% silicon than in remelting pig iron of lower percentages of silicon. 
He also points out the possible disadvantage of using ferro-silicons contain- 
ing as high a percentage of combined carbon as 0.70% to overcome the bad 
effects of combined carbon in other irons. 

The Scotch irons generally contain much more phosphorus than is desired 
in irons to be employed in making the strongest castings. It is a mistake to 
mix with strong low-phosphorus irons an iron that would increase the 
amount of phosphorus for the sake of adding softening qualities, when soft- 
ness can be produced by mixing irons of the same low phosphorus. 

(For further discussion of the influence of silicon see page 365.) 

Shrinkage of Castings.—The allowance necessary for shrinkage 
varies for different kinds of metal, and the different conditions under which 
they are cast. For castings where the thickness runs about one inch, cast 
under ordinary conditions, the following allowance can be made: 


For cast-iron, 4% inch per foot. For zine, 5/16 inch per foot. 
ee brass, 3/ 6 6 be 6e oe tin, 1 12 66 66 ee 
66 steel, 1% 6 66 6 6 aluminum, 3/16 6s 73 73 
‘© mal. iron, ry Li ag he i r*) BEICARINA, wAsSe S57 4% eo 


Thicker castings, under the same conditions, will shrink less, and thinner 
ones more, than this standard. The quality of the material and the manner 
of moulding and cooling will also make a difference. 

Numerous experiments by W. J. Keep (see Trans. A. S. M. E., vol. xvi.) 
showed that the shrinkage of cast iron of a given section decreases as the 
percentage of silicon increases, while for a given percentage of silicon the 
shrinkage decreases as the section is increased. Mr. Keep gives the follow- 
ing table showing the approximate relation of shrinkage to size and per- 
centage of silicon: 





Sectional Area of Casting. 




















Percentage 
of 14” oO 1” o 1’ A g" QV D 3” o 4” Oo 
Silicon. 
Shrinkage in Decimals of an inch per foot of Length. 
1. 183 .158 .146 .130 113 102 ~ 
1.5 Se! 145 133 «117 .098 .087 
2. 159 .133 Sia | .104 085 074 
2.5 147 121 108 .092 07 060 
3. 135 .108 .095 077 .059 045 


3.5 128 .095 082 065 046 032 





952 THE FOUNDRY. 


Mr. Keep also gives the following ‘‘ approximate key for regulating four- 
dry mixtures’’ so as to produce a shrinkage of )¥ in, per ft. in castings of 
different sections: 

SiZeCLOL CASLING ie iscsqaecte bayenrs - % 1 2 3 4 in. sq. 

Silicon required, per cent..... 3.X9 2.75 2.25 1.75 1.25 per cent. 

Shrinkage sf a -in, test-bar. .125 1385 145 155 .165 in, per ft. 

Weight of Castings determined from Weight of Pattern. 
(Rose’s Pattern-maker’s Assistant.) 





Will weigh when cast in 





A Pattern weighing One Pound, ; 
Yellow} Gun- 


made of— Cast ; x 
Iron Zine. |Copper. Brass. | metal. 
lbs. lbs Ibs. Ibs lbs 
Mahogany—Nassau................ 10.7 10.4 12.8 12.2 12.5 
4 Honduras.... .....-. 12.9 12.7 15.3 14.6 15. 
° Spanishvs sy .sesssees o- 8.5 8.2 10.1 9.7. 9.9 
Pine, red......- 24s. age te Se 12.5 12.1 14.9 14.2 14.6 
+ WIT GG ys ear boteucievsnese stele aa gherses Bat 16.7 16.1 19.8 19.0 19.5 
ret VCLIOW aint s cieie nxatlsiasiotsg/ctcek Te s 14.1 13.6 16.7 16.0 16.5 


Moulding Sand. (From a paper on ‘The Mechanical Treatment of 
Moulding Sand,’’ by Walter Bagshaw, Proc. Inst. M. E. 1891.)—The chemical 
composition of sand will affect the nature of the casting, no matter what 
treatment it undergoes. Stated generally, good sand is composed of 94 parts 
silica, 5 parts alumina, and traces of magnesia and oxide of iron. Sand con- 
taining much of the metallic oxides, and especially lime, is to be avoided. 
Geographical position is the chief factor governing the selection of sand; 
and whether weak or strong, its deficiencies are made up for by the skill of 
the moulder. For this reason the same sand is often used for both heavy and 
light castings, the proportion of coal varying according to the nature of the 
casting. A common mixture of facing-sand consists of six parts by weight 
of old sand, four of new sand, and one of coal-dust. Floor-sand requires 
only half the above proportions of new sand and coal-dust to renew it. Ger-. 
man founders adopt one part by measure of new sand to two of old sand; 
to which is added coal-dust in the proportion of one tenth of the bulk for 
large castings, and one twentieth for small castings. A few founders mix 
street-sweepings with the coal in order to get porosity when the metal in 
the mould is likely to be a long time before setting. Plumbago is effective in 
preventing destruction of the sand; but owing to its refractory nature, it 
must not be dusted on in such quantities as to close the pores and prevent 
free exit of the gases. Powdered French chalk, soapstone, and other sub- 
stances are sometimes used for facing the mould; but next to plumbago, oak 
charcoal takes the best place, notwithstanding its liability to float occasion- 
ally and give a rough casting. ‘ 

For the treatment of sand in the moulding-shop the most primitive method 
is that of hand-riddling and treading. Here the materials are roughly pro- 
portioned by volume, and riddled over an iron plate in a flat heap, where 
the mixture is trodden into a cake by stamping with the feet; it is turned 
over with the shovel, and the process repeated. Tough sand can be obtained 
in this manner, its toughness being usually tested by squeezing a handful 
into a ball and then breaking it; but the process is slow and tedious. Other 
things being equal, the chief characteristics of a good moulding-sand are 
toughness and porosity, qualities that depend on the manner of mixing as 
well as on uniform ramming. 

Toughness of Sand.—In order to test the relative toughness, sand 
mixed in various ways was pressed under a uniform load into bars 1 in. sq. 
and about 12 in. long, and each bar was made to project further and 
further over the edge of a table until its end broke off by its own weight, 
Old sand from the shor floor had very irregular cohesion, breaking at all 
lengths of projections from 44 in. to 14in. New sand in its natural state 
held together until an overhang of 234 in. was reached. A mixture of old 
sand, new sand, and coal-dust 


Mixéd under rollers. 577) agemee s+. soe. - broke at 2 to 24 in. of overhang. 
«in the centrifugal machine....... so USS Qi 214 Sass sf 
“through a riddle..... Tieeetsescees “Se ae aug Seams Se 


SPEED OF CUTTING-TOOLS IN LATHES, ETC. 953 


Bho~inzg as a mean of the tests only slight differences between the last 
three methods, but in favor of machine-work. In many instances the frac- 
sures were so uneven that minute measnrements were not taken, 
Dimensions of Foundry Ladles.—The following table gives the 
dimens Ons. inside the lining, of ladles from 25 Ibs. to 16 tons capacity. All 
the ladies are supposed to have straight sides. (Am. Mach., Aug. 4, 1892.) 

















Capacity. | Diam. | Depth. Capacity. Diam. Depth. 
in. in. in. in. 
TOONS Proc eechas os 54 56 SA COM sect ewse 20 20 
Laemee Vi osach ose tas 52 53 Eda oeebe 17 fi 
pO: ee CORE cae na 49-. 50 TAs tee Eee ae 13 1314 
NOS iG iciets cide cha "465 48 300 pounds.... 11 11% 
& She seeeeorees 43 44 250 A eccse 1084 11 
89 40 200 ss soles 10 10% 
34 35 150 es iS eres 9 914 
31 82 100 s i afele 8 814 
eke a fe : Sher % ff 
oe e p4 5 eons 614 6 
1 eeesepoevescnee 22 | 22 35 oo eee Bid ee 





THE MACHINE-SHOP. 


SPEED OF CUTTING-TOOLS IN LATHES, MILLING 
MACHINES, ETC, | 


Relation of diameter of rotating tool or piece, number of revolutions, 
and cutting-speed : 
Let d = diam. of rotating piece in inches, n = No. of revs. per min.; 
S = speed of circumference in feet per minute; 


gn Tan S 8828 | 3.829 
an, 12 ‘OhiGd ne Danesh vil 5 


Approximate rule: No. of revs. per min. = 4 X speed in ft. per min. 
diam, in inches. 

Speed of Cut for Lathes and Planers, (Prof. Coleman Sellers, 
Shiai Indicator, April, 1892.)—Brass may be turned at high speed like 
wood. 

Bronze.—A speed of 18 feet per minute can be used with the soft alloys— 
pay 8 to 1, while for hard mixtures a slow speed is required—say 6 feet per 
minute, 

Wrought Iron can be turned at 40 feet_per minute, but planing-machtnes 
that are used for both cast and forged iron are operated at 18 feet per 
minute. 

Machinery Steel.—Ordinary, 14 feet per minute; car-axles, etc., 9 feet per 
minute, 

Wheel Tires.—6 feet per minute; the tool stands well, but many prefer 
to run faster, say 8 to 10 feet, and grind the tool more frequently. 

Lathes.--The speeds obtainabie by means of the cone-pulley and the back 
rearing are in geometrical progression from the slowest to the fastest. In 
a well-proportioned machine the speeds hold the same relation through all 
the steps. Many lathes have the same speed on the slowest of the cone and 
the fastest of the back-gear speeds. 

The Speed of Counter-shafi of the lathe is determined by an assumption 
of a slow speed with the back gear, say 6 feet per minute, on the largest 
diameter that the lathe will swing. 

Exampue.—A 30-inch lathe will swing 80 inches =, say, 90 inches circumfer- 
ence = 7 6’; the lowest triple gear should give a speed of 5 or 6 per minute. 

In turning or planing, if the cutting-speed exceed 30 ft. per minute, so 
much heat will be produced that the temper will be drawn from the tool. 
The speed of cutting is also governed by the thickness of the shaving, and 
by the hardness and tenacity of the metal which is being cut; for instance, 
in cutting mild steel, with a traverse of 34 in. per revolution or stroke, and 
with a shaving about 5 in. thick, the speed of cutting must be reduced to 
about 8 ft. per minute. A good average cutting-speed for wrought or cast 


= .2618dn3; n= 


954 THE MACHINE-SHOP, 


fron is 20 ft. a minute, whether for the lathe, planing, shaping, or slotting 
machine. (Proc. Inst. M. E., April, 1883, p. 248.) 


Table of Cutting=speeds, 





Feet per minute, 


Minhas.” 5 | 10 | 1 | 2 | 2% | 20 | 25 | 40 | 45 | 50 


Revolutions per minute. 








152.8} 229.2) 305.6) 882.0) 458.4) 534.8) 611.2) 687.6] 764.9 





76.4 
4 50.9 | 101.9} 158.8] 203.7| 254.6) 3805.6) 356.5) 407.4) 458.3) 509.3 
, 88.2 | %6.4) 114.6) 152.8] 191.0) 229.2) 267.4) 305.6} 343.8) 382.0 
d% 80.6 | 61.1] 91.7) 122.2) 152.8) 183.4] 213.9) 244.5! 275.0} 305.6 
24 25.5} 50.9) %6.4{ 101.8) 127.3) 152.8) 178.2) 203.7) 229.1) 254.6 
i 21.8] 43.7) 65.5) 87.3) 109.1} 130.9) 152.8) 174.6) 196.4) 218.3 
1 19.1} 388.2) 57.8) 76.4) 95.5) 114.6] 133.7) 152.8) 171.9] 191.0 
14% 17.0] 34.0) 50.9) 67.9} 84.9; 101.8) 118.8) 135.8) 152.8} 169.7 
14 15.8} 30.6] 45.8] 61.1) 76.4) 91.7) 106.9) 122.2) 187.5) 152.8 
13g 13.9} 27.8} 41.7| 55.6) 69.5) 83.3) 97.2) 111.1] 125.0) 188.9 
14% 12.% | 25.5] 88.2) 50.9) 63.6) 76.4) 89.1) 101.8} 114.5) 127.2 
134 10.9 | 21.8} 82.7) 48.7) 54.6) 65.5) 6.4) 87.3) 98.2) 109.2 
2 9.6 | 19.1) 28.7) 38.2) 47.8! 57.3) 66.9) 76.4) 86.0) 95.5 
2 8.5) 17.0) 25.5) 84.0} 42.5) 50.9] 59.4) 67.9) 76.4) 84.9 
2 %.6} 15.8) 229; 30.6} 38.2) 45.8) 53.5) 61.1) 68.8] 76.4 
234 6.9} 13.9) 20.8] 27.8] 34.7) 41.7] 48.6) 55.6) 62.5) 69.5 
8 6.4) 12.7) 19.1] 25.5) 31.8] 88.2) 44.6) 50.9) 57.3) 63.7 
844 5.5 | 10.9) 16.4] 21.8) 27.3) 32.7) 88.2) 43.7) 49.1] 54.6 
4 4.8 9.6) 14.3) 19.1] 23.9) 28.7] 83.4) 388 2) 43.0) 47.8 
416 4.2 8.5] 12.7] 17.0) 21.2) 25.5) 29.7) 34.0) 388.2) 42.5 
5 8.8 .6) 11.5) 15.3) 19.1] 22.9) 26.7) 30.6) 34.4) 38.1 
514 3.5 6.9} 10.4] 13.9] 17.4) 20.8] 24.8) 27.8) 381.2) 34.7 
6 8.2 6.4, 9.5) 12.7) 15.9) 19.1) 22.3) 25.5) 28.6) 381.8 
vg 2.7 5.5) 8.2] 10.9) 13.6] 16.4) 19.1) 21.8) 24.6) 27.3 
8 2.4 4.8) 7.2) 9.6) 11.9) 14.38) 16.7) 19.1] 21.5) 23.9 
Q 2.1 4.2} 6.4] 8.5) 10.6) 12.7) 14.8; 17.0) 19.1) 21.2 
10 1.9 8.8) 5.7) %.6) 9.6) 11.5] 18.8) 15.3] 17.2) 19.1 
11 1.7 8.5) 5.2} 6.9) 8.7) 10.4) 12.2) 138.9) 15.6; 17.4 
12 1.6 8.2} 4.8] 6.4, 8.0) 9.5) 11.1) 12.7) 14.3} 15.9 
13 1.5 2.9) 4.4) 5.9) 7.3) 8.8) 10.3) 11.8) 13.2) 14.7 
14 1.4 2.7) 4.1 5.5) 6.8) 8.2] 9.5) 10.9) 12.3) 13.6 
15 1.3 2.5) 8.8] 6.1| 6.4) 7.6; 8.9) 10.2) 11.5) 12.7 
16 1.2 2.4, 8.6] 4.8) 6.0; 7.2] 8.4) 9.5) 10.7) 11.9 
18 1.1 2.1] 8.2] 4.2) 5.8) 6.47 7.4) 8.5) 9.5) 10.6 
20 1.0 1.9} § 2.9] °3.8) 4.8) °° 827) | O.77 | 726} 98812 9.6 
22 9 1.7, 2.6) 8.5) 4.8) 5.2) 6.1) 6.9)° 7.8! 8.7 
24 8 1.6; 2.4) 8.2} 4.0] 4.8] 5.6) 6.4) 7.2) 8.0 
26 2 1.5} 2.2; 2.9) 8.7; 4.4) 5.2) 5.9). 6.6) -7.3 
28 2 1.4, 2.0] 2.7] 38.4) 4.1) 4.8) 5.5) 6.1) 6.8 
30 6 1.8; 1.9) 2.5) 8.2) 8.8 4.5) 5.1) 5.7) 6.4 
36 5 1.1)°.1.6) 2.2) 2.7) 3.2] 8.7) 4.21 94.8) 5.8 
42 5 9 61.4, 1.8 2.8) 2.7) 8.2) 8.6) 4.1) 4.5 
48 4 8) 1.2) (1.8) 2.0) 2.4) 2.8 Biel ee GP 4 wD 
54 4 (ae 1.4, 1.8) 2.1) 2.5) 2.8) 38.2) 3.5 
60 3 AU CAH ei eshte be 139) 93.2). Ria) 28) -B2 





Speed of Cutting with Turret Lathes,.—Jones & Lamson Ma- 
thine Co. give the following cutting-speeds for use with their flat turret 
lathe on diameters not exceeding two inches: Ft Halt 

. per minute. 
Tool steel and taper on tubing,........ ccccece-eoe- ae ; 0 
Thr sadin& < Machineires. ss .c.. +05: vcce pete ecndccncieebtcetcoss 15 
VOT Y, BOP UUECE yn. | o- + vs coccgnetcc, cane teehemaacetnoe cco annem 

Turning Cut which reduces the stock to 14 of its original diam.. - 20 

machinery Cut which reduces the stock to 3 of its original diam.. 25 
steal Cut which reduces the stock to % of its original diam.. 80 to 35 
" Cut which reduces the stock to 15/16 of its original diam. 40 to 45 
Turning very soft machinery steel, light cut and cool work.... ..... 50 to 60 


GEARING OF LATHES. 95 


Forms of Metal-cutting Tools.—“ Hutte,” the German Engi- 
neers’ Pocket-book, gives the following cutting-angles for using least power: 


Top Rake. Angle of Cutting-edge, 


Wrought 1r0m.... cccccvcccccccces eese 8° 51° 
CASUITON -2 acces tote ces owes tecaese- 4° 51¢ 
IBIORZe. ..... secu cses @eoeoeeseeeeeseseers es qe 66°? 


The American Machinist comments on these figures as follows: We are 
not able to give the best nor even the generally used angles for tools, 
because these vary so much to suit different circumstances, such as degree 
of hardness of the metal being cut, quality of steel of which the tool is 
made, depth of cut, kind of finish desired, ete. The angles that cut with 
the least expenditure of power are easily determined by a few experiments, 
but the best angles must be determined by good judgment, guided by expe. 
rience. In nearly all cases, however, we think the best practical angles are 
greater than those given. 

For illustrations and descriptions of various forms of cutting-tools, see 
articles on Lathe Tools in App. Cyc. App. Mech., vol. ii.,and in Modern 
Mechanism. 

Cold Chisels,—<Angle of cutting-faces (Joshua Rose): For east steel, 
about 65 degrees; for gun-metal or brass, about 50:degrees; for copper and 
soft metals, about 30 to 35 degrees, 

Rule for Gearing Lathes for Screw-cutting. (Garvin Ma- 
chine Co.)—Read from the lathe index the number of threads per inch cut 
by equal gears, and multiply it by any number that will give for a product 
a gear on the index; put this gear upon the stud, then multiply the number 
of threads per inch to becut by the same number, and put the resulting gear 
upon the screw. 

ExaMPLE.—To cut 1114 threads per inch. We find on the index that 48 into 
48 cuts 6 threads per inch, then 6 x 4 = 24, gear on stud, and llw x 4 = 46, 
gear on screw. Any multiplier may be used so long as the products include 
gears that belong with the lathe. For instance, instead of 4 as a multiplier 
we may use 6. Thus, 6 X 6 = 36, gear upon stud, and 11144 x 6 = 69, gear 
upon screw. 

Rules for Calculating Simple and Compound Gearing 
where there is no index. (4m Mach.)—If the Jathe is simple- 
geared, and the stud runs at ‘the same speed as the spindle, select some gear 
for the screw, and multiply its number of teeth by the number of threads 
per inch in the lead-screw, and divide this result by the number of threads 
per inch to be cut. This will give the number of teeth in the gear for the 
stud. If this result isa fractional number, or a number which is not among 
the gears on hand, then try some other gear for the screw. Or, select the 
gear for the stud first, then multiply its number of teeth by the number of 
threads per inch to be cut, and divide by the number of threads per inch on 
the lead-screw. This will give the number of teeth for the gear on the 
screw. If the lathe is compound, select at random all the driving-gears, 
multiply the numbers of their teeth together; and this product by the num- 
ber of threads to be‘eut. Then:select at random all the driven gears except 
one; multiply the numbers of their teeth together, and this product by the 
number of threads per inch in the lead-screw. Now divide the first result by 
the second, to obtain the numberof teeth in the remaining driven gear. Or, 
select at random all the driven gears. Multiply the numbers of their teeth 
together, and this product by the number of threads per inch in the lead- 
serew. Then select at random all the driving-gears except one. Multiply 
the numbers of their teeth together, and this result by the number of threads 
per inch of the screw to be cut. Divide the first result by the last, to obtain 
the number of teeth in the remaining driver. When the gears on the com- 
pounding stud are fast together, and cannot be changed, then the driven one 
has usually twice as many teeth as the other, or driver, in which case in the 
ealculations consider the lead-screw to’have twice as many threads per inch 
as it actually nas, and then ignore the compounding entirely. Some lathes 
are so. constructed that the stud on which the first driver is placed revolves 
only half as fast as the spindle. This can be ignored in the calculations by 
doubling the number of threads of the lead-screw. If both the last -ondi- 
tions are present ignore them in the calculations by multiplying the numsbe1r 
of threads per inch in the lead-screw by four. If the thread to. be cut is a 
fractional one,-or if the.pitch of the lead-screw is fractional, or if both are 
fractional, then reduce the fractions to a common denominator, and use 
the numerators of these fractions as if thev eauailed the pitch of the screw 


956 THE MACHINE-SHOP, 


to be cut, and of the lead-screw, respectively. Then use that part of the rule 
given above which applies to the lathe in question. For instance, suppose 
jt is desired to cut a thread of 25/32-inch pitch, and the lead-screw has 4 
threads per inch. Then the pitch of the lead-screw will be 14 inch, which is 
equal to 8/32 inch. We now have two fraction, 25/32 and 8/32, and the two 
screws will be in the proportion of 25 to 8, and the gears can be figured by 
the above rule, assuming the number of threads to be cut to be 8 per inch, 
and those on the lead-screw to be 25 per inch. But this latter number may 
be further modified by conditions named above, such as a reduced speed of 
the stud, or fixed compound gears. In the instance given, if the lead-screw 
had been 214 threads per inch, then its pitch being 4/10 inch, we have the 
fractions 4/10 and 25/32, which, reduced to a common denominator, are 
64/160 and 125/160, and the gears will be the same asif the lead-screw had 125 
threads per inch, and the screw to be cut 64 threads per inch. ° 

On this subject consult also ‘*‘ Formulas in Gearing,” published by Brown 
& Sharpe Mfg. Co., and Jamieson’s Applied Mechanics. 

Change-gears for Screw-cutting Lathes.—tThere is a lack of 
uniformity among lathe-builders as to the change-gears provided for screw- 
cutting. W.R. Macdonald, in Am. Mach., April 7, 1892, proposes the follow- 
ing series, by which 33 whole threads (not fractional) may be cut by changes 
of only nine gears: 














3 Spindle. 

m Whole Threads. 
1 20 | 80 | 40 50 60 40 110 12 130 

20 8 6144/5) 4/)33/7| 22/11] 2] 1 11/18) 2] 11 | 22 | 44 
30 18 9\7 1/5) 6|51/7| 88/11) 3 | 2 10/138) 3 | 12] 24 | 48 
40 24) 16] 12|9 3/5 8|66/%7) 44/11; 4] 3 9/13) 4] 13] 26 | 52 
50 BOM -20))) 15> fee den 10 {84/7} 5 5/11] 5) 4 8/138) 5 | 14] 28 | 66 
60 36 } 24 | 18 |14 2/5 10 2/7} 6 6/11) 6} 5 7/138) 6] 15 | 80 } 72 
WO 42 | 28 | 21 116 4/5) 14 }...... @ 7/11) 7 )]6 6/13) 7] 16] 383 | 78 
110 66 | 44 | 33 126 2/5) 22 118 6/7|..... .. 11 |10 2/13) 8} 18 | 36 
120 G2} 48 | 86 [28 4/5) 24 |20 4/7) 18 1/11]....]11 1/13] 9 | 20 | 39 
130 78 | 52 | 39 131 1/5] 26 }22 3/7] 14 2/11| 13 |........] 10 | 21 | 42 





Ten gears are sufficient to cut all the usual threads, with the exception of 
perhaps 1114, the standard pipe-thread; in ordinary practice any fractional 
thread between 11 and 12 will be near enough for the customary short pipe- 
thread; if not, the addition of a single gear will give it. 

In this table the pitch of the lead-screw is 12, and it may be objected to as 
too fine for the purpose. This may be rectified by making the real pitch 6 
or any other desirable pitch, and establishing the proper ratio between the 
lathe spindle and the gear-stud. 

Metric Screw-ethreads may be cut on lathes with inch-divided lead- 
ing-screws, by the use of change-wheels with 50 and 127 teeth; sor 127 
centimetres = 50 inches (127 * 0.38937 == 49.9999 in.). 

Rule for Setting the Taper ina Lathe. (4m. Mach.)—No 
rule cax be given which will produce exact results, owing to the fact that 
the centres enter the work an indefinite distance. If it were not for this cir- 
cumstance the following would be an exact rule, and it is an approximation 
as itis. To find the distance to set the centre over: Divide the difference in 
the diameters of the large and small end of the taper by 2, and multiply this 
quotient by the ratio which the total length of the shaft bears to the length 
of the tapered portion, Example: Suppose a shaft three feet long is to har’ 
a taper turned on the end one foot long, the large end of the taper being two 


inches and the small end one inch diameter, ; = 14% inches. 


Electric Drilling-machines—Speed of Drilling Holes in 
Steel Plates. (Proc. Inst. M. E., Aug. 1887, p. 329.)—In drilling holes in 
the shell of the S.S. ‘‘ Albania,’ after a very small amount of practice the 
men working the machines drilled the %-inch holes in the shell with great 
rapidity, doing the work at the rate of one hole every 69 seconds, inclusive of 
the time occupied in altering the pusition of the machines by means of differ- 
ential pulley-blocks, which were not conveniently arranged as slings for 
this purpose. Repeated trials of these drilling-machines have also shown 
that, when using electrical energy in both holding-on magnets and motor 





MILLING-CUTTERS., 957 


amounting to about 34 H.P., they have drilled holes of 1 inch diameter 
through 114 inch thickness of solid wrought iron, or through 15 inch of mild 
steel in two plates of 18/16 inch each, taking exactly 134 min. for each hole. 

Speed of Drills. (Morse Twist-drill and Machine Company.)—The fol- 
lowing table gives the revolutions per minute for drills from 1/16 in. to 2 in. 
diameter, as usually applied: 


: Speed for] Speed : Speed for} Speed 
eS eer Wrouchtl’ for pee Diameter Wrought for oped 


fr) r 
Drills, in.} "on and| Cast | Brass. Drills, in.| ron and| Cast | Brags, 





Steel. Tron. teel. Tron. 

1/16 1712 2383 3544 1 1/16 ve 108 180 
14 855 1191 ih 1% 68 102 aly 

3/16 571 G94 1181 1 3/16 64 97 161 
14 897 565 855 14 58 89 150 

5/16 318 452 684 1'5/16 55 84 143 
3 265 37 570 13% 53 81 136 

7/16 227 323 489 1 7/16 50 V7 130 
4% 183 267 412 1% 46 74 12 

9/16 163 238 867 1 9/16 44 71 117 
147 214 830 154 40 66 1138 

11/16 133 194 300 1 TRYAS: 38 63 109 
34 112 168 265 134 387 61 105 

13/16 103 155 244 1 18/16 36 59 101 
y 96 144 227 1% 33 55 98 

15/16 89 134 212 1 15/16 32 53 95 
1 %6 115 191 2 81 51 92 


One inch to be drilled in soft cast iron will usually require: for 1%4-in. 
drill, 160 revolutions; for 14-in. drill, 140 revolutions; for 34-in. drill, 100 
revolutions; for 1-in. drill, 95 revolutions. These speeds should seldom be 
exceeded. Feed per revolution for 4-in. drill, .005 inch; for 14-in. drill, 
-007 inch; for 34-in. drill .010 inch. 

Tne rates of feed for twist drills are thus given by the same company: 





Diameter of drill........... 1/16 % 38% 34 1 1h; 

= Z aes ea a. 

‘evs, per inch depth of hole. 125 125 120to 140 1 inch feed per min. 
MILLING-CUTTERS, 


George Addy, (Proc. Inst. M. E., Oct. 1890, p. 537), gives the following: 

Analyses of Steel.—The following are analyses of milling-cutter 
blanks, nade from best quality crucible cast steel and from self-hardening 
“Ivanhoe” steel : 


Crucible Cast Steel, Ivanhoe Steel, 





per cent. per cent, 
Carbon ~@e@ee erteseee eee te. 2e8e8 1) 1.67 
SillCOls ccs c aecwlessicaws succes sles 0.112 0.252 
ISNOSPHOLUS|oessainecawceices eects 0.018 0.051 
Man PFANCSGicc assists els sce ce eiacne 0.36 2.557 
Sulphurcsecsascctisccccsscccascse am sls, 0.01 
Tungsten...... Hale tie e bye‘ wive calesnepemetsiae le : 4.65 
Tron, by difference......... ... 98.29 90.81 

100.000 100.000 


The first analysis is of a cutter 14 in. diam., 1 in. wide, which gave very 
good service at a cutting-speed of 60 ft. per min. Large milling-cutters are 
sometimes built up, the cutting-edges only being of tool steel. A cutter 22 in. 
diam. by 514 in. wide has been made in this way, the teeth being clamped 
between two cast-iron flanges. Mr. Addy recommends for this form of 
tooth one with a cutting-angle of 70°, the face of the tooth being set 10° back 
of a radial line on the cutter, the clearance-angle being thus 10°. At the 
Clarence Iron-works, Leeds, the face of the tooth is set 10° back of the radia! 
line for cutting wrought iron and 20° for steel. 

Pitch of Teeth.—For obtaining a suitable pitch of teeth for milling- 
cutters of various diameters there exists no standard rule, the pitch being 
usually decided in an arbitrary manner, according to individual taste, 


958 THE MACHINE-SHOP. 


For estimating the pitch of teeth in a cutter of any diameter from 4 in. to 15 
in., Mr. Addy has worked out the following rule, which he has found capa- 
ble of giving good results in practice: 


Pitch in inches = (diam. in inches x 8) X 0.0625 = .177 diam. 


J. M. Gray gives a rule for pitch as follows: The number of teeth in a 
milling-cutter ought to be 100 times the pitch in inches; that is, if there 
were 27 teeth, the pitch ought to be 0.27 in. The rules are practically the 
same, for if d = pate n = No. of teeth, p = pitch, c = circumference, c = 
pn; da Pm = WP" _ 31.9802; p = W0814d = 177 Vad; No. of teeth, n, =. 


7 us 
3.14d + p. 

Number of Teethin Mills or Cutters, (Joshua Rose.)—The teeth 
of cutters must obviously be spaced wide enough apart to admit of the emery- 
wheel grinding one tooth without touching the next one, and the front faces 
of the teeth are always made in the plane of a line radiating from the axis of 
the cutter. In cutters up to 3 in. in diam. it is good practice to provide 8 
teeth per in. of diam., while in cutters above that diameter the spacing 
may be coarser, as follows: 


Diameter of cutter, 6 in.; number of teeth in cutter, 40 
oe 66 66 ve be (73 66 66 oe 66 45 
66 66 66 Ss 66 66 66 ee 6b 66 50 


Speed of Cutters.—The cutting speed for milling was originally fixed 
very low; but experience has shown that with the improvements now in 
use it may with advantage be considerably increased, especially with cutters 
of large diameter. The following are recommended as safe speeds for cut- 
ters of 6 in. and upwards, provided there is not any great depth of material 
to cut away: 


Steel. Wrought iron. Cast iron. Brass. 
Feet per minute..... . 86 48 60 
Feed, inch permin... 4% 1 1% 224 

Should it be desired to remove any large quantity of material, the same 
cutting-speeds are still reeommended, but with a finer feed. A simple rule ~ 
for cutting-speed is: Number of revolutions per minute which the cutter 
spindle should make when working on cast iron = 240, divided by the diam- 
eter of the cutter in inches. 

Speed of Milling-cutters. (Proc. Inst. M. E., April, 1883, p. 248.)— 
The cutting-speed which can be employed in milling is much greater than 
that which can be used in any of the ordinary operations of turning in the 
lathe, or of planing, shaping, or slotting. A milling-cutter with a plentiful 
supply of oil, or soap and water, can be run at from 80 to 100 ft. per min., 
when cutting wrought iron. The same metal can only be turned in a lathe, 
with a tool-holder having a good cutter, at the rate of 30 ft. per min., or at 
about one third the speed of milling. A milling-cutter will cut cast steel at 
the rate of 25 to 30 ft. per min. 

The following extracts are taken from an article on speed and feed of 
milling-cutters in Hng’g, Oct. 22, 1891: Milling-cutters are successfully em- 
ployed on cast iron at a speed of 250 ft. per min.; on wrought iron at from 
80 ft. to 100 ft. per min. The latter materials need acopious supply of good 
lubricant, such as oil or soapy water. These rates of Speed are not ap- 
proached by other tools. The usual cutting-speeds on the lathe, planing, 
shaping, and slotting machines rarely exceed about one third of those given 
above, and frequently average about a fifth, the time lost in back strokes not 
being reckoned. 

The feed in the direction of cutting is said by one writer to vary, in ordi- 
nary work, from 40 to 70 revs. of a 4-in. cutter per in. of feed. It must always 
to an extent depend on the character of the work done, but the above gives 
shavings of extreme thinness. For example, the circumference of a 4-in. 
cutter being, say, 12% in., and having, say, 60 teeth, the advance corre- 
sponding to the passage of one cutting-tooth over the surface, in the coarser 
of the above-named feed-motions, is 1/40 x 1/60 = 1/2400 in.; the finer feed 
gives an advance for each tooth of only 1/70 x 1/60 = 1/4200in. Such fine 
feeds as these are used only for light finishing cuts, and the same author- 
ity recommends, also for finishing, a cutter about 9 in. in circumference, or 
nearly 3 in. in diameter, which should be run at about 60 revs. per min. to 
cut tough wrought steel, 120 for ordinary cast iron, about 80 for wrought 


MILLING-MACHINES. ' 959 


fron, and from 140 to 160 for the various qualtities of gun-metal and brass. 
With cutters smaller or larger the rates of revolution are increased or 
diminished to accord with the following table, which gives these rates of 
cutting-speeds and shows the lineal speed of the cutting-edge: 


Steel. Wrought Iron. Cast Iron. Gun-metal. Brags. 
Feet per minute... 45 60 90 105 120 


These speeds are intended for very light finishing cuts, and they must be 
reduced to about one half for heavy cutting. 

The following results have been found to be the highest that could be at- 
tained in ordinary workshop routine, having due consideration to econom 
and the time taken to change and grind the cutters when they become dull: 
Wrought iron—36 ft. to 40 ft. per min.; depth of cut, 1 in.; feed, 5g in. per 
min. Soft mild steel—About 30 ft. per min.; depth of cut, 144 in.; feed, 34 
in. per min. Tough gun-metal—80 ft. per min.; depth of cut, % in.; feed, 34 
in. permin, Cast-iron gear-wheels—26\% ft. per min.; depth of cut, % in.; 
feed, 34 in. permin. Hard, close-grained cast iron—30 ft. per min.; depth 
of cut, 214 in.; feed, 5/16 in. per min. Gun-metal joints, 53 ft. per min.; 
depth of cut, 13gin.; feed, 5g in. per min. Steel-bars—21 ft. per min.; depth 
of cut, 1/32 in.; feed, 34 in. per min. 

A stepped milling-cutter, 4 in. in diam. and 12 in. wide, tested under two 
conditions of speed in the same machine, gave the following results: The 
cutter in both instances was worked up to its maximum speed before it gave 
way, the object being to ascertain definitely the relative amount of work 
done by a high speed and a light feed, as compared with a low speed and a 
heavy cut. The machine was used single-geared and double-geared, and in 
both cases the width of cut was 10% in. 

Single-gear, 42 ft. per min.; 5/16 in. depth of cut; feed, 1.8 in. per min. = 
4.16 cu. in. per min. Double-gear, 19 ft. per min.; 3gin. depth of cut; feed, 
5g in. per min. = 2.40 cu. in, per min. 

Extreme Results with Milling-machines.— Horace L. 
Arnold (Am. Mach., Dec. 28, 1893) gives the following results in flat-surface 
milling, obtained in a Pratt & Whitney milling-machine: The mills for the 
flat cut were 5/’ diam., 12 teeth, 40 to 50 revs. and 4%’’ feed per min. One 
single cut was run over this piece at a feed of 9/’ per min., but the mills 
showed plainly at the end that this rate was greater than they could endure. 
At 50 revs. for these mills the figures are as follows, with 4%” feed: Surface 
speed, 64 ft., nearly; feed per tooth, 0.00812’: cuts per inch, 123. And with 
9’ feed per min.: Surface speed, 64 ft. per min.; feed per tooth, 0.015’; cuts 
per inch, 66%. 

Ata feed of 4%” per min. the mills stood up well in this job of cast-iron 
surfacing, while with a 9’ feed they required grinding after surfacing one 
piece; in other words, it did not damage the mill-teeth to do this job with 
123 cuts per in. of surface finished, but they would not endure 6624 cuts per 
inch, In this cast-iron milling the surface speed of the mills does not seem 
to be the factor of mill destruction: it is the increase of feed per tooth that 
prohibits increased production of finished surface. This is precisely the re- 
verse of the action of single-pointed lathe and planer tools in general: with 
such tools there is a surface-speed limit which cannot be economically ex- 
ceeded for dry cuts, and so long as this surface-speed limit is not reached, 
the cut per tooth or feed can be made anything up to the limit of the driv- 
ing power of the lathe or planer, or to the safe strain on the work itself, 
which can in many cases be easily broken by a too great feed. 

In wrought metal extreme figures were obtained in one experiment made 
in cutting key ways 5/16’ wide by 14” deep in a bank of 8 shafts 114” diam. 
at once, on a Pratt & Whitney No. 3 column milling-machine. The 8 mills 
were successfully operated with 45 ft. surface speed and 19% in. per min. 
feed; the cutters were 5” diam., with 28 teeth, giving the following figures, 
in steel: Surface speed, 45 ft. per min.; feed per tooth, 0.02024/’; cuts per 
inch, 50, nearly. Fed with the revolution of mill. Flooded with oil, that is, 
a large stream of oil running constantly over each mill. Face of tooth 
radial. The resulting keyway was described as having a heavy wave or 
cutter-mark in the bottom, and it was said to have shown no signs of being 
heavy work on the cutters or on the machine. As a result of the experiment 
it was decided for economical steady work to run at 17 revs., with a feed of 
4’’ per min., flooded cut, work fed with mill revolution, giving the following 
eens 2 ee speed, 2214 ft. per min.; feed per tooth, 0,0084’’; cuts per 
inch, 119, 


960 THE MACHINE-SHOP, 


An experiment in milling a wrought-iron connecting-rod of a locomotive 
on a Pratt & Whitney double-head milling-machine is described in the Iron 
Age, Aug. 27, 1891. The amount of metal removed at one cut measured 314 
in. wide by 1 3/16 in. deep in the groove, and across the top 4 in. deep by 4% 
in. wide. This represented a section of nearly 414sq.in. This was done at 
the rate of 134 in. per min. Nearly 8 cu. in. of metal were cut up into chips 
every minute. The surface left by the cutter was very perfect. The cutter 
moved in a direction contrary to that of ordinary practice; that is, it cut 
down from the upper surface instead of up from the bottom. 

Milling ** with® or *‘ against the Feed.—Tests made with 
the Brown & Sharpe No. 5 milling-machine (described by H. L. Arnold, in 
Am, Mach., Oct. 18, 1894) to determine the relative advantage of running 
the milling-cutter with or against the feed—‘t with the feed’’ meaning that 
the teeth of the cutter strike on the top surface or ‘‘scale’’ of cast-iron 
work in process of being milled, and ‘‘against the feed ’’ meaning that the 
teeth begin to cut in the clean, newly cut surface of the work and cut up- 
wards toward the scale—showed a decided :advantage in favor of running 
the cutter against the feed. The result is directly opposite to that obtained 
in tests of a Pratt & Whitney machine, by experts of the P. & W. Co. 

In the tests with the Brown & Sharpe machine the cutters used were 6 
inches face by 414 and 3 inches diameter respectively, 15 teeth in each mill, 
42 revolutions per minute in each case, or nearly 50 feet per minute surface 
speed for the 44-inch and 33 feet per minute for the 3-inch mill. The revo- 
lution marks were 6 to the inch, giving a feed of 7 inches per minute, and a 
cut per tooth of .011/7.. When the machine was forced to the limit of its 
driving the depth of cut was 11/32 inch when the cutter ran in the ‘old ” 
way, or against the feed, and only 4 inch when it ran in the “‘new”’ way, 
or with the feed. The endurance of the milling-cutters was much greater 
when they were run in the ‘‘ old’ way. 

Spiral Milling-cutters,—There is no rule for finding the angle of 
the spiral; from 10° to 15° is usually considered sufficient; if much greater 
the end thrust on the spindle will be increased to an extent not desirable for 
some machines. 

Milling-cutters with Inserted Teeth.—When it is required to 
use milling-cutters of a greater diameter than about 8 in., it is preferable to 
insert the teeth in a disk or head, so as to avoid the expense of making 
solid cutters and the difficulty of hardening them, not merely because of 
the risk of breakage in hardening them, but also on account of the difficulty 
in obtaining a uniform degree of hardness or temper. 

Milling - machine versus Planer. — For comparative data of 
work done by each see paper by J. J. Grant, Trans. A. 8. M. E., ix. 259. He 
says: The advantages of the milling machine over the planer are many, 
among which are the following : Exact duplication of work; rapidity of pro- 
duction — the cutting being continuous; cost of production, as several 
machines can be operated by one workman, and he not a skilled mechanic; 
and cost of tools for producing a given amount of work. 


POWER REQUIRED FOR MACHINE TOOLS. 


Resistance Overcome in Cutting Metal. (Trans. A.S. M. E. 
viii. 808.)—Some experiments made at the works of William Sellers & Co 
showed that the resistance in cutting steel in a lathe would vary from 
180,000 to 700,000 pounds per square inch of section removed, while for 
cast iron the resistance is about one third as much. The power required to 
remove a given amount of metal depends on the shape of the cut and on 
the shape and the sharpness of the tool used. [ff the cut is nearly square in 
section, the power required is a minimum; if wide and thin, a maximum, 
The dulness of a tool affects but little the power required for a heavy cut. 

Heavy Work on a Planer.—Wm. Sellers & Co. write as follows 
to the American Machinist ; The 120’ planer table is geared to run 18 ft. per 
minute under cut, and 72 feet per minute on the return, which is equivalent, 
without allowance for time lost in reversing, to continuous cut of 14.4 feet 
per minute. Assuming the work to be 28 feet long, we may take 14 feet as 
the continuous cutting speed per minute, the .8 of a foot being much more 
than sufficient to cover time loss in reversing and feeding. The machine 
carries four tools. At 1@’’ feed per tool, the surface planed per hour would 
be 35 square feet. The section of metai cut at 34’ depth would be .75” x 
135’ X 4 = .875 square inch, which would require approximately 30,000 lbs, 


’ 
. 


POWER REQUIRED FOR MACHINE TOOLS. 961 


pressure to remove it. The weight of metal removed per hour would be 
14 X 12 x .875 X .26 X 60 = 1082.8 lbs. Our earlier form of 36’ planer has 
removed with one tool on 34’’ cut on work 200 lbs. of metal per hour, and 
the 120’7 machine has more than five times its capacity. The total pulling 
power of the planer is 45,000 Ibs. 

Horse-power Required to Run Lathes. (J. J. Flather, An. 
Mach., April 23, 1891.)—The power required to do useful work varies with 
the depth and breadth of chip, with the shape of tool, and with the nature 
and density of metal operated upon; and the power required to run a ma- 
chine empty is often a variable quantity. 

For instance, when the machine is new, and the working parts have not 
become worn or fitted to each other as they will be after running a few 
months, the power required will be greater than will be the case after the 
running parts have become better fitted. 

Another cause of variation of the power absorbed is the driving-belt; a 
tight belt will increase the friction, hence to obtain the greatest efficiency 
of a machine we should use wide belts, and run them just tight enough to 
prevent slip. The belts should also be soft and pliable, otherwise power is 
consumed in bending them to the curvature of the pulleys. 

A third cause is the variation of journal-friction, due to slacking up or 
tightening the cap-screws, and also the end-thrust bearing screw. 

Hartig’s investigations show that it requires less total power to turn off a 
given weight of metal ina given time than it does to plane off the same 
amount; and also that the power is less for large than for small diameters. 

The following table gives the actual horse-power required to drive a lathe 
empty at varying numbers of revolutions of main spindle. 


HOoRSE-POWER FOR SMALL LATHES. 


























Without Back Gears. With Back Gears. 
jel lee H.P. 
aevndle required Ree aie required Remarks. 
erat to drive per min to drive 
Pp : empty. : empty. 
132.72 0145 14.6 .126 A 
219.08 197 24°33 141 20” Fitchburg lathe. 
365.00 .310 38.42 2274 
47.4 2159 4.84 132 Smallla the (1314’’), Chem- 
125.0 259 12.8 187 nitz. Germany. New 
188 .339 19.2 .230 machine. 
54.6 -206 6.61 157 ” 
122 "339 14/8 lope (Bae heaton Oo New 
183 455 el ~249 ; 
a 
82.2 326 10.8 087 








If H.P., = horse-power necessary to drive lathe empty, and N= number 
of revolutions per minute, then the equation for average small lathes is 
H.P.») = 0.095 + 0.0012N. 

For the power necessary to drive the lathes empty when the back gears 
are in, an average equation for lathes under 20’ swing is 


H.P.9 = 0.10 + 0.006N. 


The larger lathes vary so much in construction and detail that no general 
rule can be obtained which will give, even approximately, the power re- 
quired to run them, and although the average formula shows that at least 
0.095 horse-power is needed to start the small lathes, there are many Amer- 
ican lathes under 20’ swing working on a consumption of less than 05 
horse-power, 


962 THE MACHINE-SHOP, 


The amount of power required to remove metal in a machine is determin. 
able within more accurate limits. 

Referring to Dr. Hartig’s researches, H.P.; = CW, where C is a constant, 
and W the weight of chips removed per hour. 

Average values of C are .030 for cast-iron, .032 for wrought-iron, .047 for 
steel. 

The size of lathe, and, therefore, the diameter of work, has no apparent 
effect on the cutting power. If the lathe be heavy, the cut can be increased, 
and consequently the weight of chips increased, but the value of C appears 
io Pe about the same for a given metal through several varying sizes of 

athes. 


HORSE-POWER REQUIRED TO REMOVE Cast IRON IN A 20-INCH LATHE. 
(J. J. Hobart.) 








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R= wy Ss © mS wos | KES | S 
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a Boy 
B15 Seal Be 1 8S | Pek | Pale lego 
AIA <j a < < < > 
1 | 22 |Side tool........... 37.90 | .125 015 342 18.30 | 2025 
2 | 15 |Diamond...:2:..:. 80.50 | .125 015 218 10.70 | .020 
3 | 17 |Round nose........ 42.61 125 015 352 14.95 | .0238 
4 2 |Left- hand round 
MOSGta ne oe esi 26.29 | .125 015 237 9.22 | .026 
5 4 |Square- faced tool 
16” broad........| 25.82 | .015 125 255 9.06 | .028 
6 1 ee 25.27 | .048 .048 -200 10.89 | .018 
7 1 eS Ro.044 4125 .015 246 8.99 | .027 


7 


The above table shows that an average of .26 horse-power is required to 
turn off 10 pounds of cast-iron per hour, from which we obtain the average 
value of the constant C = .024. 

Most of the cuts were taken so that the metal would be reduced 14” in 
diameter; with a broad surface cut and a coarse feed, as in No. 5, the power 
required per pound of chips removed in a given time was a maximum; the 
least power per unit of weight removed being required when the chip was 
square, as in No. 6, 


HORSE-POWER REQUIRED ig REMOVE METAL IN A 29-INCH LATHE. 








R. H. Smith.) 
a P | 
M4 , ee -o | 83 
cS te Geet eS eer baleen hia: 3 
= ® oad | BO 
uy 2¢g Ss ere xs sS fe) 
oR fed 6) a= 2.| 22 wee oO 
=| Metal. D ta a = od DH > 
5 5 x2 | 3 | Qe ] P47 er5)] Ss 
e& ao | 4 | Shel 32 oclledauiure 
ge tm 6. BO | 556 | Soe > 
SR; Ss ® BS POS | res 
A o A <q < <j 
ae Cast iron 12.7 | .05 046 | .105 | 5.49 | .019 
4 Cast iron 11.1 135 046 217 | 12.96 .017 
2 Cast iron 12.85 .04 038 098 3.66 027 
4 Wrought iron 9.6 .03 046 059 2.49 .023 
4 Wrought iron 9.1 .06 046 138 4.72 .029 
4 Wrought iron 7.9 14 .046 186 9.56 .019 
2 Wrought iron 9.35 .045 -038 092 2.99 .031 
4 Steel 6.00 .02 .046 .043 1.03 .042 
4 Steel 5.8 04 .046 085 2.00 .042 
4 Steel 5.1 .06 046 108 2.64 .040 





POWER REQUIRED FOR MACHINE TOOLS. 963 


The small values of C, .017 and .019, obtained for cast iron are probably 
due to two reasons: the iron was soft and of fine quality, known as pulley 
metal, requiring less power to cut; and, as Prof. Smith remarks, a lower 
cutting-speed also takes less horse-power. 


Hardness of metals and forms of tools vary, otherwise the amount of ~ 


chips turned out per hour per horse-power would be practically constant, the 
higher cutting-speeds decreasing but slightly the visible work done. 

Taking into account these variations, the weight of metal removed per 
hour, multiplied by a certain constant, is equal to the power necessary to do 
the work. 

This constant, according to the above tests, is as follows: 


Cast Iron. Wrought Iron. Steel. 


FIALEIS ae cnt se cre eters sete eise cee .030 082 .047 
SIME. lots fick cesses wees - +023 028 042 
FLODALE fee ace sos feos > see Scenes O24 

PVOLALO sien shes bose iece elses oe, 6026 0380 044 


The power necessary to run the lathe empty will vary from about .05 to .3 
H.P., which should be ascertained and added to the useful horse-power, to 
obtain the total power expended. 

Power used by Machine-tools,. (R.E. Dinsmore, from the Elec- 
trical World.) 


1. Shop shafting 2 3/16’ x 180 ft. at 160 revs., carrying °° pulleys 

from 6” diam. to 86’, and running 20 idle machine belt ....... 1,32 HP, 
2. Lodge-Davis upright back-geared drill-press with ta le, 28’ 

swing, drilling 3g’’ hole in cast iron, with a feed of 1 nu. per 


TAMIVICE AS MOLL Ct iok area ensaies ee wuersaaes aeiee eerste Sue nae 0.78 H.V. 
3. Morse twist-drill grinder No. 2, carrying 2’’ x 6’” wheels t 3200 

Taye Meet. Sa AL Saat Sete bys ca Cue udu ab abie hee Rutten ees 0.29 H.P. 
4, Pease planer 30” x 36’, table 6 ft., planing cast iron, ci | 14” 

deep, planing 6 sq. in. per minute, at 9 reversals... ....... .... 1.06 H.P. 


5. Shaping-machine 22” stroke, cutting steel die, 6’ stroke 1%” 


deep, shaping at rate of 1.7 square inch per minute.... ... fo MOLoe EH. P. 
6. Engine-lathe 17’ swing, turning steel shaft 23g” diam., cut v/16 

deen feeding’ 7.02 inch per MINULS aie es fee cea tat eae menenny 0.43 H.P. 
7%. Engine-lathe 21’ swing, boring cast-iron hele 5’’ diam., cut 3/16 

diam), feeding 0:8?pet mINNLe so. ods cans os ORE EE eek 0.23 H.P. 
8. Sturtevant No. 2, monogram blower at 1800 revs. per minute, 

TVG BANE cia x. toss sca. a SUT vAAMD SID aie 50 SR ANDI VIR 2a cee be oh 0.8 H.P. 
9. Heavy planer 28” x 28” x 14 ft. bed, stroke 8”, cutting steel, 

oO? reversals Dér MIMUtO is Joes i oelSlodbes, cours va bh Pate adh leads Dab 3.2 H.P. 


The table on the next page compiled from various sources, principally 
from Hartig’s researches, by Prof. J. J. Flather (Am. Mach., April 12, 1894), 
may be used as a guide in estimating the power required to run a given 
machine; but it must be understood that these values, although determined 
by dynamometric measurements for the individual machines designated, 
are not necessarily representative, as the power required to drive a machine 
itself is dependent largely on its particular design and construction. The 
character of the work to be done may also affect the power required ta 
operate; thus a machine to be used exclusively for brass work may be 
speeded from 10% to 15% higher than if it were to be used for iron work of 
similar size, and the power required will be proportionately greater: 

Where power is to be transmitted to the machines by means of shafting 
and countershafts, an additional amount, varying from 30% to 50% of the total 
power absorbed by the machines, will be necessary to overcome the friction 
of the shafting. 

Horse-power required to drive Shafting.—Samuel Webber, 
in his ‘‘ Manual of Power” gives among numerous tables of power required 
to drive textile machinery, a table of results of tests of shafting. A line of 
214” shafting, 342 ft. long, weighing 4098 lbs., with pulleys weighing 5331 lbs., 
or a total of 9429 lbs., supported on 47 bearings, 216 revolutions per minute, 
required 1.858 H.P. to drive it. This gives a coefficient of friction of 5.52%. 
In seventeen tests the coefficient ranged from 8.34% to 11.4%, averaging 
5.73%. 


964 THE MACHINE-SHOP. 


Hurse-power Required to Drive Machinery. 





ead 


Observed Horse-power. 





Name of Machine. 
ie, Running Light. 





Small screw-cutting lathe 1314” swing, B.G...... 0.41 |0.18; 0.15*-0.34t 
Screw-cutting lathe 1714’’, B. G.... 2... cee cee ee: 0.867 |0.207; 0.16-0.466 
Screw-cutting lathe 20’ (Fitchburg), B. G..........- 0.47 10.12; 0.12 to 0.31 
Screw-cutting lathe 26/7, B. G.........ccececassescee- 0.462 |0.05; 0.03 to 0.33 
Lathe, 80’ face plate, will swing 108’’, T. G.......... 0.53 0.187; 0.12to0.66 
Large facing lathe, will swing 68’, T. G............- 0.91 {0.3873 0.39 to 0.81 
Wheel lathe\60’ swing. .ceniocs col eee torn 0.23 to 3.40 
Small shaper (stroke 4’, traverse 11’’),.............- 0.16 0.086 to 0.26 
Small shaper, Richards (914// K 22/’).........eceeee- 0.24 | 0.07; 0.07 to 0.12 
Shaper (15’’ stroke Gould & Eberhardt). ............ 0.63 |0.21; 0.01 to 0.47 
Large shaper, Richards (29/" & 91/’)...........220008- 1.14 0.26; 0.15 to 0.73 
Crank planer (capacity 23/7 & 27’ x 2814” stroke). .} 0.24 |0.12; 0.12 to 0.40 
Planer (capacity 86” < 386’ < 11 feet)..... .. ....... 0 84 OL2T 
Large planer (capacity 76” x 76’ x 57 feet.......... 1.47 0.60 
Smallidrill press, acini sah ok) ee eee Tenens eas 0.62 0.39 
Upright slct drilling mach. (will drill 2144” diam.)....} 0.41 ]0.15; 0.15 to 0.48 
Medium: drillpress 2a... to: sn oer neo seen ea 1.33 0.62 
Lareeldrill press. cn. ithulse tres «cidets site. nene Abed: 1.22 0.62 
Radial drill 6 feet swing......... soobioosr: ACSA MD AL 0.53 | 0.44; 0.1*-0.44+ 
Radial drill 84 feet swing......... dds sem tdeaote Malou 0.67 |0.80; 0.12*-0.80t 
Radial drill press........,....00 ates Aealelt siete OR 20 eel US 0.46 
Slotter (8 stroke) .......cc.00- puie cretela Pettisle baeleerin cece 0.28 |0.09; 0.05 to 0.25 
Slotter (914” stroke)............ 2000. UU, ea whet ereh 0.44 |0.22; 0.15 to 0.65 
Blosters(5/ Stroke)... ..bsiaeeccacis tesa weet Sa tee 0.95 10.57; 0.48 to 0.94 
Universal milling mach (Brown & Sharpe No. 1)....} 0.28 | 0.01; 0.003-0.13 
Milling machine (13’’ cutter-head, 12 cutters)... .... 0.66 |0.26; 0.26 to 0.55 
Small head traversing milling machine (cutter-head 

ive diameter, 16 Cutters) tne. eee ck eet eee oe ck 0.18 0.10 
Gear cutter will cut 20’ diameter................ ..- 0.28 0.11 
Horizontal boring machine for iron, 2214’ swing....| 0 98 Diba toda ( 
Hydraulic shearing machine....................0006. 1.52 0 37 
Large plate shears—knives 28” long, 3/’ stroke..... 7.12 0.67 
Large punch press, over-reach 28/’, 3’” stroke, 114” 

stockican:be punched. ans ents. tae ee 4.41 1.00 
Small punch and shear comb’d, 714’ knives. 114” str.}| 0.79 0.16 
Circular saw for hot iron (8014 diameter of saw)...| 4.12 0.61 
Plate-bending rolls, diam. of rolls 13’, length 914 ft.| 2.70 54 
Wood planer 1314” (rotary knives, 2 hor’] 2 vert. ...] 4.24 3.35 
Wood planer 24” (rotary knives)......... ..... Bein wisi xt Bt 1 42 
Wood planer 1714” (rotary knives)........... Adar Aree 4.63 1.25 
Wood planer 28’ (rotary knives)..............06 oe. 5.00 0.74¢-0.17§ 
Wood planer 28” (Daniel’s pattern).................. 3.20 1.45 
Wood planer and matcher (capacity 144% x 434”)...| 6.91 4.18 
Circular saw for wood (23/7 diameter of saw)........ 3.23 0.70 
Circular saw for wood (35’’ diameter of saw)........ 5.64 1.16 
Band saw for wood (384/’ band wheel)..........2..... 0.96 0.19 
Wood-mortising and boring machine................ 0.49 0.34 
Hor’l wood-boring and mortising machine, drill 4/’ 

diam., mortise 8144 deep X 1114” long .......... 3.68 | 1.67; 0.65 to 2.6 
Tenon and mortising machine...................00.- 2.11 1.42 
Tenon and mortising machine....... .........0. 00. 2.73 0.61 
Tenon and mortising machine............ ........8. 2.25 2.17 
Edge-molder and shaper. (Vertical spindle)........ 2.00 1.30 
Wood-molding mach. (cap. 744 X 244). Hor. spindle} 2.45 2.00 
Grindstone for tools, 31/’ diam., 6’ face. Velocity 

680, ft per, minutes os; cise eee ede). oe. oes deen 1.55 0.32 


Grindstone for stock, 42/712". Vel. 1680 ft. per min.! 3.11 0.24 
Emery wheel 1116” diameter x 14’. Saw grinder. | 0.56 0.40 


Ee ee a ee 
* With back gears. + Without back gears. + For surface cutters.. § With 
side cutters. B.G., back-geared. T. G.. triple-geared. 


ABRASIVE PROCESSES, 965 


Horse-power consumed in Machine-shops,—How much 
power is required to drive ordinary machine-tools? and how many men can 
be employed per horse-power? are questions which it is impossible to answer 
by any fixedrule. The power varies greatly according to the conditions in 
each shop. The following table given by J. J. Flather in his work on Dyna- 
mometers gives an idea of the variation in several large works. The percen- 
tage of the total power required to drive the shafting varies from 15 to 80, 
and the number of men employed per total H.P. varies from 0.62 to 6.04. 


Horse-power; Friction; Men Employed. 























Horse-power. gs 3 
Ds |o ext 
ln | aearal ae Sl petiiee 
~ pay ey ty o i 
p "Soon Ce, o 15, | 2A 
Kind wlio & wo| = 2 
Name of Firm, of iss SG ler el Saba ie ate 
Work. SHISE| eo] Sis") as 
.(/Lsl|Qoj as tH Te 
_ — & Bes o vo v et a 
Si smiss|/9n)| 2 |9 ° 
Big |e |s | Fle {sg 
AG Z |Z, a) 
Hane’& Bodley W938 «ist Ue E.'.& W. W.| 58 1323/2527 
UTA May A Core oes. hi W. W. 100} 15 | 85 15 3800}3.00} 3.53 
Union Tron Works......... E., M. M. 400} 95 |305 23 | 1600}4.00} 5.24 
« Frontier Iron & Brass W’ks!| M. E., etc. 25 Sulelae| sz 150|6.00| 8.82 
Paylon MistCor nium. 2.55! E. 95 230|2.42 
Baldwin Loco. Works.. ... L. 2500/2000 |500 | 80 | 4100/1.64] 8.20 
W. Sellers & Co. (one de- 

Pariment)>..2o)2 wie . ok, H. M. 102; 41} 61 | 40] 300/2.93) 4.87 
Pond Machine Tool Co.... Mas 180} 75 }105 } 41 432/2.40] 4.11 
Pratt & Whitney Co....... ‘ee 120 725|6.04 
Brown & Sharpe Co....... $f 230 900/3.91 
Yale & Towne Co.......... C. & L. 135) 67 | 68 | 49 | 700)5.11]10.25 
Ferracute Machine Co..... P. & D. 35} 11) 24) 31 90}2.571 3.7 
DEBS WiOOdlS| SONS at. estes - PINs: iby 80)2.50. . 
Bridgeport Forge Co...... H. F. 150} 75 | 75 | 50} 130) .86| 1.72 
Singer Mfg. Co.... 2.50.65. Ss. M. 1300 8500/2.69 
Howes Mic! Cou...osea.o% se 850 1500)/4.28 
Worcester Mach. Screw Co M.S. 40 80/2.00 
Hartford le Sore Se SS 400) 100 |3800 | 25 | 250)0.62) 0.83 
Nicholson File Co.......... F. 350 400|1.14} , 

AVE ACS fey ieee ne | PRAY, PR LSE 346.4 38 .67%/818.3/2.96| 5.13 





Abbreviations: E., engine; W.W., wood-working machinery; M. M., min- 
ing machinery; M. E., marine engines; L., locomotives; H. M., heavy ma- 
chinery; M. T., machine tools; C. & L., cranes and locks; P. & D., presses 
and dies; P. & S., pulleys and shafting; H. F., heavy forgings; S. M., sewing: 
machines; M. S., machine-screws: F., files. 

J.T. Henthorn states (Trans. A. 8. M. E., vi. 462) that in print-mills which 
he examined the friction of the shafting and engine was in 7 cases below 
20% and in 35 cases between 20% and 30%, in 11 cases from 30% to 35% and in 2 
cases above 35%, the average being 25.9%. Mr. Barrus in eight cotton-mills 
found the range to be between 18% and 25.%%, the average being 22%. Mr. 
Flather believes that for shops using heavy machinery the percentage of 
power required to drive the shafting will average from 40% to 50% of the total 
power expended. This presupposes that under the head of shaftiug are 
included elevaters, fans, and blowers. 


ABRASIVE PROCESSES. 


Abrasive cutting is performed by means of stones, sand, emery, glass, 
corundum, carborundum, crocus, rouge, chilled globules of iron, and in some 
cases by soft, friable iron alone. (See paper by John Richards, read before 
the Technical Society of the Pacific Coast, Am. Mach., Aug. 20, 1891, and 
Eng. & M. Jour., July 25 and Aug. 15, 1891.) . 


966 THE MACHINE-SHUP 


The ** Cold Saw.2?—For sawing any section of iron whilé cou the 
cold saw is sometimes used. This consists simply of a plain soft steel or 
iron disk without teeth, about 42 inches diameter and 3/16 inch thick. The 
velocity of the circumference is about 15,000 feet per minute. One of these 
saws will saw through an ordinary steel rail cold in about one minute. In 
this saw the steel or iron is ground off by the friction of the disk, and is not 
cut as with the teeth of anordinary saw. It has generally been found more 
profitable, however, to saw iron with disks or band-saws fitted with cutting- 
teeth, which run at moderate speeds, and cut the metal as do the teeth of a 
milling-cutter. 

Reese’s Fusing-disk.—Reese’s fusing-disk is an application of the 
cold saw to cutting iron or steel in the form of bars, tubes, cylinders, etc., 
in which the piece to be cut is made to revolve at a slower rate of speed 
than the saw. By this means only a small surface of the bar to be cut is 
presented at a time to the circumference of the saw. The saw is about the 
same size as the cold saw above described, and is rotated at a velocity of 
about 25,000 feet per minute. The heat generated by the friction of this saw 
against the small surface of the bar rotated against it is so great that the 
particles of iron or steel in the bar are actually fused, and the ‘‘sawdust ”’ 
welds as it fallsintoasolid mass, This disk will cut either cast iron, wrought 
tron, or steel. It will cut a bar of steel 134 inch diameter in one minute, in- 
cluding the time of setting it in the machine, the bar being rotated about 
200 turns per minute, 

Cutting Stone with Wire.—A plan of cutting stone by means of a 
wire cord has been tried in Kurope. While retaining sand as the cutting 
agent, M. Paulin Gay, of Marseilles, has succeeded in applying it by mechan- 
ical means, and as continuously as formerly the sand-blast and band-saw, 
with both of which appliances his system—that of the ‘‘ helicoidal wire 
cord ’’—has considerable analogy. An engine puts in motion a continuous 
wire cord (varying from five to seven thirty-seconds of an inch in diameter, 
according to the work), composed of three mild-steel wires twisted at a cer- 
tain pitch, that is found to give the best results in practice, at a speed of 
from 15 to 17 feet per second. 

The Sand-blast.—In the sand-blast, invented by B. F. Tilghman, of 
Philadelphia, and first exhibited at the American Institute Fair, New York, 
in 1871, common sand, powdered quartz, emery, or any sharp cutting mate- 
rial is blown by a jet of air or steam on glass, metal, or other comparatively 
brittle substance, by which means the latter is cut, drilled, or engraved 
To protect those portions of the surface which it is desired shall not be 
abraded it is only necessary to cover them with a soft or tough material, 
such as lead, rubber, leather, paper, wax, or rubber-paint. (See description 
in App. Cyc. Mech.; also U.S. report of Vienna Exhibition, 1873, vol. iii. 316.) : 

A ‘“‘jet of sand” impelled by steam of moderate pressure, or even by the 
blast of an ordinary fan, depolishes glass in afew seconds; wood is cut quite 
rapidly; and metals are given the so-called ‘‘ frosted’? surface with great 
rapidity. With a jet issuing from under 300 pounds pressure, a hole was 
cut through a piece of corundrum 114 inches thick in 25 minutes. 

The sand-blast has been applied to the cleaning of metal castings and 
sheet metal, the graining of zinc plates for lithographic purposes, the frost- 
ing of silverware, the cutting of figures on stone and glass, and the cutting 
of devices on monuments or tombstones, the recutting of files, ete. The 
time required to sharpen a worn-out f4-inch bastard file is about four 
minutes. About one pint of sand, passed through a No. 120 sieve, and four 
horse-power of 60-lb. steam are required for the operation. For cleaning 
castings compressed air at from 8 to 10 pounds pressure per square inch is 
employed. Chilled-iron globules instead of quartz or flint-sand are used 
with good results, both as to speed of working and cost of material, when 
the operation can be carried on under proper conditions. With the expen- 
diture of 2 horse-power in compressing air, 2 square feet of ordinary 
scale on the surface of steel and iron plates can be removed per minute. 
The surface thus prepared is ready for tinning, galvanizing, plating, bronz- 
ing, painting, etc. By continuing the operation the hard skin on the surface 
of castings, which is so destructive to the cutting edges of milling and 
other tools, can be removed. Small castings are placed in a sort of slowly 
rotating barrel, open at one or both ends, through which the blast is 
directed downward against them as they tumble over and over. No portion 
of the surface escapes the action of the sand. Plain cored work, such as 
valve-bodies, can be cleaned perfectly both. inside and out. 100 lbs. of cast- 
ings can be cleaned in from 10 to 15 minutes with a blast created by 2 horse- 


-—"5 


EMERY-WHEELS AND GRINDSTONES. 967 


power. The same weight of small forgings and stampings can be scaled in 
from 20 to 30 minutes.— fron Age, March 8, 1894. 


EMERY-WHEELS AND GRINDSTONES. 


The Selection of Emery-wheels.—A pamphlet entitled ‘‘ Emery- 
wheels, their Selection and*Use,’’ published by the Brown & Sharpe Mfg. 
Co., after calling attention to the fact that too much should not be expected 
of one wheel, and commenting upon the importance of selecting the proper 
wheel for the work to be done, says: 

Wheels are numbered from coarse to fine; that is, a wheel made of No. 
60 emery is coarser than one made of No. 100. Within certain limits, and 
other things being equal, a coarse wheel is less liable to change the tem- 
perature of the work and less liable to glaze than a fine wheel. Asarule, 
the harder the stock the coarser the wheel required to produce a given 
finish. For example, coarser wheels are required to produce a given sur- 
face upon hardened steel than upon soft steel, while finer wheels are re- 
quired to produce this surface upon brass or copper than upon either 
hardened or soft steel. 

Wheels are graded from soft to hard, and the gradeis denoted by the 
letters of the alphabet, A denoting the softest grade. A wheel is soft or 
hard chiefly on account of the amount and character of the material com. 
bined in its manufacture with emery or corundum. But other character: 
istics being equal, a wheel that is composed of fine emery is more compact 
and harder than one made of coarser emery. For instance, a wheel of No, 
100 emery, grade B, will be harder than one of No. 60 emery, same grade. 

The softness of a wheel is generally its most important characteristic. A 
soft wheel is less apt to cause a change of temperature in the work, or to 
become glazed, than a harder one. It is best for grinding hardened steel, 
cast-iron, brass, copper, and rubber, while a harder or more compact wheel 
is better for grinding soft steel and wroughtiron. As a rule, other things 
being equal, the harder the stock the softer the wheel required to produce 
a given finish. 

Generally speaking, a wheel should be softer as the surface in contact 
with the work is increased. For example, a wheel 1/16-inch face should be 
harder than one 44-inch face. If awheel is hard and heats or chatters, it 
can often be made somewhat more effective by turning off a part of its 
cutting surface; but it should be clearly understood that while this will 
sometimes prevent a hard wheel from heating or chattering the work, such 
a wheel will not prove as economical as one of the full width and proper 
grade, for it should be borne in mind that the grade should always bear the 
proper relation to the width. (See the pamphlet referred to for other in- 
formation. See also lecture by T. Dunkin Paret, Pres’t of The Tanite Co., 
on Emery-wheels, Jour. Frank. Inst., March, 1890.) 


Speed of Emery-wheels,--The following speeds are recommended 
by different makers : 





~ g Revolutions per minute. 4 R Revolutions per minute. 
Be| —_—_-__--OoooO:T_— 0200 ot” me 

= 2 * § . uO ° ° ° 
@ 5 3 S ES 9 [Se] ao S Es 3 
S| BO | oS | eEco | EO fer] gO | oS | gBo) 80 
ai| s= | @E | £53) SF (82) Se | BS | £23) Se 
ar oo: = ers 23 [es so, E OES Pale 
Ei) Bx H OF a = E pl ra SF <3] 
1 19,000 Tater ch saree foe 10 | 1,950 | 2,160 | 2,200 | 2,200 
144; 12,500] 14,400 |........ 12,000 § 12 | 1,600 1,800 1,800 1,850 
2 9500" 10; S00 VFS. 2.25 10,000 § 14 | 1,400 1,5 1,600 1,600 
214 7,600 8,640 5000 #16 | 1,200 1,350 1,400 1,400 
3 6,400 7,200 7,400 7,400 # 18 | 1,050 1,222 1,250 1,250 
4 4,800 5,400 5,400 5,450 § 20 950 1,080 1,100 1,100 
5 3,800 4,320 4,400 4,400 § 22 75 1,000 1,000 1,000 
6 3,200 3,600 3,600 3,600 § 24 800 917 925 925 
q 2,700 3,080 3,200 3,150 § 26 (50=S wales 600 825 
8 2,400 2,700 2,700 2,750 § 30 75 733 500 735 
9 2,150 | 2,400 2,400 | 2,450 E 36 550 611 400 550 


‘* We advise the regular speed of 5500 feet per minute.’? (Detroit Emery- 
wheel Co.) 


** Experience has demonstrated that there is no advantage in running 


§68 THE MACHINE-SHOP. 


solid emery-wheels at a higher rate than 5500 feet per minute peripheral 
speed.’ (Springfield E. W. Mfg. Co.) 

‘“‘ Although there is no exactly defined limit at which a wheel must be run 
to render it effective, experience has demonstrated that, taking into account 
safety, durability, and liability to heat, 5500 feet per minute at the periphery 
gives the best results. All first-class wheels have the number of revolutions 
necessary to give this rate marked on their Jabels, and a column of figures 
in the price-list gives a corresponding rate. Above this speed all wheels 
are unsafe. If run much below it they wear away rapidly in proportion to 

-what they accomplish.’’ (Northampton E. W. Co.) 

Grades of Emery.—The numbers representing the grades of emery 
run from 8 to 120, and the degree cf smoothness of surface they leave may 
be compared to that left by files as follows: 


8and 10 represent the cut of a wood rasp. 
46 90 eo 66 66 


16 * a coarse rough file. 

# z 30 om xe ; I en rey rough file. 
6 40 |. Oy ‘ a bastar e. 

46 ‘** 60 ss “se a second-cut file. 

Chie dfs) Le Sse ee eee SIMOOUN we 

90 ** 100 ee ss SSa snpernine |. 


120Fand FF ‘* ss 6&6 g dead-smooth file. 
Speed of Polishing-wheels. 


Wood covered with leather, about..... MI DOTL I Mees 7000 ft. per minute 
a ns ‘Shwe hair brush; BbOUbLE.] bss cee aes cee 2500 revs, ror larges 
md SS 114’ to 8’ diam., hair 1/’ to 114” long, ab. 4500 ** ‘“* smalles: 

Walrus-hide: wheels, about... 62.) eeu DA os Waele aes 1 8000 ft. per minute 

Rag-wheels, 4 to 8 in. diameter, about...... . _.-.. ZO00sS Sr iM 


Stress per sq. in. of section of a grindstone = (.7071D x N)? x .0000795 
es eadriy’ ay Se aac’ y ‘“* an emery-wheel = (.7071D X NV)? X .00010226 

D = diameter in feet, N = revolutions per minute. 

He takes the weight of sandstone at .078 lb. per cubic inch, and that of an 
emery-wheel at 0.1 lb. per cubic inch; Ohio stone weighs about .081 Ib. and 
Huron stone about .089 lb. per cubic inch. The Ohio stone will bear a speed 
at the periphery of 2500 to 3000 ft. per min., which latter should never be 
exceeded. The Huron stone can be trusted up to 4000 ft., when properly 
clamped between flanges and not excessively wedged in setting. Apart 
from the speed of grindstones as a. cause of bursting, probably the majority | 
of accidents have really been caused by wedging them on the shaft and over. 
wedging to true them. The holes being square, the excessive driving ol 
wedges to true the stones starts cracks in the corners that eventually run 
out until the centrifugal strain becomes greater than the tenacity of the 
remaining solid stone. Hence the necessity of great caution in the use ol 
wedges, as well as the holding of large quick-running stones between large 
flanges and leather washers. 


Strains in Grindstones, 
LIMIT OF VELOCITY AND APPROXIMATE ACTUAL STRAIN PER SQUARE INCH Ot 
SECTIONAL AREA FOR GRINDSTONES OF MEDIUM TENSILE STRENGTH. 


Revolutions per minute. 











UB Df 0 Sa prec l  n_)_h RE 2 SR co E & eoekes Bo, 
wor 100 150 200 | 250 300 350 400 
feet. lbs. Ibs. lbs. lbs. Tbs. ~ Tbs. ~ Tbs. 
2 1.58 3.57 6.35 9.93 14.30 18.36 25.42 
2144 2.47 ONG 9.88 15.49 22.29 28.64 39.75 
3 3.57 8.94 14.28 22.34 pap amsg Ci Le ten 9 2 Sh - 
38% 4.86 10.93 19.44 30.38 CARAS Ss Seer eee siiaises wet 
4 6.35 14.30 high” -|  dvie.c cg ghetdlll peasant cee ee ee Ids: oo “ae 
4 8.04 | 18.08 | 32.16 | 
5 .93 22.34 |... ... Approximate breaking strain te. 
6 14.30 82.17 | oe. times the strain for size opposiu 
z 19244 hee eons +» «++ | the bottom figure in each column, 
; . 














EMERY-WHEELS AND GRINDSTONES. 969 


The figures at the bottom of columns designate the limit cf velocity (in 
revolutions per minute), at the head of the columns for stones of the diam- 
eter in the first column ooposite the designating figure. 

A general rule of safety for any size grindstone that has a compact and 
strong grain is to limit the peripheral velocity to 47 feet per second. 

There is a large variation in the listed speeds of emery-wheels by different 
makers—4000 as a minimum and 5600 maximum feet per minute, while 
others claim a maximum speed of 10,000 feet per minute as the safe speed 
of their best emery-wheels. Rim wheels and iron centre wheels are special- 
ties that require the maker’s guarantee and'assignment of speed. 


. Strains.in Emery-wheels. 


ACTUAL STRAIN PER SQUARE INCH OF SECTION IN EMERY-WHEELS AT THE 
VELOCITIES AT HEAD OF COLUMNS FOR SIZES IN FirsT COLUMN. 














ig Revolutions per minute. 

5 | 

ze 600 800 | 1000 | 1200 | 1400 | 1600 | 1800 | 2000 | 2200 | 2400 | 2600 
PELE Si teuet WEP OS Pais es i eben kas Wa aie | vessee|eeeee-| 22.67] 27.43] 32.64] 38.31 
Geet tetoarohiccseweheniedt lecdes lever tye 51.18] 61.86] 73.62] 86.40 
Rieter: als pee .| 22.67] 32.65) 44.45| 58.05] 73.47] 90.71/109.76]130.62/153.30 
POR Sree Al bkiera ve 35.47| 51.08] 69.51; 90.81/114.94/141.90/171.71]......]...... 
12 | 18.40] 32.72] 51.12] 73.62/100.21/180.88/165.65|......]..... eb CRaehk wate 
14 | 24.80| 43.90] 68.70] 99.211134.65)175.60|......|..... 

16 | 32.57] 57.65] 90.24]130.31/177.80)... ..J......1... .-\Diam| Revs. Per 
18 | 41.41| 73.62/115.03/165.65|......].. ee eo aheaes Lode aie min, 

My} 50-08b" 90281 141. 22ers. sc boos ec eo oreleetc los ones ; aS Ti Beh 
22] 61.81] 109.41]171.23]......]. Ce NOR tidy paral Mae eee in. | 2800 | 3000 
Oat iets Ge D0. SB ack cals leer e 2b Wee EL 

OG t= RESO PA2-Solier ete oo ivsees loo recelcelcki liege: 4 | 44.43] 51.12 
REVEL TOOL eet Aoteat hee eee ar are 6 |100.21/115.03 
SERN COREE rete ere tains hy eeceters obit ROTOTBDlen Pee 








Joshua Rose (Modern Machine-shop Practice) says: The average speed of 
grindstones in workshops may be given as follows: 
Circumferential Speed of Stone. 


For grinding machinists’ tools, about ...... 900 feet per minute. 
ce & carpenters’ ‘ S Soa tote ae GOO) peo peett + 
The speeds of stones for file-grinding, and other similar rapid grinding is 


thus given in the ‘‘ Grinders’ List.”’ 
Diam? fer. 2. 1% q 6144 6 514 5 4% 4 34% 3 
Revs. permin. 135 144 154 166 180 196 216 240 270 308 360 
The following table, from the Mechanical World, is for the diameter of 
stones and the number of revolutions they should run per minute (not to be 
exceeded), with the diameter of change of shift-pulleys required, varying 
each shift or change 24% inches, 214 inches, or 2 inches in diameter for each 
reduction of 6 inches in the diameter of the stone. 





Shift of Pulleys, in inches. 








Diameter Revolutions 
of Stone. per minute. Sea 
2% 214 Pe 
ft. in. 

8 nO 135 40 36 32 
7 mG 144 3114 3334 30 
% 0 154 35 31144 28 
6 66 166 3214 2914 26 
Gano 180 30 27 24 
5 6 196 27 2434 22 
Ses 0. 216 25 2216 20 
4 6 240 2216 2014 18 
4 0 270 20 18 16 
Cs hiencnn 306 1714 1534 14 
3 0 360 15 1314 12 





97C THE MACHINE-SHOP, 


Columns 8, 4, and 5 are given to show that if westart an 8-foot stone with, 
say, a countershaft pulley driving a 40-inch pulley on the grindstone spindle, 
and the stone makes the right number (135) of revolutions per minute, the 
reduction in the diameter of the pulley on the grinding-stone spindle, when 
the stone has been reduced 6 inches in diameter, will require to be also re- 
duced 214 inches in diameter, or to shift from 40 inches to 37% inches, and so 
on similarly for columns 4 and 5, Any other suitable dimensions of pulley 
may be used for the stone when eight feet in diameter, but the number of 
inches in each shift named, in order to be correct, will have to be propor- 
tional to the numbers of revolutions the stone should run, as given in column 
2 of the table. 


Varieties of Grindstones,. 
(Joshua Rose.) 


For GRINDING MACHINISTS’ TOOLS. 





Name of Stone. Kind of Grit. |Texture of Stone.| Color of Stone. 


t All kinds, from | All kinds, from | Blue or yellowisk 

finest to coarsest |hardest to softest] gray 

se ad clic light 
ue 





Nova Scotia, 


Bl eee Medium to finest] Soft and sharp 


Liverpool or Melling.| Medium to fine | Soft, with sharp | Reddish. 
grit 


For Woop-woRKING TOOLS. 


Wickersley.......... Medium to fine | Very soft Grayish yellow ; 
Liverpool or Melling.| Medium to fine ; Ces sharp | Reddish 


at eavatenat (New t Medium to finest] Soft and sharp | Uniform light blue 


Huron, Michigan ... | Fine Soft and sharp | Uniform light blue 


For GRINDING BROAD SURFACES, AS SAWS OR IRON PLATES. 











Coarse to med’m| The hard ones Yellow 
Independence........ Coarse Hard to medium] Grayish white 
Massillon: steels. Coarse Hard to medium} Yellowish white’  - 


TAP DRILLS. 
Taps for Machine-screws. (The Pratt & Whitney Co.) 














Approx. Approx. 
Diameter, | Wire | No. of Threads § Diameter, | Wire | No. of Threads 
fractions | Gauge. to inch. fractions | Gauge. to inch. 
of an inch. of an inch, 
No. 1 60, 72 No. 13 | 20. 24 
2 48, 56, 64 4% 14 | 16, 18, 20, 22, 24 
3 40, 48, 56 15) |) 18, 203424 
7/64 4 32, 386, 40 17/64 16 | 16, 18; 20, 22 
5 80, 32, 36, 40 9/382 18 } 16, 18, 20 
9/64 6 30, 382, 36, 40 19 16, 18, 20 
7 24, 30, 32 5/16 20 | 16, 18, 20 
5/32 8 24, 30, 32, 36, 40 22 | 16.18) 
9 24, 28, 30, 32 34 24 | 14, 16, 18 
8/16 10 20, 22, 24, 30, 32 26 | 16 
11 22, 24 28 | 16 
7/32 12 20, 22, 24 30 | 16 





The Morse Twist Drill aud Machine Co. gives the following table showing 
the different sizes of drills that should be used when a suitable thread is io 
be tapped in a hole. The sizes given are practically correct, 


971 


TAP DRILLS. 

















PR bees Fae 5 9/ SFA eee id 
eersecee Cvvics es $9/EP I $9/IF I g SP 08/TE I econ eerere eevee eles 6 eecce $9/6¢ ee oe g ee/e i 
eoeecte eseeeee 79/IP I 9/62 L G Sp 9I/SI I o.etee eeece evens oeoee eoeee ¥9/1S oe oe 8 9I/T I 
eeccoee eoeree +9/68 I £9/21E T G OP 08/66 I cove eeeee eeees Se.6 ele eeoee #9/G¢ ee oo 8 oe/1 I 
Sat <7" | P9/2eT $9/e8 T Saou, DEN Cee ee eee | es ” geen) ORT. 2 St ray I 
ooeecoe eeresee cate eee 79/C8 I ee hy Ne Ve oeee eooee ereee essen ecere 91/81 oe eo 6 68/TE 
ces eee) we twleeee ecrewece $9/ee L oe 91/81 I eee ere ee ereee seoece 8 evrve ae/GS ee ae 9I/SI 

6 

6 


eeesecce @eoccee eeeesee FO/IET re &/GZ T cess eeeee es eeee ereee $9/6P Ve we OL ZE/6S 
eorecee “KI eeeeeee $9/62 I oe 8 
| 





Yel Poss St OAPs POY eebies yo? —ot 9% 
eetoeee eereece $9/62 I $9/22 I Sig 28/82 I eee e@reee els.«. 46 erore Le. weeee $9/CPp oe oe OL Be/LE 
OV/IL I asec eecce aevce kate ae o% dle £9/&h oe cee 9I/el 
CG/ TET core sets sa /ey  eelic  POFiP @I IL OL | &&/s3 

Soph ct tt 86-1 49/th = 4 -49/6E 1 et It or % 
2e/6L T core ev5cce evcce Sie ee $9/6E &/6L oe ZL IL 2e/8s 
9/6 I eece eoeoe coooee eoeee 79/18 91/6 ee al II 9I/IL 
CE/LL EE Coho Sse ee) 50/Ge. BS/21 we Ore LE IL Ot | ag/ie 

Hip p9/eg *'°°° | $9/se ot £9/Te SL IL OL BG 
2e/Gl I esce eee a6 ocewe igus il oH $9/1E Pet FL ar o2/61 
QI/2 EB otte 7° -$9/68 | “878? «79/68 OT/2 "* FL St | 91/6 
Ce/SL LL ett oe ee ee OW dems P/ Le carer FL &L aL | B&/2E 

Serhccss 2e/et °° 199/66 = AN % PL SI Sl % 
ee/U T eeoe oesee eevee eeeee %6 $9/&2 =e oI FL 2e/Gl 
91/S I coee eee S o. 2 e em 2e/TL i) ee OI al 9T/2 
CE/6 ELS a a ee ae ai/s N SI OL FL | 88/SI 

aa Sto ON eee W 72/6 9/21 Sl OL FL 84 
2E/2 1 eevee @ecee eovee S aueveus #9/2L1 wy at SI 9I “e/T 
91/2 I e200 re) evees eeoee ~9/GI Be/), aay SI Oo 9I/G 
COG POS ase ea! ae @ ¥9/el 91/8 02 Si OL | 28/6 

Pe LcOh/ 82 aan ates: GI $9/It 3e/g 0% SI Ol % 


Beet Be Hes, $9/L0 1 #9/9¢ I 54g 
OR dag i ae ¥9/GG 1 ¥9/Ee 1 “4G 
$9/S3 B °2""” $9/e6 1 ¥9/18T Hg 
eeeeeee eeecese erences ¥9/8% I ee 
ce seeeee eoceeece cere oee FOU/IET oe 
eoeeeee eereeee eorecee 79/6L L ee 
eae oe OTC. E oo ocieee” POs 2. a se 
eetoece © 60-6 se erecoece oe/L 1 ee 
ereeeee eerreee eree oe 9I/E I ee 
ss eeeee oreo cserece 2e/G fT ee 
eovscee F9/IL e918: eat a as ee 
pee hae. seeeeee BGM T ae 
eeerseee eeorovce eeereee F9/L 1 ee 
eee eee eee cee eoeeeee ¥9/GT ee 
eet eoee #9/E I se eereee $9/Et oo 
ecos ce eercosee 79/@ T P9/L T 8 
eeecees wereeee F9/L T 9/89 8 

8 

8 





wiciteeihte! "a ePWelere's $9/¢89 $9/19 
seeeeee £9/T9 $9/19 9/63 


Bede Pe Pele Wh HOO OH 01 10191919. 


























2 ‘a'g° “‘peogL A ‘your 0} =| ‘dey, Jo “peal , ‘your o} =| ‘dey, Jo} 

Peoria. * fos Tid speoiqL ON | ‘wed | ‘S's ‘A sos aq | PPL ATOSUMC | spvargy on | ‘werd | 

| eee ee a ee nn a a RS RS ROOT Gi STITT TERS SRT TI | 
CoD eurgory] pue [Iq ISIM J, essoyy oy.) 


*sItig dex, 


9%2 THE MACHINE-SHOP, 


TAPER BOLTS, PINS, REAMERS, ETC. 


Taper Bolts for Locomotives,.—Bolt-threads, U. S. standard, 
except stay-bolts and boiler-studs, V thieads, 12 per inch; valves, cocks, and 
plugs, V threads, 14 per inch, and 4g-iuch taper per 1 inch. Standard bolt 
taper 1/16 inch per foot. 

Taper Heamers,.—The Pratt & Whitney Co. makes standard taper 
reamers for locomotive work taper 1/16 inch per foot from 144 inch diam.; 
4 in. length of flute to 2 in. diam.; 18 in. length of flute, diameters advancing 
by 16ths and 82ds. P.& W.Co.’s standard taper pin reamers taper 14 in. 
per foot, are made in 14 sizes of diameters, 0.135 to 1.009 in.; length of fiute 
1 5/16 in, to 12 in. 


DIMENSIONS OF THE PRatT & WHITNEY ComMPANY'’S REAMERS FOR MorsE 
STANDARD-TAPER SOCKET. 


Diameter | Diameter Gauge Gauge |Length Total Taper 
No. {Small End,|Large End,|Diam.,la’ge|L’ngth,| Flute, L’ngth per foot, 























inches. inches, jend, inches} inches.| inches. inches, 
0.365 0.525 0.475 21g 3 514 0.600 
2 0.573 0.749 0.699 246 3144 614 0.602 
3 0.779 0.982 0.936 35/16 4 7% 0.602 
4 1.026 1.283 1.281 4 5 834 0.623 
5 1.486 1.796 1.746 5 6 10 0.630 
6 2.117 2.566 2.500 "4 8144 } 1214 0.626 


Standard Steel TWaper-pins.—The following sizes are made by 

The Pratt & Whitney Co.: 
Number: 
0 1 2 3 4 5 6 7 8 9 10 


Diameter large end: 
156 172° 11938 .219 .250 :,289 | :341° .409 492) 591 | .706 


Approximate fractional sizes: 
5/32: 11/64 38/16 7/82 14 19/64 11/82 138/82 14 19/82 238/32 


mesa Saute 9/3 Spadns 84 4 
4 34 4) SSaee 4 4 4 1k Fle Le 
To* 1 144 1% 13% 2 244 34 3834 446 «25% 6 
Diameter small end of standard taper-pin reamer:t 

eles 5146" °.162 ~. 18354208 9.240) 7279") dal wcS08h. ase foal 


Standard Steel Miandrels, (The Pratt & Whitney Co.)—These 
inandrels are made of tool-steel, hardened, and ground true on their cen. 
tres. Centres are also ground to true 60° cones. The ends are of a form 
best adapted to resist injury likely to be caused by driving. They are 
slightly taper. Sizes, 14 in. diameter by 8% in. long to 2 in. diam. by 145g 12. 
long, diameters advancing by 16ths. 


PUNCHES AND DIES, PRESSES, ETC. 


Clearance between Punch and Die. —For computing the amount 
of clearance that a die should have, or, in other words, the difference in 
size between die and punch, the general rule is to make the diameter of 
die-hole equal to the diameter of the punch, plus 2/10 the thickness of the 
plate. Or, D=d-+.2t, in which D = diameter of die-hole, d = diameter of 
punch, and ¢ = thickness of plate. For very thick plates some mechanics 
prefer to make the die-hole a little smaller than called for by the above rule. 
For ordinary boiler-work the die is made from 1/10 to 3/10 of the thickness 
of the plate larger than the diameter of the punch; and some boiler-makers 
advocate making the punch fit the die accurately. For punching nuts, the 
punch fits in the die. (Am. Machinist.) 

Kennedy’s Spiral Punch. (The Pratt & Whitney Co.)—B. Martell, 
Chief Surveyor of Lloyd’s Register, reported tests of Kennedy’s spjral 
punches in which a %-inch spiral punch penetrated a 5¢-inch plate at a pres- 
sure of 22 to 25 tons, while a flat punch required 33 to 35 tons. Steel boiler- 
plates punched with a flat punch gave an average tensile strength of 58,579 





* Lengths vary by 4” each size. + Taken 14” from extreme end. Each 
gize overlaps smaller one about 9”. Taper 14” to the foot, are 


FORCING AND SHRINKING FITS. 943 


Ibs. per square inch, and an elongation in two inches across the hole of 5.2, 
while plates punched with a spiral punch gave 63,929 lbs., and 10.6% elonga- 
tion. 

The spiral shear form is not recommended for punches for use in metal of 
a thickness greater than the diameter of the punch. This form is of great- 
est benefit when the thickness of metal worked is less than two thirds the 
diameter of punch. 

Size of Blanks used in the Drawing=-press,. Oberlin Smith 
(Jour. Frank. Inst., Nov. 1886) gives three methods of finding the size of 
blanks. The first is a tentative method, and consists simply in a series of 
experiments with various blanks, until the proper one is found. This is for 
use mainly in complicated cases, and when the cutting portions of the die 
and punch can be finally sized after the other work is done. The second 
method is by weighing the sample piece, and then, knowing the weight of 
the sheet metal per square inch, computing the diameter of a piece having 
the required area to equal the sample in weight. The third method is by 


computation, and the formula is 2 = /d? + 4dh for sharp-cornered cup, 
where x = diameter of blank, d = diameter of cup, h = height of cup. For 
round-cornered cup where the corner is small. say radius of corner less than 


¥% height of cup, the formula is # = ( /d?2 + 4dh) — r, about; r being the 
radius of the corner. This is based upon the assumption that the thickness 
of the metal is not to be altered by the drawing operation. 

Pressure attainable by the Use of the Drop-press, (R. H. 
Thurston, Trans. A.S. M. E., v. 58.)—A set of copper cylinders was prepared, 
of nue Lake Superior copper; they were subjected to the action of presses 
of different weights and of different heights of fall. Companion specimens 
of copper were compressed to exactly the same amount, and measures were 
obtained of the loads producing compression, and of the amount of work 
done in producing the compression by the drop. Comparing one with the 
other it was found that the work done with the hammer was 90% of the work 
which should have been done with perfect efficiency. That is to say, the 
work done in the testing-machine was equal to 90% of that due the weight of 


the drop falling the given distance. ; : 
la: M PeeeUa in Drandaie eee ee ee eC IERCy. 
Roma en eam P Ys i compression. J 


For pressures per square inch, divide by the mean area opposed to crush- 
fng action during the operation. 

Flow of Metals. (David Townsend, Jour. Frank. Inst., March, 1878.) 
~In punching holes 7/16 inch diameter through iron blocks 134 inches thick, 
it was found that the core punched out was only 11/16 inch thick, and its 
volume was only about 32% of the volume of the hole. Therefore, 68% of the 
metal displaced by punching the hole flowed into the block itself, increasing 
its dimensions. 


FORCING AND SHRINKING FITS, 


Forcing Fits of Pins and Axles by Hydraulic Pressure. 
—A 4-ineh axle is turned .015 inch diameter larger than the hole into which 
it is to be fitted. They are pressed on by a pressure of 30 to 385 tons. (Lec- 
ture by Coleman Sellers, 1872.) 

For forcing the crank-pin into a locomotive driving- wheel, when the pin- 
hole is perfectly true and smooth, the pin should be pressed in with a, pres- 
sure of 6 tons for every inch of diameter of the wheel fit. When the hole is 
not perfectly true, which may be the result of shrinking the tire on the 
wheel centre after the hole for the crank-pin has been bored, or if the hole is 
not perfectly smooth, the pressure may have to be increased to 9 tons for 
every inch of diameter of the wheel-fit. (Am. Machinist.) 

Shrinkage Fits.—In 1886 the American Railway Master Mechanics? 
Association recommended the following shrinkage allowances for tires of 
standard locomotives. The tires are uniformly heated by gas-flames, slipped 
over the cast-iron centres, and allowed to cool. The centres are turned to 
the standard sizes given below, and the tires are bored smaller by the 
amount of the shrinkage designated for each: 


Diameter of centre, in.... 38 44 50 56 62 66 
Shrinkage allowance,in.. .040 .047 .053 .060 .066 .070 
This shrinkage allowance is approximately 1/80 inch per foot, or 1/960. A 
common allowance is 1/1000, Taking the modulus of elasticity of steel at 


O74. : THE MACHINE-SHOP. 


30,000,000, the strain caused by shrinkage would be 30,000 Ibs. per square 
inch, less an uncertain amount due to compression of the centre. 


SCREWS, SCREW-THREADS, ETC.* 


Efficiency of a Screw.—Let a= angle of the thread, thatis, the 
angle whose tangent is the pitch of the screw divided by the circumference 
of a circle whose diameter is the mean of the diameters at the top and 
bottom of the thread. Then for a square thread 


1—ftana 
1+ / cotan a’ 
in which f is tue coefficient of friction. (For demonstration, see Cotterill and 
Slade, Applied Mechanics, p, 146.) Since cotan = 1 + tan, we may substitute 


for cotan a the reciprocal of the tangent, or if » = pitch, and c = mean cir- 
cumference of the screw, 


Efficiency = 


1-72 
Efficiency — ee ays 
14+f< 
p 
EXAMPLE.—Efficiency of square-threaded screws of 44 in. pitch. 
Diameter at bottom of thread,in.... 1 2 3 4 
6 be top es bé 66 any 1% 2146 344 41g 
Mean circumference ‘‘ ‘* Wi ed Os Oee 7.069 10.21 13.35 
Cotangent @=C+DP............-: Safi elie! 14.14 20.42 26.70 
Vansent =i! Cr, von tiesto el ete 0707 .0490 .0375 
Efficiency tf fF = 10's cee csc = 55.8% 41.2% 32.7% 27.2% 
a 9 panty ith rie Peiccticn = 45% 31.7% 24.4% 19.9% 


The efficiency thus increases with the steepness of the pitch. 

The above formule and examples are for square-threaded screws, and 
consider the friction of the screw-thread only, and not the friction of the 
vollar or step by which end thrust is resisted, and which further reduces the 
efficiency. The efficiency is also further reduced by giving an inclination te 
the side of the thread, as in the V-threaded screw. For discussion of this 
subject, see paper by Wilfred Lewis, Jour. Frank. Inst. 1880; also Trans. 
A. S. M. E., vol. xii. 784. 

Efficieney of Screw-bolts.—Mr. Lewis gives the following approx- 
imate formula for ordinary screw-bolts (V threads, with collars); p = 
pitch of screw, d = outside diameter of screw, #’= force applied at circum- 
ference to lift a unit of weight, H = efficiency of screw. For an averige 
case, in which the coefficient of friction may be assumed at .15, 


p+d p 
f= KE= ° 
p+d 


For bolts of the dimensions given above, \%-in. pitch, and outside dlam> 
eters 114, 244, 314, and 4% in., the efficiencies according to this formula 
would be, respectively, .25, .167, .125, and .10. 

James McBride (Trans. A. 8. M. E.. xii. 781) describes an experiment with 
an ordinary 2-in. screw-bolt, with a V thread, 414 threads per inch, raising 
a weight of 7500 Ibs., the force being applied by turning the nut. Of the 
power applied 89.8% was absorbed by friction of the nut on its supporting 
washer and of the threads of the bolt in the nut. The nut was not faced, 
and had the flat side to the washer. 

Prof. Ball in his ‘‘ Experimental Mechanics”’ says: ‘‘Experiments showed 
in two cases respectively about %4 and 34 of the power was lost.” 

Trautwine says: ‘‘In practice the friction of the screw (which under 
heavy loads becomes very great) make the theoretical calculations of but 
little value.” 

Weisbach says: ‘' The efficiency is from 19% to 30%.” 

Efficiency of a Differential Screw,.—A correspondent of the 
American Machinist deseribes an experiment with a differential screw- 
punch, consisting of an outer screw 2 in. diam., 3 threads per in., and an 
inner screw 13 in. diam., 34 threads per inch. The pitch of the outer screw 











* For U.S. Standard Screw-threads, see page 204, , 





HRPRAM Hee 95 


being 4 in. and that of the inner screw 2/7 in., tue punch would ad- 
vance In one revolution 4 — 2/7 = 1/21 in. Experiments were made to de- 
termine the force required to punch an 11/16-in. hole in iron 44 in, thick, the 
force being applied at the end of a lever-arm of 4734in. The leverage would 
be 4734 X 2m X 21 = 6300. The mean force applied at the end of the lever 
was 95 lbs., and the force at the punch, if there was no friction, would be 
6300 x 95 = 598,500 Ibs. The force required to punch the iron, assuming a 
shearing resistance of 50,000 lbs. per sq. in., would be 50,000 x 11/16 x 7 x 
14 = 27,000 lbs., and the efficiency of the punch would be 27,000 -- 598,500 = 
ouly 4.5%. With the larger screw only used as a punch the mean force at 
the end of the lever was only 82 lbs. The leverage in this case was 4734 x 
27 X 3 = 900, the total force referred to the punch, including friction, 900 x 
82 = 73,800, and the efficiency 27,000 -- 73,800 = 36.7%. The screws were of 
tool-steel, well fitted, and lubricated with lard-oil and plumbago. 

Powell’s New Screw-thread.—aA. M. Powell (Am. Mach., Jan. 24, 
1895) has designed a new screw-thread to replace the square form of thread, 
giving the advantages of greater ease in making fits, and provision for *‘ take 
up”? in case of wear. The dimensions are the same as those of square- 
thread screws, with the exception that the sides of the thread, instead of 
being perpendicular to the axis of the screw, are inclined 1414° to such per- 
pendicular; that is, the two sides of a thread are inclined 29° to each other. 
The formule for dimensions of the thread are the following: Depth of 
thread = 14 + pitch; width of top of thread = width of space at bottom = 
.3:07 + pitch; thickness at root of thread = width of space at top = .6293 + 
pitch. The term pitch is the number of threads to the inch, 


PROPORTIONING PARTS OF MACHINES IN A SERIES 
i OF SIZES. 


(Stevens Indicator, April, 1892.) 


The following method was used by Coleman Sellers while at William Sellers 
& Co.’s to get the proportions of the parts of machines, based upon the 
size obtained in building a large machine and a small one to any series of 
machines. This formula is used in getting up the proportion-book and ar- 
ranging the set of proportions from which any machine can be constructed 
of intermediate size between the largest and smailest of the series. 

Rule to Establish Construction Formulz.—Take difference 
between the nominal sizes of the largest and the smallest machines that 
have been designed of the same construction. Take also the difference be- 
tween the sizes of similar parts on the largest and smallest machines se- 
lected. Divide the latter by the former, and the result obtained will be a 
‘factor,’ which, multiplied by the nominal capacity of the intermediate 
machine, and increased or diminished by a constant ‘* increment,’ will give 
the size of the part required. To find the ‘increment :”’ Multiply the nomi- 
nal capacity of some known size by the factor obtained, and subtract the 
result from the size of the part belonging to the machine of nominal ca- 
pacity selected. 

EXxAMPLE.—Suppose the size of a part of a 72-in. machine is 3 in., and the 
corresponding part of a 42-in. machine is 1%, or 1.875 in.: then 72 — 42 = 
30, and 3 in. — 1% in. = 14% in. = 1.125. 1.125 + 380 = .0375 = the ‘ factor,” 
and .0875 & 42 = 1.575. Then 1.875 — 1.575 = .3 = the ‘“‘inerement’”’ to Le 
added. Let D = nominal capacity; then the formula will read: x2 = 
DX .0375 + .3. 

Proof: 42 * .0375 + .8 = 1.875, or 1% the size of one of the selected parts. 

Some prefer the formula: aD +c = x, in which D= nominal capacity in 
inches or in pounds, c is a constant increment, a is the factor, and # = the 
part to be found. 


KEYS. 


Sizes of Keys for Mill-gearing. (Trans. A. S. M. E., xiii. 229.)—K. 
G. Parkhurst’s rule: Width of key = diam. of shaft, depth = 1/9 diam. of 
shaft; taper 1g in. to the foot. 

Justom in Michigan saw-mills: Keys of square section, side = 14 diam. of 
shaft. or as nearly as may be in even sixteenths of an inch. 

J. T. Hawkins’s rule: Width = 14 diam. of hole; depth of side abutment 
in shaft = 4 diam. of hole. 

W.S. Huson’s rule: 14-inch key for 1 to 114 in. shafts, 5/16 key for 114 to 
1 in, shafts, 3g in. key for 144 to 134 in. shafts, and soon. Taper } in. to 

e foot. Total thickness at large end of splice, 4/5 width of key. 


976 THE MACHINE-SHOP, 


Unwin (Elements of Machine Design) gives: Width = 4d -+ in. Thick. 
ness = id -+ 1 in., in which d = diam. of shaft in inches. When wheels or 
pulleys transmitting only asmall amount of power are keyed on large shafts, 
he says, these dimensions are excessive. In that case, if H.P. = horse- 
power transmitted by the wheel or pulley, N = revs. per min, P = force 
acting at the circumference, in lbs., and R = radius of pulley in inches, take 


/iEP,  3/PR 
ad= N or 630- 


Prof. Coleman Sellers (Stevens Indicator, April, 1892) gives the following ; 
The size of keys, both for shafting and for machine tools, are the propor- 
tions adopted by William Sellers & Co., and rigidly adhered to during a pe- 
riod of nearly forty years. Their practice in making keys and fitting them 
is, that the keys shall always bind tight sidewise, but not top and bottom; 
that is, not necessarily touch either at the bottom of the key-seat in the 
shaft or touch the top of the slot cut in the gear-wheel that is fastened te 
the shaft ; but in practice keys used in this manner depend upon the fit of 
the wheel upon the shaft being a forcing fit, or a fit that is so tight as to re- 
quire screw-pressure to put the wheel in place upon the shaft. 


Size of Keys for Shafting. 


Diameter of Shaft, in. Size of Key, in. 

14 TGAGC er Lea I16F eeu ohh icodoins 16x 3% 

SIG /G 29/160. ee eee cae 7/16 x 3 
2/1 ROM LSS he OE. UE ee £ eo 9/16 x 
Q11/16 9215/16" 836M RBN716Ete...., - 2 11/16x 34 
SHS/IG Vai / LO a al G/ 1G ebis cae cece wok 13/16x % 
DOUG) 515/16) VO 1LOmsenmiesasee = cence 15/16x1 
615/16 77/16 715/16 8 7/16 8 15/16.. 1 1/16x1% 


Length of key-seat for coupling = 14% X nominal diameter of shaft. 
Size of Keys for Machine Tools. 
Diam. of Shaft, in. %!2¢°£ Key, | piam. of Shaft, in, Size of Key, 


in, sq. in. sq. 
15/16 and under........ li 4 to? pi7yig Maes 13/16 
Pea oi ye Ry Bee 3/16 Big to 6 15/16... .... 15/16 
184 to 177165 Oe 14 F StOCB IS ACe Shee 1 1/16 
Hato WLIO. S 0 ele 5/16 9 to10 15/16......... 1 3/16 
132 to B'B/18)). cs. ss ctee 7/16 11% to TRS igi Ls 1 5/16 
Biz to 201/16" 0.. 5... sok 9/16 13 to 14 15/16......... 1 7/1t' 
284 'to'S'15/16",...... 00. 11/16 


John Richards, in an article in Cassier’s Magazine,writes as follows: There 
are two kinds or system of keys, both proper and necessary, but widely dif- 
ferent in nature. 1. The common fastening key, usually madein width one 
fourth of the shaft’s diameter, and the depth five eighths to one third the 
width. These keys are tapered and fit on all sides, or, as it is commonly de- 
scribed, ‘‘ bear all over.”’ They perform the double function in most cases 
of driving or transmitting and fastening the keyed-on member against 
movement endwise on the shaft. Such keys, when properly made, drive 
as a strut, diagonally from corner to corner. 

2. The other kind or class of keys are not tapered ard fit on their sides 
only,a slight clearance being left on the back to insure against wedge action 
or radial strain. These keys drive by shearing strain. 

For fixed wo:k where there is no sliding movement such keys are com- 
iwnonly made of square section, the sides only being planed, so the depth is 
more than the width by so much as is cut away in finishing or fitting. 

For sliding bearings, as in the case of drilling-machine spindles, the depth 
should be increased, and in cases where there is heavy strain there should 
be two keys or feathers instead of one. 

The following tables are taken from proportions adopted in practical use. 

Flat keys, as in the first table, are employed for fixed work when the 
parts are to be held not only against torsional strain, but also against move- 
ment endwise ; and in case of heavy strain the strut principle being the 
strongest and most secure against movement when there is strain each way, 
as in the case of engine cranks and first movers generally. The objections 


HOLDING-POWER OF KEYS AND SET-SCREWS. 977 


to the system for general use are, EW feedeuba the work out of truth, the care 
and expense required in fitting, and destroying the evidence of good or bad 
fitting of the keyed joint. When a wheel or other part is fastened with a 
tapering key of this kind there is no means of knowing whether the work is 
well fitted or not. For this reason such keys are not employed by machine- 
tool-makers, anc in the case of accurate work of any kind, indeed, cannot 
be, because of the wedging strain, and also the difficulty of inspecting com- 
pleted work. 


T, DIMENSIONS OF FLAT Krys, IN INCHES. 








Diam. of shaft........ 1 | 114| 114] 134] 2 12%) 3 |a1 41 5 | 6 | 7/8 
Breadth of keys .....| 4 |5/16| 3617/16] 34 | 54 34 | 24) 1] 116 | 134 |116|184 
Depth of keys........ 5/32|3/16| 14|9/32|5/16| 3417/16] 1415¢|11/16|12/16| 2%) 1 





® II, DIMENSIONS OF SQUARE KEys, IN INCHES. 





Diam. of shaft..... 1 144 11% |184 {2 24 «3 34 «4 
Breadth of keys...| 5/32} 7/32] 9/32] 11/32] 13/32] 15/32] 17/82) 9/16 | 11/16 
Depth of keys.....| 3/16) 14 5/16} 36 | 7/161 % 9/16 | 5% 34 


III. DIMENSIONS OF SLIDING FEATHER-KEYS, IN INCHES. 


Diam. of shaft....| 11%4| 114/134 _ |2 a4} ate 38) | (alg). ld 4\, 
Breadth of keys..| %4| 14| 5/16 | 5/16| 36 | 8 | % | 9/16| 9/16 | 6% 


Depth of keys....| 36] 3¢| 7/16 | 7/16 | % lg 5g | 34 34 % 


P. Pryibil furnishes the following table of dimensions to the Am. Machin. 
ist. Hesays: On special heavy work and very short hubs we put in two 
keys in one shaft 90° apart. With special long hubs, where we cannot use 
keys with noses, the keys should be thicker than the standard. 


Diameter of Shafts, | Width,} Thick- f Diameter of Shafts, | Width,} Thick- 





inches. inches. |ness, in. inches. inches. |ness,in,. 
34 to 1 1/16 3/16 3/16 3 7/16 to3 11/16 % 56 
1 to 1 5/16 5/16 Y% 8 15/16 to 4 3/16 1 11/16 
t 7/16 to1 11/16 36 5/16 47/16 to4 11/16 1% 34 
1 15/16 to 2 3/16 VY 36 4% to 53% 114 15/16 
27/16 to2 11/16 5g 4% 5% to 634 14 1 
2 15/16 to3 3/16 34 9/16 6% to 73% 134 1% 





Keys longer than 10 inches, say 14 to 16’, 1/16” thicker; keys longer than 
10 inches, say 18 to 20’, 14’’ thicker; and so on. Special short hubs to have 
two keys. f 

For description of the Woodruff system of keying, see circular of the 
Pratt & Whitney Co.; also Modern Mechanism, page 455, 


HOLDING-POWER OF KEYS AND SET-SCREWS. 


Tests of the Holding-power of Set-screws in Pulleys, 
\@. Lanza, ‘rans. A. S. M. E., x. 230.)—These tests were made by using a 

ulley fastened to the shaft by two set-screws with the shaft keyed to the 
faders: then the load required at the rim of the pulley to cause it to slip 
was determined, and this being multiplied by the number 6.037 (obtained by 
adding to the radius of the pulley one-half the diameter of the wire rope, 
and dividing the sum by twice the radius of the shaft, since there were two 
set-screws in action at a time) gives the holding-power of the set-screws. 
The set-screws used were of wrought-iron, 54 of an inch in diameter, and ten 
threads to the inch; the shaft used was of steel and rather hard, the set- 
screws making but little impression upon it. They were set up with a 
force of %5 lbs. at the end of a ten-inch monkey-wrench. The set-screws 
used were of four kinds, marked respectively A, B,C, and D. The results 
were as follows; ) 


978 DYNAMOMETERS. 


A, ends perfectly flat, 9/16-in. diameter, 1412 to 2294 Ibs.; average 2064. 
B, radius of rounded ends about 1% inch, 2747 ‘ 3079 ‘ ss 2912. 

id #87 10988 x s SS EGO a 1902: S80 COS Th Ota: 
D ends cup-shaped and case-hardened, 1962 ‘* 2958 ‘* 2470, 


RemMarRkKs.—A. The set-screws were not entirely normal to the shaft ; hence 
they bore less in the earlier trials, before they had become flattened by 
wear. 

B. The ends of these set-screws, after the first two trials, were found to 
be flattened, the flattened area having a diameter of about 14 inch. 

C. The ends were found, after the first two trials, to be flattened, as in B. 

D. The first test held well because the edges were sharp, then the holding- 
power fell off till they had become flattened in a manner similar to B, when 
the holding-power increased again. 

Tests of the Holding-power of Keys. (Lanza.)—The load 
was applied as in the tests.of set-screws, the shaft being firmly keyed to the 
holders. The load required at the rim of the pulley to shear the keyg was 
determined, and this, multiplied by a suitable constant, determined in #&im- 
ilar way to that used in the case of set-screws, gives us the shearing strength 
per square inch of the keys. 

The keys tested were of eight kinds, denoted, respectively, by the letters _ 
A, B, C, D, E, F, G and H, and the results were as follows: A, B, D and F, ~ 
each 4 tests; EH, 3 tests; C, G, and H, each 2 tests. 


A, Norway iron, 2’’ X 14” X 15/82’’, 40,184to 47,760 lbs.; average, 42,726. 
38 


B, refined iron, 2’ « 14” & 15/32”, 36,482 ‘* 39,254; sf 059. 
C, tool steel, 1”’ x 14” & 15/82”, 91,344 & 100,056. 
D, machinery steel, 2’ x 14” x 15/32/’, 64,630to 70,186; %, 66,875. 
E, Norway iron, 1144” x 36” x 7/16”, 86,850 ** 37,222; S 37,036. 
F, cast-iron, 2’ & 14” & 15/827’, 30,278 °° 86,944; fs 33,034. 
G, cast-iron, 1144” « 36’ < 7/16”, 37,222 & 38,700. 
H, cast-iron, 1” x 14” X 7/16”, 29,814 & 38,978. 


_ In A and B some crushing took place before shearing. In EK, the keys be- 
ing only 7/16 in. deep, tipped slightly in the kev-way. In H, in the first test, 
there was a defect in the key-way of the pulley. 


DYNAMOMETERS. 


Dynamometers are instruments used for measuring power. They are of 
several classes, as: 1. Traction dynamometers, used for determining the 
power required to pull a car or other vehicle, or a plough or harrow. 
2. Brake or absorption dynamometers, in which the power of a rotating 
shaft or wheel is absorbed or converted into heat by the friction of a brake; 
and, 3. Transmission dynamometers, in which the power in a rotating shaft 
is measured during its transmission through a kelt or other connection to 
another shaft, without being absorbed. 

Traction Dynamometers generally contain two principal parts: 
(1) A spring or series of springs, through which the pull is exerted, the exten- 
sion of the spring measuring the amount of the pulling force; and (2) a paper- 
covered drum, rotated either at a uniform speed by clockwork, or at a speed 
proportional to the speed of the traction, through gearing, on which the ex- 
tension of the spring is registered by a pencil. From the average height of 
the diagram drawn by the pencil above the zero-line the average pulling 
force in pounds is obtained, and this multiplied by the distance traversed, 
in feet, gives the work done, in foot-pounds. The product divided by the 
time in minutes and by 33,000 gives the horse-power. 

The Prony brake is the typical form of absorption dynamometer. 
pee i 16%, from Flather on Dynamometers and the Measurement of 

ower. 

Primarily this consists of a lever connected tv a revolving shaft or pulley 
in such a manner that the friction induced between the surfaces in contact 
will tend to rotate the arm in the direction in which the shaft revolves. This 
rotation is counterbalanced by weights P, hung in the scale-pan at the end 
of the lever. In order to measure the power for a given number of revolu- 
tions of pulley, we add weights to the scale-pan and screw up on bolts bb 
until the friction induced balances the weights and the lever is maintained 


THE ALDEN ABSORPTION-DYNAMOMETER. 979 


In its horizontal position while the revolutions of shaft per minute remain 
constant. 

For small powers the beam is generally omitted—the friction being mea- 
sured by weighting a band or strap thrown over the pulley. Ropes or cords 
are often used for the same purpose. 

Instead of hanging weights in a scale-pan, as in Fig. 167, the friction may be 
weighed on a platform-seale; in this 
case, the direction of rotation being 
the same, the lever-arm will be on the 
opposite side of the shaft. 

In a modification of this brake, the 
brake-wheel is keyed to the shaft, 
and its rim is provided with inner 
flanges which form an annular trough 
for the retention of water to keep the 
pulley from heating. A small stream 
of water constantly discharges into 
tue trough and revolves with the Fia. 167 
pulley—tr.- centrifugal force of the 4 5 
particles or water overcoming the action of gravity; a waste-pipe with its 
end flattened is so placed in the trough that it acts as a scoop, and removes 
all surplus water. The brake consists of a flexible strap to which are fitted 
blocks of wood forming the rubbing-surface; the ends of the strap are con- 
nected by an adjustable bolt-clamp, by means of which any desired tension 
may be obtained. 

The horse-power or work of the shaft is determined from the following: 


Let W = work of shaft, equals power absorbed, per minute; 

P= unbalanced pressure or weight in pounds, acting on lever-arm 
at distance L; 

LI = length of lever-arm in feet from centre of shaft; 

V = velocity of a point in feet per minute at distance L, if arm were 
allowed to rotate at the speed of the shaft; 

N = number of revolutions per minute; 

H.P. = horse-power. 


Then will W = PV = 2aLNP. 
Since H.P, = PV + 33,000, we have H.P. = 24 L NP + 33,000, 


33 . L 2 2 aes 
to oa We obtain H.P. = [000° 33 +27 is practically 5 ft.3 in., a value 


eften used in practice for the length of arm. 

If the rubbing-surface be too small, the resulting friction will show great 
irregularity—probably on account of insufficient lubrication—the jaws be- 
mg allowed to seize the pulley, thus producing shocks and sudden vibra- 
tions of the lever-arm. 

Soft woods, such as bass, plane-tree, beech, poplar, or maple are all to be 
referred to the harder woods for brake-blocks. The rubbing-surface should 
e wel) lubricated with a heavy grease. 

The Alden Absorption-dynamometer, (G. I. Alden, Trans. 
A.S. M. E., vol. xi, 958; also xii, 700 and xiii. 429.)—This dynamometer is a 
friction-brake, which is capable in quite moderate sizes of absorbing large 
powers with unusual steadiness and complete regulation, A smooth cast- 
iron disk is keyed on the rotating shaft. This is enclosed in a cast-iron - 
shell, formed of two disks and a ring at their circumference, which is free 
to revolve on the shaft. To the interior of each of the sides of the shell is 
fitted a copper plate, enclosing between itself and the side a water-tight 
space, Water under pressure from the city pipes is admitted into each of 
these spaces, forcing the copper plate against the central disk. The 
chamber enclosing the disk is filled with oil. To the outer shell is fixed a 
weighted arm, which resists the tendency of the shell to rotate with the 
shaft, caused by the friction of the plates against the central disk. Four 
brakes of this type, 56 in. diam., were used in testing the experimental 
locomotive at Purdue University (Trans. A.S.M.E., xiii. 429). Each was 
designed for a maximum moment of 10,500 foot-pounds with a water-press- 
ure of 40 lbs. per sq. in. 

The area in effective contact with the copper plates on either side is rep- 
resented by an annular surface having its outer radius equal to 28 inches, 
and its inner radius equal to 10 inches. The apparent coefficient of friction 
between the plates and the disk was 319%. 





ss er, 





980 DYNAMOMETERS. 


W. W. Beaumont (Proce. Inst. C. E. 1889) has deduced a formula by means ~ 
of which the relative capacity of brakes can be compared, judging from the 
amount of horse-power ascertained by their use. 

If W = width of rubbing-surface on brake-wheel in inches; V = vel. of 
point on circum. of wheel in feet per minute; K = coefficient; then 


K= WV + H.P. 


Capacity of Friction-brakes.—Prof. Flather obtains the values 
of K given in the last column of the subjoined table: 








b Brake- ¢ 
id Wend sade BO hq 
FE |m, jeu} os ‘ x) 
Sains a le¥l/Se = Design of Brake. © 
db ie ie 3 = 
nm |ais |gsolse 0 s 
oe Tees Bie e 
m |e & IA i 
21 | 150 vg 5 | 33” Royal Ag. Soc., compensating....... .| 785 
19 | 148.5| 7 5 | 33.38’ |McLaren, compensating ........... .| 858 
2 146 5 ] 32.19” = water-cooled and comp..... 802 
40 180 410.5) 5 7 32” Garrett, oc ee oer aats ore imate di 
33 150 410.5) 5 | 382” 4 ce Si Py GABAA (TE) 
150 | 150 {10 ia peice ah Schoenheyder, water-cooled.......... 282 
24 142 12 6.4 688.3144) Balk... oceaciinssi ea eons Ser Meee alae oe 1385 
180 | 100 |24 5 1126.1/" | Gately & Kletsch, water-cooled.......| 209 
475 76.2] 24 re Nha Ge ee Webber, water-cooled .........-....ce« 84.7 
a t a 24 4 | 63” Westinghouse, water-cooled..........| 465 
rast! sooy [18 | 4 | 2734” “ + ros ee 847 





The above calculations for eleven brakes give values of K varying from 
84 7 to 1385 for actual horse-powers tested, the average being K = 655. 

Instead of assuming an average coefficient, Prof. Flather proposes the 
following: 

Water-cooled brake, non-compensating, K = 400; W = 400 H.P. + V. 

Water-cooled brake, compensating, K = 150; W = 750 H.P. + V. 

Non-cooling brake, with or without compensating device, K = 900; 
W = 900 H.P. + V. 


Transmission Dynamometers are of various forms, as the 
Batchelder dynamometer, in which the power is transmitted through a 
“train-arm”’ of bevel gearing, with its modifications, as the one described 
by the author in Trans. A. I. M. E., viii. 177, and the one described by 
Samuel Webber in Trans. A. S. M. E., x. 514: belt dynamometers, as the 
Tatham; the Van Winkle dynamometer, in which the power is transmitted 
from a revolving shaft to another in line with it, the two almost touching, 
through the medium of coiled springs fastened to arms or disks keyed to 
the shafts; the Brackett and the Webb cradle dynamometers, used for 
measuring the power required to run dynamo-electric machines. Descrip- 
tions of the four last named are given in Flather on Dynamometers. 

Much information on various forms of dynamometers will be found in 
Trans. A. 8S. M. E., vol. vii. to xv., inclusive, indexed under Dynamometers 


OPERATIONS OF A REFRIGERATING-MACHINE, 981 


ICE-MAKING OR REFRIGERATING MACHINES. 


References,—An elaborate discussion of the thermodynamic theory of 

the action of the various fluids used in the production of cold was published by 
M. Ledoux in the Annales des Mines, and translated in Van Nostrand’s Magu- 
zine in 1879. This work, revised and additions made in the light of recent ex- 
perience by Professors Denton, Jacobus. and Riesenberger, was reprinted in 
1892. (Van Nostrand’s Science Series, No. 46.) The work is largely mathe- 
matical, but it also contains much information of immediate practical value, 
from which some of the matter given below is taken. Other references are 
Wood’s Thermodynamics, Chap. V., and numerous papers by Professors 
Wood, Denton, Jacobus, and Linde in Trans. A. S. M. E., vols. x. to xiv.; 
Johnson’s Cyclopedia, article on Refrigerating-machines; also Hng’g, June 
18, July 2 and 9, 1886; April 1, 1887; June 15, 1888; July 31, Aug. 28, 1889; Sept. 
11 and Dec. 4, 1891; May 6 and July 8, 1892. For properties of Ammonia and 
Sulphur Dioxide, see papers by Professors Wood and Jacobus, Trans. A. 8. 
M. E.,. vols. x. and xii. 
' For illustrated articles describing refrigerating-machines, see Am. Mach., 
May 29 and June 26, 1890, and Mfrs. Record, Oct. 7, 1892; also catalogues of 
builders, as Frick & Co., Waynesboro, Pa.; De La Vergne Refrigerating-ma- 
chine Co., New York; and others. 

Operations ofa Refrigerating-machinme,.—Apparatus designed 
for refrigerating is based upon the following series of operations: 

Compress a gas or vapor by means of some external force, then relieve it 
of its heat so as to diminish its volume; next, cause this compressed gas or 
vapor to expand so as to produce mechanical work, and thus lower its tem- 
perature. The absorption of heat at this stage by the gas, in resuming its 
original condition, constitutes the refrigerating effect of the apparatus. 

A refrigerating-machine is a heat-engine reversed. 

From this similarity between heat-motors and freezing-machines it results 
that all the equations deduced from the mechanical theory of heat to deter- 
mine the performance of the first, apply equally to the second. 

abe efficiency depends upon the difference between the extremes of tem- 
perature. 

The useful effect of a refrigerating-machine depends upon the ratio 
between the heat-units eliminated and the work expended in compressing 
and expanding. 

This result is independent of the nature of the body employed. 

Unlike the heat-motors, the freezing-machine possesses the greatest effi- 
ciency when the range of temperature is small, and when the final tempera- 
ture is elevated. 

If the temperatures are the same, there is no theoretical advantage in em- 
ploying a gas rather than a vapor in order to produce cold. 

The choice of the intermediate body would be determined by practical 
considerations based on the physical characteristics of the body, such as the 
greater or less facility for manipulating it, the extreme pressures required 
for the best effects, etc. 

Air offers the double advantage that it is everywhere obtainable, and that 
we can vary at will the higher pressures, independent of the temperature of 
the refrigerant. But to produce a given useful effect the apparatus must 
be of larger dimensions than that required by liquefiable vapors. 

The maximum pressure is determined by the temperature of the con- 
denser and the nature of the volatile liquid: this pressure is often very high. 

When a change of volume of a saturated vapor is made under constant 
bee ahiy the temperature remains constant. The addition or subtraction of 

eat, which produces the change of volume, is represented by an increase or 
a diminution of the quantity of liquid mixed with the vapor. 

On the other hand, when vapors, even if saturated, are no longer in cun- 
tact with their liquids, and receive an addition of heat either through com- 
pression by a mechanical force, or from some external source of heat, they 
comport themselves nearly in the same way as permanent gases, and be- 
come superheated. 

It results from this property, that refrigerating-machines using a liquefi- 
able gas will afford results differing according to the method of working, 


582 ICH-MAKING OR REFRIGERATING MACHINES. 


and depending upon the state of the gas, whether it remains constantly sat- 
urated, or is superheated during a part of the cycle of working. 

The temperature of the condenser is determined by local conditions. The 
interior will exceed by 9° to 18° the temperature of the water furnished to 
the exterior. This latter will vary from about 52° F., the temperature of 
water from considerable depth below the surface, to about 95° F., the tem- 
perature of surface-water in hot climates. The volatile liquid employed in 
the machine ought not at this temperature to have a tension above that 
which can be readily managed by the apparatus. 

On the other hand, if the tension of the gas at the minimum temperature 
is too low, it becomes necessary to give to the compression-cylinder large 
dimensions, in order that the weight of vapor compressed by a single stroke 
of the piston shall be sufficient to produce a notably useful effect. 

These two conditions, to which may be added others, such as those de- 
pending upon the greater or less facility of obtaining the liquid, upon the 
dangers incurred in its use, either from its inflammability or unhealthful- 
ness, and finally upon its action upon the metals, limit the choice to a small 
number of substances. 

The gases or vapors generally available are: sulphuric ether, sulphurous 
oxide, ammonia, methylic ether, and carbonic acid. 

The following table, derived from Regnault, shows the tensions of the 
oro of these substances at different temperatures between — 22° and + 

° . 


Pressures and Boiling-points of Liquids available for 
Use in Refrigerating-machines, 


Temp. of 


Ebullition. Tension of Vapor, in Ibs. per sq. in., above Zero. 
Sul- f : ; 

Deg. PF Sulphur ., |Methylic | Carbonic; Pictet 
Fahr. | Piuric | Dioxide, |AM™monia.| Ether, | Acid. | Fluid. 
wen A Ee ae cic OT ayo anit aed ain « 10.88): Lith ds mocohapedepiecets «lpl-m seen 
ae Blo. Diiahecasece win ello vahkes tart satya ® 13.23 gisbes 
— 22 ; : 5.56 16.95 TD Oe eciasisctacctolipapine ate P 
me $8 dy chia cn Bieeibe 7.23 21.51 13.85 sy I Toa a 2 

— 4 1.30 9.27 27.04 17,06 292.9 13.5 

5 1.70 11.76 33.67 20.84 340.1 16.2 

14 2.19 14.75 41.58 25.27 393.4 19.3 

23 2.7 18.31 50.91 80.41 453.4 22.9 

32 8.55 22.53 61.85 36.34 520.4 26.9 

41 4.45 27.48 74.55 43.13 594.8 31.2 

50 5.54 33.26 89.21 50.84 76.9 36.2 

59 6.84 39.93 105.99 59 56 766.9 41.7 

68 8.38 47.62 125.08 69.35 864.9 48.1 

GT 10.19 56.39 146.64 80.28 971.1 55.6 

86 12.31 66.37 170.83 92.41 1085.6 64.1 

95 14.%6 77.64 pA Aaa ea (RR pe oe 1207.9 73.2 

104 17.59 90.32 296.0 chalets 1338.2 82.9 





The table shows that the use of ether does not readily lead to the produc: 
tion of low temperatures, because its pressure becomes then very feeble. 

Ammonia, on the contrary, is well adapted to the production of low tem- 
peratures. 

Methylic ether yields low temperatures without attaining too great pres- 
sures at the temperature of the condenser. Sulphur dioxide readily affords 
temperatures of — 14 to — 5, while its pressure is only 8 to 4 atmospheres 
at the ordinary temperature of the condenser. These latter substances then 
lend themselves conveniently for the production of cold by means of 
mechanical force. : 

The ‘ Pictet fluid” is a mixture of 97% sulphur dioxide and 3% carbonic 
acid. At atmospheric pressure it affords a. temperature 14° lower than 
sulphur dioxide. 

Carbonic acid is as yet (1895) in use but to a limited extent, but the rela- 
tively greater compactness of compressor that it requires, and its inoffensive 


THE AMMONIA ABSORPTION-MACHINE. 983 


sharacter, are leading to its recommendation for service on shipboard, where 
economy of space is important. 

Certain ammonia plants are operated with asurplus of liquid present dur- 
ing compression, so that superheating is prevented. This practice is known 
as the ‘‘cold system ’’ of compression. 

Nothing definite is known regarding the application of methylic ether or 
of the petroleum product chymogene in practical refrigerating service. The 
inflammability of the latter and the cumbrousness of the compressor 
required are objections to its use. 

¢¢¥ee-melting Effect.°°—It is agreed that the term ‘‘ice-melting 
effect’ means the cold produced in aminsulated bath of brine, on the as- 
sumption that each 142.2 B.T.U.* represents one pound of ice, this beitig the 
latent heat of fusion of ice, or the heat required to melt a pound of ice at! 
82° to water at the same temperature. 

The performance of a machine, expressed in pounds or tons of ‘‘ ice-melt- 
ing capacity,’’ does not mean that the refrigerating-machine would make 
the same amount of actual ice, but that the cold produced is equivalent to 
the effect of the melting of ice at 32° to water of the same temperature. 

In making artificial ice the water frozen is generally about 70° F. when sub- 
mitted to the refrigerating effect of a machine; second, the ice is chilled from 
12° to 20° below its freezing-point; third, there is a dissipation of cold, from 
the exvosure of the brine tank and the manipulation of the ice-cans: there- 
fore the weight of actual ice made, multiplied by its latent heat of fusion, 
142.2 thermal units, represents only about three fourths of the cold produced 
in the brine by the refrigerating fluid per I.H.P. of the engine driving the 
compressing-pumps. Again, there is considerable fuel consumed to operate 
the brine-circulating pump, the condensing-water and feed-pumps, and to 
reboil, or purify, the condensed steam from which the ice is frozen. This 
fuel, together with that wasted in leakage and drip water, amounts to about 
one half that required to drive the main steam-engine,. Hence the pounds 
of actual ice manufactured from distilled water is just about half the equiv- 
alent of the refrigerating effect produced in the brine per indicated horse- 
power of the steam-cylinders. 

When ice is made directly from natural water by means of the ‘‘ plate 
system,” about half of the fuel, used with distilled water, is saved by avoid- 
ing the reboiling, and using steam expansively in a compound engine. 

Ether-machines, used in India, are said to have produced about 6 
Ibs. of actual ice per pound of fuel consumed. 

The ether machine is obsolete, because the density of the vapor of ether, 
at the necessary working-pressure, requires that the compressing-cylinder 
shall be about 6 times larger than for sulphur dioxide, and 17 times larger 
than for ammonia. 

Air=-machines require about 1.2 times greater capacity of compress- 
ing cylinder, and are, as a whole, more cumbersome than ether machines, 
but they remain in use on ship-board. In using air the expansion must take 
place in a cylinder doing work, instead of through a simple expansion-cock 
which is used with vapor machines, The work done in the expansion-cylin- 
der is utilized in assisting the compressor. 

Ammonia Compression-machines,.—‘‘Cold” vs, ‘Dry Systems 
of Compression.—In the ** cold’’ system or ‘*humid’’ system some of the 
ammonia entering the compression-cylinder is liquid, so that the heat. de- 
veloped in the cylinder is absorbed by the liquid and the temperature of the 
ammonia thereby confined to the boiling-point due to the condenser-pres- 
sure. No jacket is therefore required about the eylinder. 

In the ‘‘ dry ”’ or ‘‘ hot’’ system all ammonia entering the compressor is 
gaseous, and the temperature becomes by compression several hundred de- 
grees greater than the boiling-point due to the condenser-pressure, A water- 
jacket is therefore necessary to permit the cylinder to be properly lubri- 
cated, 

Relative Performance of Ammonia Compression= and 
Absorption-machines, assuming no Water to be En= 
trained with the Ammonia-gas in the Condenser. (Denton 
and Jacobus, Trans. A. 8. M. E., xiii.)—It is assumed in the calculation for 
both machines that 1 1b. of coal imparts 10,000 B.T.U. to the boiler. The 





* The latent heat of fusion of ice is 144 thermal units (Phil, Mag., 1871, 
xttasay but it is customary to use 142. (Prof. Wood, Trans, A. 8. M. E., 
xi. 834, 


984 ICE-MAKING OR REFRIGERATING MACHINES. 


condensed steam from the generator of the absorption-machine is assumed 
to be returned to the boiler at the temperature of the steam entering the 
generator, The engine of the compression-machine is assumed to exhaust 
through a feed-water heater that heats the feed-water to 212° F. The engine 
.is assumed to consume 2614 lbs. of water per hour per horse-power. The 
figures for the compression- machine include the effect of friction, which is 
taken at 15% of the net work of compression. 





























Refrigerat- Pounds of Ice-melting Effect 63 
Condenser. ing oils. “ per lb. of Coal. _ > 
cs Si i es AE 
3 D ”% | Compress. Absorption- 2 if 3 
e. ~ D Machine. machine.* o.4 3 
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59.0) 106.0 5 | 83.7 | 59.0) 39.8 | 74.6 38.3 33.9 967 
59.0] 106.0 5 | 83.7 | 130.0] 39.8 | 74.6 39.8 30.1 931 
59.0] 106.0) —22 | 16.9 9.0} 28.4 | 43.9 36.3 31.5 1000 
86.0} 170.8 6) 133.7 86.0) 25.0 | 46.9 35.4 28.6 988 
86.0) 170.8 5 | 88.7 | 1380.0} 25.0 | 46.9 36.2 29.2 966 
86.0} 170.8] —22 | 16.9 86.0] 16.5 | 30.8 33.3 26.5 1025 
86.0) 170.8] —22 | 16.9 | 1380.0} 16.5 | 30.8 34.1 27.0 1002 
104.0} 227.7 5 | 83.7 | 104.0] 19.6 | 36.8 33.4 25.1 1002 
104.0] 227.7' —22 | 16.9 | 104.0} 13.5 | 25.3 31.4 23.4 1041 


The Ammonia Absorption-machine comprises a generator 
which contains a concentrated solution of ammonia in water; this gener- 
ator is heated either directly by a fire, or indirectly by pipes leading from a 
steam-boiler. The condenser communicates with the upper part of the gen- 
erator by a tube; it is cooled externally by a current of cold water. The 
cooler or brine-tank is so constructed as to utilize the cold produced; the up- 
per part of it is in communication with the lower part of the condenser. 

An absorption-chamber is filled with a weak solution of ammonia; a tube 
puts this chamber in communication with the cooling-tank. 

The absorption-chamber communicates with the boiler by two tubes: one 
leads from the bottom of the generator to the top of the chamber, the other 
leads from the bottom of the chamber to the top of the generator. Upon 
the latter is mounted a pump, to force the liquid from the absorption-cham- 
ber, where the pressure is maintained at about one atmosphere, into the gen- 
erator, where the pressure is from 8 to 12 atmospheres. 

To work the apparatus the ammonia solution in the generator is first 
heated. This releases the gas from the solution, and the pressure rises. 
When it reaches the tension of the saturated gas at the temperature of the 
condenser there is a liquefaction of the gas, and also of a small amount of 
steam. By means of a cock the flow of the liquefied gas into the refrigerat- 
ing-coils contained in the cooler is regulated. It is here vaporized by ab- 
sorbing the heat from the substance placed there to be cooled. As fast as it 
is vaporized it is absorbed by the weak solution in the absorbing-chamber. 

Under the influence of the heat in the boiler the solution is unequally sats 
urated, the stronger solution being uppermost. 

The weaker portion is conveyed by the pipe entering the top of the absorb- 
ing-chamber, the flow being regulated by a cock, while the pump sends ay 
equal quantity of strong solution from the chamber back to the boiler. 








* 5% of water entrained in the ammonia will lower the economy of theab 
gorption-machine about 15% to 20% below the figures given in the table, 


SULPHUR-DIOXIDE MACHINES. 985 


The working of the apparatus depends upon the adjustment and regula- 
tion of the flow of the gas and liquid; by these means the pressure is varied, 
and consequently the temperature in the cooler may be controlled. 

The working is similar to that of compression-machines. The absorption- 
chamber fills the office of aspirator, and the generator plays the part of 
compressor. 

The mechanical force producing exhaustion is here replaced by the affinity 
of water for ammonia gas; and the mechanical force required for compres- 
oe is replaced by the heat which severs this affinity and sets the gas at 

iberty. 

(For discussion of the efficiency of the absorption system, see Ledoux’s 
work; paper by Prof. Linde, and discussion on the same by Prof. Jacobus, 
Trans. A. S. M. E., xiv. 1416, 1436; and papers by Denton and Jaccbus, 
Trans. A. S. M. E. x. 792; xiii. 507. 

Sulphur-Dioxide Machines.—Results of theoretical calculations 
are given in a table by Ledoux showing an-ice-melting capacity per 
hour per horse-power ranging from 134 to 63 lIbs., and per pound of coa) 
ranging from 44.7 to 21.1 lbs., as the temperature correspending to the 
pressure of the vapor in the condenser rises from 59° to 104° F. The theo- 
retical results do not represent the actual. It is necessary to take into ac- 
count the loss occasioned by the pipes, the waste spaces in the cylinder, loss 
of time in opening of the valves, the leakage around the piston and valves, 
the reheating by the external air, and finally, when the ice is being made, 
the quantity of the ice melted in removing the blocks from their moulds. 
‘Manufacturers estimate that practically the sulphur-dioxide apparatus using 
water at 55° or 60° F. produces 56 lbs. of ice, or about 10,000 heat-units, per 
hour per horse-power, measured on the driving-shaft, which is about 55% of 
the theorefical useful effect. In the commercial manufacture of ice about 
7 lbs. are produced per pound of coal. This includes the fuel used for re- 
boiling the water, which, together with that wasted by the pumps and lost 
py radiation, amounts to a considerable portion of that used by the engine. 

Prof, Denton says concerning Ledoux’s theoretical results: The figures 
given are higher than those obtained in practice, because the effect of 
superheating of the gas during admission to the cylinder is not considered. 
This superheating may cause an increase of work of about 25%. There are 
other losses due to superheating the gas at the brine-tank, and in the pipe 
leading from the brine-tank to the compressor, so that in actual practice a 
sulphur-dioxide machine, working under the conditions of an absolute 
‘pressure in the condenser of 56 lbs. per sq. ir. and the corresponding tem- 
perature of 77° F., will give about 22 Ibs. of ice-melting capacity per pound 
of coal, which is about 60% of the theoretical amount neglecting friction, or 
70% including friction. The following tests, selected from those made by 
Prof. Schréter on a Pictet ice-machine having a compression-cylinder 11.3 
in. bore and 24.4 in. stroke, show the relation between the theoretical and 
actual ice-melting capacity. 


Temp. in degrees Fahr. 
corresponding to 
pressure of vapor. 


Ice-melting capacity per pound of coal, 
assuming 3 lbs. per hour per H.P. 


pty: of Per cent loss due to 
est. ‘ Theoretical cylinder super- 
Condenser.| Suction. friction Actual. heating, or differ- 
included.* ence between 
cols. 4 and 5. 

11 97.3 28.5 41.3 3a.1 19.9 

12 76.2 14.4 31.2 24.1 22.8 

13 75.2 —2.5 23.0 55 23.9 

14 80.6 —15.9 16.6 10.1 39.2 


The Refrigerating Coils of a Pictet ice-machine described by 
Ledoux had 79 sq. ft. of surface for each 100,000 theoretic negative heat-units 
produced per hour. The temperature corresponding to the pressure of the 
dioxide in the coils is 10.4° F., and that of the bath (calcium chloride solu- 
tion) in which they were immersed is 19 4°. 





* Friction taken at figure observed in the test, which ranged from 23% to 
26% of the work of the steam-cylinder. 


ICE-MAKING OR REFRIGERATING MACHINES. 


986 





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AMMONIA COMPRESSION-MACHINES. 











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AUNSSHUY ALN IOSAY ‘Sa 19° OL HOOD WIAWIG V HOAOUHL GHINVdX@Y VINONWY dO ‘aT [90Bl° HO “La “AO | do LOMUY ONILVUROIUETY 


(xnoaw]) *soinjesoduoeg, WSUIPUOD SNOTABA 7B SOUTWIVUI-UOISsoIduI0D BVIUOTIULY Jo AWMIOMODm  _ 


988 1ch-MAKING OR REFRIGERATING MACHINES, 


The following is a comparison of the theoretical ice-melting capacity of an 
ammonia compression machine with that obtained in some of Prof. 
Schriter’s tests on a Linde machine having a compression-cylinder 9 9-in. 
bore and 16.5 in. stroke, and also in tests by Prof. Denton on a machine 
having two single-acting compression cylinders 12 in. < 30 in.: 


Temp. in Degrees F. Ice-melting Capacity per lb. of Coal, 





Corresponding to assuming 3 lbs per hour per 
No Pressure of Vapor. Horse-power. 
of ' 
Test. Theoretical, of beh ee to 
Condenser.| Suction. | Friction * in- | Actual. Cylinder 

cluded. Superheating. 

8/1 72.3 26.6 50.4 40.6 19.4 

232 70.5 14.3 37.6 30.0 20.2 

S13 69.2 0.5 29.4 22.0 "25.2 

ala 68.5 —11.8 22.8 16.1 29.4 

8 (24 84.2 15.0 27.4 24.2 11.7 

e < 26 82.7 — 3.2 21.6 17.5 19.0 

& (25 84.6 —10.8 18.8 14.5 22.9 





Refriverating Machines using Vapor of Water. (Ledoux.) 
—In these machines, sometimes called vacuum macbines, water, at ordt- 
nary temperatures, is injected into, or placed in connection with, a chambeg 
in which a strong vacuum is maintained. A portion of the water vaporizes, 
the heat to cause the vaporization being supplied from the water not vapor- 
ized, so that the latter is chilled or frozen to ice. If brine is used instead of 
pure water, its temperature may be reduced below the freezing-point of 
water. The water vapor is coinpressed from, say, a pressure of one tenth 
of a pound per square inch to one and one half pounds, and discharged into 
acondenser. It is then condensed and removed by means of an ordinary 
air-pump. The principle of action of such a machine is the same as thai of 
volatile-vapor machines. 

A theoretical calculation for ice-making, assuming a lower temperature 
of 32° F., a pressure in the condenser of 144 lbs. per square inch, and a coal 
consumption of 3 lbs. per I.H.P. per hour, gives an ice-melting effect of 34.5 
lbs. per pound of coal, neglecting friction. Ammonia for ice-making condi- 
tions gives 40.9 lbs. The volume of the compressing cylinder is about 150 
times the theoretical volume for an ammonia machine for these conditions. 

Relative Efficiency of a Refrigerating Machine.—tThe effi- 
ciency of a refrigerating machine is sometimes expressed as the quotient cf 
the quantity of heat received by the ammonia from the brine, that is, the 
quantity of useful work done, divided by the heat equivalent of the mechan- 
ical work done inthe compressor. Thus in column 1 of the table of perform- 
ance of the 75-ton’ machine (page 998) the heat given by the brine to the 
ammonia per minute is 14,776 B.T.U. The horse-power of the ammonia cylin- 
‘der is 65.7, and its heat equivalent = 65.7 < 33,000 +778 = 2786 B.T.U. Then 
14.776 -:- 2786 = 5.304, efficiency. The apparent paradox that the efficiency 
is greater than unity, which is imposslble in any machine, is thus explained. 
The working fluid, as ammonia, receives heat from the brine and rejects 
heat into the condenser. (If the compressor is jacketed, a portion is rejected 
into the jacket-water.) The heat rejected into the condenser is greater than 
that received from the brine; the difference (plus or minus a small difference 
radiated to or from the atmosphere) is heat received by the ammonia from 
the compressor. The work to be done by the compressor is not the mechan- 
ical equivalent of the refrigeration of the brine, but only that necessary to 
supply the difference between the heat rejected by the ammonia into the con- 
denser and that received from the brine. If cooling water colder than the 
brine were available, the brine might transfer its heat directly into the cool- 
ing water, and there would be no need of ammonia or of a compressor; but 


* Friction taken at figures observed in the tests, which range from 14% to 
20% of the work of the steam-cylinder. 








EFFICIENCY OF REFRIGERATING-MACHINES. 989 


since such cold water is not available, the brine rejects its heat. into the 
colder ammonia, and then the compressor is required to heat the ammonia 
to such a temperature that it may reject heat into the cooling water. 

The efficiency of a refrigerating plant referred to the amount of fuel 
consumed is 


of brine or other 


x specific heat x range circulating fluid. 


of temperature 


1 Pounds circulated per hour 
Ice-melting capacity t + ce a ne neg a ae 
per pound of fuel. 142.2 X pounds of fuel used per hour. 


The ice-melting capacity is expressed as follows: 


24 X pounds 
Tons (of 2000 Ibs.) 1 X specific heat bor brine circulated per hour. 
ice-melting ca- x range of temp. 
pacity per 24 hours 142.2 « 2000 


The analogy between a heat-engine and a refrigerating-machine is as fol- 
lows: A steam-engine receives heat from the boiler, converts a part of it 
into mechanical work in the cylinder, and throws away the difference into 
the condenser. The ammonia in a compression refrigerating-machine re- 
ceives heat from the brine-tank or cold-room, receives an additional amount 
of heat from the mechanical work done in the compression-cylinder, and 
throws away the sum intothe condenser. The efficiency of the steam-engine 
= work done + heat received from boiler. The efficiency of the refrigerat~- 
ing-machine = heat received from the brine-tank or cold-room =~ heat re- 
quired to produce the work in the compression-cylinder, In the ammonia 


Cold Water 


xX 2° Brine Outlet 






Compressor 


—> 
Brine Tank 
Condenser Cold Room 
Ammonia 
Coils 
od 
° X ' 
| | 85 * Heat received 14° Tnlet 
Warm Water from compression, _ Heat received 
Heat rejected from brine 
_. DIAGRAM OF AMMONIA COMPRESSION MACHINE. 
—— 2S 
| | se a " 
== Cold 
Room 
Condenser 
<i 21S 
aed 
| I} 80° Force Pump 


DIAGRAM OF AMMONIA ABSORPTION MACHINE, 


absorption-apparatus, the ammonia receives heat from the brine-tank and 
additional heat from the boiler or generator. and rejects the sum into the 
condenser and into the cooling water cat to the absorber. The effi- 
ciency <> heat received from the brine + heat received from the boiler. 


990 ICE-MAKING OR REFRIGERATING MACHINES. 


TEST-TRIALS OF REFRIGERATING-MACHINES, 
(G. Linde, Trans. A. S. M. E., xiv. 1414.) 


The purpose of the test is to determine the ratio of consumption and pro. 
duction, so that there will have to be measured both the refrigerative effect 
and the heat (or mechanical work) consumed, also the cooling water. The 
refrigerative effect is the product of the number of heat-units (Q) abstracted 
Tc — 





i; in which Te = abso- 


lute temperature at which heat is transmitted to the cooling water, and T’ = 
absolute temperature at which heat is taken from the body to be cooled. . 

The determination of the quantity of cold wiil be possible with the proper 
exactness only when the machine is employed during the test to refrigerate 
a liquid; and if the cold be found from the quantity of liquid circulated per 
unit of time, from its range of refrigeration, and from its specific heat. 
Sufficient exactness cannot be obtained by the refrigeration of a current of 
circulating air, nor from the manufacture of a certain quantity of ice, nor 
from a calculation of the fluid circulating within the machine (for instance, 
the quantity of ammonia circulated by the compressor). Thus the refrig- 
eration of brine will generally form the basis for tests making any pretension 
to accuracy. The degree of refrigeration shou!d not be greater than neces- 
sary for allowing the range of temperature tc be measured with the neces- 
sary exactness; a range of temperature of from 5° tc v° Fahr. will suffice. 

The condense: measurements for cooling water and its temperatures will 
be possible with sufficient accuracy only with submerged condensers, 

The measurement of the quantity of brine circulated, and of the cooling 
water, is usually effected by water-meters inserted into the conduits. If the 
necessary precautions are observed, this method is admissible. For quite 
precise tests, however, the use of two accurately gauged tanks must be ad 
vised, which are alternately filled and emptied. 

To measure the temperatures of brine and cooling water at the entrance 
and exit of refrigerator and condenser respectively, the employment of 
specially constructed and frequently standardized thermometers is indis- 
pensable; no less important is the precaution of using at each spot simul- 
taneously two thermometers, and of changing the position of one such 
thermometer series from inlet to outlet (and vice versa) after the expiration 
of one half of the test, in order that possible errors may be compensated. 

It is important to determine the specific heat of the brine used in each 
instance for its corresponding temperature range, as small differences in the 
composition and the concentration may cause considerable variations. 

As regards the measurement of consumption, the programme will not have 
any special rules in cases where only the measurement of steam and cooling 
water is undertaken, as will be mainly the case for trials of absorption-ma- 
chines. For compression-machines the steam consumption depends both 
on the quality of the steam-engine and on that of the refrigerating-machine, 
while it is evidently desirable to know the consumption of the former sep- 
arately from that of the latter. Asa rule steam-engine and compressor are 
coupled directly together, thus rendering a direct measurement of the power 
absorbed by the refrigerating-machine impossible, and it will have to suffice 
to ascertain the indicated work both of steam-engine and compressor. By 
further measuring the work for the engine running empty, and by compar- 
ing the differences in power between steam-engine and compressor resulting 
for wide variations of condenser-pressures, the effective consumption of 
work Le for the refrigerating-machine can be found very closely. In gen- 
eral, it will suffice to use the indicated work found in the steam-cylinder, 
especially as from this observation the expenditure of heat can be directly 
determined. Ordinarily the use of the indicated work in the compressor- 
cylinder, for purposes of comparison, should be avoided; firstly, because 
there are usually certain accessory apparatus to be driven (agitators, etc.), 
belonging to the refrigerating-machine proper; and secondly, because the 
external friction would be excluded. 

Heat Balance.—We possess an important aid for checking the cor- 
rectness of the results found in each trial by forming the balance in each 
ease for the heat received and rejected. Cnly such tests should be re- 
garded as correct beyond doubt which show a sufficient conformity in the 
heat balance. It is true that in certain instances it may not be easy to 
account fully for the transmission of heat between the several varts of the 
machine and its environment by radiation and convection, but generally 


from the body to be cooled, and the quotient 


TEMPERATURE RANGE. 991 


{particularly for compression-machines) it will be possible to obtain for the 
heat received and rejected a balance exhibiting small discrepancies only. 

Report of Test.—Reports intended to be used for comparison with 
the figures found for other machines will therefore have toembrace at least 
the following observations : 


Refrigerator: 
Quantity of brine cirenlated per hour...........- Se Pee ebob acti 
Brine temperature at inlet to refrigerator........ stale arerd bia blawaliclglea ec clarais 
Brine temperature at outlet of refrigerator... ....... aaatiee ae sWeako pact 
Specific gravity of brine (at 64° Fahr.), .......ccccccc ces ce suis ba etseree ae 
Specie hen tio’ ripen sea at acs cees catia on eis uci ceind pakistan ee 
Heat abstracted (cold produced)..... ae tusanicges otett oe eee ee emer Qe 


Absolute pressure in the refrigerator. ....cesccosscccseccerccs cnc. ce ove 
Condenser: 


Quantity of cooling water per hour .....2. obec cccestecw se cedecnstecce 
Temperature at inlet to condenser...........ccceecceee sie sleeewin st pee F) 
Temperature at outlet of condenser.............20. s-0e- sdevsiseceeaesel 
RiGee eDSUreCreds acs g2 ga) tts a-ha. Sdeie sb ct Vases} ese Paces lp ee an eeae Q1 
Absolute pressure in the condenser.. ............0e- sbaees eles Sal te nateloals 
Temperature of gases entering the condenser.... ..... dG kia: oheye cic ateatets 


ABSORPTION-MACHINE. 
Still : 
Steam consumed per hour...... 
Abs. pressure of heating steam. 


Temperature of condensed 
steam at outlet.... .......... 
Heat imparted to still....... We 


Absorber: 

Quantity of cooling water per 
HOUT, ence chet OAT eer a 

Temperature at inlet ...... Noes 
Temperature at outlet......... 
Heat removed................ 

PP for Ammonia Liquor: 
Indicated work of steam-engine 
Steam-consumption for pump.. 


COMPRESSTON-MACHINE. 
Compressor : 
Indicated work.......... «... Lt 
Temperature of gases at inlet.. 
Temperature of gases at exit.. 
Steam-engine : 
Feed-water per hour........... 
Temperature of feed-water.... 
Absolute steam-pressure before 
steam-enpine:.........-..... 
Indicated work of apeain engine 
é 
Condensing water per hour.... 


Temperature of da........ ...+6 
Total sum of losses by radiation 
and convection... ...... + Qs 


Thermal equivalent for work of Heat Balance: 


UMD. cine loath heey ALp e+ ALc = + Qs. 
Total sum of losses by radiation @ mi vs é 
and convection.......... + Q3 


Heat Balance: 
Qe + We = Q1+ V2 + Qs. 


For the calculation of efficiency and for comparison of various tests, the 
actual efficiencies must be compared with the theoretical maximum of effi- 


ciency mex, .— 


AT, Te — T 

Temperature Range, — As temperatures (JT and Tc) at which the 
heat is abstracted in the refrigerator and imparted to the condenser, it is cor. 
rect to select the temperature of the brine leaving the refrigerator and that 
of the cooling water leaving the condenser, because it is in principle impos. 
sible to keep the refrigerator pressure higher than would correspond to the 
lowest brine temperature, or to reduce the condenser pressure below that 
corresponding to the outlet temperature of the cooling water. 

Prof. Linde shows that the maximum theoretical efficiency of a com- 
pression-machine may be expressed by the formula 


os 2 ll 
AL” Te-T’ 
in which 2 = quantity of heat abstracted (cold produced); 
AL = thermal equivalent of the mechanical work expended; 
I = the mechanical work, and A = 1 + 778; 


T = absolute temperature of heat abstraction (refrigerator); 
To= a * ‘« « rejection (condenser). 


If u = ratio between the heat equivalent of the mechanical work AL, and 
the quantity of heat Q which must be imparted to the motor to produce 
the work L, then 


corresponding to the temperature range. 


992 ICE-MAKING OR REFRIGERATING MACHINES, 


AL Q <TTe-T: 
@ u, and Oita 
It follows that the expenditure of heat Q’ necessary for the production of 
the quantity of cold Q in a compression-machine will be the smaller, the 
smaller the difference of temperature Te — T. : 
Metering the Ammonia.—for a complete test of an ammonia re- 
frigerating-machiue it is advisable to measure the quantity of ammonia cir- 
culated, as was done in the test of the 75-ton machine described by Prof. 
Denton. (Trans. A. S. M. E., xii. 326.) 


PROPERTIES OF SULPHUR DIOXIDE AND 
AMWEONIA GAS. 
Ledoux’s Table for Saturated Sulphur-dioxide Gas. 
Heat-units expressed in B.T.U. per pound of sulphur dioxide. 





‘ hed ‘ a) 
wat de a4 penioe epee 2, ([s2 
FE. lEdsslecs (Sea | 28 (Exe | ae [e285 Ss 
Sao [eter eee a8 | Ben lee oe] oe lose oalce ae 
SB ewel[Saoy (Se <a ol Ss |(SHSd| sme |Seagsslhe er 
cep |s8al sq |oxgg vaiyor, 7 odtes EY m ES 
S25 Soralgos |noo | 52 leeat) ES [Soak fae 
Beso [BES Sor [ook | 25 |eos | 89 [sos orm 
pom JOS&a low D mate S dea ote gies DRO 
es < cl an 4 q a S (am) 





| | | | — | —_ —__—— 


Deg. F.| Lbs. | B.T.U.|B.T.U. | B.T.U. | B.T.U.| B.T.U.| Cu. ft. Lbs. 
—22 5.56 | 157.43 |-19.56 | 176.99 | 18.59 | 163.89 | 13.17 076 








—13 7.23 | 158.64 |—16.30 | 174.95 | 13.83 | 161.12 | 10.27 .097 
—4 9.27 |} 159.84 |—13.05 72.89 | 14.05 | 158.84 8.12 123 
5 11.76 1 161.03 |— 9.79 | 170.82 | 14.26 | 156.56 6.50 153 
14 14.74 | 162.20 |— 6.53 |] 168.73 | 14.46 | 154.27 5.25 190 
23 18.31 | 163.36 |— 3.27 | 166.63 | 14.66 | 151.97 4.29 232 
32 | 22.53 | 164.51 0.00 | 164.51 | 14.84 | 149.68 3.54 282 
41 27.48 | 165.65 3.27 | 162.38 } 15.01 | 147.37 2.93 .340 
50 | 83.25 | 166.7 6.55 | 160.23 } 15.17 | 145.06 2.45 407 
59 | 39.93 | 167.90 9.83 | 158.07 | 15.32 | 142.75 2.07 483 
68 | 47.61 | 168.99 13.11 | 155.89 | 15.46 | 140.43 4 tee .570 
77 | 56.89 | 170.09 16.39 | 153.7 15.59 | 138.11 1.49 .669 
86 | 66.36 | 171.17 19.69 | 151.49 | 15.71 | 135.78 1527 780 
9, 1 


Density of Liquid Ammonia, (D’Andreff, Trans. A. S. M. E., 
x. 641.) 


At temperature C...... -10 —5 0 5 10 15 20 
ef ¥ F...... +14 23 82 41 50 59 68 
Densiby re ssi.ses eens <8 .6492 .6429 .6364 .6298  .6230 .6160  .6089 


These may be expressed very nearly by 


6 = 0.6364 — 0.0014¢° Centigrade; 
6 = 0.6502 — 0.000777 7° Fahr. 


Latent Heat of Evarz oration of Ammonia, (Wood, Trans. 
A. S.M. E., x. 641.) 
he = 555.5 — 0.6137’ — 0.0002197? (in B.T.U., Fahr. deg.); 
Ledoux found he = 583.838 — 0.54997 — 0.00011737%. 


For experimental values at different temperatures determined by Prof, 
Denton See Trans. A. S. M. E., xii. 356. For calculated values, see 
vol. x. 646. 

Density of Ammonia Gas.—Theoretical, 0.5894; experimental}, 
0.596. Regnault (Trans. A. S8..M. E.. x. 6383). 

Specific Heat of Liquid Ammonia. (Wood, Trans. A. 5. M. E., 
x 645 )—The specific heat is nearly constant at different temperatures, and 
about equal to that of water, or unity. From 0° to 100° F,, it is 


Inalater paper by Prof, Wood (Trang, 4.S, M. B., xii. 186) he gives a higher 
value, vies me 118186 ot 0.00088. . al iK 


PROPERTIES OF AMMONIA VAPOR. 993 


LG. A. Elleau and Wm. D. Ennis (Jour. Franklin Inst., April, 1898) give the 
results of nine determinations, made between 0° and 20° C., which range 
from 0.983 to 1.056, averaging 1.0206. Von Strombeck (Jour, Franklin Inst., 
Dec. 1890) found the specific heat between 62° and 31° C, to be 1.22876. 
Ludeking and Starr (Am. Jour, Science, iii, 45, 200) obtained 0.886. Prof. 
Wood deduced from thermodynamic equations c = 1.093 at — 34° F. or 
— 38° C., and Ledoux in like manner finds c = 1,0058 + .003658¢° C, Elleau 
and Ennis give Ledoux’s equation with anew constant derived from their 
experiments, thus c = 0.9834 + 0.003658¢° C. 


Properties of the Saturated Vapor of Ammonia. 
(Wood’s Thermodynamics.) 





{ A 
Temperature. eee: Heat of | Volume | Volume | Weight 


Vaporiza- | of Vapor |of Pee of a cu. 
Ib., 


eo. Oe eae ie GO Rep Fate oe 3 ft. of 
Degs. | Abso- |Lbs.per|Lbs.per pee ti ft Aa ft. apes, 
s. 


F. lute, F.| sq. ft. | sq. in. 


ee | ee | ms | | 











— 40 | 420.66 1540.7} 10.69 579.67 24.372 0234 .0410 
— 35 | 425.66 | 1773.6) 12.31 576.69 21.319 0236 .0468 
— 30 430.66 | 2035.8) 14.13 573.69 18.697 0237 0535 
— 25 | 4385.66 | 2829.5) 16.17 570.68 16.445 0238 0608 
— 20 | 440.66 | 2657.5) 18.45 567.67 14.507 .0240 .0689 
— 15 | 445.66 | 3022.5) 20.99 564.64 12.834 », 0242 0779 
— 10 | 450.66 | 3428.0} 23.80 561.61 11.384 0243 087 
— 5 | 455.66 | 3877.2) 26.93 558.56 10.125 0244 .0988 
0 } 460.66 | 4373.5) 30.37 555.50 9.027 0246 1108 
+ 5] 465.66 | 4920.5) 34.17 552.43 8.069 0247 1239 
+ 10 | 470.66 | 5522.2) 38.34 549.35 7.229 .0249 1383 
+ 15 | 475.66 | 6182.4) 42.93 546.26 6.492 -0250 1544 
+ 20 | 480.66 | 6905.3} 47.95 543.15 5.842 0252 1712 
+ 25 | 485.66 | 7695.2) 53.43 540.03 5.269 0258 1898 
30 | 490.66 | 8556.6) 59.41 536.92 4.763 0254 .2100 
85 | 495.66 {| 9498.9) 65.93 533.78 4.313 0256 2319 
+ 40 | 500.66 ; 10512 73.00 530.63 3.914 0257 +2555 
+ 45 | 505.66 | 11616 80.66 527.47 3.559 0259 . 2809 
50 | 510.66 | 12811 88.96 524.30 8.242 0261 . 38085 
-+ 55 | 515.66 | 14102 97.93 521.12 2.958 .0263 | ' .3381 
+ 60 | 520.66 | 15494 | 107.60 517.93 2.704 0265 3698 
+ 65 | 525.66 | 16993 | 118.03 514.73 2.476 -0266 - 4039 
+ 70 | 530.66 | 18605 | 129.21 511.52 2.201 -0268 4403 
+ 75 | 535.66 | 20336 | 141.25 508.29 2.087 .0270 4793 
+ 80 | 540.66 | 22192 | 154.11 505.05. 1.920 0272 -5208 
+ 85 | 545.66 | 24178 | 167.86 501.81 1.770 0273 5650 
+ 90 | 550.66 | 26300 | 182.8 498.11 1.682 -0274 6128 
+ 95 | 555.66 | 28565 | 198.37 495.29 1.510 027 6623 
+100 | 560.66 } 30986 | 215.14 492.01 1.398 0279 7153 
+ 105 | 565.66 | 383550 |} 282.98 488 72 1.296 0281 7716 
+110 | 570.66 | 36284 | 251.97 485.42 1.208 0283 8312 
+115 | 575.66 | 39188. | 272.14 482.41 1.119 0285 8937 
+ 120 | 580.66 | 42267 | 298.49 478.7 1.045 0287 9569 
+125 | 585.66 ; 45528 | 316.16 475.45 0.970 0289 1.0309 
-+ i650 | 590.66 | 48978 | 340.42 472.11 0.905 0291 1.1049 
+135 | 595.66 | 52626 | 365.16 468.75 0.845 0293 1.1834 
+ 140 | €00.66 | 56483 | 392.22 465.39 0.791 0295 1.2642 
+ 145 | 605.66 | 60550 | 420.49 462.01 0.741 0297 1.3495 
-+ 150 | 610.66 | 64833 | 450.20 458.62 0.695 0299 1.4388 
+ 155 | 615.66 | 69341 | 481.54 455 .22 0.652 . 0302 1.5337 
-+ 160 | 620.66 | 74086 | 514.40 451.81 0.613 0304 1.6343 
+ 165 | 625.66 | 79071 | 549.04 448.39 0.577 0306 1.7333 


Specific Heat of Ammonia Vapor at the Saturation 
Point. (Wood, Trans. A.S. M.8E., x. 644.)—For the range of temperatures 
ordinarily used in engineeering practice, the specific heat of saturated am- 
monia is negative, and the saturated vapor will condense with adiabatic ex- 
pansion, and the liquid will evaporate with the compression of the vapor, 
and when.all is vaporized will superheat. ‘ 

Regnault (Rel. des. Exp., ii. 162) gives for specific heat of ammonia-gag 
0.50836. (Wood, Trans. A.S. M. E,, xii. 133.) 


994 ICE-MAKING OR REFRIGERATING MACHINES. 


Properties of Brine uscd to absorb Refrigerating Effect 
of Ammonia, (J. E. Denton, Trans, A. 8. M. E., x. 799.)—A solution of 
Liverpool salt in well-water having a spevific gravity of 1.17, or a weight 
per eubie foot of 73 lbs,, will not sensibly thicken or congeal at 0° Fahren- 

eit, 

The mean specific heat between 39° and 16° Fahr. was found by Denton to 
be 0.805. Brine of the same specific zravity has a specific heat of 0.805 at 
65° Fahr., according to Naumann. 

Naumann’s valuesare as follows (Lehr- und Handbuch der Thermochemie, 
1882): 

Specific heat.... .791 .805* .863 .895 .931 .962 .978 
Specific gravity. 1.187 1.170- 1.103 1.072 1.044 1.023 1.012 
* Interpolated. 

Chloride-of-calcium solution has been used instead of brine. Ac. 
cording to Naumann, a solution of 1.0255 sp. gr. has a specific heat of .957. 
A solution of 1.163 sp. gr. in the test reported in Hng’g, July 22, 1887, gave a 
specific heat of .827. 


ACTUAL PERFORMANCES OF ICE-MAKING 
MACHINES. 


The table given on page 996 is abridged from Denton, Jacobus, and Riesen- 
berger’s translation of Ledoux on Ice-making Machines. The following 
shows the class and size of the machines tested, referred to by letters in the 
table, with the names of the authorities: 


Dimensions. of Compres- 
sion-cylinder in inches. 








Class of Machines. Authority. 
Bore. Stroke. 
A. Ammonia cold-compression.. Schroter. 9.9 16.5 
B. Pictet fluid dry-compression. ee 11.3 24.4 
C. Bell-Coleman air ............ - es tps 28.0 23.8 
: enwic 
I). Closed cycle air...........0.. i Jaeobua! 10. 18.0 
E. Ammonia dry-compression.. Denton. 12.0 30.0 
F. Ammonia absorption ....... es sloki's SPE Se eee be mais aie 


Performance of a %5=ton Ammonia Compression« 
machine. (J. E. Denton, Trans. A.8. M. E., xii, 326,).—The machine had 
two single-acting compression cylinders 12” x 30/’, and one Corliss steam- 
cylinder, double-acting, 18’’ x 36". It was rated by the manufacturers as a 
50-ton machine, but it showed 7% tons of ice-refrigerating effect per 24 hours 
during the test. 

The most probable figures of performance in eight trials are as follows: 











wm GH te 8 ty Litto 8, mth A! t 

Ammonia Brine A neat CoBe 18°85 [8°s | 8 

<q | Pressures, Tempera- |O3s [Zs 4 |3,; to) Ue Ey 

= | Ibs. above tures, [PSR HT SaaS wets ob 

g | Atmosphere. | Degrees F. |>2, .|/554 25/9 wie |. RG og 
é See SlaoSSulokeaud o%ES| of 
S| Con- | Suc- | mniet.| Outlet. 225 218838 S282 $8iseS5| S32 
n- |S JERR SISOO a ssk asiged5) Be 

4 |densing| tion. 5 a l= 3 2 
4 151 28 36.76] 28.86 70.3 22.60 0.80 1.0 1.0 
8 161 27.5 | 386.36] 28.45 70.1 Pea a 1.09 1.0 1.0 
q 147 13.0 | 14.29) 2.29 42.0 16.27 0.83 1.70 1.66 
4 152 8.2 6.27 2.03 36.43 14.10 i tee | 1.938 1.92 
6 105 7.6 6.40} —2.22 37.20 17.00 2.00 1.91 1.88 
2 135 15.7 | 4.62 B.2r 2 2 13.20 1.25 2.59 2 57 





The principal results in four tests are given in the table on page 998. The 
fuel economy under different conditions of operation is shown in the fol- 
lowing table; 


PERFORMANCES OF ICH-MAKING MACHINES. 995 





Pounds of Ice-melting Effect with | B.T.U. per Ib. of Steam 


ul e . . 

Ms o Engines— with Engines— 

o 

uy =} 

a ae 4 Non-com- |Compound| 4 . aD 

we}? . oereeaee pound Con-| —_ Con- =I = SA 

an aS ensing. densing. densing. AS a = 8 
Cs a ae ee ee ee ee ee ‘ g (oe) 

ees Patt se al ae 62 | 3 | a3 

g2\ss Sis poedis seis... /68 |] 95 ‘I ag 

=I 2  S 1 ® 8 u ® 2,8 + © 5 o 3 

S) 2 S52 | Be Sal ork eS) ree ° oO Oo 

oO wR oe) A, 2 0 A, 2 AO a, A 














2.90 | 30 3.61 | 87.5 | 4.51 393 518 640 
150 7 | 14 1.69 | 17.5 { 2.11 | 21.5 | 2.58 240 300 366 
105 } 28 | 34.5 | 4.16 | 43 5.18 | 54 6.50 591 720 923 
105 7 | 22 2.65 | 27.5 | 3.31 | 384.5 | 4.16 76 470 591 


The non-condensing engine is assumed to require 25 lbs. of steam per 
horse-power per hour, the non-compound condensing 20 lbs., and the com- 
densing 16 Ibs., and the boiler efficiency is assumed at 8.3 lbs. of water per 
lb. coal under working conditions. The following conclusions were derived 
from the investigation : 

1. The capacity of the machine is proportional, almost entirely, to the 
weight of ammonia circulated. This weight depends on the suction- 
pressure and the displacement of the compressor-pumps. The practical 
suction-pressures range from 7 lbs. above the atmosphere, with which a 
temperature of 0° F. can be produced, to 28 lbs. above the atmosphere, with 
which the temperatures of refrigeration are confined to about 28° F. At the 
lower pressure only about one half as much weight of ammonia can be cir- 
culated as at the upper pressure, the proportion being about in accordance 
with the ratios of the absolute pressures, 22 and 42 lbs. respectively. For each 
cubic foot of piston-displacement per minute a capacity of about one sixth 
of a ton of ‘*‘ refrigerating effect’ per 24 hours can be produced at the lower 
pressure, and of about one third of a ton at the upper pressure. No other 
elements practically affect the capacity of a machine, provided the cooling- 
surface in the brine-tank or other space to be cooled is equal to about 
36 sq. ft. per ton of capacity at 26 lbs. back pressure. For example, a differ- 

-ence of 100% in the rate of circulation of brine, while producing a propor- 
tional difference in the range of temperature of the latter, madeno practical 
difference in capacity. 

The brine-tank was 1014 « 18 x 1084 ft., and contained 8000 lineal feet of 
1-in. pipe as cooling-surface. The condensing-tank was 12 « 10 x 10ft., and 
contained 5000 lineal feet of 1-in. pipe as cooling-surface. 

2. The economy in coal-consumption depends mainly upon both the suc- 
tion-pressures and condensing-pressures. Maximum economy, with a given 
type of engine, where water must be bought at average city prices, is 
obtained at 28 lbs. suction-pressure and about 150 lbs. condensing-pressure. 
Under these conditions, for a non-condensing steam-engine, consuming coal 

- at the rate of 3lbs. per hour per 1.H.P. of steam-cylinders, 24 lbs. of ice- 
refrigerating effect are obtained per lb. of coal consumed. For the same 
condensing-pressure, and with 7 lbs. suction-pressure, which affords tem- 
peratures of 0° F., the possible economy falls to about 14 Ibs. of *‘ refrigerat- 
ing effect”? per lb. of coal consumed. The condensing-pressure is determined 
by the amount of condensing-water supplied to liquefy the ammonia in the 
condenser. If thelatter is about 1 gallon per minute per ton of refrigerating 
effect per 24 hours, a condensing-pressure of 150 lbs. results, if the initial tem- 
perature of the water is about 56°F. Twenty-five per cent less water causes 
the condensing-pressure to increase to 190 lbs. The work of compression is 
thereby increased about 20%, and the resulting ‘‘economy”’ is reduced to 
about 18 lbs. of ‘‘ ice effect’? per lb. of coal at 28 lbs. suction-pressure and 
11.5 at 7lbs. Tf, on the other hand, the supply of water is made 3 gallons 
per minute, the condensing-pressure may be confined to about 105 lbs. The 
work of compressionds thereby reduced about 25%,and a proportional increase 
of economy results. Minor alterations of economy depend on the initial 
temperature of the condensing-water and variations of latent heat, but these 
are confined within about 5% of the gross result, the main element of control 
being the work of compression, as affected by the back pressure and con- 
densing-pressure, or both. If the steam-engine supplying the motive power 
may use a condenser t¢ secure a vacuum, an increase of economy of 252% is 
available over the above figures, making the lbs. of ‘ice effect”’ per lb. of 








& 


996 ICE-MAKING OR REFRIGERATING MACHINES. 


coal for 150 lbs. condensing-pressure and 28 lbs. suction-pressure 30.0, and 
for 7 lbs. suction-pressure, 17.5. It is, however, impracticable to usé a con-~ 
denser in cities where water is bought. The latter must be practically 
free of cost to be available for this purpose. In this case it may be assumed 
that water will also be available for condensing the ammonia to obtain as 
low a condensing-pressure as about 100 lbs., and the economy of the refrig- 
erating-machine becomes, for 28 lbs. back-pressure, 43.0 lbs. of ‘ice effect ” 
per lb. of coal, or for 7 lbs. back-pressure, 27.5 lbs. of ice effect per Ib. 
of coal. If a compound condensing-engine can be used with a steam-con- 
sumption per hour per horse-power of 16 lbs. of water, the economy of the 
refrigerating-machine may be 25% higher than the figures last named, mak- 
ing for 28 lbs. back pressure a refrigerating effect of 54.0 lbs. per lb. of coal, | 
and for 7 lbs. back pressure a refrigerating effect of 34.0 lbs. per:lb. of coal. 


Actual Performance of Ice-making Machines, 
ke 



































+ fy a ‘ oo 
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Sls /2lslele} |ale| S/eelss| sess sles] a2 
Slelcgisi/siales/3i1e)e2ie3 BS) 6 33 $525 ay 
Shiels Sito SiS l2 1/5/3516 len ohl oases sia $2} oa 
BA NO) BbOul @ hSheOrl Sebo lane Sage mia 
(AS eeulil oo) (0m ue 27 43} 37/44.9)17.9)14.4126.2/40.63} 380.8 |19.1) 54.8 
ee alelo Lindos G 14 28) 23/45.1/18.0)16.7/19.5;380.01] 383.5 |20.2] 53.4 
lee |, 128) 380) | 69 1 14 9/45.1]16 8/16.0)18.3/22.03] 87.1 125 2) 50.3 
se) 4 | 126) 22 | 68 |—12 O}— 5/44.8)15.5)19.5) 9.0)16.14) 42.9 29.1) 44.7 
oe On| 200) 42] 95 14 28} 23/45.0/24.1)10.5}16.5/19.07) 86.0 |28.5) 77.0 
se) 6 | 186° 60 2 30 44 7/45.2/17.9}10.7/29.8/46.29] 28.5 {19.9] 56.8 
Sal lodiedomn Gl 18 28} 23/45.1]/18.0/12.1/21.6/338.238] 381.3 [21 9} 56.4 
ss) 8 | 126, 24 | 68 |— 9 O|— 6/44.7/15.6)18.0) 9 9117.55) 41.1 |28.3) 46.1 
‘s} 9 | 117) 41 | 64 13 28] 23)/45.0/16.4/138.5/20.0/338.77| 383 1 122.9) 50.6' 
**1 10 | 130) 60 | 70 31 43} 37|81.7/12.0)14.8]19.5/45.01) 85.2 |23.8) 52.0 
B| 11 57) 21 | 77 28 43 757 0/21 .5/22.9/25.6/83.07} 89.9 |22.2)| 24.1 
aon kee 56] 15 | 7 14 28] 23/56.8)/20.6)22.9)17.9)24.11) 41.3 |24.0) 238.1 
col lS. 55| 10 | 75 |— 2 14 9/57 .1|18.5)24.0/11.6]17.47| 42.2 |25.2] 20.4 
“) 14 60) 7 / 81 |—16 O}— 6/57.6)/15.7/25.7| 5.7|/10.14) 54.5 1|38.5) 16.8 
a8 t53 91} 15 \104 14 28} 23/59 3/27.2)16.9)15.7/16.05) 36.2 |238.1) 31.5 
CO Hea (33 61] 22 | 81 31 44} 37/57.3/21 6)14.0/28.1/86.19] 338.4 122.5) 26.8 
3a bee 59} 16 | 80 16 28] 23/57.5/20.5)12.8)19.3/26.24) 384.6 |25.0} 25.6 
“) 18 59} 7} 79 |—16 0|— 6/57.8/15.9)21.1) 6.8]11.93 “.5 183.4] 18.0 
SUNS Ee) 54] 22 | 75 31 43 7/85 .3)12.4/22.3)17.0/88.04] 39.5 |22.6) 22.6 
st) 20 89) 16 |103 16 28) 23/42.9/19.9}14 7/11.9]16.68) 37.7 1|27.0| 32.7 
ST 62) 6 | 82 |—17 0|— 5)34.8} 9.9)24.3] 3.5] 9.86) 54.2 189.5) 17.7 
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D]} 23 | 175] 54 | 81*;/—40*)._..). 93 .4/38.1/32.1]} 4.9} 3.0 80. 63. | 89.2 
H| 24 | 166} 43 | 84 15 87| 28/58 1185.0)22.7/73.9/24.16] 32.8 111.7) 65.9 
‘*) 25 | 167] 23 | 85 |—11 6 2/57.7/72.6)18.6/87.9)14.52] 37.4 |22.7| 57.6 
‘| 26 | 162) 28 | 838 |— 3 14 2/57.9)73.6)19.3/46.5|17.55) 34.9 |18.6) 59.9 
‘+! Q7 | 176] 42 | 88 14 36; 28/58.9/88.6)19.7/74.4/28.31} 30.5 |13.5) 70.5 
F} 28 | 152’ 40 | 79 13 en | 2 2s a0) veteran 42.2/20.1 7.8 Sia:|2 4a 








* Temperature of air at entrance and exit of expansion-cylinder. 

+ On a basis of 3 lbs. of coal per hour per H.P. of steam-cylinder of com- 
pression-machine and an evaporation of 11.1 lbs. of water per pound of 
combustible from and at 212° F’. in the absorption-machine. 

+ Per cent of theoretical with no friction. 

§ Loss due to heating during aspiration of gas in the compression-cylinder 
and to radiation and superheating at brine-tank. : 

| Actual, including resistance due to inlet and exit valves. 


PERFORMANCES OF ICE-MAKING MACHINES. 997 


Iu class A, a German machine, the ice-melting capacity ranges from 46.29 
to 16.14 lbs. of ice per pound of coal, according as the suction pressure 
varies from about 45 to 8 lbs. above the atmosphere, this pressnre being: the 
condition which mainly controls the economy of compression-machines. - 
These results are equivalent to realizing from 72% to 57% of theoretically per- 
fect performances. The higher per cents appear to occur with the higher 
suction-pressures, indicating a greater loss from cylinder-heating (a phe- 
nomenon the reverse of cylinder condensation in steam-engines), as the 
range of the temperature of the gas in the compression-cylinder is 
greater. 

In BE, an American compression-machine, operating on the “ dry system,” 
the percentage of theoretical effect realized ranges from 69.5% to 62.6%. 
The friction losses are higher for the American machine. The latter’s higher 
efficiency may be attributed, therefore, to more perfect displacement. 

The largest ‘‘ ice-melting capacity’? in the American machine is 24.16 lbs. 
This corresponds to the highest suction-pressures used in American practice 
for such refrigeration as is required in beer-storage cellars using the direct- 
expansion system. The conditions most nearly corresponding to American 
brewery practice in the German tests are those in line 5, which give an “‘ ice- 
melting capacity ” of 19.07 lbs. 

For the manufacture of artificial ice, the conditions of practice are those 
of lines 3 and 4, ana lines 25 and 26. In the former the condensing pressure 
used requires more expense for cooling water than is common in American 
practice. The ice-melting capacity is therefore greater in the German ma- 
chine, being 22.03 and 16.14 lbs. against 17.55 and 14.52 for the American 
apparatus. . 

Ciass B. Sulphur Dioxide or Pictet Machines.—No records are available 
for determination of the ‘‘ice-melting capacity’ of machines using pure 
sulphur dioxide. This fluid is in use in American machines, but in Europe 
it has given way to the ‘*‘ Pictet fluid,’ a mixture of about 97% of sulphur 
dioxide and 3% of carbonic acid. The presence of the carbonic acid affords 
a temperature about 14 Fahr. degrees lower than is obtained with pure sul- 
phur dioxide at atmospheric pressure. The latent heat of this mixture has 
Pde been determined, but is assumed to be equal to that of pure sulphur 

ioxide. 

For brewery refrigerating conditions, line 17, we have 26.24 lbs. ‘‘ice- 
melting capacity,’? and for ice-making conditions, line 13, the ‘‘ ice-melt- 
ing capacity’ is 17.47 lbs. These figures are practically as economical 
as those for ammonia, the per cent of theoretical effect realized ranging 
from 65.4 to 57.8. At extremely low temperatures, —15° Fahr., lines 14 and 
18, the per cent realized is as low as 42.5. 

Cylinder-heating.—In compression-machines employing volatile 
vapors the principal cause of the difference between the theoretical and the 
practical result is the heating of the ammonia, by the warm cylinder walls, 
during its entrance into the compressor, thereby expanding it, so that to 
compress a pound of ammonia a greater number of revolutions must be 
made by the compressing-pumps than corresponds to the density of the 
ammonia-gas as it issues from the brine-tank. 

Tests of Ammonia A bsorption-machine used in storage-ware- 
houses under approaches to the New York and Brooklyn Bridge. (Hng’g, 
July 22, 1887.)—The circulated fluid consisted of a solution of chloride of cal- 
cium of 1.163 sp. gr. Its specific heat was found to be .827. 

The efficiency of the apparatus for 24 hours was found by taking the 
product of the cubic feet of brine circulating through the pipes by the aver- 
age difference in temperature in the ingoing and outgoing currents, as 
observed at frequent intervals by the specific heat of the brine (.827) and its 
weight per cubic foot (73.48). The final product, applying all allowances for 
corrections from various causes, amounted to 6,218,816 heat-units as the 
amount abstracted in 24 hours, equal to the melting of 43,565 lbs. of ice in 
the same time. 

The theoretical heating-power of the coal used in 24 hours was 27,000,000 
heat-units; hence the efficiency of the apparatus was 23%. This is equivalent 
to an ice-melting effect of 16.1 lbs. per 1b. of coal having a heating value of 
10,000 B.T.U. per lb. , 

A test of « 35-ton absorption-machine in New Haven, Conn., by Prof. 
Denton (Trans. A.S. M. E., x. 792), gave an ice-melting effect of 20.1 lbs. per 
lb. of coal on a basis of boiler economy equivalent to 3 lbs. of steam per 
1.H.P. in a good non-condensing steam-engine. The ammonia was worked 
between 188 and 23 lhs, pressure above the atmosphere, 


998 ICE-MAKING OR REFRIGERATING MACHINES, 


Performance of a 75-ton Refrigerating-machine. 


TH 
a= 
ae 
oS 
235 
RES 
ae 
aoe 
3A 
=) 
Ay. high ammonia press. above atmos..... 151 lbs. 
Av. back ammonia press. above atmos..... 28 * 
Av. temperature brine inlet.... ... ....... 36.76° 
Av. temperature brine outlet............ peel, eee. BOS 
Av. range of temperature. .... ene 0% 
Lbs. of brine circulated. per minute........ 2281 
Av. temp. condensing-water at inlet........ 44.65° 
Av. temp. condensing-water at outlet...... 83.66° 
Av. range of temperature..............5... 89.01° 
Lbs. water circulated p. min. thro’ cond’ser| 442 
Lbs. water per min. through jackets....... 25 
Range of temperature in jackets.... ...... 24.0° 
Lbs. ammonia circulated per min.... ..... #28 .17 
Probable temperature of liquid ammonia, 
entrance to brine-tank,... ....... ....... #71. 3° 


Temp. of amm. corresp. to av. back press. |-+14° 
Av. temperature of gas leaving brine-tanks| 34.2° 
Temperature of gas entering compressor..| *39° 
Av. temperature of gas leaving compressor] 213° 
Av. temp. of gas entering condenser.. 200° 


Temperature due to condensing pressure..| 84.5° 
Heat given ammonia: 
By brine, B.T.U. per miniute.... ...... 14776 
By compressor, B.T.U. per minute..... 2786 
By atmosphere, B.T.U. per minute..... 140 


Total heat rec. by amm., B.T.U. per min..| 17702 
Heat taken from ammonia: 


By condenser, B.T.U. per min.......... 17242 
By jackets, B.T.U. per min......... et 608 
By atmosphere, B.T.U. per min........ 182 
Total heat rej. by amm., B.T.U. per min. 18082 
Dif. of heat ree’d and rej., B.T.U. per min. 330 
% work of compression removed by jackets. 22% 
Av. revolutions per min..................5. 48.09 


Mean eff. press. steam-cyl., Ibs. persq.in..| 32.5 
Mean eff. press. amm.-cyl., lbs. per sq. in. 65.9 


Av. H.P. steamtoylinder ,« 234.0: ..9.2enk so 85.00 
Av. H.P. ammonia-cylinder................ 65.7 
Friction in per cent of steam. H.P.......... 23.0 
Total cooling water, gallons per'min. per 

ton per 24 CE 5 el aia ae 0.75 
Tons ice-melting capacity per 24 hours..... 74.8 
Lbs. ice- refrigerating eff. per lb. coal at 3 

Ibs\per, HPS pemmoubes: 2...... .%ceeae 24.1 
Cost coal per ton of ice-refrigerating effect 

At.H4 POL. LON Lh. MeMPRB Me pied cca ated? E $0.166 
Cost water per ton of ice-refr igerating effect 

atapleper 1000 cu. Eucmmementen.. ss... 5.25 see $0.128 
Total cost of 1 ton of ice-refrigerating eff...| $0.294 





lbs. 


Economy at Zeroa, 


Brine, and 8 


Back Pressure. 
Maximum Capacity and 


Maximum Capacity and 











54.7 
24.0 


1.185 
36.43 


i4.i 
$0.283 


$0.200 
$0.483 








13 Ibs. Back 


Economy for Zero, 
Pressure. 


Brine, 


8824 
2518 
167 
11409 


17.27 
$0.231 


$0.136 
$0.467 


Economy at 27.5 lbs. 


Maximum Capacity and 
Back Pressure. 





$0. 169 
$0.389 





Figures marked thus (*) are obtained by calculation; all other figures are 
obtained from experimental data ; temperatures are in Fahrenheit degrees, 


ARTIFICIAL ICE-MANUFACTURE. 999 


Ammonia Compression-machine, 
AcTUAL RESULTS OBTAINED AT THE Municyu TEstTs. 
(Prof. Linde, Trans, A. S. M. E., xiv. 1419.) 





NOOR LeSG ei. 28 andes ee Oey a: 1 2 3 4 5 











Temp. of refrig- | Inlet, deg. F...... 48.194 | 28.844 | 13.952|—0.279) 28.251 
erated brine ) Outlet, t deg. F...| 37.054 | 22.885 | 8.771/—5.879| 28.072 
Specific heat of brine.... .......... 0.861 0.851) 0.843) 0.837) 0.851 
Quantity of brine circ. per h., cu. ft.| 1,039.38} 908.84 623.89 |414.98 |800.93 
Cold produced, B.T.U. per hour.... | 342,909 | 263,950 | 172,776) 121,474) 220,284 
Quant, of cooling water per h., c. ft./888.76 1260.83 |187.506)139.99 | 97.76 
I.H.P. in steam-engine cylinder (Le).| 15.80 16.47 15.28 | 14.24 | 21.61 
Cold pro-) Per I.H.P. in comp.-cyl.| 24,813 | 18,471 | 12,770 | 10,140 | 11,15t 
duced per | Per I.H.P. in steam-cyl.| 21,703 | 16,026 | 11,807 | 8,530] 10,194 


Per lb. of steam........ 1,100.8 1785.6 564.9 [4385.82 1512.12 


Means for Applying the Cold. (M. C. Bannister, Liverpool 
Eng’g Soc’y, 1890.) —The most useful means for applying the cold to various 
uses is a saturated solution of brine or chloride of magnesium, which 
remains liquid at 5° Fahr. The brine is first cooled by being circulated in 
contact with the refrigerator-tubes, and then distributed through coils of 
pipes, arranged either in the substances requiring a reduction of tempera- 
ture, or in the cold stores or rooms prepared for them; the air coming in 
contact with the cold tubes is immediately chilled, and the moisture in the 
air deposited on the pipes. It then falls, making room for warmer air, and 
so circulates until the whole room is at the temperature of the brine in the 

ipes. 

: In a recent arrangement for refrigerating made by the Linde British Re- 
Srigeration Co., the cold brine is circulated through a shallow trough, in 
which revolve a number of shafts, each geared together, and driven by me- 
chanical means. On the shafts are fixed a number of wrought-iron disks, 
partly immersed in the brine, which cool them down to the brine tempera- 
ture as they revolve; over these disks a rapid circulation of air is passed by 
a fan, being cooled by contact with the plates; then it is led into the cham- 
bers requiring refrigeration, from which it is again drawn by the same fan; 
thus all moisture and impurities are removed from the chambers, and de- 
posited in the brine, producing the most perfect antiseptic atmosphere yet 
invented for cold storing; while the maximum efficiency of the brine tem- 
perature was always available, the brine being periodically concentrated by 
suitable arrangements. 

Air has also been used as the circulating medium. The ammonia-pipes 
refrigerate the air in a cooling-chamber, and large wooden conduits are used 
to convey it to and return it from the rooms to be cooled. An advantage of 
this system is that by ita room may be refrigerated more quickly than by 
brine-coils. The returning air deposits its moisture in the form of snow on 
the ammonia-pipes, which is removed by mechanical brushes. 


ARTIFICIAL ICE-MANUFACTURE. 


Under summer conditions, with condensing water at 70°, artificial ice-ma- 
chines use ammonia at about 190 lbs. above the atmosphere condenser- 
pressure, and 15 lbs. suction-pressure. 

In a compression type of machine the useful circulation of ammonia, 
allowing for the effect of cylinder-heating, is about 13 lbs. per hour per in- 
dicated horse-power of the steam-cylinder. This weight of ammonia pro- 
duces about 32 lbs. of ice at 15° from water at 70°. If the ice is made from 
distilled water, as in the ‘‘can system,”’ the amount of the latter supplied 
by the boilers is about 33% greater than the weight of ice obtained. This 
exvwess represents steam escaping to the atmosphere, from the re-boiler and 
steam-condenser, to purify the distilled water, or free it from air; also, the 
loss through leaks and drips, and loss by melting of the ice in extracting it 
from thecans. The total steam consumed per horse-power is, therefore, 
about 32 X 1.33 = 43,0 lbs. About 7.0 lbs. of this covers the steam-consump- 
tion of the steam-engines driving the brine circulating-pumps, the several 


1000 ICE-MAKING OR REFRIGERATING MACHINES. 


cold-water pumps, and leakage, drips, etc. Consequently, the main steam. 
engine must consume 36 lbs. of steam per hour per I.H.P., or else live steam 
must be condensed to supply the required amount of distilled water. There 
is, therefore, nothing to be gained by using steam at high rates of expansion 
in the steam-engines, in making artificial ice from distilled water. If the 
cooling water for the ammonia-coils and steam-condenser is not too hard for 
use in the boilers, it may enter the latter at about 175° F., by restricting the 
uantity to 114 gallons per minute per ton of ice. With good coal 8% lbs. af 
eed -water may then be evaporated, on the average, per lb. of coal. 

The ice made per pound of coal will then be 32 + (43.0 +- 8.5) = 6.0 Ibs. 
This corresponds with the results of average practice. , 

If ice is manufactured by the ‘‘ plate system,’ no distilled water is used 
for freezing. Hence the water evaporated by the boilers may be reduced to 
the amount which will drive the steam-motors, and the latter may use steam 
expansively to any extent consistent with the power required to compress 
the ammonia, operate the feed and filter pumps, and the hoisting machinery. 
The latter may require about 15% of the power needed for compressing the 
ammonia. 

Yf a compound condensing steam-engine is used for driving the com- 
pressors, the steam per indicated steam horse-power, or per 32 lbs. of net 
ice, may be 14 lbs. per hour. The other motors at 50 lbs. of'steam per horse- 
power will use 7.5 lbs. per hour, making the total consumption per steam 
horse-power of the compressor 21.5 lbs. Taking the evaporation at 8 lbs., 
the feed-water temperature being limited to about 110°, the coal per horse- 
power is 2.7 Ibs. per hour. The net ice per lb. of coal is then about 32+ 2.7 = 
11.8 Ibs. The best results with ‘‘ plate-system ” plants, using a compound 
steam-engine, have thus far afforded about 1014 Ibs. of ice per Ib. of coal. 

In the “‘ plate system” the ice gradually forms, in from 8 to 10 days, to a 
thickness of about 14 inches, on the hollow plates, 10 x 14 feet in area, in 
which the cooling fluid circulates. 

In the ‘‘can system ”’ the water is frozen in blocks weighing about 300 lbs. 
each, and the freezing is completed in from 40 to 48 hours. The freezing- 
tank area occupied by the ‘“‘plate system” is, therefore, about twelve 
times, and the cubic contents about four times as much as required in the 
‘*can system.”” re 

The investment for the “plate” is about one-third greater than for the 
‘‘can’’ system. In the latter system ice is being drawn throughout the 24. 
hours, and the hoisting is done by hand tackle. Some ‘‘can”’ plants are 
equipped with pneumatic hoists and on large hoists electri¢ cranes are used 
to advantage. In the ‘plate system” the entire daily product is drawn, 
cut, and stored in a few hours, the hoisting being performed by power. 
The distribution of cost is as follows for the two systems, taking the cost 
for the ‘can ”’ or distilled-water system as 100, which represents an actual 
cost of about $1.25 per net ton: 


Hoisting and storing ice. ....2...... Je eee cee 





Engineers, firemen, and coal-passer. .......... 15.0 13.9 
Coalat/$3:50/ per gross tons: 2.20220 Poe.e ase. ok 42,2 20.0 
Water pumped directly from a natural source 
at 5 cts. per 1000 cubic feet.................6. 1.3 2.6 
Interest and depreciation at 10%... .... Sennen 246 82.7 
RE DADS cates ace Madaeiees sisisie «Westone ayere stakes slate 2.7 3.4 
—_——s 
100.00 75.4 


A compound condensing engine is assumed to be used by the ‘‘ plate sys. 
tem.” 

Nest of the New Work Hygeia Ice-making Plant.—(By 
Messrs. Hupfel, Griswold, and Mackenzie; Stevens Indicator, Jan. 1894.) 

The final results of the tests were as follows: 


Net ice made per pound of coal, in poundS..........secscececcececees Vale 
Pounds of net ice per hour per horse-power..........0..ceecccesectes 37.8 
Net ice manufactured per day (12 hours) in tonS............-2+22+ se: 97 
Av. pressure of ammonia-gas at condenser, lbs. per sq. in. ab. atmos. 135.2 
Average back pressure of amm.-gas, lbs. per sq. in. above atmos.... 15.8 
Average temperature of brine in freezing-tanks, degrees F.......... 19.7 
Total number of cans filled per week ... ........-....2. eee cee, «... 4889 


Ratio of cooling-surface of coils in brine-tank to can-surface....... . 7told 


MARINE ENGINEERING. 1001 


Ratio of brine in tanks to water in cans ...... ..........020e at dee ae LatORyS 
Ratio of circulating water at condensers to distilled water.......... 26 tol 
Pounds of water evaporated at boilers per pound of coal..... ...... 8.085 
Total horse-power developed by compressor-engines..... ........66. 444 
Percentage of ice lost in removing from Cans..........0..ce0ceee cece 2.2 
APPROXIMATE DIVISION OF STEAM IN PER CENTS OF TOTAL AMOUNT. * 

COMPRESSOMMENL INES Anse cars /sy Sale te odicie a oles ents Sate Seltie ae sie weiss ccs aaGOd 
Live steam admitted directly to condensers..........20.c0:cecccseses 19.7 
Steam for pumps, agitator, and elevator engineS,.......,..02 eecseee 7.6 
Live steam for reboiling distilled water.... ............... Be eirocncagio 6.5 
Steam for blowers furnishing draught at boilers........ eens Ad Se ae 5,6 
Sprinklers for removing ice from cans......... oie ita se crafa beh Ate: pate toad 0 | OS 


The precautions taken to insure the purity of the ice are thus described: 

The water which finally leaves the condenser is the accumulation of the 
exhausts from the various pumps and engines, together with an amount-of 
live steam injected into it directly from the boilers. This last quantity is 
used to make up any deficit in the amount of water necessary to supply the 
iwe-cans. This water on leaving the condensers is violently reboiled, and 
afterwards cooled by running through a coil surface-cooler. It then passes 
through an oil-separator, after which it runs through three charcoal-filters 
and deodorizers, placed in series and containing 28 feet of charcoal. It next 
passes into the supply-tank in which there is an electrical attachment for 
detecting salt. Nitrate-of-silver tests are also made for salt daily. From 
this tank it is fed to the ice-cans, which are carefully covered so thet the 
water cannot possibly receive any impurities, 


MARINE ENGINEERING. 


Rules for Measuring Dimensions and Obtaining Ton= 
mage of Vessels, (Record of American & Foreign Shipping. American 
Bureau of Shipping, N. Y. 1890.)—The dimensions to be measured as follows: 

I. Length. L.—From the fore side of stem to the after side of stern-post 
measured at middle line on the upper deck of all vessels, except those hav- 
ing a continuous hurricane-deck extending right fore and aft. in which the 
length is to be measured on the range of deck immediately below the hurri- 
cane-deck. 

Vessels having clipper heads, raking forward, or receding stems, or rak. 
ing stern-posts, the length to be the distance of the fore side of stem from 
aft-side of stern-post at the deep-load water-line measured at middle line, 
(The inner or propeller-post to be taken as stern-post in screw-steamers. 

II. Breadth, B.—To be measured over the widest frame at its widest part; 
in other words, the moulded breadth. 

III. Depth, D.—To be measured at the dead-flat frame and at middle line 
of vessel. It shall be the distance from the top of floor-plate to the upper 
side of upper deck-beam in all vessels except those having a continuous 
hurricane-deck, extending right fore and aft, and not intended for the 
American coasting trade, in which the depth is to be the distance from top 
of floor-plate to midway between top of hurricane deck-beam and the top 
of deck-beam of the deck immediately below hurricane-deck. 

In vessels fitted with a continuous hurricane deck, extending right fore 
and aft. and intended for the American coasting trade, the depth is to be 
the distance from top of floor-plate to top of deck-beam of deck immedi- 
ately below hurricane-deck. 

Rule for Obtaining Tonnage.—Multiply together the length, 
breadth, and depth, and their product by .75; divide the last product by 100; 


the quotient will be the tonnage. EX expxe = tonnage. 


The U.S. Custom-house Tonnage Law, May 6, 1864, provides 
that ‘‘ the register tonnage of a vessel shall be her entire internal cubic 
capacity in tons of 100 cubic feet each.’? This measurement includes all the 
space between upper decks, however many there may be. Explicit direc- 
tions for making the measurements are given in the law. F 

The Displacement of a Vessel (measured in tons of 2240 lbs.) is 
the weight of the volume of water which it displaces. For sea-water it is 
equal to the volume of the vessel beneath the water-line, in cubic feet, 
divided by 35, which figure is the number of cubic feet of sea-water at 60° 


1002 MARINE ENGINEERING, 


F. in a ton of 2840 lbs. For fresh water the divisor is 85.938. The U.S. reg- 
ister tonnage will equal the displacement when the entire internal cubig 
capacity bears to the displacement the ratio of 100 to 35. . 

he displacement or gross tonnage is sometimes approximately estimated 
as follows: Let Z denote the length in feet of the boat, B its extreme 
breadth in feet, and D the mean draught in feet; the product of these three 
dimensions will give the volume of a parallelopipedon in cubie feet. Put- 
ting V for this volume, we have V= LX BX D. 

The volume of displacement may then be expressed as a percentage of 
the volume V, known as the ‘ block coefficient.” This percentage varies for 
different classes of ships. In racing yachts with very deep keels it varies 
trom 22 to 33; in modern merchantmen from 55 to 75; for ordinary small 
boats probably 50 will give a fair estimate. The volume of displacement in 
cubic feet divided by 35 gives the displacement in tons, 

Coefficient of Fimemess.—A term used to express the relation be- 
tween the displacement of a ship and the volume of a rectangular prism or 
box whose lineal dimensions are the length, breadth, and draught of the 


ship. 
; feral Os ci ; ‘ ‘ 
Coefficient of fineness = Lupo D being the displacement in tons 


of 35 cubic feet of sea-water to the ton, the length between perpendiculars, 
B the extreme breadth of beam, and W the mean draught of water, all in 
feet. 

Coefficient of Water-limes,—An expression of the relation of the 
displacement to the volume of the prism whose section equals the midship 
section of the ship, and length equal to the length of the ship. 

5 


Coefficient of water-lines = Dx3 


S = area of immersed water section xL S°8%0P 
gives the following values: 


Coefficient Coefficient of 
of Fineness, Water-lines. 


Pinsly-shaped BAIS o0..- se dvseesens Sasentibacas . 0.55 0.63 
Wairly-shaped SHIPS. .. 2. 0060. sine -serwccccccerace 61 0.67 
Ordinary merchant steamers for speeds of 10 to 

TUREN OLS Ut Wc ccs ay es ene pee ea bene 0.65 0.72 
Cargo steamers, 9 to 10 knots.......... Meenas es 0.70 0.76 
Modern cargo steamers of large size........... 0.78 0.83 


Resistance of Ships.—tThe resistance of a ship passing through 
water may vary from a number of causes, as speed, form of body, displace. 
ment, midship dimensions, character of wetted surface, fineness of lines, 
etc. The resistance of the water is twofold: 1st. That due to the displace. 
ment of the water at the bow and its replacement at the stern, with the 
consequent formation of waves. 2d. The friction between the wetted sur- 
face of the ship and the water, known as skin resistance. A Common ap 
proximate formula for resistance of vessels is 


Resistance = speed? x 4/ displacement? xX a constant, or R= S2D3 D3 me 6 


If D = displacement in pounds, S = speed in feet per minute, R = resist- 
ance in foot-pounds per minute, R = CS?D%, The work done in overcom. 


ing the resistance through a distance equal to Sis R X S= CS8D3; ana 

if His the efficiency of the propeller and machinery combined, the indicated 
Lip. = —CS*2! 

horse-power 1L.H.P. = BE x< 33.000" 


If S = speed in knots, D = displacement in tons, and Ca constant which 
includes all the constants for form of vessel, efficiency of mechanism, etc., 
33 
ee a - ie 
The wetted surface varies as the cube root of the square of the displace- 
ment; thus, let Z be the length of edge of a cube just immersed, whose dis- 


placement is D and wetted surface W. Then D= L8 or L= yD, and 
W=5xL?=5%x( {/D)*. Thatis, W varies as D4, 





MARINE ENGINEERING. 1003 


Another approximate formula is 


area of immersed midship section x S® 
K @ 


The usefulness of these two formule depends upon the accuracy of the 
30-calied ‘‘ constants ”’ C and K, which vary with the size and form of the 
ship, and probably also with the speed. Seaton gives the following, which 
may es taken roughly as the values of C and K under the conditions ex- 
pressed: 


i oO sal 





Speed, | Value | Value 
knots. | of C. | of K. 


thips over 400 feet long, finely shaped......... ... 15 to 17} 240 620 
- 800 es “ty re or ric) cli eke We 190 500 


General Description of Ship. 








ce ie i He tlaje sisiemvoseis 13 ‘* 15} 240 650 

AN Ss i fanledeeie’ acesetld *59F83] 1-260 700 
‘ships over 300 feet long, fairly shaped..............]11 “* 13} 240 650 
ay oa aa Ady cudelaasice ts ly Spiel 260 700 
ships over 250 feet long, finaly shaped....... Gob ae 13 ‘S 15} 200 580 
fn on ve twigs Go os iibtate 8 240 660 

“5 a sty Fisy Mh abiss Ba carats Bi 9, Std 260 [00 
Ships over 250 feet long, fairly shaped........... wee [1d S13); 2280 620 
Sh re see che hh versitactak ahi dole 263 OF °S AE 5 250 680 
Ships over 200 feet long, finely shaped..........-... 11,5* 42)),, 220 600 
A oe ae Marelstnere oie oteincsii Molin eal 240 640 
Shiyvs over 200 feet long, fairly shaped .............| 9 * 11} 220 620 
Ships under 200 feet long, finely shaped.... ....... 11° ** 12) 200 550 
a +6 Pete hE a 4 eaten (lO, 6%) 14 210 580 

sa as Be PT aS is Gacnascd 9 * 10} 2380 620 

Ships under 200 feet long, fairly shaped....... ....}| 9 ** 10] 200 600 


Coefficient of Performance of Vessels.--The quotient 
/ (displacement)? x (speed in knots)§ 
tons of coal in 24 hours F 


gives a quotient of performance which represents the comparative cost of 
prepulsion in coal expended. Sixteen vessels with three-stage expansion- 
epvgines in 1890 gave an average coefficient of 14,810, the range being from 
12,150 to 16,700. 

In 1881 seventeen vessels with two-stage expansion-engines gave an aver- 
age coefficient of 11,710. In 1881 the length of the vessels tested ranged from 
260 to 820, and in 1890 from 295 to 400. The speed in knots divided by the 
square root of the length in feet in 1881 averaged 0.539; and in 1890, 0.579; 
ranging from 0.520 to 0.641: (Proc. Inst. M. E., July, 1891, p. 329.) 

Defects of the Common Formula for Resistance,— Modern 
experiments throw doubt upon the truth of the statement that the resistance 
varies as the square of the speed. (See Robt. Mansel’s letters in Hngineer- 
ing, 1891; also his paper on The Mechanical Theory of Steamship Propulsion, 
read before Section G of the Engineering Congress, Chicago, 1893.) 

Seaton says: In small steamers the chief resistance is the skin resistance 
In very fine steamers at high speeds the amount of power required seems 
excessive when compared with that of ordinary steamers at ordinary speeds. 

In torpedo-launches at certain high speeds the resistance increases at a 
lower rate than the square of the eveed. 

In ordinary sea-going and river steamers the reverse seems to be the case. 

Rankine’s Formula for total resistance of vessels of the ‘*‘ wave- 
line’? type is: 


R = ALBV (1+ 4 sin? 6+ sin‘ 6), 


in which equation @ is the mean angle of greatest pee of the stream: 
iines, A is a constant multiplier, B the mean wetted girth of the surface ex: 
posed to friction, Z the length in feet, and V the speed in knots. The power 
demanded to impel a ship is thus the product of a constant to be determined 
by experiment, ths area of the wetted surface, the cube of the speed, and the 


1004 MARINE ENGINEERING. 


quantity in the parenthesis, which is known as the “ coefficient of augmen- 
tation.” The last term of the coefficient may be neglected in‘calculating the 
resistance of ships as too small to be practically important. In applying the 
formula, the mean of the squares of the sines of the angles of maximum 
obliquity of the water-lines is to be taken for sin? @, and the rule will then 
read thus: 

To obtain the resistance of a ship of good form, in pounds, multiply the 
length in feet by the mean immersed girth and by the coefficient of augmen- 
tation, and then take the product of this ‘‘augmented surface,” as Rankine 
termed it, by the square of the speed in knots, and by the proper constant 
coefficient selected from the following: 


For clean painted vessels, iron hulls........ A = .01 
For clean coppered vessels.......... SAG ROS A = .009 to .008 
For moderately rough iron vessels......... A = .011 + 


The net, or effective, horse-power demanded will be quite closely obtained 
by multiplying the resistance calculated, as above, by the speed in knots and 
dividing by 326. The gross, or indicated, power is obtained by multiplying 
the last quantity by the reciprocal of the efficiency of the machinery and 
propeller, which usually should be about 0.6. Rankine uses as a divisor in 
shis case 200 to 260. 

The form of the vessel, even when designed by skilful and experienced 
naval architects, will often vary to such an extent as to cause the above con- 
stant coefficients to vary somewhat; and the range of variation with good 
forms is found to be from 0,8 to 1.5 the figures given. 

For well-shaped iron vessels, an approximate formula for the horse-power 


required is H.P. = 00" in which S is the ‘‘augmented surface.” The ex- 


20,0 
pression lee has been called by Rankine the coefficient of propulsion. In 


the Hudson River steamer “ Mary Powell,” according to Thurston, this 
eoefiicient was as high as 23,500. 
3 





The expression has been called the locomotive performance. (See 


Rankine’s Treatise on Shipbuilding, 1864; Thurston’s Manual of the Steam- - 
engine, part ii. p. 16; also paper by F. T. Bowles, U.S.N., Proc. U.S. Naval 
Institute, 1883.) 

Rankine’s method for calculating the resistance is said by Seaton to give 
more accurate and reliable results than those obtained by the older rules, 
but it is criticised as being difficult and inconvenient of application. 

Dr. Kirk’s Method.—This method is generally used on the Clyde. 

The general idea proposed by Dr. Kirk is to reduce all ships to so definite 
and simple a form that they may be easily compared; and the magnitude of 
pereln features of this form shall determine the suitability of the ship for 
speed, etc. 

The form consists of a middle body, which isarectangular parallelopiped, 
and fore body and after body, prisms having isosceles triangles for bases, 
as shown in Fig. 168. 





Fic. 168. 


This is called a block model, and is such that its length is equal to that of 
the ship, the depth is equal to the mean draught, the capacity equal to the 
displacement yolume, and its area of section equal to the area of im- 


MARINE ENGINEERING. 1005 


mersed midship section. The dimensions of the block model may be obtained 
as follows: 


Let AG = HB = length of fore- or after-body = F; 


GH = length of middle body 4! fH 
KL = mean draught Rod iF 
area of immersed midship section 
HK = ETE EE PIT PET Fe = B. 

s 


Volume of block = (F'-+ M)xX BX BH; 
Midship section = B X H; 
Displacement in tons = volume in cubic ft. + 35. 


AH = AG+ GH= F-+M= displacement x 35 + (B X H), 


The wetted surface of the block is nearly equal to that of the ship of the 
seme length, beam and draught; usually 2% to 5% greater. In exceedingly 
fine hollow-line ships it may be 8% greater. 


Area of bottom of block = (F'+ M) x B; 
Area of sides = 2M X H. 


\ 2 
Area of sides of ends = u/s + (=) x Gy 
Tangent of half angle of entrance = a2 = - 


From this, by a table of natural tangents, the angle of entrance may be 
obtained: 


Angle of Entrance Fore-body in 
of the Block Model. parts of length. 


Ocean-going steamers, 14 knots and upward. 18° to 15° .3 to .36 
ee . 12 to 14 knots......... 21 to 18 -26 to .3 
*$ cargo steamers, 10 to 12 knots.. 30 to 22 622 to .26 


KE. R. Mumford’s Method of Calculating Wetted Surfaces 
is given in a paper by Archibald Denny, Eng’g, Sept. 21, 1894. The following 
is his formula, which gives closely accurate results for medium draughts, 
beams, and finenesses: 


S=(LXDx19)+(LxBxOQ), 


in which S = wetted surface in square feet; 
L = Jength between perpendiculars in feet; 
D = middle draught in feet; 
B = beam in feet; 
C = block coefficient. 


The formula may also be expressed in the form S = Z(1.7D + BC). : 

In the case of twin-screw ships having projecting shaft-casings, or in the 
ease of a ship having a deep keel or bilge keels, an addition must be made 
for such projections. The formula gives results which are in general much 
more accurate than those obtained by Kirk’s method. It underestimates 
the surface when the beam, draught, or block coefficients are excessive; but 
the error is small except in the case of abnormal forms, such as stern-wheel 
steamers having very excessive beams (nearly one fourth the length), and 
also very full block coefficients. The formula gives a surface about 6% too 
small for such forms. 

To Find the Indicated Horse-power from the Wetted 
Surface. (Seaton.)—In ordinary cases the horse-power per 100 feet of 
wetted surface may be found by assuming that the rate for a speed of 10 
knots is 5, and that the quantity varies as the cube of the speed. For exam- 
ple: To find the nuniwer of I.H.P. necessary to drive a ship at a speed of 15 
knots, having a wetted skin ef block model of 16,200 square feet: 


The rate per 100 feet = (15/10)3 x 5 = 16.875. 
Then I.H.P. required = 16.875 < 162 = 2734, 


1006 MARINE ENGINEERING. 


When the ship is-exceptionally well-proportioned, the bottom quite ciean, 
and the efficiency of the machinery high, as low a rate as 4 I.H.P. per 100 
feet of wetted skin of block model may be allowed 

The gross indicated horse-power includes the power necessary to over- 
come the friction and other resistance of the engine itself and the shafting, 
and also the power lost in the propellor. In other words, I.H.P. is no meas- 
ure of the resistance of the ship, and can only be relied on as a means of 
deciding the size of engines for speed, so long as the efficiency of the engine 
and propellor is known definitely, or so long as similar engines and propellers 
are employed in ships to be compared. The former is difficult to obtain, 
and it isnearly impossible in practice to know how much of the power shown 
in the cylinders is employed usefully in overcoming the resistance of the 
ship. The following example is given to show the variation in the efficiency 
of propellers: 


Knots. 1iH.P. 


H.M.S. *‘ Amazon,’’ with a 4-bladed screw, gave,........... 12.064 with 1940 
H.M.S. ‘‘ Amazon,”’ with a 2-bladed serew, increased pitch, 

and less revolutions per Minute...........-. se sccceceecee: 12.3896 ‘* 1663 
H.M.S. ‘‘Iris,’’ with a 4-bladed secrew.......:...00--seeeseee 16.577 ‘“* %503 
H.M.S. ‘“‘Iris,’? with 2-bladed screw, increased pitch, less 

PEVOLITIONS: Per MOL. waectecteeton. fe > ces coins cts eee ee tetas es 18:58 Toot 


Relative Horse-power Required for Different Speeds of 
Vessels, (Horse-power for 10 knots = 1.)—The horse-power is taken usually 
to vary as the cube of the speed, but in different vessels and at different 
speeds it may vary from the 2.8 power to the 3.5 power, depending upor the 
lines of the vessel and upon the efficiency of the engines, the propeller, etc. 








a | | ee | | ee | | | |. | ee — | ee | a 











HP 
S2'8 | 0769] .289] .5385)/1./1.666/2.565/3.729|5.185/6.964/9.095/11 .60/14.52]17.87/21 .67 
S2°2 | 0701] .227) .524/1.|1.697/2.653/3.908)5.499}7 .464/9.841/12.67/15.97}19.80/24.19 
S$ | .0640}.216} .512/1./1.728/2.744/4.096/5.832/8. 10.65/13 .82}17.58)21.95|27. 
S31 | .0584| .205} .501/1./1.760/2.838]4 .293/6.185/8.574]11.52/15.09}19.34/24.33/30.14 
S3-2 | .0533} . 195) .490/1. |1.792}2.935)4.500}6.559}9.189)12.47/16.47/21 . 28/26. 97/33. 63 
§3°3 | 0486} .185} .479)1. |1.825/3.036/4.716/6.957/9 849/13. 49/17. 98)23.41|29.90|387.54 
S3°4 | 0444] .176} .468)1./1.859/3. 189]/4.943/7.378/10.56]14 .60/19.62/25.76|33.14/41 .96 
1.893/3.247/5.181/7 824/11 .31)15. 79/21 .42)28 .34/36.73/46.77 





S3°5 | 0405]. 167] .458/1. 


EXAMPLE IN USE OF THE TABLE.—A certain vessel makes 14 knots speed 
with 587 1.H.P. and 16 knots with 900 1.H.P. What I.H.P. will be required at 
18 knots, the rate of increase of horse-power with increase of speed remain- 


ing Se ? The first step is to find the rate of increase, thus: 147 : 16” :: 
x log 16 — x log 14 = log 900 — log 587; 
(0.204120 — 0.146128) = 2.954243 — 2.768638, 


whence x (the exponent of Sin formula H.P. «S®) = 3.2. 

From the table, for S%'? and 16 knots, the 1 H.P. is 4.5 times the I.H.P. at 
10 knots, .°. H.P. at 10 knots = 900 + 4.5 = 200. 

From the table, for S32 and 18 knots, the I.H.P. is 6.559 times the I.H.P. at 
10 knots: .°. H.P. at 18 knots = 200 *« 6.559 = 1312 HP. 

Resistance per Horse-power for Different Speeds, (One 
horse-power == 33,000 Ibs, resistance overcome through 1 ft. in 1 min.)—The 
resistances per horse-power for various speeds are as follows: For a speed of 
1 knot, or 6080 feet per hour = 10114 ft. per min., 33,000 + 10114 = 325.658 Ibs. 
per horse-power; and for any other speed 325.658 lbs. divided by the speed 
in knots; or for 


1 knot 325.66lbs. 6 knots 54.28lbs. 11 knots 29.61 lbs. 16 knots 20.35 lbs. 
2 knots 162.83 ‘°° FSG 52 oS’ 12 668 WOT Pes hpogrum Serty ig elke 
BSc) 4108.55 8a “Uaea0eaias* 618) | SS On Ob Sees’. > 18 09m 
48 81.41 ‘“ 9) Sonic 3° | 14" SOnes ONO gmAnCeee eS. 11" [ence 
Siaate 65.13 $8 10" eee oie 15 “oy Se. 88) 16 Somes 


MARINE ENGINEERING, 


100” 


Results of Trials of Steam-vessels of Various Sizes. 


(From Seaton’s Marine Engineering.) 





























Re ‘3 £ 3 : 3 
s| 8 ¢| 8 x | Oe 
Ge) fe | we | we | Hk] We 
Ms) UE) we | Ap) we | ae 
al S) fi a mi ms 
: i f = 2 S 
Length, perpendiculars..... ... 90’ 07 171 9’ 1307 0/1286" 0” 230/ 0/1327 o” 
Breadth, extreme., ..........-.: 10’ 6”) 18? 9//| 217 044) 34¢ 3/7) 29% 0/71 (35% 07 
Mean draught water............- 2161167 946/7| 8C 10" > 6" 07118776") 13% Ot 
Displacement (tons)..... BS icoe ae te 29.73) 280 370 800 | 1500 | 1900 
Area Immersed mid, section....| 24? 99 148 200 340 336 
7 g Wetted skin...... ... i ae 903 | 8793 | 3754 | 8222 | 10,075 | 15,782 
as Length, fore-body......... 45/ 0/172" 00’"| 42’ 6/1143’ 0’) 79’ 6/1129" 0” 
> 
Ba Angle of entrance. .......|12°40’| 11° 30’| 28° 50’! 18° 21’) 17° 0” | 11° 26! 
ee ee aS 0.481] 0.576) 0.608] 0.489| 0.671| 0.605 
Length xX Imm, mid area 
Bpeed (KNOtS)a. 2... sede erie caste. ts 2201 [15.8 | 10.74.) 17.20 | 10.04 | 17-8 
Indicated horse-power..... oe 460 798 fi 1490 | 503 | 4751 
[.H.P. per 100 ft. wetted skin..../50.9 | 21.04} 9.88 | 18.12} 5.00 | 30.00 
{.H.P. per 100 ft. wetted skin, re- 
duced to 10 knots.............. 48a Dee | 2 .9¢ 3.56} 4.90 | 5.32 
D2 x S83 9 |4R0 99 
Tih Riot cain aie 223 192 |172.8 | 293.7 ] 266 182 
Jmmersed mid area XS’ | 55621 445 | 495 | 683 | 690 | 399 
res hees 
an se pee RE 
ae] Bg | 2% qg| vg 35 
Seisei se | 2e) 8 |S 
ma | | ae ies ax 
ot as as ce ae 0d 6s 
Length, perpendiculars.. ....... 270’ 0/7/8300’ 0’/300" 0/370 0””|392 0/1450" 0” 
Breadth, extremes. acces sce 42/ 0! 464 04) 46% .0741412°0/"| 89 0/7) 45” 27° 
Mean draught water. ...........{18/ 10”) 18’ 2’) 18” 2/118" 11/7; 217 4/7) 23° 7/4 
Displacement (toms)............. 3057 | 8290 | 3290 | 4635 | 5767 8500 
Area Imm. mid. section.... .... 682 700 700 656 738 926 
5 Wetted Skinz .caen ee ssc. 16,008} 18,168 | 18,168 | 22,633 | 26,235 | 32,578 
aS Length, fore-body..... .»- {1017 0°'|135’ 6//}135’ 6/1123’ 0/7/118" 0/7|129" 0” 
at) 
qh Angle of entrance... ...... 18° 44’|16° 16’ |16° 16” | 16° 4” |16° 30’ | 17° 16” 
Displacement 70081 22) c1)onieeo bY 0.548) 0.848 | 0.668) 0.608-1" O°714 
Length X Imm. mid area 
Speeds (kMOts) i215 TEE ede dcets ae 14.966 | 18.578) 15.746] 13.80 |12.054 | 15.045 
Indicated horse-power........... 4015 714 | 3958 2500 | 1758 4900 
I.H.P. per 100 ft. wetted skin....} 25.08 | 42.46 | 21.78 | 11.04] 6.7 | 15.04 
I.H.P. per 100 ft. wetted skin, re- 
duced to 10 knots............. 7.49| 6.634; 5.58]; 4.20| 3.88] 4.42 
ps x S8 9 9 5) 
THRE pad vaeias Ane ee 175.8 |183.7 {218.2 292 820 |289.3 
; 3 
Immersed JUG area > 9) yee: 527.5 |581.4 [690.5 | 689 | 735 |642.5 


#4.P. 








1008 MARINE ENGINEERING. 


Results of Progressive Speed Trials in Typical Vessels. 
(Zing’g, April 15, 1892, p. 463.) 






































Oo Journ lle oeie lesa ae = - 
2 Bey oes te O's Slike ers D ,* 
é (883-| 5 | 35 | 85 | £5 | BS 
3 posh! S- |e. | oC |e. ees 
alos’ s| 25] SO] Ad | 25 [Bag 
5m 8) 55] 55/25) M5 SSR 
a el ene eR Loni Pee ys 
Length (in feet)..........-0.-6+ 185 230 265 | 300 860 | 37 525- 
Bread thse ind nee. Oso RAS on 14 27 41 | 43 60 65 63 
Draught (mean) on trial....... BY 1/7) 8738/7 116", 6”) 167 27 /238% 941254, 97 2143 
Displacement (tons)........... 103 735 2800] 3330 | 7390 | 9100 | 11550 
TEBE 10 KnOUssctes 1 ee eae 110 450 700} &00 | 1000} 1500}; 2000 
fer A EEE cai gvel 3 prelsisisipis ole 260 1100 2100) 2400 | 8000} 4000] 4600 
a TOD sate sitioeeiegesaresise | O80 MicoUU 6400} 6000 | 7500 | 9000 | 10000 
RE OO Wer ty esate alogetet ae 1130 } 8500 | 10000] 9000 | 11000 | 12500 | 14500 
Ratio of 
Speed speed3 
10 le Ratio of H.P.=| 1 1 1 1 1 1 1 
14 2.744 - ef |) Pool) 2.44 3 3 3 2°67 1-253 
18 5.832 *f = Ve01) ho-b6 tae EY Riel ee daisa |) Nid 5 
20 8. ae AT Utd et fite! 14.14) 11.25) 11 8.42 | 7.25 
Admiralty coeff. 10 knots.| 200 181 284.| 279 | 3880 | 290 | 255 
D3 <S3 i ba 232 202 259 255 347 298 804 
C =—_ Tae 147 190 181 | 217 | 295} 282) 297 
I.H.P. 20 “ | 156] 186 | 159| i98| 276 | 278] 281 


The figures for IL.H.P. are ‘‘round.’”’ The ‘‘ Medusa’s”’ figures for 20 knots 
are from trial on Stokes Bay, and show the retarding effect of shallow water. 
The figures for the other ships for 20 knots are estimated for deep water. 

More accurate methods than those above given for estimating the 
horse-power required for any proposed ship are: 1. Estimations calculated 
from the results of trials of ‘‘ similar’’ vessels driven at ‘‘ corresponding ”’ 
speeds; ‘similar’? vessels being those that have the same ratio of length to 
breadth and to draught, and the same coefficient of fineness, and ‘* corre- 
sponding ’’ speeds those which are proportional to the square roots of 
the lengths of the respective vessels. Froude found that the resistances of 
such vessels varied almost exactly as wetted surface x (speed)?. 

2. The method employed by the British Admiralty and by some Clyde 
shipbuilders, viz., ascertaining the resistance of a model of the vessel, 12 to 
20 ft. long, in a-tank, and calculating the power from the results obtained. 

Speed on Canals.—A great loss of speed occurs when a steam-vessel 
passes from open water into a more or less restricted channel. The average 
speed of vessels in the Suez Canal in 1882 was only 514 statute miles per hour. 
(Hng’g. Feb. 15, 1884, p. 139.) 

Estimated Displacement, Horse-power, etc.—The table on 
the next page, calculated by the author, will be found convenient for mak- 
{ng approximate estimates. d 

The figures in ‘th column are calculated by the formula H.P. = S3D3 = ¢, 
in which ec = 200 for vessels under 200 ft. long when C = .65, and 210 
when C = .55; c = 200 for vessels 200 to 400 ft. long when C = .75, 220 when 
C = .65, 240 when C = .55; c = 230 for vessels over 400 ft. long when C = .75, 
250 when C = .65, 260 when C = .55. 

aay figures in the 8th column are based on 5 H.P. per 100 sq. ft. of wetted 
surface. 

The diameters of screw in the 9th column are from formula D= 
3.31 4/1H.P., and in the 10th column from formula D = 2.71 4/LHLP. 


To find the diameter of screw for any other speed than 10 knots, revolu- 
tions being 100 per minute, multiply the diameter given in the table by the 
5th root of the cube of the given speed + 10. For any other revolutions per 
minute than 100, divide by the revolutions and multiply by 100. 

To find the approximate horse-power for any other speed than 10 knots, 
multiply the horse-power given in the table by the cube of the ratio of the 
given speed to 10, or by the relative figure from table on p. 1006, 





MARINE ENGINEERING, 1009 


Estimated Displacement, Horse-power, etc., of Steam-= 
vessels of Various Sizes, 























F = Sita, | Displace- | Estimated Horse- | Diam. of Screw for 10. 
au 3% =A 2 20} ment. |Wetted Surface _Power at 10 knots. knots speed and 100 
wey 4 Zs ei f LBD xX CiLd.7D+ BC)| Cale. ‘Cale. trom) _ Tvs. per minute. 
er ae}] £2, os38 35 sq. ft, from Dis-| Wetted |If Pitch =, If Pitch = 

ae i=) | oO tons, placem’t.| Surface, | Diam. 1.4 Diam, 
12 3 1.5! .55 85 48 4.3 2.4 4.4 3.6 
16 3 1.5} .55 1.13 64 532 3.2 4.6 3.8 
j 4 2 65 2.38 96 8.9 4.8 a | 4.2 
20 3 1.5) .55 1.41 80 6.6 4.0 4.7 3.9 
: 4 2 65 2.97 120 10.3 6.0 5.3 4.3 
94 3.5] 1.5) °.55 1.98 104 Wao 5.2 5 4.1 
| 4.5] 2 .65 4.01 152 12.6 (As) 5.5 4.5 
30 4 2 .55 3.77 168 M25 8.4 5.4 4.4 
j 5 2.5) .65 6.96 224 18.2 11.2 5.9 4.8 
40 4.5] 2 .55 5.66 235 15.1 11.8 Oks 4.7 
} 6 2.5| .65 11.1 326 24.9 16.3 6.3 5.2 
50 6 3 .55 14.1 420 7.8 21.0 6.4 5.4 
} 8 3.5] .65 26 558 43.9 27.9 (sa 5.8 
60 » 8.5) .55 26.4 621 42.2 31.1 ia0) Bie 
} 10 | 4 .65 44.6 798 62.9 39.9 7.6 6.2 
nO 10 | 4 .55 44 861 59.4 43.1 7.5 6.1 
: ; 127144. 5? 65 70.2 1082 85.1 54.1 8.1 6.6 
80 12 4.5) .55 67.9 1140 49.2 57.0 7.9 6.5 
; 14 5 65 104.0 1408 111 70.4 8.5 7.0 
13 5 Rs) 91.9 1408 97 70.4 8.3 6.8 
90 4 16 | 6 | .65 | 160 1854 | 147 92.7 | 9 7.3 
‘ 13 5 55 102 1565 104 78.3 8.4 6.9 
100< |15 5.5) .65 153 1910 143 Deo 8.9 7.3 
17 6 vis) 219 2295 202 ais, 9.6 7.8 
14 5.5} .55 145 2046 13 102 8.8 72 
120< |16 6 65 214 2472 179 124 9.4 a0) 
18 6.5] . 301 2946 250 147 10 8.2 
16 6 55 211 2660 169 133 9.2 7.4 
140< |18 6.5) .65 306 3185 227 159 9.8 8.0 
20) | 7 vis) 420 3766 312 188 10.5 8.5 
ile 6.5) .55 278 264 203 1638 $.6 7.8 
160< |19 tf 65 395 8880 269 194 10.1 8.3 
al (Ae 540 4560 368 228 10.8 8.8 
20 q 55 | 3896 4122 257 206 10.1 8.2 
180< |22 7.5) .65.|. 552 4869 337 243 10.6 8.7 
24 8 G5 TA1 5688 455 284 11.3 9.2 
22 a 55 484 4800 256 240 10.1 8.2 
200 |25 8 65 743 5970 373 299 10.8 8.8 
28 9 75 | 1080 4260 526 363 11.6 9.5 
28 8 55 880 7250 383 363 10.9 8.9 
250< |382 |10 65 | 1486 9450 592 47 11.9 9.7 
36 12 .75 | 23814 11850 87 593 12.8 10.5 
82 {10 55 | 1509 10380 548 519 zh Ard 9.6 
800< |36 {12 65 | 2407 13140 806 657 12.6 10.4 
40 |14 75 | 8600 17140 1175 857 13.6 iii) 
{ 38 }12 55 | 2508 14455 769 723 12.5 10.2 
250< |42 {14 65 | 3822 17885 1111 894 13.5 11.0 
(146 |16 | .%5 | 5520 21595 |1562 1080 14.4 11.8 
44 |14 55 | 3872 19200 1028 960 13.3 10.8 
400< |48 |16 65 | 5705 23360 1451 1168 14.2 11.6 
52118 75 | 8023 27840 2006 1392 15.2 12.4 
50 116 .55 | 5657 24515 1221 1226 13 11.2 
450< |54 18 65 | 812 29565 1616 1478 14.5 11.9 
58 {20 ism poptsr¢g 84875 2171 1744 15.4 12.6 
\ 52), 118 55 | 7354 29600 1454 1480 14.2 11.6 
500< |56 |20 65 10400 35200 1966 1760 15:1 12.4 
] 60 }22 75 114143 41200 2543 2060 15.9 13.0 
56 {20 .55 | 9680 86245 1747 1812 14.7 12.0 
550< |60 22 .65 1138483 é 12.7 
64 (24 .75 118103 : 13.4 
60 {22 .55 }12416 2 12.5 
600 |64 {24 665 117115 13.1 
68 26 | 175 [22781 58020 13.8 


1010 MARINE ENGINEERING. =! | | 


THE SCREW-PROPELLER, 


The ‘‘pitch’’ of a propeller is the distance which any point in a blade, 
describing a helix, will travel in the direction of the axis curing one revolus 
tion, the point being assumed to move around the axis. The pitch of a 
propeller with a uniform pitch is equal to the distance a propeller will 
advance during one revolution, provided there is no slip. In acase of this 
kind, the term ‘‘ pitch’’ is analogous to the term ‘‘pitch of the thread” of 
an ordinary single-threaded screw. 

Let P = pitch of screw in feet, R = number of revolutions per second, 
V = velocity of stream from the propeller = P x R, v = velocity of the ship 
in feet per second, V —v= slip, A = area in square feet of section of stream 
from the screw, approximately the area of a circle of the same diameter, 
A> V= volume of water projected astern from the ship in cubic feet per 
second. Taking the weight of a cubic foot of sea-water at 64 lbs., and the 
force of gravity at 82, we have from the common formula for force of accel- 


W. 
eration, viz.: = 3 == ai or # = Ae ,» when ¢ = 1 second, v, being 


the acceleration. ee 
Thrust of screwin pounds = tan (VY —v) = 2AV(V — v). 


Rankine (Rules, Tables, and Data, p. 275) gives the following: To calculate 
the thrust of a propelling instrument (jet, paddle, or screw) in pounds, 
multiply together the transverse sectional area, in square feet, of the stream 
driven astern by the propeller; the speed of the stream relatively to the ship 
in knots; the real slip, or part of that speed which is impressed on that 
stream by the propeller, also in knots; and the constant 5.66 for sea-water, 
or 5.5 for fresh water. If S =speed of the screw in knots, s = speed of ship 
in knots, A = area of the stream in square feet (of sea-water), 


Thrust in pounds = A x S(S — s) X 5.66. 


The real slip is the velocity (relative to water at rest) of the water pro- 
jected sternward; the apparent slip is the difference between the speed of 
the ship and the speed of the screw; i.e., the product of the pitch of the 
screw by the number of revolutions, 

This apparent slip is sometimes negative, due to the working of the screw 
in disturbed water which has a forward velocity, following the ship. Nega- 
tive apparent slip is an indication that the propeller is not suited to the 
ship. 

The apparent slip should generally be about 8% to 10% at full speed in well- 
formed vessels with moderately fine lines; in bluff cargo boats it rarely 
exceeds 5%. 

The effective area of a screw is the sectional area of the stream of water 
laid hold of by the propeller, and is generally, if not always, greater than 
the actual area, in a ratio which in good ordinary examples is 1.2 or there- _ 
abouts, and is sometimes as high as 1.4; a fact probably due to the stiffness 
of the water, which communicates motion laterally amongst its particles. 
(Rankine’s Shipbuilding, p. 89.) 

Prof, D. S. Jacobus, Trans. A. S. M. E., xi. 1028, found the ratio of the ef- 
erie to the actual disk area of the screws of different vessels to be as 
follows: 


Tug-boat, with ordinary true-pitch screw...............26.0% ae hE hate 1.42 
Bs ** screw having blades projecting backward............... Or 
Ferryboat “* Bergen,’’ with or- at speed of 12.09 stat. miles per hour. 1.53 
dinary true-pitch screw Ti ee 613.4 ae ah « say wleas 
Steamer ‘** Homer Ramsdell,’’ with ordinary true-pitch screw........... 1.20 


Size of Screw.—Seaton says: The size of a screw depends on so many 
things that it is very difficult to lay down any rule for guidance, and much 
must always be left to the experience of the designer, to allow for all the 
circumstances of each particular case. The following rules are given for 
ordinary cases. (Seaton and Rounthwaite’s Pocket-book): 

101333 : : : 

R100 — a)" in which S = speed in knots, 
RF = revolutions per minute, and # = percentage of apparent slip. 
112.69 


ze * 


P = pitch of propeller in feet = 


For a slip of 10%, pitch = 





THE SCREW PROPELLER, 1011 


Hole he 


D = diameter of propeller = K 7PXR\3? K being a coefficient given 


100 





/ TH. 
in the table below. If K = 20, D = 20000 / fae i 


Yotal developed area of blades = of/ a, in which C is a coefficient 


to be taken from the table. 
Another formula for pitch, given in Seaton’s Marine Engineering, is 


Gest. P. : x ; . 
=> pa? in which C = 7237 for ordinary vessels, and 660 for slow- 


speed cargo vessels with full lines, 





‘as 
Thickness of blade at root = A a 3 x k, in which d = diameter of tail 


shaft in inches, » = number of blades, b = breadth of blade in inches where 
it joins the boss, measured parallel to the shaft-axis; k = 4 for cast iron, 1.5 
for cast steel, 2 for gun-metal, 1.5 for high-class bronze. 

Thickness of blade at tip: Cast iron .04D-+- .4in.; cast steel .083D + .4in.3 
gun-metal 03D + .2in.; high-class bronze .02D-+.3 in., where D = diameter 
of propeller in feet. 


Propeller Coefficients. 














o ‘ 
@ 3, (s,e1 . : 
. . = aed 5 
Ol - Oi. w@ oy ta} 
aoe 5B (522 cS) ‘S SO 3 
Description of Vessel. |S 2=| 22 [2 eH 8 . saa 
EQ = 9 Siaa| L, s 5 Som 
Si Shem edeetiae Ss c Pie 
<q a > P 
Bluff cargo boats....... 8-10} One 4 | 37 ~-17.5) 19 -17.5) Cast iron 
Cargo, moderate lines. ..}| 10-13} ‘ A Sie — 193 al G15 SL ial sy SS 
Pass. and mail, fine lines.| 13-17} * AV} 1905-20. 5t 5/13 0} C. Teor St 
~ Seren’ SS Aiea 13-17) Twinh) |) 4) 20).5--21—-5) (14 -6-12.5) 0% 88 
se MG very fine.| 17-22) One 4 | 21 -22 | 12.5-11 |G.M. orB 
Er SSS SSS SS SO ie ole wit mmo ues) =a. LO0L5— 9 CO Lr aK S 
Naval vessels, ‘* SO 16-22\6 aoe 4 | 21 -22.5) 11.5-10.5 sedew | SE ee 
se oe be 66 16-22 1) 2 29 93.5) 8.5- 7 66 oe bb 
Torpedo-boats, **  ‘* | 20-26] One 3 25 7-6 |BrorF.s 


C. I., cast iron; G. M., gun-metal; B., bronze; S., steel; F.S., forged steel. 


LHP: 737 | 8/LELP. 
. -- 9 —— a ? 
From the formulee D == 20000 ae XR and P= R Di 


——— 


and R = 100, we obtain D = 4/400 X LHP. = 331 LHP 
LHP. =? 


6; 

If P = 1.4D and R = 100, then D = 9/145.8 X LHP. = 2.V1V LHP. 

From these two formule the figures for diameter of screw in the table on 
page 1009 have been calculated. ‘They may be used as rough approximations 
to the correct diameter of screw for any given horse-power, for a speed of 
10 knots and 100 revolutions per minute. 

For any other number of revolutions per minute multiply the figures in 
the table by 100 and divide by the given number of revolutions. For any 
other speed than 10 knots, since the I.H.P. varies approximately as the cube 
of the speed, and the diameter of the screw as the 5th root of the I.H.P., 
multiply the diameter given for 10 knots by the 5th root of the cube of one 
tenth of the given speed. Or, multiply by the following factors; 


For speed of knots: 
4 5 


/ (S + 10)8 


= .577 .660 .786 .807 .875 .939 1.059 1.116 1.170 1.224 1.275 1.32% 











7 8 oe 11 12°" Sees 15 


1012 MARINE ENGINEERING. 


Speed: 
18.180 5: 20 | QI. 22 “2B. 62404525 Vy 6 nmi Oty ee 88 


ripe bathed, 
WS + 10) 
== 1.875 1.423 1.470 1.515 1.561 1.605 1.648 1.691 1.733 1.774 1.815 1.855 


For more accurate determinations of diameter and pitch of screw, the 
formule and coefficients given by Seaton, quoted above, should be used. 

Emfciency of the Propeller.—According to Rankine, if the slip of 
the water be s, its weight W, the resistance R, and the speed of the ship v, 


Y, 
R= yea, poe 
g g 


This impelling action must. to secure maximum efficiency of propeller, be 
effected by an instrument which takes hold of the fluid without shock or 
disturbance of the surrounding mass, and, by a steady acceleration, gives it 
the required final velocity of discharge. The velocity of the propeller over- 
coming the resistance & would then be 








PECTS) Sy 48; 


and the work performed would be 


the first of the last two terms being useful, the second the minimum lost 
work; the latter being the wasted energy of the water thrown, backward. 
The efficiency is 


H=vu-+ (v+5); 


and this is the limit attainable with a perfect propelling instrument, which 
limit is approached the more nearly as the conditions above prescribed are 
the more nearly fulfilled. The efficiency of the propelling instrument is 
probably rarely much above 0.60, and never above 0.80. 

In designing the screw-propeller, as was shown by Dr. Froude, the best 
angle for the surface is that of 45° with the plane of the disk; but as all 
parts of the blade cannot be given the same angle, it should, where practi- 
cable, be so proportioned that the ‘‘ pitch-angle at the centre of effort”’ 
should be made 45°. The maximum possible efficiency is then, according 
to Froude, 77%. 

In order that the water should be taken on without shock and discharged 
with eee SEUSS backward velocity, the screw must have an axially increas- 
ing pitch. 

The true screw is by far the more usual form of propeller, in all steamers, 
Big torte: and naval. (Thurston, Manual of the Steam-engine, part ii., 
p. 176. 

The combined efficiency of screw, shaft, engine, etc., is generelly taken 
at 50%. In some cases it may reach 60% or 65%. Rankine takes the effective 
H.P. to equal the I.H.P. + 1.63. 


Pitch-ratio and Slip for Screws of Standard Form. 































: : Real Slip of F watt Real Slip of | 
Pitch-ratio. Boren’ Pitch-ratio. Se ee 
p es 1.7 ts 
“ys 1.8 21. 
1.0 16.88 1.9 22.4 
1.1 17.55 2.0 22.9 
1.2 18.2 2.1 23.5 
1.3 18.8 2.2 24.0 
is Bt z a3 
. : : 5. 
1.6 20.4 2.5 25.4 








THE PADDLE-WHEEL. 1013 


Results of Recent Researches on the efficiency of screw-propel- 
fers are summarized by S. W. Baruaby, in a paper read before section G of 
the Engineering Congress, Chicago, 1898. He states that the following gen- 
eral principles have been established: 

(a) There is a definite amount of real slip at which, and at which only, 
maximum efficiency can be obtained with a screw of any given type, and 
this amount varies with the pitch-ratio. The slip-ratio proper to a given 
ratio of pitch to diameter has beep discovered and tabulated for a screw 
of a standard type, as below (see table on page 1012): 


(6) Screws of large pitch-ratio, besides being less efficient in themselves, 
add to the resistance of the hull by an amount bearing some proportion to 
their distance from it, and to the amount of rotation left in the race. 

(c) The best pitch-ratio lies probably between 1.1 and 1.5. 

(ad) The fuller the lines of the vessel, the less the pitch-ratio should be. 

(e) Coarse-pitched screws should be placed further from the stern than 
fine-pitched ones. 

(Ff) “adele negative slip is a natural result of abnormal proportions of 
propellers. 

(g) Three blades are to be preferred for high-speed vessels, but when the 
diameter is unduly restricted, four or even more may be advantageously 
employed. 

(h) An efficient form of blade is an ellipse having a minor axis equal ta 
four tenths the major axis. 

(i) The pitch of wide-bladed screws should increase from forward to aft, 
but a uniform pitch gives satisfactory results when the blades are narrow, 
and the amount of the pitch variation should be a function of the width of 
the blade. 

(1) A considerable inclination of screw-shaft produces vibration, and with 
right-handed twin-screws turning outwards, if the shafts are inclined at 
all, it should be upwards and outwards from the propellers. 

For results of experiments with screw-propellers, see F.C. Marshall, Proc. 
Inst. M. E. 1881; R. E. Froude, Trans. Institution of Naval Architects, 1886; 
G. A. Calvert, Trans. Institution of Naval Architects 1887; and S. W. Bar- 
naby, Proc. Inst. Civil Eng’rs 1890, vol. cii. 

One of the most important results deduced from experiments on model 
screws is that they appear to have peat iga ly, equal efficiencies throughout 
a wide range both in pitch-ratio and in surface-ratio; so that great latitude 
is left to the designer in regard to the form of the propeller. Another im- 
portant feature is that, although these experiments are not a direct guide to 
the selection of the most efficient propeller for a particular ship, they sup- 
ply the means of analyzing the performances of screws fitted to vessels, and 
of thus indirectly determining what are likely to be the best dimensions of 
screw for a vessel of a class whose results are known. Thus a great ad- 
vance has been made on the old method of trial upon the ship itself, which 
was the origin of almost every conceivable erroneous view respecting the 
screw-propeller. (Proc. Inst. M. E., July, 1891.) 


THE PADDLE-WHEEL. 


Paddle-wheels with Radial Floats. (Seaton’s Marine En- 
zineering.)—The effective diameter of a radial wheel is usually taken from 
the centres of opposite floats; but it is difficult to say what is absolutely 
that diameter, as much depends on the form of float, the amount of dip, 
and the waves set in motion by the wheel. The slip of a radial wheel is 
from 15 to 30 per cent, depending on the size of float. 


Area of one float = uae KC. 


D is the effective diameter in feet, and C is a multiplier, varying from 
0.25 in tugs to 0.175 in fast-running light steamers. 

The breadth of the float is usually about 14 its length, and its thickness 
about its breadth. The number of floats varies directly with the diam- 
eter, and there should be one float for every foot of diameter, 

(For a discussion of the action of the radial wheel, see Thurston, Manual 
of the Steam-engine, part ii., p, 182.) 

Feathering Paddle=wheels. (Seaton.)—The diameter of a 
feathering-wheel is found as follows: The amount of slip varies from 12 to 
20 per cent, although when the floats are small or the resistance great it 


1014 MARINE ENGINEERING, 


is as high as 25 per cent; a well-designed wheel on a well-formed ship should 
not exceed 15 per cent under ordinary circumstances. 

If K is the speed of the ship in knots, S the percentage of slip, and R the 
revolutions per minute, 


K(100 +- 8) 
3.14%: B.- 


The diameter, however, must be such as will suit the structure of the 
ship, so that a modification may be necessary on this account, and the 
revolutions altered to suit it. 

The diameter will also depend on the amount of ‘‘ dip” or immersion of 
float. 

When a ship is working always in smooth water the immersion of the top 
edge should not exceed 4 the breadth of the float; and for general service 
at sea, an immersion of 4 the breadth of the float is sufficient. If the ship 
is intended to carry cargo, the immersion when light need not be more than 
2 or 3 inches, and should not be more than the breadth of float when at the 
deepest draught; indeed, the efficiency of the wheel falls off rapidly with 
the immersion of the wheel. fife 


Diameter of wheel at centres = 





ma iC. 


Cis a multiplier, varying from 0.3 to 0.85; Dis the diameter of the wheel 
to the float centres, in feet. 


The number of floats = L6(D + 2). 

The breadth of the float = 0.35 x the length. 

The thickness of floats = 1/12 the breadth. 

Diameter-of gudgeons = thickness of float, 
Seaton and Rounthwaite’s Pocket-book gives: 


Number of floats = NE 


I 
Area of one float = 


where F& is number of revolutions per minute. 


L.H.P. x 33000 x K 
NCD eae 





Area of one float (in square feet) = 


where NV = number of floats in one wheel. 

For vessels plying always in smooth water K = 1200. For sea-going 
steamers K = 1400. For tugs and such craft as require to stop and start 
frequently in a tide-way K = 1600. 

It will be quite accurate enough if the last four figures of the cube 
(D X &)* be taken as ciphers. 

For illustrated description of the feathering paddle-wheel see Seaton’s 
Marine Engineering, or Seaton and Rounthwaite’s Pocket-book. The diam- 
eter of a feathering -wheel is about one half that of a radial wheel for equal 
efficienev. (Thurston.) 

Efficiency of Paddie-wheels.—Computations by Prof. Thurston 
of the efficiency of propulsion by paddle-wheels give for light river steamers 
with ratio of velocity of the vessel, v, to velocity of the paddle-fioat at 
a = .: with a dip = 3/20 radius of the wheel, and 
a slip of 25 per cent, an efficiency of .714; and for ocean steamers with 


the same slip and ratio of — and a dip = radius, an efficiency of .685. 


centre of pressure, V, or 


JET-PROPULSION. 


Numerous experiments have been made in driving a vessel by the 
reaction of a jet of water pumped through an orifice in the stern, but 
they have all resulted in commercial failure. Two jet-propulsion steamers, 
the ‘*‘ Waterwitch,” 1100 tons, and the ‘Squirt,’ a small torpedo-boat, 
were built by the British Government. The former was tried in 1867, and 
gave an efficiency of apparatus of only 18 per cent. The latter gave a speed 
of 12 knots, as against 17 knots attained by a sister-ship having a screw and 
equal steam-power. The mathematical theory of the efficiency of the jet 
was discussed by Rankine in The Engineer, Jan. 11, 1867, and he showed that 
{ae greater the quantity of water operated on by a jet-propeller, the greater 


RECENT PRACTICE IN MARINE ENGINES, 1015 


is the efficiency. In defiance both of the theory and of the results of earlier 
experiments, and also of the opinions of many naval engineers, more than 
$200,000 were spent in 1888-90 in New York upon two experimental boats, the 
* Prima Vista’ and the ‘‘ Evolution,” in which the jet was made of very small 
size, in the latter case only 5¢-inch diameter, and with a pressure of 2500 
lbs. per square inch. As had been predicted, the vessel was a total failure, 
(See article by the author in Mechanics, March, 1891.) 

The theory of the jet-propeller is similar to that of the screw-propeller. 
{f A = the area of the jet in square feet, V its velocity with reference to the 
orifice, in feet per second, v = the velocity of the ship in reference to the 
earth, then the thrust of the jet (see Screw-propeller, ante) is zAV (V — v). 
The work done on the vessel is 2AV(V— v)v, and the work wasted on the 
rearward projection of the jet is 45 X 2AV(V = v)%. The efficiency is 


et aaldearahe 4 =”. This expression equals unity wh 

294V(V—vv+AV(V—-vp V+ P a a aie 
V = v, that is, when the velocity of the jet with reference to the earth, or 
V — v, = 0; but then the thrust of the propeller is also0. The greater the 
value of V as compared with v, the less the efficiency. For V = 20v, as was 
proposed in the ‘* Evolution,” the efficiency of the jet would be less than 10 
per cent, and this would be further reduced by the friction of the pumping 
mechanism and of the water in pipes. 

The whole theory of propulsion may be summed up in Rankine’s words: 
‘“*That propeller is the best, other things being equal, which drives astern 
the largest body of water at the lowest velocity.” 

It is practically impossible to devise any system of hydraulic or jet propul- 
sion which can compare favorably, under these conditions, with the screw 
or the paddle-wheel. 

Reaction of a Jet.—If a jet of water issues horizontally from a ves- 
sel, the reaction on the side of the vessel opposite the orifice is equal to the 
weight of a column of water the section of which is the area of the orifice, 
and the height is twice the head. 

The propelling force in jet-propulsion is the reaction of the stream issuing 
from the orifice, and it is the same whether the jet is discharged under 
water, in the open air, or against a solid wall. For proof, see account of 
frials by ©: J. Everett, Jr., given by Prof. J. Burkitt Webb, Trans. A. 8. M. 

., xii. 904. 


RECENT PRACTECE IN MARINE ENGINES. 


(From a paper by A. Blechynden on Marine Engineering during the past 
Decade, Proc. Inst. M. E., July, 1891.) 


Since 1881 the three-stage-expansion engine has become the rule, and the 
boiler-pressure has been increased to 160 lbs. and even as high as 200 Ibs. per 
square inch. Four-stage-expansion engines of various forms have also been 
adopted. 

Forced Draught has become the rule in all vessels for naval service, 
and is comparatively common in both passenger and cargo vessels. By this 
means it is possible considerably to augment the power obtained from a 
given boiler; and so long as it is kept within certain limits it need result in 
no injury to the boiler, but when pushed too far the increase is sometimes 
purchased at considerable cost. 

In regard to the economy of forced draught, an examination of the ap- 
pended table (page 1018) will show that while the mean consumption of coal 
in those steamers working under natural draught is 1.573 lbs. per indicated 
horse-power per hour, it is only 1.336 lbs. in those fitted with forced draught. 
This is equivalent to an economy of 15%. Part of this economy, however, 
may be due to the other heat-saving appliances with which the latter 
steamers are fitted. 

Woilers.—As a material for boilers, iron is now a thing of the past, 
though it seems probable that it will continue yet awhile to be the material 
for tubes. Steel plates can be procured at 132 square feet superficial area 
and 14% inches thick. For purely boiler work a punching-machine has be- 
come obsolete in marine-engine work. 

The increased pressures of steam have also caused attention to be directed 
to the furnace, and have led to the adoption of various artifices in the shape 
of corrugated, ribbed, and spiral flues, with the object of giving increased 
‘strength against collapse without abnormally increasing the thickness of 
the plate. A thick furnace-plate is viewed by many engineers with great 


1016 MARINE ENGINEERING. 


= 


suspicion; and the advisers of the Board of Trade have fixed the limit of 
thickness for furnace-plates at 5g inch; but whether this limitation will 
stand in the light of prolonged experience remains to be seen. It is a fact 
generally accepted that the conditions of the surfaces of a plate are far 
greater factors in its resistance to the transmission of heat than either the 
material or the thickness. With a plate free from lamination, thickness 
being a mere secondary element, it would appear that a furnace-plate night 
be increased from 1% inch to 34 iuch thickness without increasing its resist- 
ance more than 114%. So convinced have some engineers become of the 
soundness of this view that they have adopted flues 34 inch thick. 

Pistom=valves.—Since higher steam-pressures have become common, 
piston-valves have become the rule for the high-pressure cylinder, and are 
not unusual for the intermediate. When well designed they have the great 
advantage of being almost free from friction, so far as the valve itself is 
concerned. In the earlier piston-valves it was customary to fit spring 
rings, which were a frequent source of trouble and absorbed a large amount 
of power in friction; but in recent practice it has become usual to fit spring- 
less adjustable sleeves. 

For low-pressure cylinders piston-valves are not in favor; if fitted with 
spring rings their friction is about as great as and occasionally greater than 
that of a well-balanced slide-valve; while if fitted with springless rings there 
is always some leakage, which is irrecoverable. But the large port-clear- 
ances inseparable from the use of piston-valves are most objectionable; 
and with triple engines this is especially so, because with the customary 
late cut-off it becomes difficult to compress sufficiently for insuring econo- 
ay and smoothness of working when in “full gear,’ without some special 

evice, 

Steam-pipes.—tThe failures of copper steam-pipes on large vessels 
have drawn serious attention both to the material and the modes of con- 
struction of the pipes. As the brazed joint is liable to be imperfect, it is 
proposed to substitute solid drawn tubes, but as these are not made of large 
sizes two or more tubes may be needed to take the place of one brazed tube. 
Reinforcing the ordinary brazed tubes by serving them with steel or copper 
wire, or by hooping them at intervals with steel or iron bands, has been 
tried and found to answer perfectly. 

Auxiliary Supply of Fresh Water—Evaporators.—To make 
un the losses of water due to escape of steam from safety-valves, leakage at 
glands, joints, etc., either a reserve supply of fresh water is carried in tanks, 
or the supplementary feed is distilled from sea-water by special apparatus 
provided for the purpose. In practice the distillation is effected by passing 
steam, say from the first receiver, through a nest of tubes inside a still or 
evaporator, of which the steam-space is connected either with the second 
receiver or with the condenser. The temperature of the steam inside the 
tubes being higher than that of the steam either in the second receiver or in 
the condenser, the result is that the water inside the still is evaporated, and 
passes with the rest of the steam into the condenser, where it is condensed 
and serves to make up the loss. This plan localizes the trouble of the de- 
posit, and frees it from its dangerous character, because an evaporator can- 
not become overheated like’a boiler,even though it be neglected until it 
salts up solid; and if the same precautions are taken in working the evapo- 
rator which used to be adopted with low-pressure boilers when they were 
fed: with salt water, no serious trouble should result. 

Weir’s Feed=-water Heater.—tThe principle of a method of heating 
feed-water introduced by, Mr. James Weir and widely adopted in the 
marine service is founded on the fact that, if the feed-water as it is drawn 
from the hot-well be raised in temperature by the heat of a portion of steam 
introduced into it from one of the steam-receivers, the decrease of the coal 
necessary to generate steam from the water of the higher temperature bears 
a greater ratio to the coal required without feed-heating than the power 
which would be developed in the cylinder by that portion of steam would 
bear to the whole power developed when passing all the steam through all 
the cylinders. Suppose a triple-expansion engine were working under the 
following conditions without feed-heating: boiler-pressure 150 lbs,; I.H.P. in 
high-pressure cylinder 398, in intermediate and low-pressure cylinders to- 
gether 790, total 1188. The temperature of hot-well 100° F. Then with feed- 
heating the same engine might work as follows: the feed might be heated to 
220° F., and the percentage of steam from the first receiver required to heat 
it would be 10.9%; the I.H.P. in the h.p. cylinder would be as before 398, and 
in the three Gvlinders it would be 1108, or 93% of the power developed withont 


RECENT PRACTICH IN MARINE ENGINES. 1017 


feed-heating. Meanwhile the heat to be added to each pound of the feed-water 
at 220° F. for converting it into steam would be 1005 units against 1125 units 
with feed at 100° F., equivalent to an expenditure of only 89.4% of the heat 
required without feed-heating. Hence the expenditure of heat in relation 
to power would be 89.4 + 93.0 = 96.4%, equivalent to a heat economy of 3.6%. 
If the steam for heating can be taken from the low-pressure receiver, the 
economy is about doubled. : 


Passenger Steamers fitted with Twin Screws. 











tea e 
Sas Cylinders, two sets e e 
Ais in all. Sart eo 
Vessels. age ; »esl 24 
wee] & 3G?) 32 
as g. Bi Diameters. | Stro./3 a2 =m 
Ghee ae Feet | Feet Inches in. | dubs. |e B: 
ity of Ne or ; 7 
oS Paris ence 525 | 6314 | 45,71, 113 | 60 | 150 | 20,000 
TEI trae hsteeeie oss 565 |58 | 43,68,110 | 60 | 180} 18,000 
Normannia.........2.0.00) 500 5716 | 40, 67, 106 66 160 } 11,500 
STAN en eal a 46314 | 55g | 41, 66,101 | 66 | 160| 12,500 
Empress of India ‘ 
eS PUES Oe Ae: 440 51 2, 51, 82 54 160 | 10,125 
Sa ** China 
NOOR AOE ane wrk ss acess 5 oe 415 48 34, 54, 85 51 160 | 10,000 
Beat a at vn te Achebe 400 lewd b3416 (6746, 92 |. 260 wih, 170th a1, 656 





Comparative Results of Working of Marine Engines, 
1872, 1881, and 1891. 








Boilers, Engines, and Coal, 1872. 1881. 1891. 
Boiler-pressure, lbs. per Sq. in .........0...-- 52.4 G74 158.5 
Heating-surface per horse-power, sq. ft...... 4.410 3.917 8.275 
Revolutions per minute, revs.... .......02.--- 55.67 59.76 63.75 
Piston-speed, feet per min........ AAs ati cha 376 467 529 
Coal per horse-power per hour, lbs.....- oh alate 2.110 1.828 1ip22 





Weight of Three =-stage - expansion Engines in Nine 
Steamers in Helation to Indicated Horse-power and 
to Cylinder-capacity. 




















Weight of ; é : 

2 Machinery Relative Weight of Machinery. 

® 

: Per Indicated Hor e Bak | Bem 1 f 
> | 1 ‘ n se- Os Oe155 ype 0 
| Saale eles power. e“s 2/3 +8 $|Machinery. 
a hans col ead b5a 8/2088 

i =| Ke & 2 i= 3 f a ta op Aca = 
i) | Engine-] Boiler- Total 0d ~ SS a, em 
Zz room. | room. |*O'@'|a SS “im Bo 

tons. | tons.,|tons.} Ibs. Ibs. lbs. | tons. | tons 

1 681 662 1343 226 220 446 1.30 3.75 | Mercantile 
2 638 619 1257 259 251 510 1.46 4.10 oP 

8 134 128 262 207 198 405 1.23 38.23 “e 

4 38.8] 46.2 85 170 203 37% 1.29 3.30 g 

5 (aly 695 1414 167 162 829 1.41 3.44 se 

6 75.2} 107.8) 183 141 202 343 1.37 38.30 $6 

Go qed 61, | 1051 uate 108 | 185 | 1.21 | 2.724}, a 
8 73.5} 109 182.5 78 116 194 roa 2.78 do. 

‘ ~ Naval 
9 | 262 | 429 691 62.5 102 165 | 0.82 2.70 vertical 





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CONSTRUCTION OF BUILDINGS, 1019S 


Dimensions, Indicated Horse - power, and Cylinder e 
capacity of Three-stage -expansion Engines in Nine 
































Steamers. 

“ g a9 ae hea ye i 

S| &5 Cylinders, | §5 | ¢S| SE | 5B] Heating-sur- 

pa | 05 Ba) 52) 38 13% face. 

Sa | we Be [n#2| Bo | 22. 

gS] 24 Be |SES| 2 18s Per 

Lae alg Diameters. |Stroke Pe a K ae va Total. | 1. H.P, 

ins. ins, | revs. | lbs. | I.H.P. |cu.ft.| sq. ft. | sq. ft. 

1 Single |40 66 100) 7% 64.5} 160 | 6751 522 17,640 | 2.62 
2 wh 39 G1 9%] 66 67.8| 160] 5525 | 436 15,107 | 2.73 
3 $$ 23 388 G61] 42 83 160 | 1450 | 109 8,973 | 2.73 
4 ss 17 =. 2644 42} 24 90 150 510 30 1,403 | 2.75 
5 Twin {82 54 82) 54 88 160 | 9625 | 508 20,193 | 2.10 
6 > 15-24. 888) 27 113 150 1194 55 8,200 | 2.68 
q Single {20 380 45) 24 191 145 1265 36.3} 2,227 1.7 
8 Twin 1814 29 43) 24 182.5} 140] 2105 66.2] 3,928 | 1.87 
2 ss 18344 4974] 89 145 150 | 9400 | 319 15,882 | 1.62 


CONSTRUCTION OF BUILDINGS.* 


(Extract from the Building Laws of the City of New York, 1893.) 
Walis of Warehouses, Stores, Factories, and Stables,.— 
25 feet or less in width between walls, not less than 12 in. to height of 40 ft. 
If 40 to 60 ft. in height, not less than 16 in. to 40 ft., and 12 in. thence to top; 
60 to 80 $6 66 66 6 $6 90 66 95 oo 16 66 “ee 
75 to 85 % * o 6 2406-20 ft.3 20 in, to 60 ft., and 16 in, 


to top3 

85 to 100 ft. in height, not less than 28 in, to 25 ft.3 24 in. to 50 ft.3 20 in’ 
to 75 ft., and 16 in. to top; 

Over 100 ft. in height, each additional 25 ft, in height, or part thereof, next 
above the curb, shall be increased 4 inches in thickness, the upper 100 
feet remaining the same as specified for a wall of that weight. 

If walls are over 25 feet apart, the bearing-walls shall be 4 inches thicker 
than above specified for every 1214 feet or fraction thereof that said walls 
are more than 25 feet apart. 

Strength of Floors, Roofs, and Supports. 
Floors calculated to bear 


less'than’s 222°) 22% Rete Se es ca oleae cae aces %0 Ibs 
Floors of office-building, not less than........c.ccccsco. see cces 100 * 
4 public-assembly building, not less than......... Ree 120 * 
is store, factory, warehouse, ete., not less than....... 150 “ 
Roofs of all buildings, not less than........... 12.2.0 Anessa 50 * 


Every floor shall be of sufficient strength to bear safely the weight to be 
imposed thereon, in addition to the weight of the materials of which the 
floor is composed. 

Columns and Posts.—tThe strength of all columns and posts shall 
be computed according to Gordon’s formule, and the crushing weights in 
pounds, to the square incl of section, for the following-named materials, 
shall be taken as the coefficients in said formulee, namely: Cas’ iron, 80,000; 


* The limitations of space forbit any extended treatment of this subject. 
Much valuable information upon it will be found in Trautwine’s Civil Engi- 
neer’s Pocket-book, and in Kidder’s Architect’s an | Builder’s Pocket-book. 
The latter in its preface mentions the following works of reference: ‘* Notes 
on Building Construction,’’ 3 vols., Rivingtons, publishers, Boston; ‘‘Building 
Superintendence,” by T. M. Clark (J. R. Osgood & Co., Boston.); ‘*The 
American House Carpenter,”? by R. G. Hatfield; ‘* Graphical Analysis of 
Roof-trusses,”’ by Prof. C. E. Greene; *‘ The Fire Protection of Mills,” by C. 
J. H. Woodbury; *‘ House Drainage and Water Service,” by James C, 
Bayles; “The Builder’s Guide and Estimator’s Price-book,” and ‘‘ Plaster- 
ing Mortars and Cements,”’ by Fred. T. Hodgson; ‘‘ Foundations and Con- 
crete Works,” and “Art of Building,’ by E. Dobson, Weale’s Series, London, 
y. H. Woodbury; ‘rouse Drainage and Water Service,” by James co, 
Bayles; ‘The Builder’s Guide and Estimator’s Price-book,” and ‘* Plaster- 
ing Mortars and Cements,” by Fred. T. Hodgson; “Foundations and Con- 
erete Works.” and ‘*‘ Art of Building.” by E. Dobson, Weale’s Series. London, 


1020 CONSTRUCTION O# BUILDINGS. 


wrought or rolled iron, 40,000; rolled steel, 48,000; white pine and spruce, 
3500; pitch or Georgia pine, 5000; American oak, 6000, The breaking strength 
of wooden beams and girders shall be computed according to the formule 
in which the constants for transverse strains for central load shall be as 
follows, namely: Hemlock, 400; white pine, 450; spruce, 450; pitch or Georgia 
pine, 550; American oak, 550; and for wooden beams and girders carrying a 
uniformly distributed load the constants will be doubled. The factors of 
safety shall be as one to four for all beams, girders, and other pieces subject 
to a trausverse strain; as:one to four for all posts, columns, and other 
vertical supports when of wrought iron or rolled steel; as one to five for 
other materials, subject to a compressive strain; as one to six for tie- 


rods, tie-beams, and other pieces subject to a tensile strain. Good, solid, 


_ natural earth shall be deemed to safely sustain a load of four tons to the 
superficial foot, or as otherwise determined by the superintendent of build- 
ings, and the width of footing-courses shall he at least sufficient to meet this 
requirement. In computing the width of walls, a cubic foot of brickwork 
shall be deemed to weigh 115 lbs. Sandstone, white marble, granite, and 
other kinds of building-stone shall deemed to weigh 160 lbs. per cubic foot. 
The safe-bearing load to apply to good brickwork shall be taken at 8 tons 
per superficial foot when good lime mortar is used, 1114 tons per superficial 
foot when good lime and cement morta. mixed is used, and 16 tons per sup- 
erficial foot when good cement mortar is used. 

Fire-proof Buildings—Iroa and Steel Columns,—aAll cast- 
tron, wrought-iron, or rolled-steel columns shall be made true and smooth 
at both ends, and shall rest on iron cr sveel bed-plates, and have iron or 
steel cap-plates, which shall also be made truc. Alliron or steel trimmer: 
beams, headers, and tail-beams shall be suitably framed and connected to- 
gether, and the iron girders, columns, beams, trusses, and all other ironwork 
of all floors and roofs shall be strapped, bolted, anchored, and connected to- 
gether, and to the walls, in a strong and substantial manner. Where beams 
are framed into headers, the angle-irons, which are bolted to the tail-beams, 
shall have at least two bolts for all beams over 7% inches in depth, and three 
bolts for all beams 12 inches and over in depth, and these bolts shall not b3 
less than 34 inchin diameter. Each one of such angles or knees, when boltei 
to girders, shall have the same number of bolts as stated for the other leg, 
The angle-iron in no case shall be less in thickness than the header or trim~ 


mer to which it is bolted, and the width of angle in no case sha!! be less than | 


one third the depth of beam, excepting that no angle-knee shall be less than 
214 inches wide, nor required to be more than 6 inches wide. All wrought- 
iron or rolied-steel beams 8 inches deep and under shall have bearings equal 
to their. depth, if resting on a wall; 9 to 12 inch beams shall have a bearing 
of 10 inches, and all beams more than 12 inches in depth shall have bearings 
of not less than 12 inches if resting on a wall. Where beams rest on iron 
supports, and are properly tied to the same, no greater bearings shall be re- 
quired than one third of the depth of the beams. Iron or steel floor-beams 
shall be so arranged as to spacing and length of beams that the load to be 
supported by them, together with the weights of the materials used in the 
construction of the said floors, shall not cause a deflection of the said beams 
of more than 1/30 of an inch per linear foot of span; and they shall be tied 
together at intervals of not more than eight times the depth of the beam. 

Under the ends of all iron or steel beams, where they rest on the walls, a 
stone or cast-iron template shall be built into the walls. Said template shall 
be 8 inches wide in 12-inch walls, and in all walls of greater thickness said 
template shall be 12 inches wide; and such templates, if of stone, shall not be 
in avy case less than 2% inches in thickness, and no template shall be less 
than 12 inches Jong. 

No cast-iron post or column shall be used in any building of a less average 
thickness of shaft than three quarters of an inch, nor shall it have an un- 
supported length of more than twenty times its least lateral dimensions or 
diaineter. No wrought-iron or rolled-stee] column shall have an unsupported 
length of more than thirty times its least lateral dimension or diameter, nor 
shall its metal be less than one fourth of an inch in thickness. 

Lintels, Bearings and Supports,—All iron or steel lintels shall 
have bearings proportionate to the weight to be imposed thereon, but no 
lintel used to span any opening more than 10 feet in width shall have a bear- 
ing less than 12 inches at each end, if resting on a wall; but if resting on an 
jron post, such lintel shall have a bearing of at least 6 inches at each end, 
by the thickness of the wall to be supported 

Strains on Girders and Rivets.—Rolled iron or steel beam gir- 


a a es 


oe a ee 


STRENGTH OF FLOORS. 1021 


ders, or riveted iron or steel plate girders used as lintels or as girders. 
carrying a wall or floor or both, shall be so proportioned that the loads 
which may come upon them shall not produce strains in tension or com- 
pression upon the flanges of more than 12,000 lbs, for iron, nor more than 
15,000 lbs. for steel per square inch of the gross section of each of such 
flanges, nor a shearing strain upon the web-plate of more than 6000 lbs. per 
square inch of section of such web-plate, if of iron, nor more than %000 
pounds if of steel; but no web-plate shall be less than 14 inch in 
thickness. Rivets in plate girders shall not be less than 5 inch in diameter, 
and shall not be spaced more than 6 inches apart in any case. They shall be 
so spaced that their shearing strains shall not exceed 9000 Ibs. per square 
inch, on their diameter, multiplied by the thickness of the plates through 
which they pass. The riveted plate girders shall be proportioned upon the 
supposition that the bending or chord strains are resisted entirely by the 
upper and lower fianges, and that the shearing strains are resisted entirely 
by the web-plate. No part of the web shall be estimated as flange area, nor 
more than one half of that portion of the angle-iron which lies against the 
web. The distance between the centres of gravity of the flange areas will 
be considered as the effective depth of the girder. 

The building laws of the City of New York contain a great amount of de- 
tail in addition to the extracts above, and penalties are provided for viola- 
tion. See An Act creating a Department of Buildings, ete., Chapter 275, 
Laws of 1892. Pamphlet copy published by Baker, Voorhies & Co., New 


York. 
MAXIMUM LOAD ON FLOORS, 

(Eng’g, Nov. 18, 1892. p. 644.)\—Maximum load per square foot of floor 
surface due to the weight of a dense crowd. Considerable variation is 
apparent in the figures given by many authorities, as the following table 
shows: 


. Weight of Crowd, 
Authorities. lbs. per sq. ft. 

French practice, quoted by Trautwine and Stoney ........... 41 
Hatfield (** Transverse Strains,’’ p. 80)........-... Ma rialnddareete %0 
Mr. Page, London, quoted by Trautwine........ pra acte's oi 84 
Maximum load on American highway bridges according to 

Waddell’s general specifications............ tastenigecltecsiels 100 
Mz. Nash, architect of Buckingham Palace. ........sscecscece 120 
Hexperiments by Prof. W. N. Kernot, at Melbourne ..... .... a 1 
Experiments by Mr. B. B. Stoney (‘* On Stresses,” p. 617). ... 147.4 


The highest results were obtained by crowding a number of persons pre- 
viously weighed into a small room, the men being tightly packed so as to 
resembie such a crowd as frequently occurs on the stairways and platforms 
of a theatre or other public building. 


STRENGTH OF FLOORS, 


(From circular of the Boston Manufacturers’ Mutual Insurance Co.) 
- The following tables were prepared by C. J. H. Woodbury, for determining 
safe loads on floors. Care should be observed to select the figure giving the 
yreatest possible amount and concentration of load as the one which may 
be put upon any beam or set of floor-beams; and in no case should beams be 
subjected to greater loads than those specified, unless a lower factor of 
safety is warranted under the advice of a competent engineer. 

Whenever and wherever solid beams or heavy timbers are made use of in 
the construction of a factory or warehouse, they should not be painted, var- 
nished or oiled, filled or encased in impervious concrete, air-proof plastering, 
or metal for at least three years, lest fermentation should destroy them by 
what is called * dry rot.” 

It is, on the whole, safer to make floor-beams in two parts, with a small 
open space between, so that proper ventilation may be secured, even if the 
outside should be inadvertently painted or filled. 

These tables apply to distributed loads, but the first can be used in respect 
to floors which may carry concentrated loads by using half the figure given 
in the table, since a beam will bear twice as much load when evenly distrib- 
uted over its length as it would if the Joad was concentrated in the centre 
of the span. 

The weight of the floor should be deducted from the figure given in the 
table, in order to ascertain the net load which may be placed upon any floor, 
The weight of spruce may be taken at 36 lbs. per cubic foot, and that of 
Southern pine at 48 lbs, per cubic foot, 


1022 CONSTRUCTION OF BUILDINGS. 


Table I was computed upon a working modulus of rupture of Southern 
pine at 2160 lbs., using a factor of safety of six. It can also be applied to 
ascertaining the strength of spruce beams if the figures given in the table 
are multiplied by 0.78; or in designing a floor to be sustained by spruce 
beams, multiply the required load by 1.28, and use the dimensions as given 
by the table. 

Theses tables are computed for beams one inch in width, because the 
strength of beams increases directly as the width when the beams are broad 
enough not to cripple. 

EXxAMPLE.—Required the safe load per square foot of floor, which may be 
safely sustained by a floor on Southern pine 10 X 14 inch beams, 8 feet on 
centres, and 20 feet span. In Table lai X 14inch beam, 20 feet span, will 
sustain 118 lbs. per foot of span; and for a beam 10 inches wide the load 
would be 1180 Ibs. per foot of span, or 14714 lbs. per square foot of floor for 
Southern-pine beams. From this should be deducted the weight of the fioor, 
which would amount to 17% lbs. per square foot, leaving 130 ibs. per square 
foot as a safe load to be carried upon such a floor, If the beams are of 
spruce, the result of 14714 Ibs. would be multiplied by 0.78, reducing the load 
to 115 lbs. The weight of the floor, in this instance amounting to 16 lbs., 
would leave the safe net load as 90 lbs. per square foot for spruce beams. 

Table II applies to the design of floors whose strength must be in excess 
of that necessary to sustain the weight, in order to meet the conditions of 
delicate or rapidly moving machinery, to the end that the vibration or dis- 
tortion of the floor may be reduced to the least practicable limit. 

In the table the limit is that of load which would cause a bending of the 
beams to a curve of which the average radius would be 1250 feet. 

This table is based upon a modulus of elasticity obtained from observa- 
tions upon the deflection of loaded storehouse floors, and is taken at 2,000,000 
Ybs. for Southern pine; the same table can be applied to spruce, whose 
modulus of elasticity is taken as 1,200,000 lbs., if six tenths of the load for 
Southern pine is taken as the proper load for spruce; or, in the matter of 
designing, the load should be increased one and two thirds times, and the 
dimension of timbers for this increased load as found in the table should be 
used for spruce. 

It can also be applied to beams and floor-timbers which are supported at 
each end and in the middle, remembering that the deflection of a beam 
supported in that manner is only four tenths that of a beam of equal span 
which rests at each end; that is to say, the floor-planks are two and one 
half times as stiff, cut two bays in length. as they would be if cut only one 
bay in length. When a floor-plank two bays in length is evenly loaded, 
three sixteenths of the load on the plank is sustained by the beam at each 
end of the plank, and ten sixteenths by the beam under the middle of the 
plank; so that for a completed floor three eighths of the load would be sus- 
tained by the beams under the joints of the plank, and five eighths of the load 
by the beams under the middle of the plank: this is the reason of the impor- 
tance of breaking joints in a floor-plank every three feet in order that each 
beam shall receive an identicai load. If it were not so, three eighths of the 
whoie joad upon the floor would be sustained by every other beam, and five 
eighths of the load by the corresponding alternate beams. 

Repeating the former example for the load on a mill floor on Southern- 
.pine beams 10 K 14 inches, and 20 feet span, laid 8 feet on centres: IniTable 
Ilai1 x 14inch beam should receive 61 lbs. per foot of span, or 75 Ibs. per 
isq. ft. of floor, for Southern-pine beams. Deducting the weight of the floor, 
17% lbs. per sq. ft., leaves 57 lbs. per sq. ft. as the advisable load. 

If the beams are of spruce, the result of 75 lbs. should be multiplied by 0.6, 
reducing the load to 45 lbs. The weight of the floor, in this instance amount- 
ing to 16 lbs.. would leave the net load as 29 lbs. for spruce beams. 

If the beams were two spans in iength, they could, under these conditions, 
support two and a half times as much load with an equal amount of defiec- 
tion. unless such load should exceed the limit of safe load as found by Tabie 
I, as would be the ease under the conditions of this problem. 

MEill Columns.—Timber posts offer more resistance to fire than iron 
pillars, and have generally displaced them in millwork. Experiments 
made on the testing-machine at the U. §S. Arsenal at Watertown, Mass., 
show that sound timber posts of the proportions customarily used in mill- 
work yield by direct crushing, the strength being directly as the area at the 
smallest part. The columns yielded at about 4500 lbs. per square inch, con- 
firming the general practice of allowing 600 lbs. per square inch, as a safe 
aes Square columns are one fourth stronger than round ones of the same 

meter, 


STRENGTH OF FLOORS. ~ 1023 


I, Safe Distributed Loads upon Southern-pine Beams 
One Inch in Width. 


(C. J. H. Woodbury.) 


(If the load is concentrated at the centre of the span, the beams will sus: 
tain half the amount as given in the table.) 




















+ Depth of Beam in inches, 

aa 
e}2|3|[4|[5]|6]7]s| 9] 10,11] 12] 18] 14] 15 | 16 

pe) BS Ae te al Meg ea Bote alloy aia Re A a ea a BR Ls a ee) ER ak 
a 

n Load in pounds per foot of Span. 

5 | 88! 86 | 154) 240] 346; 470) 614] 778) 960 

6 | 27 | 60 | 107] 167} 240} 327) 427) 540) 667) 807 

7 120 | 44 78}. 122} 176] 240) 3814) 3897) 490} 593} 705) 628 

8 15 | 34 60} 94} 135] 184} 240) 804] 375) 454] 540} 634) 735 

9 |....] 27 | 47] 74] 107) 145] 190} 240; 296} 359) 427) 501! 581) 667 | 759 
10 .-.| 22 | 38} 60} 86) 118/ 154) 194] 240) 290] 346; 406) 470) 540 | 614 
11 its 82} 50} 71] 97} 127) 161} 198} 240) 286} 335] 389} 446 508 
12 27; 42) 60} 82) 107) 135] 167] 202) 240) 282) 327 75 | 474 
Le md eetas, | ears 36} 51) 70} 90) 115) 142) 172) 205} 240] 27 820 | 364 
Tea reise eval eres 31; 44) 60); 7 99) 123! 148] 176} 207) 240) 276 314 
LO Gighesrea haat sete 27| 388] 52) 68) 86) 107) 129) 154} 180] 209} 240 | 273 
Oa tiahaes | Metcid Gere [doce 34} 46] 60) 76] 94] 113] 1385) 158) 184) 211 240 
UE Cl eg PRS st a 80} 41) 53 7} 83} 101] 120} 140] 163} 187 | 217 
Trev Uh ae esr Ia an 36 7] 60} V4) 90) 107) 125) 145} 167 | 190 
19 43) 54} 66). 80) 96} 112; 130; 150] 170 
20 38] 49} 60] 73) 86] 101) 118} 1385] 154 
21 44) 54) 66) 78! 92] 107/ 122] 139 
COMES sastare lieastal TSM. cisreil ech apeal ihe, sfei|iraacoguil ates 50] 60). 71) 784) 97) 2 112 127 
Shite Ew Mintel auealh| see 45] 55) 65) 77) 89! 102) 116 
4 Sa linea A reyanouhh rota) eaardto, Hack. Staslyenere ty atta t ane xallvosa3 50} 60) TO; 82 94 107 
aay eos Gold Acs dheneudh-dacol a ceubb ace TORE EOL AOD TOL nn OO. | 898 





Ii, Distributed Loads upon Southernm-pine Beams sufii= 
cient to produce Standard Limit of Defiection, 


(C. J. H. Woodbury.) 


| 








+3 Depth of Beam in inches. a 
o hi 
ee ee ee Ae ee 
4 ro 
22/3 |4|{5]6]7|s|9 || 11] 12] 13] 14| 15] 16} Be 
s Bs 
2, D-s 
2) Load in pounds per foot of Span. A 
o | 38] 10 | 28 | 44 1 771 122) 182) 259 , .0300 
Opler sl loulole pros 85) 126} 180) 247 0432 
FN I Sip a S|) 62} 93] 132} 181] 241 0588 
8 4 Ouiel 80 | 48} 71} 101) 189} 185) 240) 305 0768 
9 AL 7 | 14 | 24] 388] 56} 80} 110} 146; 190} 241] 301 | 0972 
10 Seiten ea bila ake) 80| 46) 65] 89) 118] 154! 195] 244] 300 1200 
Leica adc wake 9 | 16 25) 38) 54} 73) 98) 127) 161) 202] 248) 801) .1452 
12 |. 13 2) woel) paolmos 2) 107} 136} 169] 208} 253] .1728 
ISH spel ate € [yes 11 Key ar 38) 58) ZO} 91] 116] 144) 178) 215) .2028 
pe PN ees eet a 8 cee 16] 28} 33) 45) 60) 78) 100] 124] 153) 186) .2852 
LO L4ini| Aosta cccsailisce ete | ate ee 14] 20} 29) 40) 53) 68 7| 108} 133) 162! .2700 
NG frliacl hig iP oreeal ap stete at aaeelierase 18} 25) 35) 46] 60) 7 95] 117) 147] .38072 
Lease’ | Aakscilinnodye stl tisS tlprcke Sin arene 16} 22) 31] 41) 538] 68] 84) 104) 126) .3468 
TS 4c free pigs 5.) 27s oo: || svete |feeepeet | pean 20; 27) 387] 47] 60} 75] 93) 112] .3888 
19 18] 25) 33] 43; 54] 68) 83) 101; .4332 
PV eo Sots] ee REN Me eee ees Pome ln oe 22} 30; 388} 49) 6ll %5} 91] .4800 
Um |S est ee RIE epanved WERE Ol lod ere 20} 27] 85) 44) 55] 68] 83) .5292 
eas vile ters | eae So |i, 18 24) 32) 40) 50] 62] 75) .5808 
2B") Semele tise | te na'|,. oe ine Stoke name eee a 22} 29) 387) 46! 57) 69] .6348 
24 27| 34] 42] 52) 63] .6912 


1024 ELECTRICAL ENGINEERING, 


ELECTRICAL ENGINEERING. 


STANDARDS OF MEASUREMENT. 


C.G.S. (Centimetre, Gramme, Second) or ** Absolute 
System of Physical Measurements: 


Unit of space or distance = 1 centimetre, cm.; 
Unit of mass = 1 gramme, gm.; 
Unit of time = 1 second, s.; 


Unit of velocity = space + time = 1 centimetre in 1 second; 
Unit of acceleration = change of 1 unit of velocity in 1 second; 


Acceleration due to gravity, at Paris, = 981 centimetres in 1 second; 
Unit of force = 1 dyne = al gramme = ca Ib. = .000002247 Ib. 


A dyne is that foree which, acting on a mass of one gramme during one 
second, will give it a velocity of one centimetre per second. The weight of 
one gramme in latitude 40° to 45° is about 980 dynes, at the equator 973 dynes, 
and at the poles nearly 984 dynes. Taking the value of g, the acceleration 
due to gravity, in British measures at 32.185 feet. per second at Paris, and the 
metre = 39.37 inches, we have 


1 gramme = 82.185 x 12 + .38937 = 981.00 dynes. 


Unit of work =1erg = 1 dyne-centimetre = .00000007372 foot-pound 3; 
Unit of power = 1 watt = 10 million ergs per second, 
= .7373 foot-pound per second, 
1373 1 06 
= 9 = 746 of 1 horse-power = .00184 H.P. 


C.G.S. Unit of magnetism = the quantity which attracts or repels an 
equal quantity at a centimetre’s distance with the force of 1 dyne. 

C.G.S. Unit of electrical current = the current which, flowing through a 
length of 1 centimetre of wire, acts with a force of 1 dyne upon a unit of 
magnetism distant 1 centimetre from every point of the wire. The ampere, 
the commercial unit of current, is one tenth of the C.G.S. unit. 

The Practical Units used in Electrical Calculations are: 

Ampere, the unit of current strength, or rate of flow, represented by J. 

Volt, the unit of electro-motive force, electrical pressure, or difference of 
potential, represented by £. 

Ohm, the unit of resistance, represented by R. 

Coulomb (or ampere-second), the unit of quantity, Q. 

Ampere-hour = 3600 coulombs, Q’. 

Watt (ampere-volt, or volt-ampere), the unit of power, P. 

Joule (volt-coulomb), the unit of energy or work, W. 

Farad, the unit of capacity, represented by C. 

Henry, the unit of inductance, represented by Z. 

Using letters to represent the units, the relations between them may be 
expressed by the following formule, in which ¢ represents one second and 
T one hour: 


E 


i Q 


EH 9 

As these relations contain no coefficient other than unity, the letters may 
represent any quantities given in terms of those units. For example, if # 
represents the number of volts electro-motive force, and R the number of 
ohms resistance in a circuit, then their ratio E + R will give the number of 
amperes current strength in that circuit. 

The above six formule can be combined by substitution or elimination, 
so as to give the relations between any of the quantities. The most impor- 
tant of these are the following : 

2 
4 oe Gees, W = Int = "1 = 19Rt = Pt, 
K2 WS On 


E 
1 = TW P= = = 2R = 
E=IR, R=> RUDR=;% 


Q=t, °Q@=1T, C= W=QE, P=IE. 





STANDARDS OF MEASUREMENT. 1025 


The definitions of these units as aaopted at the International Electrical 
Congress at Chicago in 13893, and as established by Act of Congress of the 
United States, July 12, 1894, are as follows: 

The ohm is substantially equal to 10° (or 1,000,000,000) units of resistance 
of the C.G.S. system, and is represented by the resistance offered to an un- 
varying electric current by a column of mercury at 32° FP, 14.4521 grammes 
in mass, of a constant cross-sectional area, and of the length of 106.3 centi- 
metres. 

The ampere is 1/10 of the unit of current of the C.G.S. system, and is the 
practical equivalent of the unvarying current which when passed through 
a solution of nitrate of silver in water in accordance with standard speci- 
fications deposits silver at the rate of .001118 gramme per second. 

The volt is the electro-motive force that, steadily applied to a conductor 
whose resistance is one ohm, will produce a current of one ampere, and is 
practically equivalent to 1000/1434 (or .6974) of the electro-motive force be- 
tween the poles or electrodes of a Clark’s cell at a temperature of 15° C., 
and prepared in the manner described in the standard specifications. 

The coulomb is the quantity of electricity transferred by a current of one 
ampere in one second. 

The farad is the capacity of a condenser charged to a potential of one 
volt by one coulomb of electricity. 

The joule is equal to 10,000,000 units of work in the C.G.S. system, and is 
practically equivalent to the energy expended in one second by an ampere 
in an ohm. 

The watt is equal to 10,000,000 units of power in the C.G.S. system, and is 
practically equivalent to the work done at the rate of one joule per second. 

The henry is the induction in a circuit when the electro-motive force in- 
duced in this circuit is one volt, while the induciug current varies at the rate 
of one ampere per second. 

The ohm, volt, etc., as above defined, are called the ‘‘ international *’ ohm, 
volt, ete., to distinguish them from the ‘legal’? ohm, B.A. unit, ete. 

The value of the ohm, determined by a committee of the British Associa- 
tion in 1863, called the B.A. unit, was the resistance of a certain piece of 
copper wire. The so-called ‘‘legal’? ohm, as adopted at the International 
Congress of Electricians in Paris in 1884, was a correction of the B.A. unit, 
and was defined as the resistance of acolumn of mercury 1 square millimetre 
in section and 106 centimetres long. at a temperature of 382° F, 

1 legal ohm = 1.0112 B.A. units, 1B.A. unit = 0.9889 legal ohm; 

1 international ohm = 1.0136 ‘** * 1184 ee) e= 09866 int, ohm: 

1 a ** = 1.0023 legalohm, 1legalohm=0,9977 ‘“ 


DERIVED UNITs. 


1 megohm = 1 million ohms; 

1 microhm = 1 millionth of a2 ohm; 
1 milliampere = 1/1000 of an empere; 

1 micro-farad = 1 millionth of a farad. 


RELATIONS OF VARIOUS UNITS. 


Tampere........ccc-ceee.ee-- = 1 Coulomb per second; 

1 volt-ampere..........e..«.. = 1 watt = 1 volt-coulomb per second; 
= .7373 foot-pound per second, 

1 watt..... coreececses eoveee. 4 = .0009477 heat-units per second (Fahr.), 


1/746 of one horse-power; 

7373 foot-pound, 

work done by one watt in one second, 
.0009477 heat-unit; 

1055.2 joules; 

1000/746 or 1.3405 horse-powers; 
1.3405 horse-power hours, 

= 2,654,200 foot-pounds, 

= 3412 heat-units; 

= 746 watts = 746 volt-amperes, 
= 33,000 foot-pounds per minute, 


The ohm, ampere, and volt are defined in terms of one another as follows: 
Ohm, the resistance of a conductor through which a current of one ampere 
will pass when the electro-motive force is one volt. Ampere, the quantity 
of current which will flow through a resistauce of one ohm when the electro- 
motive force is one volt. Volt, the electro-motive force required to cause a 
current of one ampere to flow through a resistance of one ohm. 


Ei SOUIG, apie atte trees date ae 


1 British thermal unit ....... 
1 kilowatt, or 1000 watts..... 
1 kilowatt-hour, 


Hun NAT | 


1000 volt-ampere hours, 
1 British Board of Trade unit, 


PWOLSE2POWEL os sees sete 


ELECTRICAL ENGINEERING. 


1026 





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FLOW OF WATER AND ELECTRICITY. 1027 


Units of the Magnetic Circuit.—(See Electro-magnets, page 1052.) 

For Methods of making Electrical Measurements, Test= 
ing, etec., see Munroe & Jamieson’s Pocket-Book of Electrical Rules, 
Tables, and Data; S. P. Thompson’s Dynamo-Electric Machinery; Carhart & 
Patterson’s Electrical Measurements; and works on Electrical Engineering. 

Equivalent Electrical and Mechanical Units.—H. Ward 
Leonard published in The Electrical Engineer, Feb. 25, 1895, a table of useful 
equivalents of electrical and mechanical units, from which the table on page 
1026 is taken, with some modifications. 


ANALOGIES BETWEEN THE FLOW OF WATER AND 


ELECTRICITY. 
WATER. ELECTRICITY. 
Head, difference of level, in feet. \ Volts; eleectro-motive force; differ- 
Difference of pressure, lbs. per sq. in. ence of potential; E. or E.M.F. 


Resistance of pipes, apertures, etc., 
increases with length of pipe, with 
contractions, roughness, ete.; de- 
creases with increase of sectional 
area. 

Rate of flow, as cubic ft. per second, 
gallons per minute, etc., or volume 
divided by the time. In the mining 
regions sometimes expressed in 
‘miners’ inches.”’ 


Quantity, usually measured in cubic 
ft. or gallons, but is also equivalent 
to rate of flow x time, as cu. ft. per 
second for so many hours. 


Work, or energy, measured in foot- 
pounds; product of weight of fall- 
ing water into height of fall; in 
pumping, product of quantity in 
cubic feet into the pressure in lbs. 


epee a7 aCos aeninst which the between two points in a circuit, 


energy expended = JEHt, = I?Rt. 
Power, rate of work. Horse-power = : oe 
ft.-lbs. of work in 1 min. + 33,000,{ Watt, unit of power, P, = volts x 


; ° - = r flow 
In water flowing in pipes, rate of | ®™peres, current or rate of flo 


: ; x difference of potential. 
flow in cu. ft. per second X resist- 1 watt = .7373 foot -pound per second 
neil the flow in lbs. per sq. ft. = 1/746 of a horse-power 
+ 550. rE ; 


Ohms, resistance, R. Increases di- 
rectly as the length of the conductor 
or wire and inversely as its sectional 
area, Rel +s. It varies with the 
nature of the conductor. 

Amperes; current; current strength; 
intensity of current; rate of flow; 
1 ampere = 1 coulomb per second. 

volts 

Amperes = haw I Pp? Pi Lie 

Coulomb, unit of quantity, Q, = rate 
of flow X time, as ampere-seconds. 
1 ampere-hour = 8600 coulombs. 


Joule, volt-coulomb, W, the unit of 
work, = product of quantity by the 
electro-motive force =volt-ampere- 
second, 1 joule =.73738 foot-pound. 

If C (amperes) = rate of flow, and 
E (volts) = difference of pressure 





(eee ee ere) 


ELECTRICAL RESISTANCE, 


Laws of Electrical Resistance.—The resistance, R, of any con- 
ductor varies directly as its length, /, and inversely as its sectional area, s, 
or Re l+s. 

If r = the resistance of a conductor 1 unit in length and 1 square unit in 
sectional area, R = ri +s. The common unit of length for electrical calcu- 
lations in English measure is the foot, and the unit of area of wires is the 
circular mil = the area of a circle 0.001 in. diameter. 1 mil-foot = 1 foot 
long 1 circ.-mil area. 

ssn eteanels of 1 mil-foot of soft copper wire at 51° F. = 10 international 
onms. 

ExAMPLE.—What is the resistance of a wire 1000 ft. long, 0.1 in. diam.? 
0,1 in. diam. = 10,000 cire. mils. 


k= rl+s= 10 X 1000 + 10,000 = 1 ohm. 


Specific resistance, also called resistivity, is the resistance of a material of 
unit length and section as compared with the resistance of soft copper. 

Conductivity is the reciprocal of specific resistance, or the relative con- 
ducting power compared with copper taken at 100., 


1028 BLECTRICAL ENGINEERING. 


Relative Conductivities of Different Metals at 0° and 
100° ©, (Matthiessen.) 


























Conductivities. Conductivities. 

Metals. At 0°. |At 100° C. Metals. At 0°. |At 100°C, 

Tt SOIREE MS Lee SA SSS OC ET phone leeks 
Silver, hard...... 100 Ta. SOW ST int oe Aa Wee 12.36 8.67 
Copper, hard.... 99.95 OPA’ Bibteri als Tew omnes 8 32 5.86 
Goldy hard sce. 77.96 5ds.90 | Arsenics.:......: 4.76 3.33 
Zine, pressed... 29.02 20.67 Antimony. ..... 4.62 3.26 

Cadminumeess, o2 23.702 16.77 | Mercury, pure.. 160. ier ctsrd 
Platinum, soft... TBR OCR ee eo. Bisma'the eee 1.245 0.873 

IrOnSOGhTS . c+ LORS OG EE Ne. 





Electrical Conductivity of Different Metals and Alloys. 


The following figures of electrical conductivity. are given by Lazare Weiler 


Bure ‘Silvers, .sesssers ee eer OD Swedisianronie «cee ee: ce eee 16 
Pure copper......... APR Ayo! 100 PUNT Carbine. rete emis cea eee tila is 
Telegraphic silicious bronze.. 98 Aluminum bronze (10%)....... 5 Es 
Alloy of 4 copper, 44 silver.. 86.65 | Siemens steel.................. 12 
PurevyeOlder Git sete eed screen tee ae Pure platinunisie Slee aerate ORG 
Silicide of copper, 4% Si....... figs Copper with 10% of nickel..... 10.6 
Telephonic silicious bronze... 35 IBUNe Wea ae ce icaeh mee wack cheoniee OL SS 
PURE Cee eee cree Age EAR te 29.9 | Bronze with 20% of tin......... 8.4 
BFASS With 35% Of ZINC.n.nce eee ke, | Eure mickel. 7.000 ).mecaueee het 7.89 
ROSPDHONGL I sislesn eae hteets se BR 7.7 | Phosphor-bronze, 10%tin... .. 6.5 
Alloy of 4% gold, 1% silver...... Gs L2t CAM EIT OM Vie sae eee eee Boek: Segoe Piste! 


Conductivity of Aluminum.—J. W. Richards (Jour. Frank. Inst., 
Mar. 1897) gives for hard-drawn aluininum of purity 98.5, 99.0, 99.5, and 99.75% 
respectively a conductivity of 55, 59, 61, and 63 to 64%, copper being 1002. 
The Pittsburg Reduction Co. claims that its purest aluminum has a con- 
ductivity of over 64.5%. (Hng’g News, Dec. 17, 1896.) 

German Silver.—tThe resistance of German silver depends on its com- 
position. Matthiessen gives it as nearly 13 times that of copper, with a tem- 
perature coefficient of .0004433 per degree C. Weston, however (Proc. 
Electrical Congress 1893, p. 179), has found copper-nickel-zine alloys (German 
silver) which had a resistance of nearly 28 times that of copper, and a tem- 
perature coefficient of about one half that given by Matthiessen. 


Conductors and Insulators in Order of their Value. 





CONDUCTORS, INSULATORS (NON-CONDUCTORS). 
All metals Dry air Ebonite 
Well-burned charcoal Shellac Gutta-percha 
Plumbago Paraffin India-rubber 
Acid solutions Amber Silk 
Saline solutions Resins Dry paper 
Metallic ores Sulphur Parchment 
Animal fluids Wax Dry leather 
Living vegetable substances Jet Porcelain 
Moist earth | Glass Oils 
Water | Mica 


According to Culley, the resistance of distilled water is 6754 million times 

as great as that of copper. Impurities in water decrease its resistance. 
esistance Varies with Temperature.—For every degree Cen- 

tigrade the resistance of copper increases about 0.4%. or for every degree F. 
0.2222%. Thus a piece of copper wire having a resistance of 10 ohms at 82° 
would have a resistance of 11.11 ohms at 82° F, 

The following table shows the amount of resistance of a few substances 
used for various electrical purposes by which 1 oli is increased by a rise of 
temperature of 1° C. 


ELECTRICAT, RESISTANCE, 1029 


~ 


Pia cir ee te tare ee. ot SE OOOt PO 1d, ‘silver ens: ssiekin foes £0 OO06R 
Piasinure silver ers. eet see eee O00! (Pash RPOM ME esis ees twins t's «..-- «(0080 
German silver (see above)..... .U0044| Copper ..........--seeeeeee sees .00400 


Anmnealing.—Resistance is lessened by annealing. Matthiessen gives 
the following relative conductivities for copper and silver, ihe comparison 
being made with pure silver at 100° C.: 


Metal. Temp. C. Hard. Annealed. Ratio. 
CODDEGatenene s sien nig 95.3 97.838 Pto 1,020 
STALV. GES fogs. c reece =. 14.62 95.36 1038.33 1 to 1.084 


Dr. Siemens compared the conductivities of copper, silvcr, and brass with 
the following results. Ratio of hard to annealed: 


Copper..... eee letowl.058 Bilvers es. 1 to 1.145 IBrassuticam an 1 to 1.180 


Standard of Resistance of Copper Wire. (Trans. A.I. E. E., 
Sept. and Nov. 189).)—Matthiessen’s standard is: A hard-drawn copper wire 
1 metre long, weighing 1 gramme, has a resistance of 0.1469 B.A. unit at 0° C. 
Relative conducting power (Matthiessen): silver, 100; hard or unannealed 
copper, 99.95; soft or annealed copper, 102.21. Couductivity of copper at 
other temperatures than 0° C., Cy = Co(1 — .00387¢ +- .000009009¢?). 


The resistance is the reciprocal of the conductivity, and is 
Ry = Ro(t + .00387¢ 4- .000005977?), 
The shorter formula R, = Io(1 + -00406f) is commonly used. 


A committee of the Am. Inst. Electrical Engineers recommend the rollow- 
ing as the most correct forin of the Matthiessen standard, taking 8.89 as the 
sp. gr. of pure copper: 

A soft copper wire 1 metre long and 1 mm. diam. has an electrical resist- 
ance of .02057 B.A. unit at 0° C. From this the resistance of a soft copper 
wire 1 foot long and .001 in. diam, (.uil-foot) is 9.720 B.A. units at 0° C. 


Standard Resistance at 0° C. B.A. Units. Legal Ohms. lees 
Mc. 2-millimetre, soft copper......... .02057 02084 02029 
Cubic centimetre ‘ Se SER i star .000001616 . 000001598 .000001£93 
Mil-foot ct EL RATA aE 9.720 9.612 9.590 
1 mil-foot. of soft copper at 10°.22 C. or 50°.4 F... 10 9.7 

= ieee als ry Ds) Digg fe ets) OOP OURS, a TOR20 10.175 
cs eS ea CSAR, 66 4 s¢ 230.9 ie teat. Us 10.505 


For tables of the resistance of copper wire, see pages 218 to 220, also 
pp. 1034, 1035. 

Taking Matthiessen’s standard of pure copper as 100%, some refined metal 
has exhibited an electrical conductivity equivalent to 103%. 

Matthiessen found that impurities in copper sufficient to decrease its 
density from 8.94 to 8.90 produced a marked increase of electrical resistance. 


DIRECT ELECTRIC CURRENTS, 


Ohm/’s Law,—tThis law expresses the relation between the three fun- 
damental units of resistance, electrical pressure, and current. Itis: 


electrical pressure , E Ez 
resistance Mite > Whence H=IR, and R= T: 


In terms of the units of the three quantities, 


volts 
Amperes = ———; volts = amperes X ohms; ohms = er Olea : 
ohms amperes 
EXAMPLES: Simple Circuits.—1. If the source has an effective electrical 
pressure of 100 volts, and the resistance is two ohms, what is the current ? 
E 100 
et I= at el 
R > 50 amperes. 
2. What pressure will give a current of 50 amperes through a resistance or 
2ohms? A= JR = 50 X 2 = 100 volts. 
3. What resistance is required to obtain a current of 50 amperes when the 
pressure is 100 volts? R= H+] = 100 + 50 = 2 ohms, 
Ohm’s law applies equally to a complete electrical circuit and to any 
part thereof. 
Series Circuits.—If conductors are arranged one after the other they 


Current = 


— 


1030 ELECTRICAL ENGINEERING, 


are said to be ia series, and the total resistance of the circuit is the sum of 
the resistances of its several parts. Let A, Fig. 
170, be a source of current, such as a battery or 
generator, producing a difference of potential or 
EK. M. F. of 120 volts, measured across ab, and let 
the circuit contain four conductors whose resist 
ances, 71, 1. 173, 74, are 1 ohm each, and three 
other resistances, R;, Rp, Rs, each 2 ohms. The 
total resistance is 10 ohms, and by Ohm’s law 
the current J= H+ R= 120+ 10 = 12 amperes. 
This current is constant throughout the circuit, and a series circuit 
is therefore one of constant current. The drop of potential in the 
whole circuit from a around to b is 120 volts, or H= RI. The drop in any 
portion depends on the resistance of that portion; thus from « to R, the re- 
sistance is 1 ohm, the constant current 12 amperes, and the drop 1 X 12 
= 12 volts. The drop in passing through each of the resistances Rh,, Rg, Rs 
is 2 x 12 = 24 volts. ri . 
Parallel, Divided, or Multiple Circuits.—Let B, Fig. 171, be 
a generator producing an E. M. I’, of 220 volts across the terminals ab. The 
current is divided, so that part flows 
through the main wires ac and part 
through the *‘shunt”’’ s, having a resist- 
ance of 0.5 ohm. Also the current has 
three paths between c and d, viz , through 
the three resistances in parallel Ry, Ry, R3, 
of 2 ohms each. Consider that the resist- 
ance of the wires is so small that it may 
om be neglected. Let the conductances of 
Fia. 171, the four paths be represented by Cs, C,, 
Cg, Cz. The total conductance is Cs + C; 
+ 0C,-+ C3; = C and the total resistance R=1-+C. The conductance of 
each path is the reciprocal of its resistance, the total conductance is the sum 
of the separate conductances, and the resistance of the combined or ‘ par- 
allel’’ paths is the reciprocal of the total conductance. 








hi 7 IM ees ® Klan S| 
Ra1+ (g5+y+y+q) =148.5 = 0.286 ohm. 


The current J = H+ & = 770 amperes. 

Conductors in Series and Parallel.—Let the resistances in 
parallel be the same as in Fig. 171, with the additional resistance of 0.1 ohm 
in each of the six sections of the main,wires, ac, bd, ete., in series. The 
voltage across ab being 220 volts, determine the drop in voltage at the 
several points, the total current, and the current through each path. The 
problem is somewhat complicated. It may be solved as follows: Consider 
first the points eg; here there are two paths for the current, efgh and eg. 
Find the resistance and the conductance of each and the total resistance 
(the reciprocal of the joint conductance) of the parallel paths. Next con- 
sider the points cd ; here there are two paths—one through e and the other 
through cd. Find the total resistance as before. Finally consider the points 
ab ; here there are two paths—one through ¢, the other through s._ Find the 
conductances of each and theirsum. The product of this sum and the volt 
age at ab will be the total amperes of current, and the current through any 
path will be proportional to the conductance of that path. The resistances, 
&, and conductances, C, of the several paths are as follows * 








R C 

R, of efFshg = 0.1+22 + 0.1 = 2.2 0.4545 
fy, of efyg =e 0.5 

Joint Re = 1.048 0.9545 
Ry of ce +dg + Re lt i fe 0.8013 
f, of cR,d = 0.5 

Joint Rf = 0.7687 1.3013 
Ry of ac + bd + Rf == 0.9687 1.0332 
&, of s = 0.5 2 





ae Joint Rg + Kh = 0,380 38.0332 


ELECTRIC CURRENTS. ee 


Total current = 220 x 3.0332 = 667.38 amperes, 
Current through s = 220x 2 = 440 amp.; through c = 227.4 amp. 
a * cRyd = 227.8 x 05 -- 1.8013 = 87.34 amp. 


‘ ée = 227.3 x 0.8013 + 1.30138 = 139.96 * 
“ eRag = 189.96 x 0.5 + 0.9545 = 73.81.‘ 
2 ** fitz = 189.96 x 0.4545 + 0.9545 = 66.65 ‘ 


The drop in voltage in any section of the line is found by the formula 
E= RI, R being the resistance of that section and J the currentin it. As 
the R of each section is 0.1 ohm we find # for ac and bd each = 22.7 volts, 
for ce and dg each 14.0 volts, and for ef and gh each 6,67 volts. The voltage 
across cd is 220 — 2 x 22.7 = 174.6 volts; across eg, 174.6 — 2 x 14.0 = 146.6, 
and across fh 146.6 — 2 x 667 = 133.3 volts. Taking these voltages and the 
resistances R,R,R3, each 2 ohms, we find from J= #-+R the current 
through each of these resistances 87.3, 73.3, and 66.65 amperes, as before. 

Internal Resistance.—In a simple circuit we have two resistances, 
that of the circuit R and that of the internal parts of the source of electro- 
motive force, called internal resistance, r. The formula of Ohm’s law when 
the internal resistance is considered is f= EH + (R +71). 

Power of the Cirecuit.—The power,or rate of work, in watts = 
current in amperes X electro-motive force in volts = I xX H. Since J= H+R, 
watts = H2-+- R = electro-motive force? ~ resistance. 

ExAMPLE.—What H.P. is required to supply 100 lamps of 40 ohms resist- 
ance each, requiring an electro-motive force of 60 volts ? 


2 b | 
The number of volt-amperes for each lamp is Ars aes ‘ 


2 
.00134 H.P.; therefore a x 100 x .00134 = 12 H.P. (electrical) very nearly. 


Electrical, Brake, and Indicated Horse=power.—The power 
given out by a dynamo = volts x amperes + 1000 = kilowatts, kw. Volts x 
amperes + 746 = electrical horse-power, E.H.P. The power put into a 
dynamo shaft by a direct-connected engine or other prime mover is called 
the shaft or brake horse-power, B.H.P. If e; is the efficiency of the 
dynamo, B.H.P. = E.H.P.+e,. If e, is the mechanical efficiency of the 
engine, the indicated horse-power, I.H.P. = brake H.P. + eg = E.H.P. + 
(€; X eg). 

If e, and e, each = 9116%, ILH.P. = E.H.P. x 1.194 = kw. x 1.60, In direct- 
connected units of 250 kw. or less the rated H.P. of the engine is commonly 
taken as 1.6 x the rated kw. of the generator. 

Electric motors are rated at the H.P. given out at the pulley or belt. H.P. 
of inotor = E.H.P. supplied + efficiency of motor. 

Heat Generated by a Current.—Joule’s law shows that the heat 
developed in a conductor is directly proportional, 1st, to its resistance; 2d, 
to the square of the current strength; and 3d, to the time during which the 
current flows, or H=J?Rt. Sincel= H+ R, 


1 volt-ampere = 


EH EH Ht 
2 =_-— m4 =; =— fj = ——. 
PRt=pIkt Elt Eet R 
Or, heat = current? x resistance < time 
= electro-motive force < current < time 

= electro-motive force? x time + resistance. 
g = quantity of electricity flowing = Jt = (Ht + R). 
= HQ; or heat = electro-motive force <x quantity. 


The electro-motive force here is that causing the flow, or the difference in 
potential between the ends of the conductor. 

The electrical unit of heat, or ‘‘ joule’? = 107 ergs = heat generated in one 
second by a current of 1 ampere flowing through a resistance of one ohm = 
-239 gramme of water raised 19 C. H = I?Rt X .239 gramme calories = 
I2Rt x .0009478 British thermal units. 

In electric lighting the energy of the current is converted into heat in the 
lamps. The resistance of the lamp is made great so that the required 
quantity of heat may be developed, while in the wire leading to and from 
the lamp the resistance is made as small as is commercially practicable, so 
that as little energy as possible may be wasted in heating the wire. 

' Heating of Conductors, (From Kapp’s Electrical Transmission 
of Energy.)—It becomes a matter of great importance to determine before- 


1032 ELECTRICAL ENGINEERING. 


hand what rise in temperature is to be expected in each given case, and if 
that rise should be found to be greater than appears safe, provision must be 
made to increase the rate at which heat is carried off. This can generally 
be done by increasing the superficial area of the conductor. Say we have 
one circular conductor of 1 square inch area, and find that with 1000 amperes 
flowing it would become too hot. Now by splitting up this conductor into 
10 separate wires each one tenth of a square inch cross-sectional area, we 
have not altered the total amount of energy transformed into heat, but we 
have increased the surface exposed to the cooling action of the surrounding 


air in the ratio of 1: 4/10, and therefore the ten thin wires can dissipate more 
than three times the heat, as compared with the single thick wire. 

Prof. Forbes states that an insulated wire carriesa greater current without 
overheating than a bare wire if the diameter be not too great. Assuming ~ 
the diameter of the cable to be twice the diam. of the conductor, a greater 
current can be carried in insulated wires than in bare wires up to 1.9 inch 
diam. of conductor. If diam. of cable = 4 times diam. of conductor, this is 
the case up to 1.1 inch diam. of conductor. 

Heating of Bare Wires.—tThe following formule are given by 
Kennelly: 

rt =" x 90,000 per aela 
as , titsw.d = (44.8 Tor 


A 


T = temperature of the wire and ¢ that of the air, in Fahrenheit degrees; 
I = current in amperes, d = diameter of the wire in mils. 


If we take T — ¢ = 90° F., 4/90 = 4.48, then 


d=10/7 and I = #/d3 + 1,000. 


This latter formula gives for the carrying capacity in amperes of bare 
wires almost exactly the figures given for weather-proof wires in the Fire 
Underwriters’ table except in the case of Nos. 18 and 16, B. & S. gauge, 
for which the formula gives 8 and 11 ampere’, respectively, instead of 5 
and 8 amperes, given in the table. 

Heating of Coils,—The rise of temperature in magnet coils due to 
the passage of current through the wire is approximately proportiona! to ~ 
the watts lost in the coil per unit of effective radiating surface, thus: 
1°R F PR 

Stee ks’ 

t being the temperature rise in degrees Fahr.; S, the effective radiating 
surface; and é& a coefficient which varies widely, according to conditions. 
In electromagnet coils of small size and power, k may be as large as 0.015. 
Ordinarily it ranges from 0.012 down to 0.005; a fair average is 0.007. 
The more exposed the coil is to air circulation, the larger is the value of k; 
the larger the proportion of iron to copper, by weight, in the core and 
winding, the thinner the winding with relation to its dimension parallel 
with the magnet core, and the larger the ‘‘space factor” of the winding, 
the larger will be the value of k. The space factor is the ratio of the actual 
copper cross-section of the whole coil to the gross cross-section of copper, 
insulation, and interstices. 

See also the discussion of magnet windings under Electromagnets, p. 1050. 

Fusion of Wires.—W. H. Preece gives a formula for the current re- 


quired to fuse wires of different metals, viz., [=ad?, in which d is the 

diameter in inches and a a coefficient whose value for different metals is as 

follows: Copper, 10244; aluminum, 7585; platinum, 5172; German silver, 

oes cereals 4750; iron, 3148; tin, 1462; lead, 1379; alloy of 2 lead and 
in, 2 


tc 


ELECrin(C’ CURRENTS, 1033 


Allowable Carrying Capacity of Copper Wires. 
(Fire Underwriters’ Rules.) 

















Amperes. Amperes 
B.&S. Circular oh, Circular 
Gauge. Mils. Rubber |Weather- Mils. Rubber |Weather- 
Covered.| proof. Covered | proof. 
18 1,624 eS Ss 200,000 200 300 
16 2,583 6 8 300,000 270 400 
14 4,107 ie 16 400.000 330 500 
12 6,530 Li De 500.000 390 590 
10 10,380 24 32 600,000 450 680 
8 16,510 33 46 700,000 500 760 
6 26,250 46 651 800 000 550 840 
oy 33,100 54 Linh 900,000 600 920 
4 41,740 5 92 1,000,000 650 1,000 
3 52,630 76 110 1,100,000 690 1,080 
2 66,370 90 131 1,200,000 730 1,150 
] 83,690 107 156 1,300,000 770 1.220 
0 105,500 127 185 1,400,000 810 1,290 
00 133,100 150 220 1,600,000 890 1,430 
000 167,800 Wars 262 1,800,000 970 1,550 
0000 211,600 210 a2 2,000,000 1,050 1,670 





For insulated aluminum wire the safe-carrying capacity is 84 per cent of 
that of copper wire with the same insulation. 

Underwriters? Insuliation.—The thickness of insulation required 
by the rules of the National Board of Fire Underwriters varies with the size 
of the wire, the character of the insulation. and the voltage. The thickness 
of insulation on rubber-covered wires carrying voltages up to 600 varies from 
3s inch for a No. 18 B. & S. gauge wire to $ inch for a wire of 1 000 000 cir- 
cular mils. Weather-proof insulation is required to be slightly thicker. 
For voltages of over 600 the insulation is required to be at least 1/16 inch 
thick for‘all sizes of wire under No. 8 B..& 8. gauge, and to be at least 3/32 
inch thick for all sizes greater than No. 0000 B. & S. gauge. 

Copper-wire Table.—The table on pages 1034 and 1085 is abridged 
from one computed by the Committee on Units and Standards of the Ameri- 
can Institute of Electrical Engineers (Trans. Oct. 1893). 





ELECTRIC TRANSMISSION, DIRECT CURRENTS. 
Cross-section of Wire Required for a Given Current.— 


Let R = resistance of a given line of copper wire, in ohms’ 
i % ‘* 1 mil-foot of copper; 
L = length of wire, in feet; 
e = drop in voltage between the two ends; 
I = current, in amperes; 
A = sectional area of wire, in circular mils; 


e é rl 
then J = R R ag R= 173 whence A = oe 

The value of r for soft copper wire at 75° F. is 10.505 international ohms. 
For ordinary drawn copper wire the value of 10.8 is commonly taken, cor- 
responding to a conductivity of 97.2 per cent. ‘ 

For a circuit, going and return, the total length is 2L, and the formula 
becomes A = 21.6/L + e, Lhere being the distance from the point of supply 
to the point of delivery. : 

If E is the voltage at the generator and a the per cent of drop in the line, 
then e = Ea + 100, and A = 


7) 


ake 
i 2160P. 
If P = the power in watts, = XT, then J = = and A = es 


If Pk= the power in kilowatts, A 


ELECTRICAL ENGINEERING, 


1034 





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1035 


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1036 *®LECTRICAL ENGINEERING. 


If Lm = the distance in miles, and Ac the area in circular inches, 
Ac = 6405 PrLm + ak?. If As= area in square inches As = 5030 PkLm 
+ ak?, When the area in circular mils has been determined by either 
of these formule reference should be made to the table of Allowable Capacity 
of Wires, to see if the calculated size is sufficient toavoid overheating. For 
all interior wiring the rules of the National Board of Fire Underwriters should 
be followed. See Appendix to Vol. IT of Crocker’s Electric Lighting. 

Weight of Copper for a Given Power.—Taking the weight of 
a mil-foot of copper at .000003027 lb., the weight of copper in a circuit of 
length 22 and cross-section A, in cire. mils, is 0.000006054LA Ibs., = W. 

Substituting for A its value 2160PL + aH? we have 


W = 0.0130766PL? +. ak?; P in watts, L in ft. 
W = 13.0766 PkL2 + ak?; Pk in kilowatts, Z in ft. 
W = 364,556,000 PkL2m + aH?; Pk in kilowatts, Lm in miles. 


The weight of copper required varies directly as the power transmitted; 
inversely as the percentage of drop or loss; directly as the square of the 
distance; and inversely as the square of the voltage. 

From the last formula the following table has been calculated. 


WEIGHT OF COPPER WIRE TO CARRY 1000 KILOWATTS WITH 10% LOSS. 





Distance i 
in miles. 1 ta) 10 20 50 100 
RVoltaus Weal cinllie 











500| 145,822 | 3,645,560 
1,000 36,456} 911,390 | 3,645,560 


2,000 9,114) 227,848) 911,390 | 3,645,560 

5,000 1,458 36,456} 145,822] 593,290 | 3,645,560 
10,000 365 9,114 36,456 | 145,822; 911,390] 3,645,560 
20,000 oN 2,278 9,114 36,456 | 227,848 911,390 
AQ O00 etalon STO) 28 9,114 56 ,962 227 848 
GOEOOON Saeiseaeie || a0 iers seeders 1,013 4,051 25,316 101,266 





hr) calculating the distance, an addition of about 5 per cent should be 
made for sag of the wires. 


Short-circuiting.—From the law] = a it is seen that with any 


pressure E,the current J will become very great if Ris made very small. In 
short-circuiting the resistance becomes small and the current therefore 
great. Hence the dangers of short-circuiting a current. 

Economy of Electric Transmission.—Lord Kelvin’s rule for 
the most economical section of conductor is that for which the annual 
interest on capital outlay is equal to the annual cost of energy, wasted. 

Tables have been compiled by Professor Forbes and others in accordance 
with modifications of this rule. For a given entering horse-power the ques- 
tion is merely one as to what current density, or how many amperes per 

square inch of conductor, should be employed. Kelvin’s rule gives about 
393 amperes per square inch, and Professor Forbes’s tables give a current 
density of about 380 amperes per square inch as most economical. 

Bell (Electric Transmission of Power) shows that while Kelvin’s rule cor- 
rectly indicates the condition of minimum cost in transmission for a given 
current and line, it omits many practical considerations and is inapplicable 
to most power transmission work. Each plant has to be considered on its 
merits and very various conditions are likely to determine the line loss in 
different cases. Several cases are cited by Bell to show that neither Kel- 
vin’s law nor any modification of it is a safe guide in determining the proper 
allowance for loss of energy in the line. 

Wire Tables,.—The tables on the following page show the relation 
between load, distance, and *‘drop” or loss by voltage in a two-wire circuit 
of any standard size of wire. The tables are based on the formula 


(21.61L) +A =Drop in volts. 
I=current in amperes, L=distance in feet from point of supply to point 


of delivery. The factors J and Z, are combined in the table, in the com- 
pound factor ‘‘ampere feet,” 


WIRE TABLES. >» HOSY, 


Wire TasteE—RELATION BETWEEN Loap, Distancr, Los3, AND S1zE OF 
CONDUCTOR. 
Table I.—110-volt and 220-volt Two-Wire Circuits, 


Nore.—The numbers in the body of the tables are Ampere-Feet; 1.e., 
Amperes X Distance (length of one wire) in feet. See examples on next page. 





























Wire Sizes; Line Loss in Percentage of the Rated Voltage; and Power 
B. & 8. Gauge. Loss in Percentage of the Delivered Power. 

110 V. | 220 V. 1 14 2 3 4 5 6 8 10 

0000 |21,550 32,325 43,100/64,650/86,200 107,750] 129 ,300| 172 400/215 ,500 

000 |17,080 25,620 34,160/51,240/68,320) 85,400/102,480)136 ,640)170,800 

00 |13,550)20,325)27,100)40,650/54,200| 67,750} 81,300)108 ,400)135 ,500 

0000 0 !10,750}16,125/21,500/32,250)438,000) 53,750) 64,500} 86,000)107 ,500 

000 1 | 8,520)12,780 17,040|25,560/34,080| 42,600) 51,120, 68,160} 85,200 

00 2 | 6,750/10,140) 13,520)]20,280|27,040} 33,800) 40,560] 54,080} 67,600 

0 3 | 5,360] 8,040/10,720/16,080|21,440} 26,800) 32,160] 42,880] 53,600 

1 4 | 4,250] 6,375} 8,500|12,750)17,000| 21,250) 25,500) 34,000] 42,500 

2 5 | 3,370] 5,055} 6,740|10,110}13,480| 16,850) 20,220] 26,960] 33,700 

3 6 | 2,670| 4,005| 5,340) 8,010/10,680) 13,350} 16,020) 21,360) 26,700 

4 7 | 2,120] 3,180} 4,240) 6,360} 8,480} 10,600] 12,720] 16,960) 21,200 

5 8 | 1,680} 2,520} 3,360] 5,040] 6,720) 8,400} 10,800} 13,440) 16,800 

6 9 | 1,330] 1,995] 2,660) 3,990} 5,320) 6,650} 7,980} 10,640) 13,300 

7 10 | 1,055], 1,582) 2,110} 3,165) 4,220| 5,275) 6,330} 8,440) 10,550 

8 11 838| 1,257} 1,675} 2,514] 3,350} 4,190) 5,028) 6,700} 8,380 

9 12 665} 997] 1,330) 1,995} 2,660) 3,320) 3,990} 5,320) 6,650 

10 13 527| 790) 1,054) 1,580) 2,108} 2,635} 3,160) 4,215) 5,270 

11 14 418] 627) 836] 1,254] 1,672) 2,090} 2,508) 3,344) 4,180 

LOA ria | 332| 498] 665) 997] 1,830) 1,660} 1,995) 2,660) 3,325 

14 Alar & 209} 313] 418} 627] 836) 1,045} 1,354) 1,672) 2,090 




















Table Ei.—500, 1000, and 2000 Volt Circuits. 
































Wire Sizes; Line Loss in Percentage of the Rated Voltage; and 
B.& 8S. Gauge. Power Loss in Percentage of the Delivered Power. 
500 V. }1000 V.} 2000 V. a 14 2 24 3 4 5 

0000 0 97,960} 146 ,940|195 ,920)244 900/293 ,880/391 ,840/489 ,800 
000 1 77,690} 116,535) 155,380) 194 ,225)233 ,970|310,760/388 ,450 
00 2 61,620) 92,430)123 ,240| 154,050) 184,860) 246 ,480/308 ,100 
0000 0 3 48,880] 73,320] 97,760) 122 ,200/146 640) 195 420/244 ,400 
000 1 4 38,750} 58,125} 77,500} 96,875|116,250) 155 ,000)193,750 
00 2 5 30,760} 46,140} 61,520) 76,900] 92,280) 123 ,040)153,800 
0 3 6 24,370} 36,555} 48,740} 60,925] 73,110) 97,480)121,850 
1 4 ff 19,320} 28,980] 38,640] 48,300} 57,960) 77,280) 96,600 
2 5 8 15,320] 22,980) 30,640) 38,300) 45,960} 61,280| 76,600 
3 | 6 9 12,150] 18,225! 24,300} 30,375] 36,450] 48,300| 60,750 
4 7 10 9,640] 14,460) 19,280] 24,100] 28,920) 38,560} 48,200 
5 8 11 7,640] 11,460} 15,280] 19,100) 22,920) 30,560) 38,200 
6 9 12 6,060} 9,090) 12,120) 15,150) 18,180) 24,240) 30,300 
7 10 13 4,805| 7,207) 9,610) 12,010) 14,415) 19,220; 24,025 
8 11 14 3,810} 5,715) 7,620) 9,525) 11,480) 15,220) 19,050 
9 12 nae 3,020} 4,530} 6,040} 7,550) 9,060; 12,080) 15,100 
10 13 iG 2,395! 3,592) -4,790) 5,985) 7,185} 9,580 11,975 
11 14 Kd 1,900} 2,850} 3,800) 4,750} 5,700) 7,600) 9,500 
12 i: 5 1,510) 2e265iee3 020) 3,775! 4,530K) 6,040)" 7yo50 
14 a Ae 950} 1,425) 1,900} 2,875) 2,850} 3,800) 4,750 











| SS ee 


1038 - ELECTRIGAL ENGINEERING. 


EXAMPLES IN THE USE or THE Wire Tasies.—1. Required the 
maximum load in amperes at 220 volts that can be carried 95 feet by No. 6 
wire without exceeding 144% drop. 

Find No. 6 in the 220-volt column of Table I; opposite this in the 144% 
column is the number 4005, which is the ampere-feet. Dividing this by the 
required distance (95 feet), gives the load, 42.15 amperes. 

Example 2. A 500-volt line is to carry 100 amperes 600 feet with a drop 
not exceeding 5%; what size of wire will be required? 

The ampere-feet will be 100 x 600 =60,000. Referring to the 5% column 
of Table II, the nearest number of ampere-feet is 60,750, which is opposite 
No. 3 wire in the 500-volt column. d 

These tables also show the percentage of the power delivered to a line 
that is lost in non-i1 ductive alternating-current circuits. Such circuits are 
obtained when the load consists of incandescent lamps and the circuit wires 
lie only an inch or two apart, as in conduit wiring. 

Efficiency of Long-distance Transmission, (Ff. R. Hart, 
Power, Feb. 1892.)— The mechanical efficiency of a system is the ratio of the 
power delivered to the dynaimo-electric machines at one end of the line to 
the power delivered by the electric motors at the distant end. The com: 
mercial efficiency of a dynamo or motor varies with its load. Under the 
most favorable conditions we must expect a loss of say 9%in the dynamo 
and 9%in the motor. The loss in transmission, due to fall in electrical pres- 
sure or *‘drop”’ in the line, is governed by the size of the wires, the other 
conditions remaining the same. For a long-distance transmission plant 
this will vary from 5% upwards. With a loss of 5% in the line the total 
efficiency of transmission will be slightly under 79%. With a loss of 10% ir 
the line it will be slightly under 75%. We may call 80% the practical limit of 
the efficiency with the apparatus of to-day. The methods for long-distance 
transmission may be divided into three general classes: (1) continuous cur- 
rent; (2) alternating current; and (#) regenerating or ‘‘motor-dynamo” 
Systems. 

There are many factors which govern the selection of asystem. For each 
problem considered there will be found certain fixed and certain unfixed 
conditions. In general the fixed factors are: (1) capacity of source of 
power; (2) cost of power at source; (3) cost of power by othermeans at point 
of delivery; (4) danger considerations at motors; (5) operating conditions; 
(6) construction conditions (length of line, character of country, ete.).. The 
partly fixed conditions are: (7) power which must be delivered, i.e., the effi- 
ciency of the system; (8) size and number of delivery units. The variable 
conditions are: (9) initial voltage; (10) pounds of copper on line; (11) origi- 
nal cost of all apparatus and construction: (12) expenses, operating (fixed 
charges, interest, depreciation, taxes, insurance, etc.); (18) liability of trouble 
and stoppages; (14) danger at station and on line; (15) convenience in oper- 
ating, making changes, extensions, ete. 

The relative advantages of different systems vary with each particular 
transmission problem, but in a general way may be tabulated as below: 








System. Advantages. Disadvantages. 
1 Low voltage. |Safety, simplicity. Expense for copper. 
DF TS ee Te oe ge ee Se ee 2 ee 
a High voltage. : ‘ai Danger; difficulty of 
E Economy» IMIBUelEN building machines. 
5 Sy ee te ne ee eee 
& : Low voltage on machines : : 
rn 3-wire. and saving in copper, |Not saving enough in 
iS "| eopper for long dis- 





: : Low voltage at machines! tances. Necessity for 
Multiple-wire. and eave in copper. ‘** balanced ” system. 


| 


Cannot start under load. 
Single phase. Economy of copper. Low efficiency. 








Economy of copper, syn- 
: chronous speed unnec-|Requires more than twa 
Multiphase. essary; applicable to] wires. 

very long distances. 





High-voltage transmis- 


; a ja.) Expensive. 
Motor-dynamo. Sala voltage de bw éfficioncy: 


Alternating. 


TABLE OF ELECTRICAL HORSE-POWERS., 1039 


. 
y 


TABLE OF ELECTRICAL HORSE-POWERS. 


woe meres =H.P., or 1 volt-ampere = .0013405 H.P. 


Read amperes at top and volts at side, or vice versa. 


formula: 





Volts or Amperes. 





50 60 | 70 80 90 | 100 | 110 | 120 




















0570} .0804] .0938} .1072| .1206) .1841) 1475) .1609 
1341] .1609| .1877) .2145| .2413] .2681) .2949| (4217 
-2011| .2413] .2815) .3217| .3619| .4022) .4424/ .4826 
2681} .8217] .3753] .4290} .4826| .5362) .5898) 6434 
3351] 4022] .4692) .5362) .6032| .6708) .7373) .8043 
4022} 4826] .5630} .6434) .7239) .8043) .8847] .9652 
.4692| .5630| .6568) .7507| .8445) .9384! 1.032 | 1. 
.5362| .6434] .7507| .8579| .9652| 1.072 | 1 180 | 1.287 

1 

1 





.6032] .7239} .8445| .9652) 1.086 | 1.206 | 1.327 
6703] .8043] .9383} 1.072 | 1.206 | 1.341 | 1.475 


.7373| 8847} 1.032 | 1.180 } 1.327 | 1.475 | 1.622 | 1.769 
8043] .9652] 1.126 | 1.287 } 1.448 | 1.609 | 1.769 | 1.930 
.8713| 1.046 } 1.220 | 1.394 | 1.568 | 1.743 ) 1.917 | 2.091 
.9384! 1.126 | 1.314 | 1.501 | 1.689 | 1.877 | 2.064 | 2.252 
1.005 | 1.206 | 1.408 | 1.609 | 1.810 | 2.011 } 2.212 | 2.413 


1.072 | 1.287 | 1.501 | 1.716 | 1.980 | 2.145 | 2.359 | 2.574 
: 1.139 | 1.867 | 1.595 | 1.823 | 2.051 | 2.279 | 2.507 | 2.736 
1.206 | 1.448 | 1.689 | 1.930 | 2.172 | 2.413 | 2.654 | 2.895 
1.273 | 1.528 | 1.783 | 2.037 | 2.292 | 2.547 | 2.801 | 3.056 
1.340 | 1.609 | 1.877 | 2.145 | 2.413 | 2.681 | 2.949 | 3.217 


1.408 | 1.689 | 1.971 | 2.252 | 2.533 | 2.815 | 3.097 | 3.378 
1.475 | 1.769 | 2.064 | 2.359 | 2.654 | 2.949 | 3.244 | 3.539 
1.542 .| 1.850 | 2.158 | 2.467 | 2.775 | 3,083 | 3.391 | 8.700 
1.609 | 1.930 | 2.252 | 2.574 | 2.895 | 3.217 | 3 539 | 3.861 
1.676 | 2.011 | 2.346 | 2.681 | 3.016 | 3.351 | 3.686 | 4.022 


1.743 | 2.091 | 2.440 | 2.788 | 3.137 | 3.485 | 3.834 | 4.182 
1.810 | 2.172 | 2.534 | 2.895 | 3.257 | 3.619 | 3.981 | 4.343 
1.877 | 2.252 | 2.627 | 3.003 | 3.378 | 3.753 | 4.129 | 4.504 
1.944 | 2.332 | 2.721 | 3.110 | 3.499 | 3.887 | 4.276 | 4.665 
2.011 | 2.413. | 2.815 | 3.217 | 3.619 | 4.022 | 4.424 | 4.826 


2.078 | 2.493 | 2.909 | 3.324 | 3.740 | 4.156 | 4.571 | 4.987 
2.145 | 2.574 | 3.003 | 3 482 | 3.861 | 4.290 | 4.719 | 5.148 
2.212 | 2.654 | 3.097 | 3.539 | 3.986 | 4.424 | 4.866 | 5.308 
2.279 | 2.735 | 3.190 | 3.646 | 4.102 | 4.558 | 5.013 | 5.469 
2.346 | 2.815 | 3.284 | 3.753 | 4.223 | 4.692 | 5.161 | 5.680 
49| .05362; .5362| 1.072) 1.609) 2.145) 2.681) 3.217] 3.753) ra 4.826) 5.363} 5.898) 6.434 

















45| .06032) .6032| 1.206] 1.810] 2.413! 3.016 3.619] 4.223 5.439) 6.032] 6.635) 7.239 

59! .06703| .6703| 1.341) 2.011) 2.681] 3.351; 4.022] 4.692 6.032] 6.703) 7.37% ‘ 

55| .07373| .7373/ 1.475/ 2.212] 2.949] 3.686] 4.424| 5.161| 5.898! 6.635) 7.373/ 8 

60} (8043) .8043} 1.609) 2.413} 3.217] 4.022) 4.826] 5.630) 6.434] 7.239) 8.043) 8. 

65) 08713) .8713| 1.743) 2.614) 3.485} 4.357/ 5.228] 6.099) 6.970) 7.842) 8.713 hocos 10.46 
il 








70} 09384) .9384/ 1.877] 2.815} 3.753] 4.692) 5.630| 6.568) 7.507) 8.445) 9.384 
75| .10054] 1.005 | 2.011} 3.016] 4.021] 5.027) 6.032) 7.037) 8.043; 9.048] 10.05 


80| .10724| 1.072) 2.145) 3.217] 4.290) 5.362) 6.434) 7.507} 8.579) 9.652) 10.72 | 11.80 | 12.87 
85| .11394) 1.139] 2.279) 3.418] 4.558] 5.697| 6.836] 7.976] 9.115} 10.26 | 11.39 | 12.53 | 13.67 
90} .12065| 1.206) 2.413) 3.619] 4.826] 6.032) 7.239] 8.445} 9.652] 10.86 | 12.06 | 13.27 | 14.48 
95| 12725! 1.273] 2.547| 38.820) 5.094) 6.367) 7.641} 8.914) 10.18 | 11.46 | 12.73 | 14.01 | 15.28 
100| .1340b) 1.341) 2.681) 4.022] 5.362) 6.703) 8.043/ 9.384) 10.72 | 12.06 | 13.41 | 14.75 | 16.09 


£00| .26810] 2.681| 5.362} 8.043] 10.72 | 13.41 | 16.09 | 18.77) 21.45] 24.13) 26.81] 29.49] 32.17 
300) .40215| 4.022) 8.043) 12.06 | 16.09 } 20,11 | 24.13 | 28.15) 32.17) 36.19} 40.22! 44.24) 48.26 
400| .63620) 5.362/10.72 | 16.09 | 21.45 | 26.81 | 32.17 | 87.53} 42.90] 48.26) 53.62 58.98) 64.34 - 
500] .67025) 6.703)13.41 | 20.11 | 26.81 | 33.51 | 40.22 | 46.92) 63.62) 60.32) 67.03, 73.73) 80.43 
600] .80430) 8.048/16.09 | 24.13 | 32.17 | 40.22 | 48.26 | 56.30) 64.34) 72.39) 80.43) 88.47] 96.52 


700! .93835| 9.384] 18.77) 28.15) 37.53 | 46.92 | 56.30 | 65.68) 75.07] 84.45} 93.84! 103.2 | 112.6 
800] 1.0724) 10.72 | 21.45) 32.17] 42.90 | 53.62 | 64.34 | 75.07) 85.79] 96.52) 107.2 | 118.0 | 128.7 
900| 1.2065] 12.06 | 24.13) 36.19] 48.26 } 60.32 | 72.39 | 84.45) 96.52] 108.6 | 120.6 | 132.7 | 144.8 
1,000] 1.3405] 13.41 | 26.81} 40.22 | 53.62 | 67.03 | 80.43 | 93.84) 107.2 | 120.6 | 134.1 | 147.5 | 160.9 
2,000) 2.6810} 26.81 | 53.62) 80.43 |107.2 |134.1 |160.9 |187.7 | 214.5 | 241.3 | 268.1 | 294.9 | 321.7 


8,000} 4.0215) 40.22 | 80.43 120.6 |160.9 [201.1 [241.3 [281.5 | 321.7 | 361.9 | 402.2 | 442.4 | 482.6 
4,000] 5.4620] 53.62 |107.2 |160.9 |214.5 268.1 (321.7 |375.3 | 429.0 | 482.6 | 536.2 | 589.8 | 643.4 
5,000} 6.7025) 67.03 |134.1 201.1 |268.1 |335.1 (402.2 |469.2 | 536.2 | 603.2 | 670.3 | 737.3 | 804.9 
6,000) 8.0430, 80.43 |160.9 |241.3 |321.7 402.2 [482.6 |563.0 | 643.4 | 723.9 | 804.3 | 884.7 | 965.9 
7,000| 9.3835! 93.84 |187.7 |281.5 |375.3 /469.2 (563.0 [656.8 | 750.7 | 844.5 | 938.4 /1032 {1126 


'8,000|10.724 |107.2 |214.5 $21.7 |429.0 |536.2 (643.4 [750.7 | 857.9 | 965.2 1072 {1180 1287 
9,000/12.065 {120.6 |241.3 361.9 |482.6 [603.2 [723.9 |844.5 | 965.2 |1086 |1206 §=|1327 = 1448 
0,000|13.405 |134.1 268.1 402.2 1536.2 [670.3 |804.3 (938.3 |1072 [1206/1341 1476 1609 
i a Se = 


























1040 ELECTRICAL ENGINEERING. 


Cost of Copper for Long-distance Transmissione 
(Westinghouse El. & Mfg. Co.) 

Cost oF COPPER REQUIRED FOR THE DELIVERY OF ONE MECHANICAL HORSE4 
POWER AT Motor SHAFT WITH 1000, 2000, 3000, 4000, 5000, and 10,000 VoLts 
at Motor TERMINALS, OR AT TERMINALS OF LOWERING TRANSFORMERS. 
Loss of energy in conductors (drop) equals 20%. Motor efficiency, 90%. 
Length of conductor per mile of single distance, 11,000 ft., to allow for sag. 
Cost of copper taken at 16 cents per pound. 


_— —_— 


| 
Miles. 1000 v. 2000 v. | 3000 v. 4000 v. 5000 v. | 10,000 v. 


| | ———— =. < mate) a 














——— 


1 $2.08 $0.52 $0.23 $0.13 $0.08 $0.02 
2 8.33 2.08 0.93 0.52 0.33 0.08 
3 18.70 4.68 2.08 iPS 0.75 0.19 
4 33.30 8.32 3.70 2.08 1.33 0.33 
5 52.05 13.00 5.78 3.25 2.08 0.52 
6 74.90 18.70 8.32 4.68 3.00 0.75 
7 102.00 25.50 11.30 6.37 4.08 1.02 
8 133.25 33.30 14.80 8.32 5.33 1.33 
9 168.60 42.20 18.70 10.50 6.74 1.69 
10 208.19 52.05 23.14 13.01 8.33 2.08 
11 251.90 63.00 28.00 15.75 10.08 2.52 
12 299.80 75.00 33.30 18.70 12.00 3.00 
13 352.00 88.00 39.00 22.00 14.08 3.52 
14 408.00 102.00 45.30 25.50 16.32 4.08 
15 468.00 117.00 52.00 29.25 18.72 4.68 
16 533.00 133.00 59.00 33.30 21.32 5.33 
17 600.00 150.00 67.00 37.60 24.00 6.00 
18 675.00 169.00 75.00 42.20 27.00 6.75 
19 750.00 188.00 83.50 47.00 30.00 7.50 
20 833.00 208.00 92.60 52.00 33.32 8.33 


Cost oF COPPER REQUIRED TO DELIVER ONE MECHANICAL HORSE-POWER AT 
Moror-SHAFT WITH VARYING PERCENTAGES OF Loss IN CONDUCTORS, UPON 
THE ASSUMPTION THAT THE POTENTIAL AT Motor TERMINALS IS IN EHAcH 
Cass 3000 Vourts. 


Motor efficiency, 90%. Cost of copper equals 16 cents per pound. 
Length of conductor per mile of single distance, 11,000 ft., to allow for sag, 








—— 

















Miles. 10% 15% 20% 25% 30% 
1 $0.52 $0.33 $0.23 $0.17 $0.13 
2 2.08 1.31 0.93 0.69 0.54 
3 4.68 2.95 2.08 1.55 1.21 
4 8.32 5.25 3.70 2.77 2.15 
5 13.00 8.20 5.78 4.33 3.37 
6 18.70 11.75 8.32 6.23 4.85 
Z 25.50 16.00 11.30 8.45 6.60 
8 33.30 21.00 14.80 11.00 8.60 
9 42.20 26.60 18.75 14.00 10.90 

10 52.05 32.78 23.14 17.31 13.50 
11 63.00 39.75 28.00 21.00 16.30 
12 75.00 47.20 33.30 24.90 19.40 
13 §8.00 55.30 39.00 29.20 22.80 
14 102.00 64,20 45.30 33.90 26.40 
15 117.00 73.75 52.00 38.90 30.30 
16 133.00 83.80 59.00 44.30 34.50 
17 150.00 94.75 67.00 50.00 39.00 
18 169.00 106.00 75.00 56.20 43.80 
19 188.00 118.00 83.50 62.50 48.70 


ELECTRIC TRANSMISSION, 1041 


Systems of Electrical Distribution in Common Use, 


I, Drrecr Current. 
A. Constant Potentia 
110 to it and 520 to 250}Volts.— Distances less than, say, 1500 
eet 

For incandescent lamps. 

For arc-lamps, usually 2 in series. 

For motors of ‘moderate sizes. 

200 to 250 and 440 Volts, 3-wire.—Distances less than, say, 
5000 feet. 

For incandescent lamps. 

For arc-lamps, usually 2 in series on each branch. 

For motors 110 or 220 volts, usually 220 volts. 

500 Volts.—Distances less than, say, 20,000 feet. 
Incidentally for arc-lamps, usually 10 in series. 
For motors, stationary and street-car. 
B. Constant Current. 
Usually 5, 64, or 94 amperes, the volts increasing to several 
thousand, as demanded, for arc-lamps. 
II. ALTERNATING CURRENT. 
- Constant Potential. 
For incandescent lamps, arc-lamps, and motors. 
Ployphase Systems. 

For are and incandescent lamps, motors, and rotary con- 
verters for giving direct current. 

Ployphase—2- and 3-phase—high tension (25,000 volts and 
over), for long-distance transmission; transformed by 
step-up and step-down transformers. 

B. Constant Current. 
Usually 5 to 6.6 amperes. For arc-lamps. 

References on Power DisteihutionwAT hott. Electric Trans~- 
mission of Energy; Bell, Electric Power Transmission; Cushing, Standard 
Wiring for Incandescent Light and Power; Crocker, Electric Lighting, 2 
vols.; Poole, Electric Wiring. 


ELECTRIC RAILWAYS. 


Space will not admit of a proper treatment of this subject in this work. 
Consult Crosby and Bell, The Electric Railway in Theory and Practice ; 
Fairchild, Street Railways ; Merrill, Reference Book of Tables and Formule 
for Street Railway Engineers ; Bell, Electric Transmission of Power ; Daw- 
son, Engineering and Electric Traction Pocket-book. 


ELECTRIC LIGHTING. 


Are Lights.—Direct-current open arcs usually require about 10 am- 
peres at 45 volts. or 450 watts. The range of voltage is from 42 to 52 for 
ordinary ares. The most satisfactory light is given by 45 to 47 volts. 
Search. light projectors use from 50 to 100 amperes at 48 to 53 volts. 

The candle- power of an arc light varies according to the direction in which 
the light is measured; thus we have, 1, mean horizontal candle-power; 
2, maximum candle-power. which is usually found at an angle below the 
horizontal; 3. mean spherical candle-power; 4, mean hemispherical candle- 
power, below the horizontal. 

The nominal candle-power of an are Jamp is an arbitrary figure. A 450- 
watt are is commonly called 2000 c.-p. and a 300-watt arc is 1200 c.-p. 
These figures greatly exceed the true candle-power. Carhart found with 
an arc of 10 amperes and 45 volts a maximum c.-p. of 450, but with the 
same watts 8.4 amperes, and 54 volts he obtained 900 c.-p. Blondel. 
however, found the ¢.-p. a maximum usually below 45 volts. Crocker 
explains ‘the discrepancy as probably due to a difference in size and quality 
of the carbons. 

Current for are lighting is furnished either on the series. constant current, 
or on the parallel constant potential system. In the latter the voltage 
of the circuit is usually 110 and two lamps are connected in series. In 
currents with higher voltages more lamps are us sed in series; for instance 
10 with a 500-volt circuit 


é 


1042 ELECTRICAL ENGINEERING. 
L 


Enclosed Arcs---Direct current enclosed arcs consume about 5 amperes 
at 80 volts. or 400 watts. The chief advantages of the enclosed ares, on 
constant potential circuits are the long life of the carbons, 100 to 150 
hours, as compared with 8 to 10 hours for open ares; simplicity of con- 
struction, absence of sparks, agreeable quality and better distribution of 
light. 

Alternating-current enclosed arcs usually take a current of 6 amperes at 
70 or 75 volts. With 70 volts and 6 amperes, in a 104-volt circuit, the 
apparent watts at the lamp terminals are 625 and at the are 420, the actual 
watts being 445 and 390 respectively. The watts consumed in the inductive 
resistance average 35 to 45. ; 

Incandescent Lamps,.—Candle-power of nominal 16 c.p. 110-volt 
lamp; 

Mean horizontal 15.7 to 16.6 

Mean spherical 12.7 to 13.8 

Mean hemispherical 14.0 to 14.6 

Mean within 30° from tip 7.9 to 10.9 

- Ordinary lamps take from 3 to 4 watts per candle-power. A 16 candle- 
power lamp using 3.5 watts per candle-power or 56 watts at 110 volts takes 
a current of 56 + 110 = 0.51 ampere. For a given efficiency or watts per 
candle-power the current and the power increase directly as the candle- 
power. An ordinary lamp taking 56 watts, 13 lamps take 1 H.P. of elec- 
trical energy, or 18 lamps 1.008 kilowatts. 

Variation in Candle-Power, Efficiency, and Life.—The 
following table shows the variation in candle-power, etc., of the General 
Electric Co.’s standard 100 to 125 volts, 3.1 and 3.5 watt lamps, due to vari- 
ation in voltage supplied to them. It will be seen that if a 3.1 watt lamp 
is run at 10 per cent below its normal voltage, it may have over 9 times 
as long a life, but it will give only 53 per cent of its normal lighting power, 
and the light will cost 50 per cent more in energy per ‘candle-power. If 
it is run at 6 per cent above its normal voltage, it will give 37 per cent 
more light, will take nearly 20 per cent less energy for equal light power, 
but it will have less than one third of its normal life. 





Efficiency in : 
Per cent of} Per cent of ivatteieer Relative 


Normal |Normal Can- Life’ 3.1 
Voltage. | dle-power, | Candie, 3-1 


Efficiency in ; 
watts per Hees 

watt Lam Candle, | 25 evs 

watt Lamp. P-) 3/5 watts. | 00 watts. - 


cnr mm | a 





90 53 4.65 9.41 5.36 

91 57 4.44 7.16 5.09 

92 61 4.24 5.55 4.85 

93 65 4.10 4.35 4.63 

94 69.5 3.90 3.45 4.44 3.94 
95 74. 3.75 2.75 4.26 3.10 
96 79 3.60 2.20 4.09 2.47 
97 84 3.45 1.79 3.93 1.95 
98 89 3.34 1.46 3.78 1.53 
99 94.5 oe 1.21 3.64 1.26 
100 100 3.10 1.00 3.50 1.00 
101 106 2.99 .818 3.38 84 
102 112 2.90 681 Siasnd) 68 
103 118 2.80 .562 3.16 58 
104 124 2.70 ~A52 3.05 AT 
105 130 2.62 37. 2.95 39 
106 137 2.54 +3810 2.85 31 








The candle-power of a lamp falls off with its length of life, so that during 
the latter half of its life it has only 60 per cent or 70 per cent of its rated 
candle-power, and the watts per candle-power are increased 60 per cent or 
70 per cent. After a lamp has burned for 500 or 600 hours it is more eco- 
nomical to break it and supply a new one if the price of electrical energy 
is that usually charged by central stations, 


s 


ELECTRIC WELDING. as 1045 


Specifications for Lamps.  (Crocker.)—The initia) candle-power 
of any lamp at the rated voltage should not be more than 9 per cent above 
or below the value called for. The average candle-power of a lot should 
be within 6 per cent of the rated value. The standard efficiencies are 32.1 
3.5, and 4 watts per candle-power. Each lamp at rated voltage should 
take within 6 per cent of the watts specified, and the average for the lot 
should be within 4 per cent. The useful life of a lamp is the time it will 
burn before falling to a certain candle-power, say 80 per cent of its initial 
candle-power. For 3.1 watt lamps the useful life is about 400 to 450 
hours. for 3.5 watt lamps about 800, and 4 watt lamps about 1600 hours. 

Special Lamps.—The ordinary 16 c.-p. 110-volt is the standard 
for interior lighting. Thousands of varieties of lamps for different voltages 
and candle-power are made for special purposes, from the primary lamp, 
supplied by primary batteries using three volts and about 1 ampere and 
giving 4 ¢c.-p., and the 34 ¢c.-p. bicycle lamp, 4 volts and 0.5 ampere, to lamps 
of 100 e.p. at 220 volts. Series lamps of 1 c.-p. are used in illuminating 
signs, % ampere and 12.5 to 15 volts, eight lamps being used on a 110-volt 
circuit. Standard sizes for different voltages, 50, 110, or 220, are 8, 16, 
24, 32, 50, and 100 c.-p. as 

Nernst Lamp.—A form of incandescent ‘lamp originated by Dr. 
Walther Nernst, of Géttingen, is being developed in this country by the 
Nernst Lamp Company, Pittsburg, Pa. It depends for its operation upon 
the peculiar property of certain rare earths, such as yttrium, thorium, zir- 
conium, etc., of becoming electrical conductors when heated to a certain 
temperature; when cold, these oxides are non-conductors. ‘The lamp com- 
prises a ‘‘glower’’ composed of rare earths mixed with a binding material 
and pressed into a small rod; a heater for bringing the glower up to the con- 
ducting temperature; an automatic cut-out for disconnecting the heater 
when the glower lights up, and a ‘‘ballast” consisting of a small resistance 
coil of wire having a positive temperature-resistance coefficient. The bal- 
last is connected in series with the glower; its presence is required to com- 
pensate the negative temperature-resistance coefficient of the glower; with- 
out the ballast, the resistance of the glower ; 
would become lower and lower as its temper- 
ature rose, until the flow of current through it 
would destroyit. Fig. 171lashows the element- 
ary circuits of a simple Nernst lamp. The 
cut-out is an electromagnet connected in series 
with the glower. When current begins to flow 
through the glower, the magnet pulls up the 
armature lying across the contacts of the cut- 
out, thereby cutting out the heater. The 
heater is a coil of fine wire either located very 
near the glower or encircling it. The glower 
is from’1/32 to 1/16 inch in diameter and about 
1 inch long. 

The material of the glower is an electrolyte, 
so that this type of lamp is not well adapted 
for operation on direct-current circuits be- 
cause of the wasting away at the positive end 
and the deposition of material at the nega- Fie. 171a. 
tive end. 

The lamps are made with one glower, or with two, three, or six glowers 
Aes in parallel, and for operation on 100 to 120 and 200 to 240 volt 
circuits. 





1044 ELECTRICAL ENGINEERING. 


ELECTRIO WELDING. 


The apparatus most generally used consists of an alternating-current. 
dynamo, feeding a comparatively high-potential current to the primary coil 
of an induction-coil or transformer, the secondary of which is made so 
large in section and so short in length as to supply to the work currents 
not exceeding two or three volts, and of very large volume or rate of flow. 
The welding clamps are attached to the secondary terminals. Other forms 
of apparatus, such as dynamos constructed to yield alternating currents 
direct from the armature to the welding-clamps, are used to a limited 
extent. 

The conductivity for heat of the metal to be welded has a decided influ- 
ence on the heating, and in welding iron its comparatively low heat conduc~ 
tion assists the work materially. (See papers by Sir F. Bramwell, Proc. 
Inst. C. E., part iv., vol. cii. p. 1; and Elihu Thomson, Trans. A. I. M.E., xix. 
877.) 

Fred. P. Royce, Iron Age, Nov, 28, 1892, gives the following figures show- 
ing the amount of power required to weld axles and tires: 


AXLE-WELDING, 


Seconds. 
1-inch round axle requires 25 H.P. for........... Ailde'sleate ate teltsae pan 
l-inch square axie requires 80) Hi PStormcsacteincs eens snes fSOI CaS 
1144-inch round axle requires 35 H.P. for......... dala Celotetn el dale etl ancOO 
114-inch square axle requires 40 H.P. for........ Sina ear soGhs 70 
2-inch round axle requires 75 H.P. for............ Blatant enc.cteents 95 
2-inch square axle requires 90 H.P. for....... Shad de bck veneeetes 100 


The slightly increased time and power required for welding the square 
axle is not only due to the extra metal in it, but. part to the cave which it 
is best to use to secure a perfect alignment. 


TIRE-WELDING. 


Seconds. 
1 X 3/16-inch tire requires 11 H.P. for.......... SSS UT Re ee IS 
114 x 3é-inch tire requires 23 H.P. for............ GE. STS RE 25 
1144 X 3@-inch tire requires 20 H.P. for........ asl tElahh Ob ate Seal late eee 30 
1144 x %-inch tire requires 23 H.P, for........ Deseo triste aateln ae ohare 40 
2x 14-inch-tire requires 29 H/Poforitey eel... OEP ES ote decent ee 55 
2 x 34-inch tire requires 42 H.P. for....... PAU LEET Re eet tne 62 


The time above given for welding is of course that required for the actual 
application of the current only, and does not include that consumed by 
placing the axles or tires in the machine, the removal of the upset and 
other finishing processes. From the data thus submitted, the cost of welding 
can be readily figured for any locality where the price of fuel and cost of 
labor are known. 

In almost all cases the cost of the fuel used under the boilers for produc- 
ing power for electric welding is practically the same as the cost of fuel 
used in forges for the same amount of work, taking into consideration the 
difference in price of fuel used in either case. 

Prof. A. B. W. Kennedy found that 24-inch iron tubes 44 inch thick were 
welded in 61 seconds, the net horse-power required at this speed being 23.4 
(say 33 indicated horse-power) per square inch of section. Brass tubing re 
quired 21.2 net horse-power. About 60 total indicated horse-power would be 
required for the welding of angle-irons 3 x 3 * % inch in from two to three 
minutes. Copper requires about 80 horse-power per square inch of section, 
and ‘an inch bar can be welded in 25 seconds. It takes about 90 seconds to 
weld a stee] bar 2 inches in diameter. 


ELECTRIC HEATERS, 


Wherever a comparatively small amount of heat is desired to be auto- 
matically and uniformly maintained, and started or stopped on the instant 
without waste, there is the province of the electric heater. 

The elementary form of heater is some form of resistance, such as coils 
of thin wire introduced into an electric circuit and surrounded with a sub- 
stance, which will permit the conduction and radiation of heat, and at the 
saine time serve to electrically insulate the resistance. 

This resistance should be proportional to the electro-motive force of the 
current used aud to the equation of Joule’s law ; 


ELECTRICAL ACCUMULATORS OR STORAGE-BATTERIES. 1045 


H=I?Rt X 0.24, 
where J is the current in amperes; R, the resistance in ohms; ¢, the time in 
seconds; and H, the heat in gram-centigrade units. 

Since the resistance of metals increases as their temperature increases, a 
thin wire heated by current passing through it will resist more, and grow 
hotter and hotter until its rate of loss of heat by conduction and radiation 
equals the rate at which heat is supplied by the current. In a short wire, 
before heat enough can be dispelled for commercial purposes, fusion will 
begin; and in electric heaters it is necessary to use either Jong lengths of 
thin wire, or carbon, which alone of all conductors resists fusion. In the 
majority of heaters, coils of thin wire are used, separately embedded in 
some substance of poor electrical but good thermal conductivity. 

The Consolidated Car-heating Co.’s electric heater consists of a galvanized 
iron wire wound in a spiral groove upon a porcelain insulator. Each heater 
is 305 in. long, 8% in. high, and 65g in. wide. Upon it is wound 392 ft. of 
wire. The weight of the whole is 2314 ibs. 

Each heater is designed to absorb 1000 watts of 1 500-volt current. Six 
heaters are the complement for an ordinary electric car. For ordinary 
weather the heaters may be combined by the switch in different ways, so 
that five different intensities of heating-surface are possible, besides the 
position in which no heat is generated, the current being turned entirely off. 

For heating an ordinary electric car the Consolidated Co. states that 
from 2 to 12 amperes on a 500-volt circuit is sutficient. With the outside 
temperature at 20° to 30°, about 6 amperes will suffice. With zero or lower 
temperature, the full 12 amperes is required to heat a car effectively. 

Compare these figures with the experience in steam-heating of railway- 
cars, as follows: 

1 B.T.U. = 0.29084 watt-hours. 

6 amperes on a 500-volt circuit = 3000 watts. 

A current consumption of 6 amperes will generate 8000 + 0.29084 = 10,315 
B.T.U. per hour. 

In steam-car heating, a passenger coach usually requires from 60 lbs. of 
steam in freezing weather to 100 lbs. in zero weather per hour. Supposing 
the steam to enter the pipes at 20 lbs. pressure, and to be discharged at 200° 
F., each pound of steam will give up 983 B,T.U. to the car. . Then the 
equivalent of the thermal units delivered by the electrical-heating system in 
pounds of steam, is 10,315 + 983 = 1014, nearly. 

Thus the Consolidated Co.’s estimates for electric-heating provide the 
equivalent of 10% lbs. of steam per car per hour in freezing weather and 21 
Ibs. in zero weather. 

Suppose that by the use of good coal, careful firing, well-designed boilers, 
and triple-expansion engines we are able in daily practice to generate 
fi og delivered at the fly-wheel with an expenditure of 24% lbs. of coal per 

our. 

We have then to convert this energy into electricity, transmit it by wire 
to the heater, and convert it into heat by passing it through a resistance-coil. 
We may set the combined efficiency of the dynamo and line circuit at 85%, 
and will suppose that all the electricity is converted into heat in the resist- 
ance-coils of the radiator. Then 1 brake H.P. at the engine = 0.85 electrical 
H.P. at the resistance-coil = 1,683,000 ft.-lbs. energy per hour = 2180 heat- 
units. But since it required 214 lbs. of coal to develop 1 brake H.P., it fol- 
lows that the heat given out at the radiator per pound of coal burned in the 
boiler furnace will be 2180 + 244 = 872 H.U. An ordinary steam-heating 
system utilizes 9652 H.U. per |b. of coal for heating; hence the efficiency 
of the electric system is to the efficiency of the steam-heating system as 872 
to 9652, or about 1 toll. (Hng’g News, Aug, 9, °90; Mar, 30, 92; May 15, 93.) 


ELECTRICAL ACCUMULATORS OR STORAGE= 
BATTERIES. 


The original, or Planté, storage battery consisted of two plates of metallic 
lead immersed in a vessel containing sulphuric acid. An electric current 
being sent through the cell thesurface of the positive plate was converted into 
peroxide of lead, PbO,. This was called charging the cell, After being thus 
charged the cell could be used as a source of electric current, or discharged, 
Planté and other authorities consider that in charging, PbOg is formed on 
the positive plate and spongy metallic lead on the negative, both being con- 


1046 ELECTRICAL ENGINEERING. 


verted into lead oxide, PbO, by the discharge, but others hold that sulphate 
of lead is made on both plates by discharging and that during the charging 
PbO, is formed on the positive plate and metallic Pb on the other, sulphuric 
acid being set free. 

The acid being continually abstracted from the electrolyte as the discharge 
proceeds, the density of the solution becomes less. In the charging opera- 
tion this action is reversed, the acid being reinstated in the liquid and 
therefore causing an increase in its density. 

The difference of potential developed by lead and lead peroxide immersed 
in dilute H.SO, is about two volts. A lead-peroxide plate gradually loses 
its electrical energy by local action, the rate of such loss varying according 
to the circumstances of its preparation and the condition of the cell. 

In the Faure or pasted cells lead plates are coated with minium or 


litharge made into a paste with acidulated water. When dry these plates © 


are placed in a bath of dilute H2SO,4 and subjected to the action of the 
current, by which the oxide on the positive plate is converted into peroxide 
and that on the negative plate reduced to finely divided or porous lead. 

The initial electro-motive force of the Faure cell averages 2.25 volts, but 
after being allowed to rest some little time it is reduced to about 2.0 volts. 

The ‘‘chloride’”’ accumulator, made by the Electric Storage Battery Co., 
of Philadelphia, consists of lead plates containing cells filled with spongy 
lead or with lead peroxide. The spongy lead is formed by first casting 
into the lead plate pastilles of a mixture of lead and zine chlorides, the 
lead in which is afterwards by an electrolytic method converted into spongy 
lead, while the zinc chloride is dissolved and washed away. Plates intended 
for positive plates have the spongy lead converted into peroxide by immers- 
ing them in sulphuric acid and passing a current through them in one 
direction for about two weeks. : 

The following tables give the elements of several sizes of ‘‘chloride”’ 
accumulators. Type G is furnished in cells containing 11-125 plates, and 
type H from 21 plates to any greater number desired. The voltage of cells 
of all sizes is slightly above two volts on open circuit, and during discharge 
varies from that point at the beginning to 1.8 at the end. 

Accumulators are largely used in central lighting and power stations, in 
office buildings and other large isolated plants, for the purpose of absorbing 
the energy of the generating plant during times of light load, and for giving 
it out during times of heavy load or when the generating plant is idle. The 
advantages of their use for such purposes are thus enumerated: 


1. Reduction in coal consumption and general operating expenses, due to - 


the generating machinery being run at the point of greatest economy while 
in service, and being shut down entirely during hours of light load, the bat- 
tery supplying the whole of the current. 











RY PBs Be? (he Roe ek te cy Pe 
Size of Plates, 3X3 in. Plates, 434X4in.| Size of Plates, 6 6 in. 
ee —_—__OoS- SF 
Numiber of plates; Jac 6)... 6: )2. 3 3 5 7 3 5 7 Se ca Me 
Discharge (For 8 hours...... 5~| 114] 214] 334] 226) 5 | 724/10 11219115 
inirame Ae Baie ais is. Ye 184) 3)4} 534] 36] 7 [1014/14 {1714/21 
peres: tS Teg ae 144] 244} 5 | 74 5 110 {15 |20 [25 |30 
Normal charge rate. ....,....- 5~| 114] 214) 334] 214) 5 | 714/10 1121615 
Weight of each element, lbs..../3 | 5 | 8 |11 | 8 |14 |20 |26 {32 /38 
Outside measurement Width. |134| 2 3 4 2) 3 4 5 6 7 
of rubber jar iny Length.|/354| 434 vA va Ne 614) 614 or 614) 614 
peas: 


4 
inches: Height.|5 | 7 
Outside measurement ( Width../2'4| 3 | 4 | 54) 314) 434] 614) 734) 734 

of glass jar in <Length./4 | 514] 514) 54) 77% 774| 77%) 834] 834] 834 

inches: 614] 614] 634] 914] 914] 814] 836] 834] 836 
314| 4 5 6 914/1334|1614/1414/13 
Ths ee ..| 34, 1 | 214] 254] 214) 314] 5141 7 | 824/10 
Weight of cell complete, with 

acid, in rubber jars in lbs. ..|4 614) 1014}1414)1114]1814]26 (85 [4214/50 
Height of cell over allininches./8 |10 !10 1/10 |1216/1214611214|121¢6|1216/1214 








OPM CUeC air SECT OME AER ann eT, Ye en Ce a 




















ELECTRICAL ACCUMULATORS OR STORAGE-BATTERIES. 1047 





TYPE“ h:” 
Size of Plates, 734 x 


734 in. 




















TY PEAY By? 
Size of Plates, 
10% « 10% in. 


















































Mimtber ol DIAtesi acs Ok elo die (io cite Oem | iden io Tl pate 
Discharge ( ForShours/10 |15 |20 |25 {30 |35 |40 |50 |60 /70 |80 |90 

in a} “5D  ** 114 121 128 (135. 142° 149 «(56 170 (84° |98 {112 1126 

peres: “3 * 120 180 |40 50 |60 |70 |80 |100 /120 |140 |160 |180 
Normal charge rate....}10 {15 /20 |25 |30 '!35 /40 |50 |60 |70 {80 {90 
Weight each element, 

eSB SHEA CALS: ate : 2 Rare ay 71. «(86 = |106 }125 |145 |165 |184 

+: idth, in., ) ru ‘ g| 714] 8lé6|.... |. +4 |1634)183¢/20 | 21 
32) Lenath, ee te B14 Si4| 816] 84) Bis! Bisl.... 515 N15 115 is 
SE Height, “ § jar.ft1 lit {11 [ta Jar dar |... |S 8 117341 1734'1734]1734 
$3 (Width, “ ) ».. | 54] 684) 8 | 85g)11 11 | 9 (105¢)105g)12 |....].... 
Sf Lenath, ve ee 914) 914) 914] 914] 914] 91¢]12146]1214] 1214/1234] ....].... 

B (Height, ‘* ) gyn (1144/1124/1114]1144|1144|1114/1546]1516|1546| 1544)... |... 
Weight of acid in glass 

JAS IOS ws: ote echlie Riedy cone ler tise aot. loom (Ol, [OS cen Og eactlemes 
Weight of acid in rub- 

ber jars in Ibs........| 644) 9 |1114]1414/1714]21 ng {94 [104 [114 | 124 
Weight of cell com- Ss 

plete, with acid, in Os 

rubber jarinlbs.. ..;31 |42 [54 |66 |79 /91 302 |3839 |3876 |415 
Height of cell over all, 

ROMA GHOS Mrememe cy so 1444 Mig 46 1414/1414 ia bi 18) }18 19 T9119 

‘ TY PB? Ee? 
TYPE “G.” : : 
Size of Plates, 1544 « 1514 in. sv e Nina 

Number of plates. ....} 11 | 13 | 15 | 17 | 25 es D¥} 21 | 238 1° 25-1125 | D* 
Discharge (For 8 hrs.|100 |120 |140 |160 /240 |1240)10 [400 |440 |480 |2480/20 

in am- * 5 *S 1140 1168 |196 |224 |3386 |1736]14 (560 |616 [672 [8472/28 

peres: se 3 ** 1200 1240 |280 [320 |480 |2480)20 {800 |880 |960 |4960}40 
Normal charge rate....|100 |120 |140 |160 [240 |1240/10 {400 /440 |480 |2480/20 
Weight of each ele- 

THEN tel DSc ce eetes ose 219 |260 |300 |341 |503 |2538/20.4)790 |866 |942 |41741/38 

Outside ( Width. |151¢]1634|183¢'20 |275g) 1112] 76) 254¢/2634/283¢]1113] % 
ean Length|1934| 1934 |1934| 1934/2034 /2114]....|2114]2114|2114]21146).... 

inches. | Height | 22% | 2276 | 2276 | 2276 | 2274/2434]... .|4276|4276|4274 14874)... . 
Weight of acid in 

HPOUN AS Hse Herds hig eters 160 |179 |197 {216 )292 |1242) 9.5)515 |552 |590 /2512/19.2 
Weight of cell, com- 

plete, with acid in 

lead-lined tank in é 

OUNGS st ites roee 482 |552 |621 |689 |992 |4560/386 |1635]1769)1904/8696]68 
Height of cell over all, 

ANCHES Sie see mas ' 26 | 26 | 26 | 26] 29 45 | 45 | 45 | 46 











——— at 


*D = addition per plate from 25 to 125 plates; approximate as to dimen- 


sions and weights. 


2. The possibility of obtaining good regulation in pressure during fluctua. 
tions in load, especially when the day load consists largely of elevators and 


similar disturbing elements. 


3. To meet sudden demands which arise unexpectedly, as in the case of 
darkness caused by storm or thunder-showers; also in case of emergency 
due to accident or stoppage of generating-plant. 

4. Smaller generating-plant required where the battery takes the peak of 
the load, which usually only lasts for a few hours, and yet where no battery 
is used necessitates sufficient generators, etc., being installed to provide for 
the maximum output, which in many cases is about double the normal 


output, 


1048 ELECTRICAL ENGINEERING. 


The Working Current, or Energy Efficiency, of a storage- 
cell is the ratio between the value of the current or energy expended in the 
charging operation, and that obtained when the cell is discharged at any 
specified rate. 

In a lead storage-cell, if the surface and quantity of active material be 
accurately proportioned, and if the discharge be commenced immediately 
after the termination of the charge, then a current efficiency of as much as 
98% may be obtained, provided the rate of discharge is low and well regu- 
lated. In practice it is found that low rates of discharge are not economica!, 
and as the current efficiency always decreases as the discharge rate in- 
creases, it is found that the normal current efficiency seldom exceeds 90%, 
and averages about 85%. 

As the normal discharging electro-motive force of a lead secondary cell 
never exceeds 2 volts, and as an electro-motive force of from 2.4 to 2.5 
volts is required at its poles to overcome both its opposing electro-motive 
force and its internal resistance, there is an initial loss of 20% between the 
energy required to charge it and that given out during its discharge. 

As the normal discharging potential is continually being reduced as 
the rate of discharge increases, it follows that an energy efficiency of 80% 
can never be realized. As a matter of fact,a ma imum of 75% anda 
mean of 60% is the usual energy efficiency of lead-sulphuric-acid storage-cells. 

Important General Rules.—Storage cells should not be 
allowed to stand idle when charged, and must not stand idle when uncharged 
or aiter being discharged. If a battery is to be put out of commission 
for any length of time, it should be fully charged, the electrolyte all drawn 
off, the cells filled with pure water and then discharged slightly—say until 
the E.M.F. is 1.95 volts. The cells should then be emptied, and the plates 
dried in a warm atmosphere. 

In mixing the electrolyte, the acid should always be poured into the 
water. The mixing must be very gradual in order to avoid excessive 
heating. The acid solution must be cooled before the cells are filled with 
it. The acid should be tested for impurities before mixing the electrolyte. 

Tests for Impurities.—To test for copper and arsenic, add a small quantity 
of dilute acid to an equal quantity of fresh sulphide of hydrogen (H.S). 
The presence of copper will cause a black precipitate; that of arsenic, a 
yellow precipitate. 

To test for iron, add a few drops of nitric acid to a small quantity of 
dilute acid and heat the mixture; after cooling add a few drops of potassium 
pene pe solution. ‘The presence of iron will be indicated by a deep 
red color. 

Charging and Discharging.—Charging should be stopped when the voltage 
is 26 volts per cell and gas is given off, except in the first charging, when 
2.7 should be reached. Discharging should be stopped and the cells re- 
charged when the voltage is down to 1.8 volts per cell when discharging at 
normal rate. 


ELECTROLYSIS, 


The separation of a chemical compound into its constituents by means 
of an electric current. Faraday gave the nomenclature relating to elec- 
trolysis. The compound to be decomposed is the Electrolyte, and the 
process Electrolysis. The plates or poles of the battery are Electrodes. 
The plate where the greatest pressure exists is the Anode, and the other 
pole is the Cathode. ‘The products of decomposition are Ions. 

Lord Rayleigh found that a current of one ampere will deposit 0.017253 
grain, or 0.001118 gramme, of silver per second on one of the plates of a 
silver voltameter, the liquid employed being a solution of silver nitrate 
containing from 15% to 20% of the salt. The weight of hydrogen similarly 
set free by a current of one ampere is .00001088 gramme per second. 

Knowing the amount of hydrogen thus set free, and the chemical equiva- 
lents of the constituents of other substances, we can calculate what weight 
of their elements will be set free or deposited in a given time by a given 
current. Thus, the current that liberates 1 gramme of hydrogen will liberate 
8 grammes of oxygen, or 107.7 grammes of silver, the numbers 8 and 107.7 
being the chemical equivalents for oxygen and silver respectively. 

To find the weight of metal deposited by a given current in a given time, 
find the weight of hydrogen liberated by the given current in the given 
time, and multiply by the chemical equivalent of the metal, “ 


ELECTRO-CHEMICAL EQUIVALENTS, 1049 


ELECTRO-CHEMICAL EQUIVALENTS. 


























+ rts 
#15 |s5e : 
9 oy =Pe nan, 3 Lp 3 
Elements. » Oo oa 2eaee a, ons 
e. E = OB E's ae RO 
~~ ae] 1 © g = Qs On 
oO 2 S = iS) & at E gs | 2 
A 5 S§ |/ser31 Ss Se 
a o- Oo SMO st = g 
3 mS qs a ) 3 ae} 
> < 3) cs} s) O 
ELECTRO-POSITIVE. 
EVO LOP EM ge 'siac serie oes H, 1.00 1.00 | .010384 | 96293.00 | 0.03738 
Potassium........ rane dt Sep]. O90. |. 89.04 4) 2840539 2467.50 | 1.45950 
Sodium .-..< aye tavera (reise Nagi) eesno | es oo -23873 4188.90 | 0.85942 
AIMIMIMUM A teehee aan Als Iki etca 9.1 09449 1058.30 | 0.34018 
Magnesium..... ......] Mzg| 23.94 ]' 11.97 . 12480 804.038 | 0.44747 
(Oe) ti MSS eRe Sree [Ae je LOO. 2 65.4 -67911 1473.50 | 2.44480 
PL VOLaias ai tis roa: case as Ag, | 107.66 | 107.66 | 1.11800 894.41 | 4.02500 
Copper (cupric)........}] Cug | 638.00] 31.5 .82709 8058.60 | 1.17700 
HY (cuprous)...... Cu, 63.00 63.00 .65419 1525.30 | 2.35500 
Mercury (mercuric)....]| Hg, | 199.8 99.9 | 1.03740 963.99 | 8.73450 
sé (mercurous)..| Hg, | 199.8 199.8 2.0747 481.99 7.46900 
ED (SUA AUC). .G 2 scec > Sn, | 117.8 29.45 | .30581 3270.00 | 1.10090 
Soe (SUATITOUS)) os 016) eieici- Sn, | 117.8 58.9 .61162 1635.00 | 2.20180 
Tron (ferric). ..2 cse-5 o-| Leg 55.9 18.64t) .19356 5166.4 0.69681 
Sel (LELYOUS) 2 c0%,. 52 ole Fe, 55.9 27.95 -29035 8445.50 | 1.04480 
INTC Ol cg wteiein oye orcs sarere'sio eI 58.6 29.3 .80425 3286.80 1.09530 
SINCE SARIS OS OO SHUSHaOS Zv9 64.9 32.45 - 33696 2967.10 1.21330 
WCAC actrees Metacs'ec ss Phg | 206.4 | 103.2 | 1.07160 933.26 | 3.85780 
ELECTRO-NEGATIVE. 
ORY PONY... wot sees she os Og 15.96 7.98 | .08286 
Chlorine... .s-27 e's corte Ole 35.387 | 35.387 | .36728 
WOGUN Gren cicre' «Jere be Seth edt (oil UP 126.53 | 126.53 | 1.31390 
IRTOUMNNG.. 2. cece es sets Br, | 79.75) "79.75-| © .82812 
Nitrogen........ ecie cles Ns | 14.01 4.67 | .04849 





* Valency is the atom-fixing or atom-replacing power of an element com- 
pared with hydrogen, whose valency is unity 

+ Atomic weight is the weight of one atom of each element compared with 
hydrogen, whose atomic weight is unity. 

t Becquerel’s extension of Faraday’s law showed that the electro-chemical 
equivalent of an element is proportional to its chemical equivalent. The 
latter is equal to its combining weight, and not to atomic weight + valency, 
as defined by Thompson, Hospitalier, and others who have copied their 
tables. For example, the ferric salt is an exception to Thompson’s rule, as 
are sesqui-salts in general. ’ 

Thus: Weight of silver deposited in 10 seconds by a current of 10 amperes 
= weight of hydrogen liberated per second x number seconds X current 
strength x 107.7 = .00001038 x 10 x 10 x 107.7 = .11178 gramme. 

Weight of copper deposited in 1 hour by a current of 10 amperes = 


-00001038 x 3600 x 10 & 31.5 = 11.77 grammes. 


Since 1 ampere per second liberates .00001038 gramme of hydrogen, 
strength of current in amperes 
_. weight in grammes of H. liberated per second 
ts -00001038 
_ _ weight of element liberated per second 
~ .00001038 x chemical equivalent of element’ 


The above table (from “ Practical Electrical Engineering ’’) is calculated 
apon Lord Rayleigh’s determination of the electro-chemical equivalents and 
Roscoe’s atomic weights, 





1050 ELECTRICAL ENGINEERING. 


ELECTR O-MAGNETS.* 
Units of Electro-magnetic Measurements. 


Umit magnetic pole is a pole of such strength that when placed at a dis- 
tance of one centimetre from a similar pole of equal strength it repels it 
with a force of one dyne. 

Gauss =unit of field strength, or density, symbol H, is that intensity of 
field which acts on a unit pole with a force of one dyne, =one line of force 
per square centimetre. A field of H units is one which acts with H dynes 
on unit pole, or H lines per square centimetre. A unit magnetic pole has 
4x lines of force proceeding from it. 

Mazxwell=unit of magnetic flux, is the amount of magnetism passing 
through every square centimetre of a field of unit density. Symbol, 

Gilbert =unit of magneto-motive force, is the amount of M.M.F., that 
would be produced by a coil of 10+ 4z or 0.7958 ampere-turns. Symbol, F. 

The M.M.F. of a coil is equal to 1.2566 times the ampere-turns. 

If a solenoid is wound with 100 turns of insulated wire carrying a current 
ont amperes, the M.M.F. exerted will be 500 ampere-turns X 1.2566 = 628.3 
gilberts. 

Oersted = unit of magnetic reluctance; it is the reluctance of a cubic centi- 
metre of an air-pump vacuum. Symbol, R 

Reluctance is that quantity in a magnetic circuit which limits the flux 
under a given M.M.F. It corresponds to the resistance in the electric cir- 
cuit. 

The reluctivity of any medium is its specific reluctance, and in the C.G.S. 
system is the reluctance offered by a cubic centimetre of the body between 
opposed parallel faces. .The reluctivity of nearly all substances, other than 
the magnetic metals, is sensibly that of vacuum, is equal to unity, and is 
independent of the flux density. 

Permeability is the reciprocal of magnetic reluctivity. It is a number, and 
the symbol is p. 

Permeance is the reciprocal of reluctance. 

Lines and Loops of Forece.—JIn discussing magnetic and 
electrical phenomena it is conventionally assumed that the attractions and 
repulsions as shown by the action of a magnet or a conductor upon iron 
filings are due to ‘‘lines of force”? surrounding the magnet or conductor. . 
The ‘‘number of lines’”’ indicates the magnitude of the forces acting. As 
the iron filings arrange themselves in concentric circles, we may assume that 
the forces may be represented by closed curves or ‘‘loops of force.’’ The 
following assumptions are made concerning the loops of force in a con- 
ductive circuit: 

1. That the lines or loops of force in the conductor are parallel to the 
axis of the conductor. 

2. That the loops of force external to the conductor are proportional in 
number to the current in the conductor, that is, a definite current gener- 
ates a definite number of loops of force. These may be stated as the 
strength of field in proportion to the current. 

3. That the radii of the loops of force are at right angles to the axis of 
the conductor. 

The magnetic force proceeding from a point is equal at all points on the 
surface of an imaginary sphere described by a given radius about that 
point. A sphere of radius 1 cm. has a surface of 4z square centimetres. If 
¢=total flux, expressed as the number of lines of force emanating from 
a magnetic pole having a strength, M, 


¢=427M; M=¢+4n. 
Magnetic moment of a magnet =product of strength of pole @ acd its 


length, or distance between its poles L. Magnetic moment = —7—* 
ua 





* Wor a very full treatment of this subject see ‘‘The Electro- Magnet, a 
published by the Varley Duplex Magnet Co., Phillipsdale, R. I. 


BRLECTRO-MAGNBITS, 105% 


If B=number of lines flowing through each square centimetre of cross- 
section of a bar-magnet, or the ‘‘specific induction,’ and A =cross-section, 


Magnetic Moment=LAB+ 47x. 


If the bar-magnet be suspended in a magnetic field of density H, and so 
placed that the lines of the field are all horizontal and at right angles to the 
axis of the bar, the north pole will be pulled forward, that is, in the direction 
in which the lines flow, and the south pole will be pulled in the opposite 
direction, the two forces producing a torsional moment or torque, 


Torque=MLH=LABH + 4z, in dyne-centimetres. 


Magnetic attraction or repulsion emanating from a point varies inversely 
as the square of the distance from that point. The law of inverse squares, 
however, is not true when the magnetism proceeds from a surface of appre- 
ciable extent, and the distances are small, as in dynamo-electric machines 
and ordinary electromagnets. 

Permeability .—Materials differ in regard to the resistance they offer 
to the passage of lines of force; thus iron is more permeable than air. The 
permeability of a substance is expressed by a coefficient, », which denotes 
its relation to the permeability of air, which is taken as 1. Jf H=number 
of magnetic lines per square centimetre which will pass through an air- 
space between the poles of a magnet, and B the number of lines which will 
pass through a certain piece of iron in that space, then »=B+H. The 
permeability varies with the quality of the iron and the degree of satura- 
tion, reaching a practical limit for soft wrought iron when B=about 18,000 
and for cast iron when B=about 10,000 C.G.S lines per square centimetre. 

The permeability of a number of materials may be determined by mears 
of the table on the following page. 

The Magnetic Circuit,—In the electric circuit 


Current =a tance’ or I[=5. 
Similarly, in the magnetic circuit 
Magnetomotive Force 
Reluctance 





Magnetic Flux = a OF -f. 


Reluctance is the reciprocal of permeance, and permeance is equal to 
permeability X path area+path length (metric measure); hence 


Ga-b. 

U ° 

One ampere-turn produces 1.257 gilberts of magnetomotive force and 
one inch equals 2.54 centimetres; hence, in inch measure, 





16.450 _ 3.192 na A t 


@.= 2oT Fo) a Sian OMA Z 


The ampere-turns required to produce a given magnetic flux in a given 


path will be 
Apa__ot_ _ 0.313392 
3.192 na oe 


Since magnetic flux+area of path=magnetic density, the ampere-turns 
required to produce a density B, in lines of force per square inch of area 
of path, will be 

A, =0.3133Bl + p. 


This formula is used in practical work, as the magnetic density must 
be predetermined in order to ascertain the permeability of the material 
under ity working conditions. When a magnetic circuit includes several 


1052 ELECTRICAL ENGINEERING. 


qualities of material, such as wrought iron, cast iron, and air, it is most 
direct to work in terms of ampere-turns per unit length of path. The 
ampere-turns for each material are determined separately, and the wind- 
ing is designed to produce the sum of all the ampere-turns. The following 
table gives the average results from a number of tests made by Dr. Samuel 
Sheldon: 


Vauurs oF B anv H. 























4 Ms Cast Iron. | Cast Steel. |WroughtIron| Sheet Metal. 
q q SD | ee eee) ee 

eH fey fy 

Bi 5.4 S wal ye ms, | ,@ 
Pads | Po my I (\ o| QQ. o a. cs a ° 
N Boe BS a z eae om & Se mo au8 co Z 228 
by ay 1 Lente kc! 1 wee =| a a 1 erie 
Sie) eee Se Seg es See ater e Moe oes 

§ <a i ING Mm |i s mM | 

10 7.95 20.2 7 NG sa are ira Wea) (422 als. 0 $3.8 | 14.3 92.2 
20 15.90 40.4 5:7 | 36.8 | 13.8 89.0 | 14.7 94.8 | 15.6 | 100.7 
30 23.85 60.6 6.5 | 41.9 | 14.9 96.1 | 15.3 98.6 | 16.2 | 104.5 
40 31.80 80.8 Had) Wo. 40.50 |) Loson | 600.05) occa Ole 2c Ol One Li ned 
50 39.75 | 101.0 7.6 | 49.0 | 16.0 | 1038.2 | 16.0 03.2 | 16.9 | 109.0 
60 47.70 | 121.2 8: Ons Ol:O01. 16.0.1 ed OG.Delt Ossie LOSs2ut ues 
70 55.65 | 141.4 8.4 | 59.2 | 16.9 | 109.0 | 16.5 | 106.5 | 17.5 | 112.9 
80 63.65 | 161.6 Sif SO. Le Lea LALO SIG eel O7 Sar used aml co 
90 71.60} 181.8 9.0 | 58.0 | 17.4 | 112.2 | 16.9 | 109.0 | 18.0 | 116.1 
100 791501 202.0 | 9:4 | 60:6 117.7 | 114.1 | 17-25) D109 B1S2 1738 
150 | 119.25] 303.0 | 10.6 | 68.3 | 18.5 | 119.2 | 18.0 | 116.1 | 19.0 | 122.7 
200 | 159.0 ADO 117 We(5.07 1 1922. | 128290 Ws vie 12008" 19 Oe colo 
250 | 198.8 505.04. 12.4) 80:05 (1 Osve el 2761 | 19201 23.98 2025 eroOr 
300 | 238.5 606.0%) 13822" Sole 2001 129.67 19s e127, 15) 20a leks 











H =1.257 ampere-turns per cm. =.495 ampere-turns per inch. 


Exampie.—A magnetic circuit consists of 12 inches of cast steel of 
8 square inches cross-section; 4 inches of cast iron of 22 square inches 
cross-section; 3 inches of sheet iron of 8 square inches cross-section; and 
two air-gaps each 4¢ inch long and of 12 square inches area. Required, 
the ampere-turns to produce a flux of 768,000 maxwells, which is to b 
uniform throughout the magnetic circuit. 

The flux density in the steel is 768,000+ 8 =96,000 maxwells; the ampere, 
turns per inch of length, according to Sheldon’s table, are 60.6, so that the 
12 inches of steel will require 727.2 ampere-turns. 

The Ray. in the cast iron is 768,000+22=34,900; the ampere-turns 
=4 40 = 160. 

The density in the sheet iron=768,000+8=96,000; ampere-turns per 
inch=30; total ampere-turns for sheet iron=90. 

The air-gap density is 768,000+12=—64,000; ampere-turns per inch= 
0.3133B; ampere-turns required for air-gap = 0.3133 x 64,000 + 8 = 2506.4. 

The entire circuit will require 727.2+160+ 90+ 2506.4 = 3483.6 ampere- 
turns, assuming uniform flux throughout. 

In practice there is considerable ‘‘leakage’’? of magnetic lines of force; 
that is, many of the lines stray away from the useful path, there being no 
material opaque to magnetism and therefore no means of restricting it to 
a given path. The amount of leakage is proportional to the permeance 
of the leakage paths available between two points in a magnetic circuit 
which are at different magnetic potentials, such as opposite ends of a 
magnet coil. It is seldom practicable to predetermine with any approach 
to accuracy the magnetic leakage that will occur under given conditions 
unless one has profuse data obtained experimentally under similar con- 
ditions. In dynamo-electric machines the leakage coefficient varies from 
1.3 to 2. 


ELECTRO-MAGNETS. 1053 


Tractive or Lifting Force of a WMagnet.—The lifting power or 
“‘pull” exerted by an electro-magnet upon an armature in actual contact 
with its pole-faces is given by the formula 


2a 

sam = Lbs. 

72,134,000 ; 

a being the area of contact in square inches and B the magnetic density 
over this area. If the armature is very close to the pole-faces, this for- 
mula also applies with sufficient accuracy for all practical purposes, but 
a considerable air-gap renders it inapplicable. The accompanying table is 
convenient for approximating the dimensions of cores and pole-faces for 
tractive magnets. 


Dimensions of Lifting Magnets. 





























Ampere-turns per Ampere-turns per 
Den: inch of length. Bull dni}: Den: inch of length. Pullin 
my Ibs. per ae lbs. per 
: : Cast’ | Cast | &4: 12: : : Cast. |. Cast | 24s 42. 
Air. Iron. | Steel. Air. Tron. | Steel. 

10,006 | 3133 18 Bil 1.38 |/29,000 | 9,086 49 6.5 11.6 
11,€00 3447 19.2 3.81 1.65 |/30,000 | 9,400 52 6.7 12.4 
12,000 3760 20.4 3.93 2 31,000 | 9,713 55 6.9 13.2 
13,000 4073 21.6 4.05 23 32,000 | 10,026 58 fie 14 
14,000 4387 22.8 4.17 Qed, 33,000 | 10,339 61 133 15 
15,000 4700 24 4.3 oar 34,000 | 10,652 64 ies 16 
16,000 5013 25.2 4.44 BD 35,000 | 10,965 68 a 17 
17,000 5326 26.5 4.58 4 36,000 | 11,278 72 7.9 18 
18,000 5640 27.9 4.72 4.5 37,000 | 11,590 76 8.1 19 
19.000 5953 29.3 4.86 | 5 38,000 | 11,904 80 8.3 20 
20,000 6266 30.7 5 bpayo 39,000 | 12,217 85 aay Mle Vall 
21,000 6580 ny ay? Cah ae 40,000 | 12,532 90 8.8 Pap 
21,500 6736 Sel 5.24 6.4 41,000 | 12,843 95 9.05 | 23 
22,000 6893 34 5.32 67 42,000 | 13,159) 100 9.3 24.25 
22,500 | 7050 35 5.4 7 43,000 | 13,472] 106 estat aids) 
23,000 | 7206 36 5.48 Tos 44,000 | 18,785} 112 9.8 26.75 
23,500 | 7363 37 5.56 7.6 45,000 | 14.098; 118 10.25 | 28 
24,000 | 7520 38 5.64 + 7.9 46,000 | 14,412} 125 10.5 29.3 
25,000 | 7833 40 5.8 8.6 47,000 | 14,725} 132 10.8 30.6 
26,000 | 8146 42 5.97 9.3 48,000 | 15,038} 140 11.15 | 31.9 
27,000 | 8459 44 6.14 | 10 49,000 | 15,350} 150 11.5 are 
28,000 | 8773 46 6.32 | 10.8 50,000 | 15,665} 160 11.9 34.6 








Magnet Windings.—Knowing the ampere-turns required to pro- 
duce the desired excitation of a magnetic circuit, the winding may be 
approximately determined as follows: 

For round cores under 1 inch in diameter make the depth or thickness 
of winding, t, equal to the core diameter; over 1 inch, let t=cube root of 
core diameter. For slab-shaped cores let the coil thickness be equal to the 
core thickness up to 1inch, and to the square root of the core thickness 
above that. 

The ampere-turns produced by any coil will be 


in which V =volts at the coil terminals, 
d2=area of the wire in circular mils, 
1=mean length in inches per turn of wire, 
k=a coefficient depending on the temperature of the coil, 


1054 ELECTRICAL ENGINEERING. 


The mean length per turn of wire is 
at+nt= lyn? 


g being the perimeter of the core. The size of wire required for a given 
excitation will be 


kA, 
ee oe ae 2 nt). 


At 140° Fahr. k=1. The table herewith gives the values of k& at various 
other practical temperatures. 


Values of k in Magnet-coil Formula,’ 








Temp. | k | Temp. k Temp. | k Temp. k 








100 | 0.923 ie 0.952 130 | 0.981 150 1.0195 
105 | 0.933 || 120 | 0.962 135 | 0.99 155 | 1,029 
0 | «(0.942 || 125 |. 0-971 1451.14.01 160 | 1.0387 





The rise above atmospheric temperature will be 


v2 
k,RS 


in which R =the resistance of the coil when hot, S=its radiating surface, 
and k; is a variable coefficient (see p. 1032). The value of k; will be about 


0.008 for electro-magnets of ordinary size not enclosed or shielded in any 
way from the surrounding air. 

For fuller treatment of the subject, see American Electrician, April and 
May, 1901, and January, 1904. 

Determining the Polarity of Electro-magnets.—lIf a wire 
is wound around a magnet in a right-handed helix, the end at which the 
current flows into the helix is the south pole. If a wire is wound around an 
ordinary wood-screw, and the current flows around the helix in the direc- 
tion from the head of the screw to the point, the head of the screw is the 
south pole. If a magnet is held so that the south pole is opposite the eye of 
the observer, the wire being wound as a right-handed helix around it, the' 
current flows in a right-handed direction, with the hands of a elock. 

Determining the Direction of a Current.—Place a wire 
carrying a current above and parallel to a pivoted magnetic needle. If 
the current be flowing along the wire from N. to S., it will cause the N.- 
seeking pole to turn to the eastward; if it be flowing from S. to N., the 
pole will turn to the westward. If the wire be below the needle, these 
motions will be reversed. , 

Maxwell’s rule. The direction of the current and that of the resisting 
magnetic force are related to each other as are the rotation and the for- 
ward travel of an ordinary (right-handed) cork-screw. 


0, 


DYNAMO-ELECTRIC MACHINES. 1055 


DYNAMO-ELECTRIC MACHINES. 


There are three classes of dynamo-electric machines, viz.: 

1, Generators, for the conversion of mechanical into electrical energy. 

2. Motors, for the conversion of electrical into meé¢hanical energy. 

Generators and motors are both subdivided into direct-eurrent and alter- 
nating-current machines. 

38. Transformers, for she conversion of one character or voltage of current 
into another, as direct into alternating or alternating into direct, or from 
one voltage into a higher or lower voltage. 

Kinds of Dynamo-electric Machines as regards Man-= 
ner of Winding. 

1. Separately-excited Dynamo.—The field-magnet coils haye no connec- 
tion with the armature-coils, but receive their current from a separate 
machine or source. 

2. Series-wound Dynamo.—The field winding and the external circuit are 
connected in series with the armature winding, so that the entire armature 
current must pass through the field-coils. 

Since in a series-wound dynamo the armature-coils, the field, and the ex- 
ternal circuit are in series, any increase in the resistance of the external 
circuit will decrease the electro-motive force from the decrease in the mag- 
netizing currents. A decrease in the resistance of the external circuit will, 
in a like manner, increase the electro-motive force from the increase in the 
magnetizing current. The use of a regulator avoids these changes in the 
electro-motive force. 

3. Shunt-wound Dynamo.—The field-magnet coils are placed in a shunt 
to the armature circuit, so that only a portion of the current generated 
passes through the field-magnet coils, but all the difference of potential of 
the armature acts at the terminals of the field-circuit. 

In a shunt-wound dynamo an increase in the resistance of the external 
circuit increases the electro-motive force, and a decrease in the resistance 
of the external circuit decreases the electro-motive force. This is just the 
reverse of the series-wound dynamo. 

In a shunt-wound dynamo a continuous balancing of the current occurs, 
the current dividing at the brushes between the field and the external cir- 
cuit in the inverse proportion to the resistance of these circuits. If the 
resistance of the external circuit becomes greater, a proportionately greater 
current passes through the field-magnets, and so causes the electro-motive 
force to become greater. If, on the contrary, the resistance of the external 
circuit decreases, less current passes through the field, and the electro- 
motive force is proportionately decreased. 

4. Compound-wound Dynamo.—The field-magnets are wound with two 
separate sets of coils, one of which is in series with the armature and the 
external circuit, and the other in shunt with the armature, or the external 
circuit. 

Motors.—The above classification in regard te winding applies also to 
motors. 

Moving Force of a Dynamo-electric Machine.—A wire 
through which a current passes has, when placed in a magnetic field, a 
tendency to move perpendicular to itself and at right angles to the lines 
of the field. The force producing this tendency is P=IBI dynes, in which 
l=length of the wire, J=the current in C.G.S. units, and B=the induc- 
tion, or flux density, in the field in lines per square centimetre. 

If the current J is taken in amperes, P=/1BI+10=/BI 10—1. 

If Pk is taken in kilogrammes, 


Pk=I1BI =~ 9,810,000 = 10.1937 7B7 10~8 kilogrammes. 


ExAMPLE.—The mean strength of field, B, of a dynamo is 5000 C.G.S. 
lines; a current of 100 amperes flows through a wire; the force acts upon 
10 centimetres of the wire=10.1937 X 10x 100 5000 xX 10~8=.5097 kilo- 


grammes. . 
In the ‘‘English” or Kapp’s system of measurement a total flow of 6000 


1056 ELECTRICAL ENGINEERING 


C.G.S. lines is taken to equal one English line. Calling Bz the induction in” 
English, or Kapp’s, lines per square inch, and B the induction in C, G. 8. 
lines per square centimetre, BE = B + 930.04; and taking 7” in inches and 
PPin pounds, PP = 531/1’BE10- pounds. ‘ 

Torque ofan Armature,—The torque of an armature is the mo- 
ment tending to turn it. In a generator it is the moment which must be 
applied to the armature to turn it in order to produce current. In a motor 
it is the turning moment which the armature gives to the pulley. 

Let J = current in the armature in amperes, /=the elect ro-motive force 
in volts, 7 = the torque in pound-feet, @ = the flux through the armature 
in maxwells, N= the number of conductors around the armature, and n = 
the number of revolutions per second. Then 


Watts = IE = 2rnT X 1.356.* 
_ In any machine if the flux be constant, H is directly proportional to the 
speed and = ¢Nn + 108; whence 


¢NI 
roe = 2"TX 1.356; 


oNI a pNI 
108 X 2 X 1.356 8.52 X 108 


Let 1 = length of armature in inches, d=diameter of armature in inches, 
B = flux density in maxwells per square inch, and let m = the ratio of the 
conductors under the influence of the pole-pieces to the whole number of 
conductors on the armature. Then 


=" XIX BX m. 





Gp pound-feet. 


These formule apply to both generators and motors. They show that 
torque is independent of the speed and varies directly with the current and 
the flux. The total peripheral force is obtained by dividing the torque by 
the radius (in feet) of the armature, and the drag on each conductor is 
obtained by dividing the total peripheral force by the number of conductors 
under the influence of the pole-pieces at one time. 

EXxAMPLE.—Given an armature of length 1 = 20 inches, diameter d=12 
inches, number of conductors N = 120, of which 80 are under the influence 


of the pole-pieces at one time; let the flux density B = 30,0CO maxwells 
per sq. in. and the current J = 400 amperes. 
127 80 
= Te xX 20 X 30,000 x ee 7,540,000. 


. 7 — 7:540,000 x 120 x 400 
8.52 X 100,000,000 


Total peripheral force = 424.8 + .5 = 849.6 lbs. 

Drag per conductor = 849.6 + 120 = 7.08 lbs. 

The work done in one revolution = torque X circumference of a circle of 
1 foot radius = 424.8 X 6.28 = 2670 foot-pounds. 

Let the revolutions per minute equal 500, then the horse-power 


2670 X 500 
ee eaGd Tee 4075. baPe 
Electro-motive Force of the Armature Cireuit.—From the 
horse-power, calculated as above, together with the amperes. we can obtain 
the E.M. F., for /H = H.P. X 746, whence E.M.F. or FE = H.P. X 746 + J. 


If H.P., as above, = 40.5, and J = 400, H = ea = 75.5 volts. 


The E.M.F. may also be calculated by the following formulx: 
I = Total current through armature; 
ea = E.M.F. in armature in volts; 
N = Number of active conductors counted all around armature? 
p = Number of pairs of poles (p = 1 in a two-pole machine); 
n = Speed in revolutions per minute; 
¢ = Total flux in maxwells. 


* 1 ft.-lb, per second = 1,356 watts, 





= 424.8 pound-feet. 





DYNAMO-ELECTRIC MACHINES. 105% 


ea = oN a 10~° for two-pole machines. 


f Electro-motive poNn 


1 i wit 
force: ake m for multipolar machines h 


10° 60 series-wound armature. 


" Strength of the Magnetic Field.—The fundamental equation 
for calculations relating to the magnetic circuit is 


Magneto-motive Force 
Flux = — 
Reluctance 


Magneto-motive force is the magnetizing effect of an electric current. 
It varies directly as the number of turns in a coil, and as the current. It 
is numerically equal to 1.257 X amperes X turns, 

Reluctance is the resistance any material offers to the setting up in itself 
of magnetic lines. It varies directly as the length and inversely as the area 
of the cross-section of the core, taken at right angles to the direction of the 
magnetic lines, and inversely as the permeability of the material. 


Let J = current in amperes, N = number of turns in the coil, A = area 
of the cross-section of the core in square centimetres, 2 = length of core in 
centimetres, m» the permeability of the core, and ¢ = flux in maxwells. 
Then 

ie 1.257NI 
(meee, HENS 


In a dynamo-electric machine the reluctance will be made up of three 
separate quantities, viz.: the reluctance of the field magnet cores, the reluc- 
tance of the air spaces between the field magnet pole-pieces and the arma- 
ture, and the reluctance of the armature. The total reluctance is the 
sum of the three. Let Li, L2, 3 be the length of the path of magnetic 
lines in the field magnet cores,* in the air-gaps, and in the armature respec- 
tively; and let A;, Ao, A3 be the areas of the cross-sections perpendicular 
to the path of the magnetic lines in the field magnet cores, the air-gaps, and 
' the armature respectively. Let the permeability of the field magnet cores 
be #1, and of the armature w3. The permeability of the air-gaps is taken 
asunity. Then the total reluctance of the machine will be 


Ty Le L3 
Ay By WE T Aoed A3 Kh3° 
The formula for magnetic flux will now read 
Hae 1.257NI 
(Ly + Aymy) + (ig + Az) + (Lg + Azns)’ 
The ampere turns necessary to create a given flux in a machine may be 
found by the formula 


[Ca + Ar m1) + he + Ao) + (L3+ Asus) 
NI = ¢ 1.257 


But the total flux generated by the field coils is not available to produce 
current in the armature. There is a leakage between the field magnets, 
and this must be allowed for in calculations. The leakage coefficient 
varies from 1.3 to 2 in different machines. The meaning of the coefficient 
is that if a flux of say 100 maxwells per square cm. are desired in the field 
coils, it will be necessary to provide ampere turns for 1.3 K 100 = 130 
maxwells, if the leakage coefficient he 1.3. 

Another method of calculating the ampere turns necessary to produce a 
given flux is to calculate the magneto-motive force required in each portion 
of the machine, separately, introducing the leakage coefficient in the caleu- 
lation for the field magnets, and dividing the sum of the magnetive-moto 
forces by 1.257. An example of this last method is appended. 

ExampLe.—Given a two-pole generator with a single magnetic circuit 
of the following dimensions; in centimetres and square centimetres: L; = 
150, Le = each.5, Lg = 25; A; = 1200, Ao = 1400, Az = 1000; leakage 


* The length of the path in the field magnet cores L; includes that portion 
of the path which lies in the piece joining the ceres of the various field 
magnets. 








1058 ELECTRICAL ENGINEBRING. 


coefficient = A = 1.32; flux in armature = 10,000,000 maxwells. Re- 
quired the ampere turns on field magnets. Let B = intensity of magnetic 
induction, or flux density, and H = intensity of the magnetic field. 


: ¢ __ 10,000,000 
Armature: B reiy 1000 = 10,000. 


From the permeability table, a = 2000 
M.M.F3 = gente _ 10, 000,000 X 25 


a Be 1000 X 2000. a 


Air-gaps: 
10,000,000 X2 X.5 
M.M.F2 = 1400 7150. 


Wield Cores: 





¢ XA _ 10,000,000 X 1.32 _ fi 
B ve BOO 10003 vs 1 1602 
_ gd, _ 10,000,000 x 1.32 x 150 
ike itt eee Ay, 1200 X 1692 See 


Total M.M.F. = 125 + 7150 + 975 = 8250. 


M.M.F. 8250 
Ampere turns = “7.257. Lay 6563. 


In a machine having a double magnetic circuit, the calculation is slightly 
varied. The total fiux is created by the two separate sets of windings, 
each set creating one half. The ampere turns are calculated for one set 
of windings. The flux, %, used in the calculation is taken as one half the 
total flux created. The areas of the air-gaps A», and of the armature A3 
are also taken as one half the actual area. Except for these changes, 
the calculation is made in the same manner as for the single magnetic cir- 
cuit; the result is the ampere turns for one set of field windings. 

In the ordinary type of multipolar machine there are as many magnetic 
circuits as there are poles. Each winding energizes part of two circuits 
The calculation is mace in the same manner as for a single magnetie circuit. 

Dynamo Design.—In the design of a motor or generator the follow- 
ing data are usually given, being determined by local conditions Class, 
viz., bipolar or multipolar. series, shunt or compound wound; size, in 
kilowatts: voltage; and current. The following is an outline of the method 
ported in the complete design. (For complete method see Wiener’s 

ynamo-electrie Machines.) 

Notation.—E = e.m.f. in external circuit in volts; H’=total e.m.f. gener- 
ated in armature in volts; e = e.m.f. necessary to overcome internal 
resistances of machine; J = current in external circuit. in amperes; I = cur- 
Tent generated in armature in amperes; 7 = current in shunt field in am- 


peres; H, = assumed flux density of field in maxwells per sq. inch; B = 
actual flux density in armature, maxwells per square inch.; L = length of 
armature’ in inches; D = diameter of armature in inches; l = length of 


active conductor (i.e., that on pole-facing surface of armature) in feet; d = 
diameter of armature conductor in mils; d? = area of armature conductor, 
circular mils; d’ = diameter of insulated armature ccnductor in inches; 
N = number of conductors on armature; p = number of pairs of poles in 
field; C = number of bars on commutator; ¢ = magnetic flux in arma- 
ture in maxwells; ¢’ = total magnetic flux: A = leakage coefficient of 
magnetic circuit; V = mean velocity of armature conductors in feet per 
second; h = available depth of winding space on armature, inches (in a 
slotted’ armature A is the depth of slot); 2; = number of wires stranded 
in parallel to make one armature conductor; ne = number of conductors 
per layer on armature; n3 = number of layers of conductor on armature; 
k, m, b = variables and factors explained in ‘the text. 

A value is first assumed for H;. This is governed by the size of the 
machine, the style of armature, the number of poles, and the material of 
the pole-pieces, magnet cores, ‘and frame. For a smooth core armature 
in a-1 kw. bipolar machine, with cast-iron pole-pieces, it may be taken as 
15,000 maxwells per sq. inch for cast- -iron; for wrought iron or steel pole- 
pieces it may be taken at 22,000 maxwells. For a 300 kw. bipolar machine 


DYNAMO-ELECTRIG MACHINES. 1059 


it may be assumed at 30,000 maxwells with cast-iron pole-pieces, and at 
45,000 with wrought-iron pole-pieces. In multipolar machines, the figureg 
are from 5000 to 7000 higher in each case. 

A formula for the length of active armature conductor is 


foe oe NS 
kX xX Hy 


The value of k is determined by multiplying 1078 by a factor ranging from 
50 to 72, depending on the percentage of polar arc, i.e.. the percentage of 
the armature subtended by the pole-pieces. If the percentage cf polar are 
is 50 the factor is 50, if the percentage is 100 the factor is 72. V varies from 
35 in a 1 kw. machine to 50 in a 200 or 300 kw. machine with a drum arma- 
ture. With ring armatures, in high speed machines. V varies from 65 in a 
1 kw. machine to 75 in a 25 kw.. 85 in a 300 kw, and 100 in a 5000 kw. ma- 
chine. On low speed dynamos the figures are approximately one half 
the above. 

E’ = (£ + e). In series machines, under 1 kw..e is from 40 to 20 per 
cent of £; in machines of from 1 to 25 kw., from 20 to 10 per cent; in 25 
to 500 kw. machines. from 10 to 4 per cent; and in machines of over 500 
kw. from 4 to 2.5 per cent of H. In shunt-wcund machines e has approxi- 
mately one half the value used in series machines ; in ecmpound-wound 
machines approximately three quarters the value used in series machines. 

The diameter of the armature core is found by means of the assumed 
velocity and the given revolutions per minute, D=(12X60V) + (r.p.m. X 7). 

The area of the conductors on the armature depends on the amount of 
current to be carried. d? = 3001’ + p. 

In a series machine J’ = J; in shunt and compound machines J’=I++7. 
The current consumed in the shunt field varies with the size of the machine 
approximately as follows 


kw. = 1 5 10 20 50 100 500 2000 
= .O8T .06L Aleve 047 .03L O2%ob -O2% .O15T 
In large machines it is better, in order to diminish the eddy currents, to 
make the armature conductors in the form of a cable, than to use single 
wires. If the conductor on the armature is a single wire the thickness of 
insulation varies from .012 to .020 inch, depending on the voltage. If the 
conductor is @ cable, each strand is insulated with a thickness of from .005 
to .01 inch and the entire cable is covered with insulation of thickness 
varying from .005 to .01 inch. 

In a small machine with but a single layer of conductors on the arma- 


ture L =1 + N. N = (1.885,000D X h) + d?. 
For drum armatures N = 2 (ng X n3) + 113 
for ring armatures N = (n2 X ng) + 14. 


A general formula given by Wiener for the length of armature is 
Pree Kombi as Dem he 
DW Go X Rg Ty Qi gh Pa a” 


The minimum number of bars on the commutator is Cmin = E’p + b. 
The value of 6 depends on the current as follows: 


Amperes: over 100 100-50 50-20 20-10 10-5 5-2 2-1 
b 10 10.5 11.5 12.5 15 20 20. 


The number which may be used, provided it does not fall below Cmin is 

C = (no X n3) + 7. 
For drum armatures the number of conductors attached to each com- 
mutator bar must be an even number. The quotient cf C, obtained as 
above, by the largest even number which will give a result greater than 
Cmin is the proper number of ecmmutator bars for drum armatures. For 
ring armatures it is the quotient of C by the largest number which will give 
a result greater than Cmin. In each case the divisor is the number of 
eonductors which should be attached to each bar. 
The flux through the armature is: 





1060 ELECTRICAL ENGINEERING, 


_6XpX EX 10° 
N X r.p.m. 
‘rhe flux density in the armature 2ore is 


BR Soe SR eee 
TXT Re XO 
where m is a factor depending on the percentage of polar arc. Assuming 
100 per cent and 50 per cent as the limits cf polar arc, the foJlcwing are 
the respective values of m at those limits’ In bipolar, "smocth armature, 
machines m = 1.00 and .70; in bipclar, tcothed armature machines 
m = 1.00 and .55; in smooth armature multipolar machines m = 1.00 
and .625, with from 4 to 12 poles: m = 1.00 and .60 with from 14 and 20 
poles. With toothed armatures the figures are slightly lower. 

The area of the field magnet ccres depends en the flux to be generated. 


p= pA, 
A value for A is assumed, which wiJ] vary with the size and type of machine. 
By means of this assumed value the principal dimensions of the magnetic 
circuit are calculated. The true value of A is next calculated by means 
of the formula 
, __ Joint permeance of useful and stray paths 


Permeance of useful path 


The permeance of a path is its magnetic conductance. 
Permeance = (Permeability X Area) + Length. 


The stray paths are those across the pole-pieces, across the magnet cores 
and between the pole-pieces and the yoke joining the magnet ccres. 

With the new value of A, ¢’ is recaleulated. If the true and assumed 
values of A give a large difference in flux then the dimensions of the circuit 
must be changed and A recaleulated. 

The areas of the various portions are found by dividing the total flux by 
the allowable flux density. The allowable flux densities in maxwells per 
square inch are as follows: Wrought iron, 90,000; cast steel. 85,000; cast 
iron, 40,000. 

The various areas being known, the winding of the magnets is ealculated 
as shown in the section on Strength of the Magnetic Field. 

ExampLe.—Design a 200 K.W. bipolar, smooth drum armature, shunt 
dynamo, with wrought-iron pole-pieces. and cast iron magnet cores and 
yoke. Volts, 500; amperes, 400; R.P.M., 450. 

Assume iy = 40,000; Vie 45> ev= 08H 46—= i025! percentage of 
polar are = 85. Then FE’ =515; I’ = 410 andk = 68 X 1078, 

tl = (515 X 1 X 100,000,000) + (68 X 45 X 40,000) = 420.7 feet. 

D = (12 X.60.X 45) + (450 X 3.1416) = 22.91 inches. 

d? = 300 X 410 + 1 = 123,000. In this size of machine it is desirable 
to use cables. Each conductor may be composed of three cables in paral- 
lel, each composed of seven wires. A No. 12 B. & S. gauge wire has an area 
of 6530 cir. mils, and 7 X 3 X 6530 = 137,130, which is near enough to a2. 

To find d’- Number of strands on a diameter = 3. Insulation on each 
strand = .005; insulation of cable = .008: diameter No. 12 wire = .080808; 
(Oh ES eh SK (0808 + 2 X .005) + (2 X .008) = .2884 inch. 

Assume h = .625; ny = 3; no = 22.91 X 3.1416 + .2884 = 249; nz = 

625 += pet he oe Then L = (12 X 3 X 420.7) + (2 X 249) = 30.41 


inches. 
Cmin=515 X¥ 1+ 10 = 51. a Oe Sane X 2 + 3) + 4 = 41 (too small); 
(249. 2.+.3) + 2 = 83... ek 
NS OP OL) cos eC 
= 6X 1X 515 X 1,000,000,000 + 332 * 450 = 20,683,000. 


iad eens ==). O4° eae), 683 000 += (3.1416 X 22, 91 X 30.41 X .94) 
ie Pa calculate A would require more space than can be spared here. As: 
sume A = 1.34. 

= 1.34 X 20,683,000 = 27,715,220. 
Area & Bick cores = 27,715,220 + 40000 = 692 sq. inches, 


Diameter of magnet cores = 692 x : = 29.8 inches. _ 


ALTERNATING CURRENTS. 1061 


ALTERNATING CURRENTS,* 


The advantages of alternating over direct currents are: 1. Greater sim- 
plicity of dynamos and mot«rs,no commutators being required; 2. The 
feasibility of obtaining high voltages, by means of static transformers, for 
cheapening the cost of transmission; 3. The facility of {transforming from 
one voltage to another, either higher or lower, for different purposes. 

A direct current is uniform in strength and direction, while an alternating 
current rapidly rises from zero to a maximum, falls to zero, reverses its 
direction, attains a maximum in the new direction, and again returns to 
zero. This series of changes can best be represented ‘by a curve the abscis- 
sas of which represent time and the ordinates either current or electro- 
motive force (e.m.f.). The curve usually chosen for this purpose is the 
sine curve, Fig. 172; ‘the best forms of alternators give a curve that is a very 
close approximation to the sine curve, and all calculations and deductions 
of formule are based on it. The equation of the sine curve is y=sin 2, in 
which y is any ordinate, and z is the angle passed over by a moving radius 
vector. 

After the flow of a direct current has been once established, the only 
opposition to the flow is the resistance offered by the conductor to the 
passage of current through it. ‘This resistance of the conductor, in treat- 
ing of alternating currents, is sometimes spoken of as the ohmic resistance. 
The word resistance, used alone, always means the ohmic resistance. In 
alternating currents, in addition to the resistance, several other quantities, 
which affect the flow of current, must be taken into consideration. These 
quantities are inductance, capacity, and skin effect. They are discussed 
under separate headings. 

The current and the e.m.f. may be in phase with each other, that is, 
attain their maximum strength at the same instant, or they may not, de- 
pending on the character of the circuit. Ina circuit containing only resist- 
ance, the current and e.m.f. are in phase; in a circuit containing induct- 
ance the e.m.f. attains its maximum value before the current, or leads the 
current. In a circuit containing capacity the current leads the e.m.f. If 
both capacity and inductance are present in a circuit, they will tend to 
neutralize each other. 

Maximum, Average, and Effective Values.—tThe strength 
and the e.m.f. of an alternating current being constantly varied, the maxi- 
mum value of either is attained only for an instant in each period. The 
maximum values are little used in calculations, except in deducing formulze 
and for proportioning insulation, which must stand. the maximum pressure. 

The average value is obtained by averaging the ordinates of the sine curve 
representing the current, and is 2 + 7m or 0.637 of the maximum value. 

The value of greatest ‘importance is the effective, or ‘‘square root of the 
mean square,’’ value. It is obtained by taking the square root of the mean 
of the squares of the ordinates of the sine curve. The effective value is 
the value shown on alternating-current measuring instruments. The prod- 
uct of the square of the effective value of the current and the resistance of 
circuit is the heat lost in the circuit. 

The comparison of the maximum, average, and effective values is as 
follows: 


Evsrec. = Evax. X 0.707; ElAver. = FN a X 0.637; Eytax. =1.41X Epic, 


Frequency.—The time required for an alternating current to pass 
through one complete cycle, as from one maximum point to the next (a 
and 6, Fig. 172)° is termed the period. The number of periods in u second 
is termed the frequency of the current. Since the current changes its direc- 
tion twice in each period, the number of reversals or alternations is double 
the frequency. A current of 120 alternations per second has a period ot 1/60 











* Only a very brief treatment of the subject of alternating currents can 
be given in this book. The following works are recommended as valuable 
for reference’ Alternating Currents and Alternating Current Machinery, by 

C. and J. P. Jackson; Standard Polyphase Apparatus and Systems, by 
M. A. Oudin; Polyphase Electric Currents, by S. P. Thompson; Electric 
Lighting, by F. B. Crocker, 2 vols.; Electric Power Transmission, by Louis 
Bell; Alternating ae by Bedell and Crehore; Alternating- current Phe- 
nomena, by Chas. P . Steinmetz. The two last named are highly mathemat- 
ical, 











1062 . ELECTRICAL ENGINEERING. 


and a frequency of 60 The frequency of a current is equal to one half the 
number of poles on the generator. multiplied by the number of revolutions 
per second Frequency is denoted by the letter Ff. 

The frequencies most generally used in the United States are 25, 40, 60, 
125, and 133 cycles per second The Standardization Report of the 

I.E.E recommends the adoption of three frequencies, viz.. 25 60.and 120. 

With the higher frequencies both transformers and conductors will be 
less costly in a circuit of a given resistance, but the capacity and inductance 
effects in each will be increased, and these tend to increase the cost. With 
high frequencies it also becomes difficult to operate alternators in parallel. 

A low-frequency current cannot be used on lighting circuits, as the hghts 
will flicker when the frequency drops below a certain figure. For are lights 
the frequency should not be less than 40. For incandescent lamps it should 
not be less than 25. If the circuit is to supply both power and hght a 
frequency of 60 is usually desirable. For power transmission to long dis- 
tances a low frequency, say 25, is considered desirable, in order to lessen 
the capacity effects If the alternating current is to be converted into 
direct current for lighting purpose, a low frequency may be used. as the 
frequency will then have no effect on the lights. 

Inductance. —A current flowing through a conductor produces a mag- 
netic flux around the conductor. If the current be changed in strength or 
direction, the flux is also changed, producing in the conductor an e.m/f. 

whose direction is opposed to that of the 
current in the conductor. This counter 
e.m.f. is the counter e.m.f. of inductance 
It is proportional to the rate of change 
of current, provided that the permeabil- 
ity of the medium around the conductor 
remains constant. The unit of induct- 
ance is the henry, symbol L. A circuit 
has an inductance of one henry if a uni- 
form variation of current at the rate of 
Fic. 172. one ampere per second produces a 

: counter e.m.f. of one volt. 

The effect of inductance on the circuit is to cause the current to lag be- 
hind the e.m.f.. as shown in Fig. 172, in which abscissas represent time, and 
ordinates represent e.m.f. and current strengths respectively. 

_ Capacity.— Any insulated conductor has the power of holding a quan- 
tity of static electricity. This power is termed the capacity of the body. The 
capacity of a circuit is measured by the quantity of electricity in it when 
at unit potential. It may be increased by means of a condenser. <A con- 
denser consists of two parallel conductors, insulated from each other by 
a non-conductor. The conductors are usually in sheet form. 

The unit of capacity is a farad, symbol C. A condenser has a capacity 
of one farad when one coulomb of electricity contained in it produces a dif- 
ference of potential of one volt. The farad is too large a unit to be conven- 
iently used in practice, and the micro-farad is used instead. 

The effect of capacity on a circuit is to cause the e.m.f. to lag behind the 
current. Both inductance and capacity may be measured with a Wheat- 
stone bridge by substituting for a standard resistance a standard of induct- 
ance or a standard of capacity. 

Power Factor.—In direct-current work the power, measured in watts, 
is the product of the volts and amperes in the circuit. In alternating-cur- 
rent work this is only true when the current and e.m.f. are in phase. If the 
current either lags or leads, the values shown on the volt and ammeters 
will not be truc simultaneous values. Referring to: Fig. 172, it will be seen 
that the product of the ordinates of current and e.m.f. at any particular 
instant will not be equal to the product of the effective values which are 
shown on the instruments. The power in the circuit at any instant is the 
product of the simultaneous values of current and e.m.f., and the volts 
and amperes shown on the recording instruments must be multiplied 
together and their product multiplied by a power factor before the true 
watts are obtained. This power factor, whichis the ratio of the volt-amperes 
noe watts, is also the cosine of the angle of lag or lead of the current. 

ug L.4 





~P=IXEX power factor = IX EXcos @ 
where @ is the angle of lag or lead of the current. 


ALTERNATING CURREN‘IS. 1063 


A watt-meter, however, gives the true power in a circuit directly. The 
method of obtaining the angle of lag is shown below, in the section on Im- 
pedance Polygons. 

Reactance, Impedance, Admittance.—In addition to the 
ohmic resistance of a circuit there are also resistances due to inductance, 
capacity, and skin effect. The virtual resistance due to inductance and 
capacity is termed the reactance of the circuit. If inductance only be 
— in the circuit, the reactance will vary directly as the inductance. 

f capacity only be present, the reactance will vary inversely as the capacity. 


Inductive reactance =27/L. 


: 1 

Condensive reactance —opfO" 

The total apparent resistance of the circuit, due to both the ohmic resistance 
and the reactance, is termed the impedance, and is equal to the square root 
of the sum of the squares of the resistance and the reactance. 


Impedance = Z =V R?2+ (2xfL)2 when inductance is present in the circuit. 


5} 
Impedance =Z = R2+ (saa) when capacity is present in the circuit. 
ia 


Admittance is the reciprocal of impedance, =1~+ Z. 

If both inductance and capacity are present in the circuit, the reactance 
of one tends to balance that of the other; the total reactance is the alge- 
braic sum of the two reactances; thus, 

1 y, 1 2 
Total rE ar Ye Z=V R i (2afL aC) : 
In all cases the tangent of the angle of lag or lead is the reactance divided by 
the resistance. In the last case 
i! 
Be GG 
R e 

Skin Effect.—Alternating currents tend to have a greater density at 
the surface than at the axis of a conductor. The effect of this is to make 
the virtual resistance of a wire greater than its true ohmic resistance. With 
low frequencies and small wires the skin effect is small, but it becomes quite 
important with high frequencies and large wires. 

The following table, condensed from one in Foster’s ‘‘ Electrical Engi- 
neers’ Pocket-book,’’ shows the increase in resistance due to skin effect. 


‘ tan, 2 = 


Skin-effect Factors for Conductors carrying Alternating 








Currents. 
Diameter Frequencies. 
an 

B.&S oS. 

Gauge 25 40 60 100 130 

Oiubein (ike aceke ght ere a eae Rees 1.001 1.005 1.008 

YQ) os ew hh RES pers Sele 1.001 1.002 1.006 1,010 

COLGTOE erapagiiad (aoe eesti 1.002 1.005 1.010 1.017 

0000 1.001 1.005 1.006 1.085 L027 

4" 1.002 1.006 1.008 1.022 1.039 

Bg” 1.007 076 1.040 1.100 1.156 

1 1.020 1.052 aT Na 1.263 1.397 

ig gi 1.053 1.138 1.239, 1.506 1.694 

14” 1.098 e223 1.420 L765 1.983 

Pits 1.265 Look 1.826 2.290 2.560 














For virtual resistance, multiply ohmic resistance by factor from this table. 


1064 ELECTRICAL ENGINEERING. 


Ohms Law applied to Alternating-current Circuits.—To 
apply Ohm’s law to alternating-current circuits a slight change is neces- 
sary in the expression of the law. Impedance is substituted for resistance. 
The law should read » 

E Hy 


VR?+ x2 4 

Impedance Polygons.—1. Series Circuits —The impedance of a cir- 
cuit can be determined graphically as follows. Suppose a circuit to contain 
a resistance R and an inductance L, and to carry a current J of frequency f/f. 
In Fig. 173 draw the line ab proportional to R, and representing the direc- 
tion of current. At b erect bc perpendicular to ab and proportional to 27fL. 
Join a and c. The line ac represents the impedance of the circuit. The 
angle 6 between ab and ac is the angle of lag of the current behind the e.m.f., 
and the power factor of the circuit is cosine 9. The e.m.f. of the circuit is 


e a R b 
. eon 
b 
a b Cc 


Fia. 173. Fie. 174. 


If the above circuit contained, instead of the inductance L,a capacity C, 
then would the polygon be drawn as in Fig. 174. The line bc would be pro- 


portional to onfC and would be drawn in a direction opposite to that of 
bc in Fig. 173. The impedance would again be Z, the e.m.f. would be 
Z XI, but the current would lead the e.m.f. by the angle @. 

Suppose the circuit to contain resistance, inductance, and capacity. Tue 
lines of the impedance polygon would then be laid off as in Fig. 175. The 
impedance of the circuit would be represented by ad, and "the angle of lag 
by 6. If the capacity of the circuit had been such that cd was less than bc, 
then would the e.m.f. have led the current. 


Cy 


Oi ale 


g 





d 


Fie. 175. Fram lsGs 
If between the inductance and capacity in the circuit in the previous ex- 
amples there be interposed another resistance, the impedance polygon will 
take the form of Fig. 176. The lines representing either resistances, in- 
ductances, or capacities in the circuit follow each other in all cases as do 
the resistances, inductances, and capacities in the circuit, each line having 
its appropriate direction and magnitude. 


Ri=15 C,=.000100 Re=12 Li =.05 





~ + = R3= 20 
Fia. 177. 


_ ALTERNATING CURRENTS. 1065 


Exampie.—A circuit (Fig. 177) contains a resistance, R,, of 15 ohms, a 
capacity, Ci, of 100 microfarads (.000100 farad). a resistance, Ry, of 12 
ohms. an inductance Lj, of .05 henrys, and a resistance Rg, of 20 ohmns. 
Find the impedance and electromotive force 
when a current of 2 amperes is sent through 
the circuit, and the current when an e.m.f. @q 
of 120 volts is impressed on the circuit fre- 
quency being taken as 60. Also find the 
angle of lag. the power factor, and the power 
in the circuit when 120 volts are impressed. 

The resistance is represented in lig. 178 
by the horizontal line ab, 15 units long. 


Ri=15 





T1ZO , lo 
The capacity is represented by the line bc, S 
drawn downwards from b. and whose = d 
length is ; R=12 
Ui 





= = = ot ° 1 iis i78. 
DBxfC, 2X3.1416xX60xX 0001 °° eiita: 


From the point ¢ a horizontal line cd, 12 units long, is drawn to represent 
R,.. From the point d the line de 1s drawn vertically upwards to represent 
the inductance L,. Its length is 
2nfL,=2X 3.1416 X60X .05=18.85. 

From the point e a horizontal line ef, 20 units long, is drawn to represent 
Rs;. The line joining a and f will represent the impedance of the circuit in 
ohms. The angle 9, between ab and af, is the angle of lag of the e.m-f. be- 
hind the current. ‘The impedance in this case is 47.5 ohms, and the angle 
of lag 1s,9° 15’. ‘ 

The e.m.f. when a current of 2 amperes is sent through is 

IZ=E=2X47.5=95 volts. . 

If an e.m.f. of 120 volts be impressed on the circuit, the current flowing 

through will be ; 
1207-31120 


ee ee e ° 
Ti Z 47.5 53 amperes 


The power factor =cos 6=cos 9° 15’ = .987. 
The power in the circuit at 120 volts is 
xX EX cos 6=2.53 X 120 X .987 = 299.6 watts. 
2. Prrallel Circwits.—If two circuits be arranged in parallel, the current 
flowing in each circuit will be inversely proportional to the impedance of 
that circuit. The e.m.f. of each circuit is 


Ri Ld the e.m.f. across the terminals at either end 
of the main circuit, where the various branches 
00000 separate. Consider a circuit, Fig. 179, con- 


sisting of two branches. The first branch 

contains a resistance R, and an inductance L, 

NOOO in series with it. The second branch con- 

tains a resistance Rg in series with an induct- 

Fre. 179 ance Ly. The impedance of the circuit may 

IG. . be determined by treating each of the two 

branches as a separate series circuit, and drawing the impedance polygon 

for each branch on that assumption. Having found the impedance the 

current flowing in either branch will be the reciprocal of the impedance 

multiplied by the e.m.f. across the terminals. The current in the entire 
? circuit is the geometrical sum of the current in the two branches. 

The admittance of the equivalent simple circuit may be obtained by 
drawing a parallelogram, two of whose adjoining sides are made parallel to 
the impedance lines of each branch and equal to the two admittances 
respectively. 

The diagonal of the parallelogram will represent the admittance of the 
equivalent simple circuit. The admittance multiplied by the e.m-f. gives 
the total current in the circuit. 

ExAmpLe.—Given the circuit in Fig, 180, consisting of two branches. 
Branch 1 consists of a resistance R,;=12 ohms, an inductance L,=.05 
henry, a resistance R,=4 ohms, and a capacity Cy, =120 microfarads 
<.00012 farad). Branch 2 consists of an inductance Lg=.015 henry, a 
resistance Rg=10 ohms, and an inductance L3;=.03 henry. An emf, 
of 100 volts is impressed on the circuit at a frequency of 60. Find the ad- 


1066 ELECTRICAL ENGINEERING. 


mittance of the entire circuit, the current, the power factor, and the power 
in the circuit. Construct the impedance polygons for the two branches 


R,=12 Li=.05 Re=4 C,=.00012 





Fie. 180. 


separately as shown in Fig. 181, a and 6b. The impedance in branch 1 is 


16.4 ohms, and the current is wax 100=6.19 amperes. The angle of 


Ro=4 





1 
Z, 7 0619 
Fre. 181. 
lead of the current is 12° 45’. The impedance in branch 2 is 19.5 ohms and, 
the current is ios X*100=5.13 amperes. The angle of lag of the current 
is 61°. . 


The current in the entire circuit is found by taking the admittances of 
the two branches, and drawing them from the point o, in Fig. 181 c, parallel 
to the impedance lines in their respective polygons. The diagonal from o 
is the admittance of the entire circuit, and in this case is equal to 0.092. 
The current in the circuit is .092 x 100=9.2 amperes. ‘The power factor 
is 0.944 and the power in the circuit is 100 x .944 X 9.2 = 868.48 watts. 

Self-inductance of Lines and Circuits.—The following formuls 
and table, taken from Crocker’s ‘‘ Electric Lighting,” give a method of cal- 
culating the self-inductance of two parallel aerial wires forming part of the 
same circuit and composed of copper, or other non-magnetic material: 


ALTERNATING CURRENTS. 1067 


Feats WL ae T am Let a cap Fe 
: C2: Me Wop | 
L per mile = (80.5+740 log =*)10-", 


in which Z isthe inductance in henrys of each wire, A is the interaxial dis- 
tance between tae two wires, and d is the diameter of each, both in inches. 
If the circuit is of iron wire, the formule become 


L por foot = (2286+140.3 log = )10-*, 
L per mile = (120704740 log 2) 10 -*. 


INDUCTANSE, IN MILLIHENRYS PER MILE, FOR EACH OF TWO PARALLEL 
COPPER WIRES. 























= th ° ° 
a8 American Wire Gauge Number 
= 2 | 0000) 000 ee ee Raed i WA Mii a Hl Bas Wl SN = a bd <a Soke 
3 |0.907|0 944/0.982]1.019/1.056/1.094/1 131/1.168]1.243]1.317)1.392|1.467 
6 |1.130/1 168]1.205 1.242) 1.280 1 317)1.354/1.392)1.466/1.540|1.615/1.690 
9 }1 260/1.298]1 3351 372;1 410)1.447/1.485)1.522|1.596)1.671!1.746}1.820 
12 |1.3853/1.391'1.428)1 465/1.502/1 540, 1 577|1.614)1.689]1.764/1.838/]1.913 
18 |1.48411.521[1.558'1.596!1.633/1.671/1.708'1.744!1.820!1 894|1.968/2.044 
24 |1.576)1.614/1 651)1 688 1.725/1.764/1.800)1.838)1.912}1.986;2 061/2.135 
30 |1.648]1 686]1 723/1.760 1.797|1.835]1 871}1 910}1 .984|2:058)}2.134/2.208 
36 |1 707|1 745)1.784/1.818 1.856}1 893)1.931)}1 .968)2.043)2.117/2.19212.266 
48 |1.799}1 836/1.874/1.911 1.949]1.986|2 023/2.061}2 135|2.209| 2.285]2.359 
60 |1.871}1 909/1 946/1 982 2.023/2.058/2.095|2 132/2.208)2.282|2.356/2.432 
72 |1.930]1 968|2.005|2.042 2.079/2 116/2.154/2.192|2 266/2.340|2.415|2.489 
84 |1.971)2.016)/2:053/2.092 2 128'2 166|2.203|2.240/2.312)2.389)2.464)/2 539 
96 |2 023/2.059/2.097/2.134 2.172|2.210/2.246|2.283/2 358/2.433 2.507/2.582 











Capacity of Conductors.—aAll conductors are included in three 
classes, viz.: 1. Insulated conductors with metailic protection: 2. Single 
aerial conductor with earth return; 3. Metallic circuit consisting of two 
parallel aerial wires. The capacity of the lines may be calculated by means 
of the following formule taken from Crocker’s “Electric Lighting "’: 


7361k 10-"° . 38.83k 107° 
Class1. C per foot= Siraed Tee C per mile = iar Day: 





7361 x10—'° Waddie s Merve 301) so 


3681 x 10—"° 
log (2A + d)’ 
lass 3. 

oH C per mile of each wire = | eee x aoe 

pe e of eac Wire oS GA = @) 


I 


C per foot of each wire 





In which C isthe capacity in farads. D the internal diameter of the metallic 
covering, d the diameter of the conductor, h the height of the conductor 
above the ground, and A the interaxiai distance between two parallel wires, 
all 1n inches; & is a dielectric constant which for air is equal to 1 and for 
pure rubber is equal to 2.5. The formule in cases 2 and 3 assume the wires 
to be bare. If they are insulated, & must be introduced 1n the numerator 


and given a value slightly greater than 1. 


1068 ELECTRICAL ENGINEERING. 


Single-phase and Polyphase Currents.—A single-phase current 
sS a simple alternating current carried on a single pair of wires, and is 
generated on a machine having a single armature winding. It is represented 
by a single sine curve. 

Polyphase currents are known as two-phase, three-phase, six-phase, or 
any other number, and are represented by a ccrresponding number of sine 
Es bas The most commonly used systems are the two-phase and three- 
phase 

1. Two-phase Currents.—In a two-phase system there are two single- 
phase alternating currents bearing a definite time relation to each other 
and represented by two sine curves (Fig. 182). The two separate currents 

may be generated by the same or by separate 
machines. If by separate machines, the arma- 
aN tures of the two should be positively coupled 
together. Two-phase currents are usually gener- 
NY, ated by a machine with two armature windings, 
each winding terminating in two collector rings. 
The two windings are so related that the two 
Fia. 182. currents will be 90° apart. For this reason two- 
phase currents are also called ‘‘quarter-phase’”’ 
currents. 

Two-phase currents may be distributed on either three or four wires. 
The three-wire system of distribution is shown in Fig. 183. One of the 
return wires is dispensed with, connection being made across to the other 
as shown. The common return wire should be made 1.41 times the area 
of either of the other two wires, these two being equal in size. 





W1 
a 
b 
Cc 
ad 
Fia. 183, Fie. 184. 


The four-wire system of distribution is shown in Fig. 184. The two 
phases are entirely independent, and for lighting purposes may be operated 
as two single-phase circuits. 

2. Three-phase Currents.—Three-phase currents consist of three alternat- 
ing currents, differing in phase by 120°, and represented by three sine 
curves, as in Fig. 185. They may be distributed by three or six wires. If 
distributed by the six-wire system, it is analogous to the four-wire, two- 
phase system, and is equivalent to three single-phase circuits. In the 
three-wire system of distribution the circuits may be connected in two 
different ways, known respectively as the Y or star connectiun, and the 4 
(delta) or mesh connection. 





Fre. 186. Fig. 186, 


ALTERNATING CURRENTS. 1069 


The Y connection is shown in Fig. 186. The three circuits are joined 
at the point 0, known as the neutral point, and the three wires carrying the 
eurrent are connected at the points a, b, and c, respectively. If the three 
circuits ao, bo, and co are composed of lights, they must be-equally loaded 
or the lights will fluctuate. If the three circuits are nerfectly balanced, the 
lights will remain steady. In this form of connection each wire may be 
considered as the return wire for the other 
two. If the three circuits are unbalanced, b 
a return wire may be run from the neutral 
point o to the neutral point of the arma- 
ture winding on the generator. The 
system will then be four-wire, and will 
work properly with unbalanced circuits. 

The A connection is shown in Fig. 187. 

Each of the three circuits ab, ac, bc, re- 

ceives the current due to a separate coil 

in the armature winding. This form of 

connection will work properly even if the c 
circuits are unbalanced; and if the cir- @ 

cuit contains lamps, they will not fluctuate 

when the circuit changes from a balanced Fic. 187. 

to an unbalanced condition, or vice versa. . 

Measurement of Power in Polyphase Circuits.—i. Two- 
phase Circuits.—The:power of two-phase currents distributed by four wires 
may be measured by two wattmeters introduced into the circuit as shown in 
Fig. 184. The sum of the readings of the two instruments is the total power. 
If but one wattmeter is available, it should be introduced first in one circuit, 
and then in the other. If the current or e.m.f. does not vary during the 
operation, the result will be correct. If the circuits are perfectly belaaced, 
twice the reading of one wattmeter will be the total power. 

The power of two-phase currents distributed by three wires may be 
measured by two wattmeters as shown in Fig. 183. The sum of the two 
readings is the total power. If but one wattmeter is available, the coarse- 
wire coil should be connected in series with the wire ef and one extremity 
of the pressure-coil should be connected to some point on ef. The other 
end should be connected first to the wire a and then to the wire d, a reading 
being taken in each position of the wire. The sum of the readings gives the 
power in the circuits. 

2. Three-phase Currents.—The power in a three-phase circuit may be 
measured by three wattmeters, connected as in Fig. 188 if the svstem is 
Y-connected, and as in Fig. 189 if the system is A-connected. The sum 


Wi 
We 





Fig. 188. Fig. 189. 


of the wattmeter readings gives the power in the system. If the circuits 
are perfectly balanced, three times the reading of one wattmeter 1s the 
total power. 

The power in a A-connected system may be measured by two wattmeters, 
as shown in Fig. 190. If the power factor of the system 1s greater than 
0.50, the arithmetical sum of the readings is the power in the circuit. If 
the power factor is less than 0.50, the arithmetical difference of the read-~ 
ings is the power. Whether the power factor 1s greate: or less than 0.50 
may be discovered by interchanging the wattmeters without disturbing the 


a 
1070 PLECTRICGAL ENGINEERING. 


relative connection of their coarse- and fine-wire ecils. If the deflections of 
the needles are reversed, the difference 
of the readings is the power. If the needles 
are deflected in the same direction as at 
first, the sum of the readings is the 
power. 

Alternating-current Genera= 
tors.—These differ little from direct- 
current generators in many respects. Any 
direct-current generator, if provided with 
collector rings instead of a commutator. 
could be used as a single-phase alternator, 
The frequency would in most cases, how- 
ever, be too low for any practical use. 
The fields of alternators are always 

Fie. 190. separately excited; the machines are 

sometimes compounded by shunting some 

of their own current around the fields through a rectifying device which 

changes. the current to pulsating direct current. In ail large machines 
the armature is stationary ard the field-magnets revclve. 


TRANSFORMERS, CONVERTERS, ETC, 


Transformers.—aA transformer consists essentially of two coils of wire, 
one coarse and one fine, wound upon an iron core. The function of a trans- 
former is to convert electrical energy from one potential to another. If 
the transformer causes a change from high to low voltage, it is known as a 
‘*step-down” transformer; if from low to high voltage, it is known as a 
‘‘step-up”’ transformer. 

The relation of the primary and secondary voltages depends on the num- 
ber of turns in the two coils. Transformers may also be used to change 
’ eurrent. of one phase to current of another 
phase. The windings and the arrangement 
of the transformers must be adapted to each 
particular, case. In Fig. 191 an arrange- 
ment is shown whereby two-phase currents 
may be converted into three-phase. Two 
transformers are required, one having its 
primary and secondary coils in the relation 
of 100 to 100, and the other having its pri- 
mary and secondary in the relation of 100 to 
86. The secondary of the 100-to-100 trans- 
former is tapped at its middle point and 
joined to one terminal of the other secondary. 
Between any pair of the three remaining ter- 
minals of the secondaries there will exist a Fic. 191. 
difference of potential of 50. 

There are two sources of loss in the transformer, viz., the copper loss and 
the iron loss. The copper loss is proportional to the square of the current, 
being the J?R loss due to heat. If J;, Ri, be the current and resistance 
respectively of the primary, and J», Ro, the current and resistance respect- 
ively of the secondary, then the total copper loss is We=1/,2R,+/,2R, and 
I,?R, +1o?Ro 









400 Vor 
100 Turns 


<100 Volt: 
100 Turns 









the percentage of copper loss is , where Wp is the energy delivered 
tothe primary. The iron loss is constant at all loads, and is due to hysteresis 
and eddy currents. 

Transformers are sometimes cooled by means of forced air or water cur- 
rents or by immersing them in oil, which tends to equalize the temperature 
jn all parts of the transformer. 

Efficiency of Transformers.—The efficiency of a transformer is the ratio 
of the output in watts at the secondary terminals to the input at the primary 
terminals. At full load the output is equal to the input less the iron and 
copper losses. The full-load efficiency of transformers is usually very high, 
being from 92 per cent. to 98 per cent. As the copper loss varies as the 
square of the load, the efficiency of a transformer varies considerably at 
different loads. Transformers on lighting circuits usually operate at full 


i 


ALTBERNATING-CURRENT MOTORS. 1071 


bat 


load but a very small part of the day, though they use some current all the 
time to supply the iron losses. For transformers operated only a part of the 
time the *‘all-day”’ efficiency ismore important than the full-load efficiency. 
It is computed by comparing the watt-hours output to the watt-hours input. 
The all-day efficiency of a 10-K.W. transformer, whose copper and iron 
losses at full load are each 1.5 per cent, and which operates 3 hours at full 
load, 2 hours at half load, and 19 hours at no load, is computed as follows: 


Tron loss, all loads=10X .015=.15 K.W. 

Copper loss, full load =10X .015=.15 K.W. 
Copper loss, 4 load=.15X (4)2= .0375 K.W. 
iron loss. K.W...hours=.15X24=8.6. 

Copper loss, full load, K.W. hours= .15X3=.45. 
Copper loss, 4% load, K.W. hours= .0375 X 2= .075. 
Output. K.W. hours= {(10X3)+(5X2) } =40. 
Input, K.W. hours=40+3.6+ .45+ .075=44.125. 
All-day efficiency = 40 + 44.125 = .907. 


The transformers heretofore discussed are constant-potential transformers 
and operate at a constant voltage with a variable current. For the opera- 
tion of lamps in series a constant-current transformer is required - There 
are a number of types of this transformer. That manufactured by the 
General Electric Co. operates by causing the primary and secondary coils to 
approach or to separate on any change in the current. 

Converters, etc.—In addition to static transformers, various machines 
are used for the purpose of changing the voltage of direct currents or the 
voltage, phase, or frequency of alternating currents, and also for changing 
alternating currents to direct or vice versa. These machines are all rotary 
and are known as rotary converters, motor-dynamos. and dynamotors. 

A rotary converter consists of a field excited by the machine itself, and 
an armature which is provided with both collector rings and a commuta- 
tor. It receives direct current and changes it to alternating, working as a 
direct-current motor, or it changes alternating to direct current. working 


as a synchronous motor. 
A motor-dynamo consists of a motor and a dynamo mounted on the same 


' base and coupled together by a shaft. 


A dynamotor has one field and two armature windings on the same core. 
One winding performs the functions of a motor armature, and the other those 
of a dynamo armature. 

A booster is a machine inserted in series in a direct-current circuit to 
change its voltage. It may be driven either by an electric motor or other- 


wise. 
ALTERNATING-CURRENT MOTORS, 


Synchronous Motors,—Any alternator may be used as a motor, 
provided it be brought into synchronism with the generator supplying the 
eurrent to it. The operation of the alternating-current motor and generator 
is similar to the operation of two generators in parallel. It is necessary to 
supply direct current to the field. The field circuit is left open until the 
machine is in phase with the generator If the motor has the same number 
of poles as the generator. it will run at the same speed; if a different number 
the speed will be that of the generator multiplied by the ratio of the number 
of poles of the motor to that of the generator. Single-phase, synchronous 
motors are not self-starting. Polyphase motors may be made self-starting 
but it is better to bring the machines to speed by independent means before 
supplying the current. The machines may be started by a small induction 
motor, the load on the synchronous motor being thrown off, or the field 
may be excited by a small direct-current generator belted to the motor, and 
this generator may be used as a motor to start the machine, current to run 
it being taken from a storage battery. If the field of a synchronous motcr 
be properly regulated to the load, the motor will exercise no inductive effect 
on the line, and the power factor will be 1. If the load varies the current 
in the motor will either lead or lag behind the e.m.f. and will vary the 
power factor. If the motor be overloaded so that there is a diminution of 
speed the motor will fall out of step with the generator and stop. | 

Synchronous motors are often put on the same circuit with induction 
motors. The synchronous motor in this case may, by increasing the field 
excitation, be made to cause the current to lead, while the induction motor 





10%2 ELECTRICAL ENGINEERING, 


will cause it to lag. The two effects will thus tend to balance each other 
and cause the power factor of the circuit to approach 1. 

Synchronous motors are best used for large units of purer at high voltages, 
where the load is constant and the speed invariable. They are unsatis- 
factory where the required apeed is variable and the Joad changes. Two 
great disadvantages of the synchronous motor are its inability to start 
under load. and the necessity of direct-current excitation. 

Induction Motors.—The distinguishing feature of an induction motor 
is the rotating magnetic field. It is thus explained: In Fig 192 let ab, cd 
be two pairs of poles of a motor, a and b being wound from 
one leg or pair of wires of a two-phase alternating circuit, 
and cand d from the other leg, the two phases being 90° 
apart. At the instant when a and 6 are receiving maxi- 
mum current, so as to make aa north pole and 6b a south 

ole, c and d are demagnetized. and a needle placed 
tween the poles would stand as shown in the cut. Dur- 
ing the progress of the cycle of the current the magnetic 
flux at a decreases and that atc increases. causing the 
Fic. 192 point of resultant maximum intensity to shift, and the 
E ; needle to move clockwise toward c. A complete rotation 
of the resultant point is performed during each cycle of the current. 
An armature placed within the ring is caused to rotate simply by the shift- 
ing of the magnetic field without the use of a collector ring. The words 
“rotating magnetic field” refer to an area of magnetic intensity and must 
be distinguished from the words ‘revolving field ’” which refer to the por- 
tion of the machine constituting the field-magnet. 

The} field or *‘ primary” of an induction motor is that portion of the 
machine to which current is supplied from the outside circuit. 

The armature or ‘“* secondary” is that portion of the machine in which 
currents are induced by the rotating magnetic field. Either the primary or 
the secondary may revolve. In the more modern machines the secondary 
revolves. The revolving part is called the “ rotor,” the stationary nart the 
“stator.” The rotor may be either of the ring orthe drum type, the drum 
type being more common. A common type of armature is the ‘‘ squirrel- 
cage.” It consists of a number of copper bars placed on the armature core 
and insulated from it. A copper ring at each end connects the bars. The 
field windings are always so arranged that more than one pair of poles 
are produced. This is necessary in order to bring the speed down to a 
practical limit. If but one pair of poles were produced, with a frequency 
of 60, the revolutions per minute would be 3600. 

The revolving part of an induction motor does not rotate as fast as the 
field. except at no load When loaded, a slip is necessary,in order that the 
lines of force may cut the conductors in the rotor and induce currents 
therein. The current required for starting an induction motor of the squir- 
rel-cage type under full load’ is 7 or 8 times as great as the current for 
running at full-load. A type of induction motor known as‘ Form L,” built 
by the General Electric Co., will start with the full load current, provided 
the starting torque is not greater than the torque when running at full load. 

Induction motors should be run as near their normal primary e.m.f. as 
possible. as the output and torque are directiy proportional to the square 
of the primary pressure A machine which will carry an overload of 50 
per cent at normal e.m.f. will hardly carry its full load at 80 per cent of the 
normal e.m.f. 

An induction motor exercises its greatest torque when standing still, and 
its least when running in synchronism with the rotating field. If it be over- 
loaded it will slow down until the induced currents in the armature are 
sufficient to carry the load. : 


ALTERNATING-CURRENT CIRCUITS. 


Calculation of Alternating-current Circuits.—The follow- 
ing formule and tables are issued by the General Electric Co. They 
afford a convenient method of caiculating the sizes of conductors for, and 
determining the losses in. alternating-current circuits. They apply to cir- 
cuits in which the conductors are spaced 18 inches apart. but a slight in- 
crease or decrease in this distance dves not alter the figutes appreciably. If 
the conductors are less than 18 inches apart, the loss of voltage is decreased 
and vice versa. 





ALTERNATING-CURRENT CIRCUITS, 1073 


Let W=total power delivered in watts; 
D=distance of transmission (one way) in feet; 
P*=per cent loss of delivered power (W); 
H=voltage between main conductors at consumer’s end of circuit: 
K=a constant; for continuous current = 2160; 
T =a variable depending on the system and nature of the load; for 
continuous current =1; 
M =a variable, depending on the size of wire and the frequency; 
for continuous current =1; 
A=a factor; for continuous current=6.04. 


: : DX Waog ln 
Area of conductor, circular mils= Se pars 
Current in main conductors = Mae it 3 


Volts lost in lines = EXEX", 
DDxXWXKXA 
P X E? X 1,000,000° 

The following tables give values for the various constants: 


Pounds copper = 








Value of K. Value of 7. 

















© 
Per cent of A Ss eA WE Les 
Power Factor. ao 
100 | 95 | 85 | 80 |100}| 95 | 85 | 80 | > 
System: 
Single-phase ........... 2160|2400|3000)3380]1.00]1.C5]1.17/1 25] 6.04 
Two-phase 4-wire ...... 1080|1200]1500]1690] .50] 53] .59] 62|12 08 
Three-phase, 3-wire..... .|1080/1200/1506)1690} .58] .61] .68] .72) 9.06 
Values of M 
25 Cycles. 60 Cycles. 125 Cycles. 
a i a i ec se a ae Ee 0 
Py = | 2a % o | 2a a a HO a) 
Sy = & os a uy cot h rr bp & a 
E ; Sib 2S ler lie SOS livess) « Sob sahiee 
O a) 2 | Ro S) oj Ho “9 i) S ° 
ES pS | oS | PS] Bly Bl] PS! sa | os] as 
x 2 au | Em | ee | Bm | ee bee | Se ee | om 
Ow Os eS Silt Bl siemipeenece | Oe os [ies 
< - BOERS | Gena ee poms Poe Bh mel ere 
@ n=Be) ie 4) ae a) ©). | Je play MENS! Sonne ° 
C) £ "a | SAY | SAY | eA | SAN | SAY | “wy | EA | OM 
4 st 4 = a 4 = = Hi = = 
0000 211,600 | 1.23] 1.33] 1.34] 1.62] 1.99] 2.09] 2 35} 3.24] 3.49 
vu00 167 805] 1.18} 1.24! 1 24) 1.49] 1.77] 1.95} 2.08) 2.77) 2 94 
00 133,079 | 1.14] 1.16} 1.16} 1.34] 1.60] 1.66] 1.86} 2.40) 2.57 
0 105,592} 1.10} 1.10} 1.09] 1.31] 1.46] 1.49] 1.71] 2.18) 2 25 
1 83 694] 1.07! 1.05) 1.03] 1.24} 1.34] 1.36} 1.56) 1.88 1.97 
2 66,373 | 1.05] 1.02] 1.00] 1.18] 1.25} 1.26} 1.45) 1.70) 1.77 
a 52,633] 1.03} 1.00} 1.00) 1.14] 1.18} 1.17] 1.35) 1.53) 1.57 
4 41,742] 1.02] 1.00} 1.00} 1.11] 1.11] 1.10} 1.27) 1.40) 1.43 
5 33,102] 1.00] 1.00] 1.00] 1.08] 1.06] 1.04] 1,21) 1.30) 1.31 
6 26,250} 1.00] 1.00] 1.00} 1.05] 1.02) 1.00} 1.16] 1.21} 1.21 
7 20,816 | 1.00} 1.00] 1.00] 1.03] 1.00} 1.00} 1.12) 1.14; 1.13 
8 16,509 | 1.00] 1.00} 1.00] 1.02] 1.00} 1.00} 1.09) 1.C9 1.07 


* P should be expressed as a whole number. not as a decimal; thus a 6 
per cent loss should be written 5 and not .05, 


1074 ELECTRICAL ENGINEERING, 


Relative Weight of Copper Required in Different 
Systems for Equal Effective Voltages. 


Direct current, ordinary two-wire system........ Opittes Tae eae 1.000 
oy a three-wire system, all wires same size............. 375 
a <f ot * oy neutral one-half size............ allies 


Alternating current, single-phase two-wire, and two-phase four-wire 1.000 
Two-phase three-wire, voltage between outer and middle wire same 4 


as in single-phase two-wire..:........... .729 

voltage between two outer wires same....... 1.457 

Whree-phase three=wite oc.cacuid © eee obec aie © entices oe ane rene .750 
A put LOUTE WINES fea ore ucha ar thane Sead ol enateact a beoie att tces. Semen. leer ae .oa3 


The weight of copper is inversely proportional to the squares of the 
voltages, other things being equal. The maximum value of an alternating 
e.m.f. is 1.41 times its effective rating. For derivation cf the above figures, 
see Crocker’s Electric Lighting, vol. ii. 


STANDARD SIZES OF ELECTRICAL MACHINES. 
(Chiefly Selected from Bulletins of the General Electric Co.) 


Direet-driven Direct-current Generators for Lighting 
and Power. 

















125 or 250 Volts. 275 Volts. 

J - Di : MARS hie Di ; 
a z S by 2 imensions. % : z § "en 4 imensions 
La Se a OG a e |ee oY 
fo) a) o Qu. 
Siw lad] B A.| B.|oG.]]) & | M lal & ale ane 
6 25} 305} 3,500 | 40 | 48 | 21 10 800 | 150 40,000 | 116] 129} 40 
6 85] 3800} 4,600 | 42 | 52 | 2: 10 400 | 150 55,000 | 132} 145) 41 
6 50) 280) 6,250 | 46 | 53 | 2 10 400 | 120 62,000 | 135] 147] 42 
6 75) 27 8,800 | 55 | 66 | 26 14 550 | -100 82,000 | 152] 180] 42 
6 | 100} 270} 11,200 | 58 | 71 | 28 18 800 | 100 95,000 73| 206} 44 
8 | 160} 230} 15,000 | 67 | 85 | 30 18 | 1,000 | 100} 115,000 | 178} 212} 46 
8 | 160} 150) 21,000 | 79 | 96 | 35 24 | 1,600; 100} 175,000 | 264] 258] 54 
8 | 200} 200) 22,000 | 79 | 96 | 35 
8 | 200) 150) 80,000 | 85 112 ai 


Direct-connected Direct-current Railway Generators, 
Form H. 575 Volts, 














- ° a2 ® : o _ . s 

“ ; : 5 ae Dimensions. Z ar a Dimensions. 
6/2/22 2A 3S 5 x 2 o 

o|M lad! & AaB: | Onk By M lad! & ast} Bales 
6 | 100} 275] 15,000 81} 95) 28 10 500 | 100 96,000 | 160) 178} 48 
6 | 150} 200} 29,000 99) 114] 85 10 500; 90} 110,000 | 161] 180) 50 
6 | 200] 200) 39,000 | 116| 133} 37 10 500 | 80) 118,000 | 162] 180} 51 
6 | 200} 150} 50,000 | 119) 136] 41 12 650} 90] 117,000 | 173] 188] 48 
6 | 200} 120) 58,000 | 121) 140} 48 12 800 | 120] 113,000 | 173} 188} 48 
8 | 800} 150) 55,000 | 125) 141] 41 14 800 | 100} 118,000 | 186] 200] 46 
8 | 300} 120) 65,000 | 129) 145} 45 14 800 | 80) 135,000 | 187) 201) 48 
8 | 300} 100} 75,000 } 180] 146} 48 16 | 1,000} 80} 150,000 | 187} 209) 50 
8 | 400] 150) 68,000 | 132) 148) 45 18 | 1,200} 80} 156,000 | 196] 221] 48 
8 | 400} 120) 79,000 | 135} 150} 48 22 (1,600) 75) 180,000 | 230) 245} 48 
8 | 400] 100} 90,000 | 138) 152) 59 26 {2.000} 75} 188,000 | 285) 812] 52 
10 | 500} 120} 81,000 | 145} 154] 45 28 12,400} 75) 225,000 | 320) 364) 52 





Dimensions in inches: A, height of frame above floor, B, diameter of 
frame at base. C, width of frame base. 


STANDARD: SIZES OF ELECTRICAL MACHINES. 1075 


Belted Generators, Compound- or Shunt-wound, 


Type CE 


Poles. | Kw. | Spee (a) (b) 





2 1% | 1,350} 12 6 || 
2 2144 | 2,100 | 18 9 |f 
2 ai, | 1,350 | 18 9 | 
2 334, | 2,100 | 30 | 15 |i 
2 334 | 1,850 | 30 | 15 
2 5146 | 1,875 | 44 22 
4 5t4 | 1,050 | 44 5 
{1 gle | 8 | 
4 7 5) 

4 | i] 1,300 | 88 | 44 |f 
4 11 850 | 88 44 t 
4 15 1,300 | 120 60 


ai Amp.| Amp. Weight] 


bs. be 
345 28 
455 31 
630 33 
870 38 
1,240 | 41 
1,660 |. 49 


(a) Full load, 125 volts; no load voltage, 120. 


load voltage, 240. 


Belted Generators, Slow Speed. 





Dimensions, Inches.* 





30 


dD. | = 
Bull SA 
5 | 4% 
5 | 4 
134| 6 
934, 7 
10 | 8% 


(b) Full load, 250 volts; no 


Form H (Four Poles). 

















Amperes, full load. ‘ Dimensions, Inches.* 
Kw. | Speed. isa 
125 V.}250 V.|500 V. ; A. iBy, CG: D. E. 
64| 950 | 52} 26] 18] 1,030 | 88 | 36 | 26 | 11 | 4% 
9 900 92 36 18 1,435 43 40 29 11% 6 
1344 | 850 108 54 27 1,900 50 | 44 33 1214; 84 
17 750 136 68 34 2,665 ay 46 35 1334 sy, 
20 700 160 80 40 3,350 61 53 39 15 104 
30 is) 240 120 60 4,935 68 59 46 20%) 11 
40 605 820 160 80 5,690 72 63 49 2234] 1544 
50 600 400 200 100 7,140 fi 66 52 23 1844 
75 550 600 300 150 8,800 92 68 56 20 2444 
Direct-current Motors. Wype CEH. : 




















RSUN 
tes: 
7a 
Rollyo) 
nS 
—_— 
oe 
Oren 
pad 
Oa 
a= 
So 
ao 
On 
on 
oo 


H. Lb 

110 V.1115 V.|125 v.|500 V. 

2 | 1,000 | 1,025 | 1,075 | 1,200 

3 | 1.700 | 1.750 | 1'840 | 15800 

3 | 1,000 | 1/025 | 1,075 | 1/200 

5 | 1.680 | 1725 | 1820 | 1.800 

5 

7 

é 


wg 
0 


1,150 
1,400 


Speed (Shunt-wound). Weight 
: 5 


Ss. 


Dimensions, Inches.* 


33 











ohghes os 

Sie hte 

Sedge ohé 

5 | 4% 

134| 6 

934.| 7 
10 | gM 





Speeds for 220, 230, and 250 volts are the same as for 110, 115, and 125 volts, 


* Dimensions in inches: A, length over allin direction of shaft, including 
pulley ; B, width or diameter at feet of frame ; C, height above floor; D, 


diameter of pulley: E, face of pulley. 


+ With rails ; includes pulley, but not wood base-frame, 


1076 


ELECTRICAL ENGINEERING, 


STANDARD BELTED MOTORS AND GENERATORS, 
(Crocker-Wheeler Electric Co., 1898.) 





{ 




















Outside Dimen- 
























































| Output. Effi- sions in inches. an of 5 
CY eal Hae Net Over All. | Pulley. |~ 
“ | Motor. | Dynamo. re! ~ roy 
i . 2 ("et alice | a a4 a : 
eee ser Uhre B teak 8] S(t et eee es Gee es 
S jo HT Ske | (Stes) se) e | wpe ys | sis 
OIA) helo bap ale 1S H sn) A | & {em 
Rp 4) 225 400|200, 450/88 |93 30000] 13838 7334 | 6714 |88 |29 {45 
150 | 6| 150 | 400/130 | 450/85 |92_ | 11800] 854g | 65tg | OF" [ae 2B [45 
100 | 4| 100 | 600} 90 | 650/88 |92' | 11000] %s%% | 5814 | 5134/23 16 [45 
q 4, 75 625 60 645 90 {92 6500 6934 5214 4676 20 114 145 
50 | 4] 50 | G50] 45 | 700/89 - jo1tg] 4500] 6116 | 4614 | 42 17 [12 [45 
35 | 4] 35 | 700) 31.5 | 750/88 |91"”| 3350) 5474 | 4044 | 8714 |15 11 45 
25 4| 25 750] 23.5 | 825/86 |8814) 2400! 46% | 365g | 33 13 9 |45 
15 4; 15 800 13 900 8216 88 1510} 41 31}6 2834 ANZ 8 (45 
10 | 2) 10 | 850) 10 |1000|83""|87 920] 3644 | 2534 | 231419 | 7 |45 
‘44 | 2} 744] 900] 7.5 |1050|83 [86 160| 33 | 2344 | 211418 | 6 |45 
5 D4 5 950 5 1100 82 185 510) 2814 | 2184 | 1944 | 7 5 45 
3 | 2} 3 | 975] 3 1175/80 |84¥4] 410) 265g | 185g | 1614 | 6 | 434/45 
2 |} 2 2 {1000} 2 1200 i 82 288} 2246 | 1534 | 1444 | 5 4 45 
4g] 3] 44 lizool ‘us.|teooler [es | tool 1738 | tesg | do4 | 3 | elas 
2 2 3 1375] “25{1800155. |¢ ol is 1054 | 856| 3 | 214/45 
176] | 1/6/1600} S72 |2200|55 [61 27] 97% | 8i4| 644 | 116] 1 
Small Belted Dynamos and Motors (4=pole). 
(Crocker-Wheeler Co.) 
Motor Dynamo rey Dimensions, Inches, 
Size Output. Speed. Speed. aoe (See foot-note on p. 10774 
iy Aspire fare ee 
1? Be = 
HIP. | Kw: logo y,|000.V.loya a. (550 Vol 1. Allaah pet ae 
8 1p 2461-975 | 1,100 14,9001 1,400 14.08 || ae 
3 41 4 | 382 | 1,800 | 1'375 | 1600 | 17501 $295 | 21 | 18 | 6 | 436 
y] 5 42 | '950 | 15100] 1,150 | 1’375 
‘ a p) ’ yiv 000 6 
ais a4 584 1,150 | 1.250 | 1.400 | 1,700 $400} 22 | 20 | 7 | 5 
od 76 646 375 925 | 1,050 | 1,150 
76 | 9% | 814 | 1,100 | 1,175 | 1,300] 1.450 (540 Rat 8 | 54 
Bi-polar Dynamos and Motors. (Crocker-Wheeler Co.) 
ha Motor Dynamo 
size, | Out Ut: Speed.) | .8pect! wrety Pulley. 
ght, 
15- 125 Lbs. s 
H.P Kw 230 V. 500 V 50 V, 550 V Diam. Trace, 
af] 3. 2 |, 975 | 1,025 | 1,800 | 1,480 DT igs ethene ila «a4 
AU Le caerca know RES d : 
1 } 1 1 1,000 | 1,050 | 1,300 | 1,450 205 4 34% 
HAY A Pera 12450 | 1,550 
lé 14 \ 1,200 | 1,350 | 1,600 | 1,750 100 8 3 
Vj ij Vy 1,400 | 1,600 | 1,800 | 17950 ni 3 O14 
1/6 | 1/6 | 110 watts! 1,600 | 1,600] 2,200] 2... or 1% 1 
VAP Meayealin. < bene A SOO5 mre = -)+ .'v's'| eat 19 146 | Grooved 

















STANDARD SIZES OF ELECTRICAL MACHINES. 1077 


Direct-connected Alternators. (General Electric Co.) 


25 CYCLEs. 
Poles. Kw. At M. Roe wil RPM [{Poles. Kw. R.P. M. ales asia R.P.M. 
12 ie 125 28 $10 107 800 9+ 


12 108 350 58 360 107 32 810 94 40 1800 7 
14 160 89214 20 540 = 150 24 1200). 125 32 2700 9 
16 240 187.5 | 24 540 = 125 oeteh UD valOe 40 = 2700 i 
20 210 150 28 540 107 382° 1200 94 40 4080 7 
20 860 = 150 a4 810 125 2 1800 107 40 6000 i 


From 260 to 810 kw. the machines are wound for 370 volts; from 72 to 
810 kw. for 480 volts; from 810 to 6000 kw. for 2300 volts; and from 360 to 6000 
kw. for 6600 and 13 5200 volts. 


60 CYcLzs. 
Poles. ee hs P.M. re, Kw. R.P.M|Poles. Kw. R.P.M, Poles. Kw. R.P.M. 
26 276 350 128.5 60 810 120 80 1800 90 


28 1 i 257 81 BOOM ede Shee c 810 100 72 2700 100 
32 160 = 225 48 540 = 150 60 1200 120 84 2700 86 
36 240 200 56 540 =128.5 | 72 1200 100 

48 240 = 150 63 540 =105 64-1800 = 11255 

48 360 =: 150 52 810 138.5 | 72 1800 100 


From ‘2 to 360 kw. the machines are wound for 240 volts ; from 72 to 
1200 kw. for 480 volts ; from 72 to 2700 kw. for 2800 volts; from 540 to 2700 
kw.some machines are wound for 6600 volts. 

The kw. ratings in the above table are based on the load that may be 
carried without arise in temperature of any part exceeding 4U° UC. above the 
surrounding atmosphere when running continuously with non-inductive full 
load. An overload of 25%, non-inductive. may le carried for two hours with- 
out heating more than 55° C. When full non inductive load is thrown off, 
with fixed normal excitation, the voltage wil] rise approximately 8%. When 
full load with 80% noes Bede § is thrown off, with fixed excitation, the rise 
will be ea hehe rahe foe 

A rating one-sixth less is given all machines for a rise of temperature not 
exceeding 35°C. above surrounding atmosphere. 


Belt-driven Alternating-current Generators. 60 Cycles, 


SIZ Oe Wile ia idthe tee 380 50 75 100 150 200 
IN@Z OL POLES ieee inert ete oe 6 6 8 8 12 12» 
Speeds I: P-Wdi thy -eeee tema 1200 1200 900 900 600 600 


Weight. with rails, Ibs..... 3000 8800 4750 5850 8100 9650 
Floor-space with rails, ins. 51 x 56 58x56 68x67 74x67 80x79 87x 
Size of pulley, ins......... Oi LOSHO RM Ole aumel 1b) 82x 19 82x23 


Induction Motors. 60 Cycles. 





HIB Sevctenntas'sisie 1 288 6 5y ico 10515) S20 S30 40 50) F100). 1505200 
ROLES aa eenisee « 4 4 4 6 6 COME Omer Oo 10.100 hk 2 ata 
Speed: .-..... —-1800-7 — 1200—~ “«—900-~ —720~ 600 600 514 
Weight ...... 210 300 375 600 700 812 1062 1500 2380 3000 3490 5220 6800 9000 11000 
Width. ins.* - 19 20 22 24 26 29 84 36 43 48 50 60 57 67 a 

Length, * 24 28 28 42 42 46 46 57 57 57 59 64 7 78 102 


Pulley, diam. 446 4446 41446 8 8 8 8 13 13 13 16 16 26°28 36 
So Width: .2)o.elG.e oode moO mmOmECemn(aee oO) etl) 13 Li era 23 


*In direction of shaft, Form K motors. Forms Land M are 4 to 10 ins. 
wider. 


10%8 ELECTRICAL ENGINEERING. 


SYMBOLS USED IN ELECTRICAL DIAGRAMS, 
a SPST Qa W 
3 E- SPDT 

steel eng MR ik San 


ch a 
ped = t>-DPDT Galvanometer. Ammeter. Voltmeter. Wattmeter 


Switches: S, singie: wn, WHITH et 
D fouls ee Non-inductive Inductive , Capacity 
} Resistance. Resistance. or Condenser. 
Lamps. Motecr Shunt-wound Motor Series- wound 
or Generator. or Generator. Motor or Generator. 


GS = (2 f6—- 


Two-phase Three-phase Battery. Trans- Compound- Separately 
Generator. Generator. former, wound Motor excited Motor 
or Generator. ' or Generator. 


APPENDIX. 


STRENGTH OF TIMBER. 


Safe Loads in Tons, Uniformly Distributed, for White= 
‘ oak Beams, 
(In accordance with the Building Laws of Boston.) 
W = safe load in pounds; P, extreme fibre- 


4PBD? stress = 1000 lbs. per square inch, for white 
Formula: W= — : P a 





3L oak; B, breadth in inches; D, depth in inches; 
IL, distance between supports in inches, 





* Distance between Supports in feet. 


12 | 14) 16) 16/17/18) 19 














“le 





— mm ef J a | ee | ee | ee J | ee 

















Safe Load in Tons of 2000 Pounds. 

2x6 | 0.67| 0.50/0.40,0.36/0.33)0. 29]0.27/0.25]0,24|0.22 | | | 
2x8 | 1.19} 0.8910.71/0.65/0.59/0.51]0.47|0.44]0.42/0.40/0.3710.34/0.381 10.28 
2x10 | 1.85] 1.39]1.11]1.01]}0.93/0.79|0.74/0.69/0.65)0.62/0.58/0.53/0.48 ]0.44(0.43 
2x12 | 2.67] 2.00]1.60}1.45}1.33/1.14)1.07]1.00/0.94/9.89,0.8410.7610.70 |0.64]0.62 
8x6 | 1.00] 0.75/0.6010.55|0.50/0. 43/0.40/0.37/0.3510.33/0.32/0.2910, 26 

8x8 | 1.73] 1.33/1.07/0.97/0.89)/0.76)0.7110.67/0.63/0.5910.56/0.51/0.46 ]0.43]0.41 
3x10 } 2.78) 2.08]1.67)1.52/1.39/1,1911.11]1 04/0. 98/0.93/0.88/0.79 0.72 10.67]0.64 
83x12 } 4.00! 3.00)2.40/2.18)2.00]1.'71/1.60)1.50/1.41/1.33]1.26]1.1411.04]0.96]0.92 
8x14 | 5.45] 4.08/3.27/2.97/2. 72)2.37/2.18)2.0411 .92]1.82/1.7211.56/1.42 ]1.81/1.25 
8x16 | 7.11) 5.83)4.27/3.88)3.56/3.05|2.84)2. 67/2.5112.371/2.25/2.03]1.86|1.7111.64 
4x10 | 3.70) 2.78)2.22|2.02]1.85/1.59)/1.48)1.39]1.3111.23)1.17)1.06/0.9710.8910.85 
4x12 | 5.33] 4.00)3.20)2.91)2.67/2.29)2.13/2.00]1.88]1.78]1.68]1.52/1.39)1.28)1.28 
4x14) 7.26] 5.44/4.36]3.96/3.63/3.1112.90/2.72/2.56/2.4212.29)2 07/1.90)1.7411.68 
4x16 | 9.48) 7.1115.6915.17/4.74/4.06/3.7913 .56/8.35/3.16)3.00/2.71/2.47/2.28/2.19 
4x18 |12.00] 9.00/7.20/6.55/6.00.5.14/4.80/4.50)4.24/4.00/3.79/3.43/3.13/2.88/2.77 





e 





For other kinds of wood than white oak multiply the figures in the table 
by a figure selected from those given below (which represent the safe stress 
per square inch on beams of different kinds of wood according to the build- 
ing laws of the cities named) and divide by 1000. 











White Yellow 
Hemlock. Spruce. pine, Oak. Dian 
New York.. ... 800 900 900 1100 1100* 
Boston decccse: toh Eee 750 TH 1000+ 1250 
DRICA LORS 0 sre ld aw ¢ seb eens eee eee. t! 900 1080 1440 
* Georgia pine. t+ White oak. 


1079 


1080 APPENDIX. 


‘ MATHEMATICS, 
Formula for Interpolation. 


in In 2} —)in—2An—3), | 
tig SO(n = 1d, -b CO a ee bas 


a, = the first term of the series; n, number of the required term; a,, the 

required term; d,, dg, dy, first terms of successive orders of differences 

between 1), Gg, U3, A4. SUCCessive terms. : , 
EXAaMPLE.—Required the log of 40.7, logs of 40, 41, 42,43 being given as 


below. 
Terms Qj, (9, M3, @4: 1.6021 1.6128 1.6232 1.6335 
‘Ist differences: 0107 .0104 # .0108 
2d AS — .0003 — .0001 
3d os -++ .0002 


For log. 40 n = 1; log 41 n = 2; log 40.7 n=1.7,n —1=0.7, 1 —2 = — 0.3, 
n—3= —.1.3. 


Gy, = 1.6021 + 0.7(.0107) + ered uae 


4 OD = ae — 1.3)(.0002) 


= 1.6021 + .00749 + .000031 + .000009 = 1.6096 ++. 


Maxima and Minima without the Calculus.—In the equation 
y = a-+ bx + ca?, in which a, b, and ¢ are constants, either positive or neg- 
ative, if c be positive y is a minimum when a2 = — b + 2c; if c be negative y 
is a maximum when aw = — 6+ 2c. In the equation y = a-+ ba+ c/a, y is 
a minimum when ba = c/a. 

APPLICATION.—The cost of electrical transmission is made up (1) of fixed 
charges, such as superintendence, repairs, cost of poles, etc., which may be 
represented by’a; (2) of interest on cost of the wire. which varies with the 
sectional area, and may be represented by ba; and (3) of cost of the energy 
wasted in transmission, which varies inversely with the area of the wire, or 
c/x. The total cost,y=a-+bx+c/x,isa minimum whenitem 2 = item 
3, O00 = 0/2, 


RIVETED JOINTS. 


Pressure Required to Drive Hot Rivets.—R. D. Wood & Co., 
Philadelphia, give the following table (1897): 


PowER TO DRIVE Rivets Hor. 





Sire Girder- | Tank- Boiler- Girder-| Tank- | Boiler- 
work. work. work. work. work. work, 
in tons tons tons tons, tons. tons. 
re 9 15 20 38 60 %5 
64 12 18 25 45 70 100 
34 15 22 33 60 85 b2o 
i 22 30 45 75 100 150 
1 30 45 60 








The above is based on the rivet passing through only two thicknesses of 
plate which together exceed the diameter of the’rivet but little, if any. 

As the plate thickness increases the power required increases approxi- 
mately in proportion to the square root of the increase of thickness. Thus, 
if the total thickness of plate is four times the diameter of the rivet, we 
should require twice the power given above in order to thoroughly fill the 
rivet-holes and do good work. Double the thickness of plate would increase 
the necessary power about 40%. 

It takes about four or five times as much power to drive rivets cold as to 
drive them hot. Thus, a machine that will drive 34-in. rivets hot will usually 
drive 3-in. rivets cold (steel). Baldwin Locomotive Works drive }<-in. soft- 
iron rivets cold with 15 tons. : 


HEATING AND VENTILATION, 1081 


HEATING AND VENTILATION. 
Table of Capacities for Hot-blast or Plenum Heating 
with Fans or Blowers. 
(Computed by F. R. Still, American Blower Co., Detroit, Mich.) 


















































z As OOo ! 
— > Oo Ro #2 4 
$ 22 fan i 5 8 Ms 
oe cs fas BHO no| 2s (38 
y eld eB} - 4 oo aS} Ba os dog 
o q a oS Raita te fe) Yso 4252) oo |=2 testy 
e | al w Pa /4E= a aS O8/ 45 |; .| a 
Oxl& | 2. )e8 lone Pe Seneliat ty) ey cane Me nos| $5 
ra 2s | Be [Sobel] SB goiter oe Os (e321 ne 
Mele i 2S] oh |[okstl 06 EOS |p men] SS qu5/ ao 
ie ea it e420 08 |e lie te Poe ASO) 48 Ip ais) iF 
oo} Ee] Selene F2ss| Bs | gze [SES] o& [355] 
8a) 8) 58 (4 [scent] sa dae [oes| Sh Saal oo 
miA]& G  |O oO = > me {x QD 
70} 42 360 | 214 6,900 415,200 | 1,021,000} 90) 7.7 | 1760 580 
80} 48 | 320 3 8,500 510,000 | 1,255,000 os D4 5 [teas | 714 
90} 54 280 4 10,500 630,000 | 1,550,000 a ll S00 ears 880 
100} 60 250 5 12,500 750,000 | 1,845,000 hy 1 so af 1050 
110} 66 230 6 15,800 948.000 | 2,335,000 sh a aay) ome a 1325 
120} 7 210 8 19,800 | 1,118,000 | 2,900,000 & eee ve 1650 
140} 84 180 | 10 26,200 | 1,572,000 | 3,870,000 i 29.1 Me 2200 
160} 96 160 | 12 33,000 | 1,980,000 | 4,870,000 O; 36.7 oa 770 
180} 108} 140 | 15 41.600 | 2,496,000 | 6,130,000 es 46.3 7 3490 
200} 120} 125 | 18 50.000. | 8,000,000 | 7.875.000 ue Dawa w 4140 
Ko) ria ane ° O° : Me ey 
yaa! A) ep ee S18 2 Ol lecao at lioeeena 
wo} ‘oO C ai) ES. fies. Se | Same ero | & aS) 
ra] c yo! =] oO |S 8 5, OH ane Pa THE 
aie 12 |e) 2128 (ee igs | G22 lap f ee8 
5 ¢ 5, || es pe ea ee oo-s volge ou" 
) = 2 Al A Eee 7 = rem) ar) 
Ie Ony ES) Eagle ar eo ign bes © =e) = 8 
Bleao | s@ |e] E ageice jes.| op 150 |'s 
Oo) oh | SO) asda aes tess isaac a S ton 
B = Su A pes el Db fet gies ep diipetest rst subs ule ogs 
So reo tos | Le Serio PS ela Omi. |\ae Sas 
aa) Eee SS Sula On Ae ier of wef .| Seon 
slag | BS 1S] 8 lo ales.-(see 2s CSS] 50_s 
CO} 6h | 85 | 2)% [se sleee lew En a gue 1 FOSS 
S| Ba | 28/8) 8 fers ear] .ee) s85 | 88 | sass 
mn) A = M | 2 | N w2 > < q 
70) 1,740 | 1055 | 314} 2 35 | 525 15 8,700 9.67 8.200 
80} 2,142 | 1295 | 4 2 43 | 645 18 10,700 13.05 10,000 
90} 2,640 | 1600 | 4146 21% 53 795 23 13,200 14.72 12,500 
100} 3,150 } 1900 | 244 63 | 945 27 15,800 17.55 15,000 
110} 38,975 | 2410 


EN 
os 
@ 
o 
nl 
cw) 
c=) 
So 
(sy) 
~ 
= 

wae 
le) 
>. 
Oo 
ris) 
ve 
an 
o 

—_ 

Bo.2) 
Ve) 
S 
o 


3 U F . 

844} 133 | 1995 57 33,100 36.80 31,400 
4 167 | 2505 G2 41,700 46.30 39,600 
4 
5 


—_ 
a 
oO 
for) 
D> 
oS 
oOo 
Coe 
Oo ilo} 
SD 
Q 
© OF Od. OT Ot 


¥6| 211 | 3165 90 52,500 58.40 50,000 
200! 12.420 | 7560 '10 


Temperature of fresh air, 0°; of air from coils, 120°; of steam, 227°. Pres- 
sure of steam, 5 lbs. 

Peripheral velocity of fan-tips, 4000 ft.; number of pipes deep in coil, 24; 
depth of coil, 60 inches; area of coils approximately twice free area. 





WATER-WHEELS. 


Water-power Plants Operating under High Pressures.— 
The foilowiug notes are contributed by the Pelton Water Wheel Co.: 

The Consolidated Virginia & Col. Mining Co., Virginia, Nev., has a 3-ft. 
steel-disk Pelton wheel operating under 2100 ft. fall, equa) to 911 Ibs. per sq. in. 
It runs at a peripheral velocity of 10,804 ft. per minute and has a capacity 
of over 100 H.P. The rigidity with which water under such a high pressure 
as this leaves the nozzle is shawn in the fact that it is impossible to cut the 


1082 .. APPENDIX. 


stream with an axe, however heavy the’ blow, as it will rebound just as it 
would from a steel rod travelling at a high rate of speed. 

The London Hydraulic Power Co. has a large number of Pelton wheels 
from 12 to 18 in. diameter running under pressure of about 1000 lbs. per. sq. 
in. from asystem of pressure-mains, The 18-in. wheels weighing 30 Ibs. have 
a capacity of over 20 H.P. (See Blaine’s ‘* Hydraulic Machinery.*’) 

Hydraulic Power-hoist of Milwaukee Mining Co., Idaho.—One cage travels 
up as the other descends; the maximum load of 5500 Ibs. at a speed of 400 
ft. per min. is carried by one of a pair of Pelton wheels (one for each cage). 
Wheels are started and stopped by opening and closing a small hydraulic 
valve at the engineer’s stand which operates the larger valves by hydraulic 
pressure. An air-chamber takes up the shock that would otherwise occur 
on the pipe line under the pressure due to 850 ft. fall. 

The Mannesmann Cycle Tube Works, North Adams, Mass., are using four 
Pelton wheels, having a fly-wheel rim, under a pump pressure of 600 Ibs. per 
sq. in. These wheels are direct-connected to the rolls through which the 
ingots are passed for drawing out seamless tubing. is 

The Alaska Gold Mining Co., Douglass Island, Alaska, has a 22-ft. Pelton 
wheel on the shaft of a Riedler duplex compressor. It is used as a fly- 
wheel as well, weighing 25,000 lbs.—and develops 500 H.P. at 75 revolutions. 
A valve connected to the pressure-chamber starts and stops the wheel 
automatically, thus maintaining the pressure in the air-receiver. 

At Pachuca in Mexico five Pelton wheels having a capacity of 600 H.P. 
each.under 800 ft. head are driving an electric transmission plant. These 
wheels weigh less than 500 Ibs. each, showing over a horse-power per pound 
of metal. 

Formule for Calculating the Power of Jet Water- 
wheels, such as the Pelton (F. K. Blue).—HP = horse-power delivered; 

= 62.36 Ibs. per cu. ft.; H = efficiency of turbine; g = quantity of water, 
cubic feet per minute; h = feet effective head; d = inches diameter of jet; 
p = pounds per square inch effective head; c = coefficient of discharge from 
nozzle, which may be ordinarily taken at 0.9. 














8 a =. 
RPS eke = .00189Egh = .00436Egp =.00496Ecd? /h3 = .0174Ecd? 4/p3, 
HP HP z 
= 529.2 = 229 —— = 2.62cd? = 3.99¢cd? 
q= 520.2 = OF = 2.62ed Vh = 3.99cd? Vp, 
Beet ogy eels cy Ge ee ay ee eee 


Ec Vh3 "Ee /p3 2 eVvh c Vp 
GAS FUEL, 


Average Volumetric Composition, Energy, etc., of Vari=- 
ous Gases. (Contributed by R. D. Wood & Co., Philadelphia, 1898.) 











Natural | Coal- | Water-| Producer-gas. fed 
Gas. Bas, 8as- | anthra.| Bitum 
CRS erent Os ten cate wine 0.50 6.0 45.0 27.0 ds Ou De ota ee 
I 8 opin ae Gee 2.18 46.0 45.0 12.0 LUPE S leaker 
(Oi s vEnerage Aan atic 92.6 40.0 2.0 1.2 ps ee eA, 
Colson. st teeter ae 0.31 ye he sie is ae UR: IND ten ae, FA se 
CON ec meinen oneree - 0.26 0.5 4.0 2.0 ao trace 
es Sees cote kee 3.61 5S 2.0 57.0 55.3 79 
Chasers Baer 0.34 0.5 0.5 0.3 0.3 21 
MAPOR: oo. crcmsls oe ne Was aoe ees a: 15) beck Rh eid eee trace 
Lbs. in 1000 cu. ft.. 45.6 32.0 45.6 65.6 65.9 76.1 
H. U. in 1000 cu. ft.} 1,100,000 435,000 | 822.000 | 187,455 | 156;910%) |. 2 ac8 


Cu.ft. from each lb. 
ofscoal approx, Bisen. eoeeee 5 25 85 78 200+ 


* The real energy of bituminous producer-gas when used hot is far in 
excess of that indicated by the above table, on account of the hydrocarbons, 
which do not show, as they are condensed in the act of collecting the gas 
for analysis. In actual practice there is found to be about 50% more effective 
energy. in bituminous gas than in anthracite gas when used hot enough te 
prevent condensation in the flues. 

t Cubic feet of air required to burn 1 lb. of coal with biast. 





STEAM-BOILERS, — 1083 


STEAM-BOILERS. 


Steam-boiler Construction, (Extract from the Pules and Speci- 
fications of the Hartford Steam Boiler Inspection & Insurance Co., 1898.) 

Cylindrical boiler shells of fire box steel, and tube-heads of best flange 
steel. Limits of tensile strength between 55,000 and 62,000 lbs. per sq. in. 

_lron rivets in steel plates, 38,000 lbs. shearing strength per sq. in. in 
single shear, and 85% more, or 70.300 Ibs., in double shear. 

Each shell-plate must bear a test-coupon which shall be sheared off 
and tested. Eachcoupon must fulfil the above requirements as to tensile 
strength, but must have a contraction of area of not less than 56% and 
an elongation of 25% in alength of 8in. It mustalso stand bending 180° 
when cold, when red hot, and after being heated red hot and quenched in 
cold water, without fracture on outside of bent portion. 

Crow-foot braees are required for boiler-heads without welds, and if of 
iron limit the strain to 7500 Ibs. per sq. in., and stay-bolts must not be sub- 
jected to a greater strain than 6000 lbs. persq.in. © 

The thickness of double butt-straps 8/10 the thickness of plates. In lap- 
joints the distance between the rows of rivets is?4the pitch. In double- 
riveted lap-joints of plates up to 4 in. thick the efficiency is 70% and in 
triple-riveted lap-joints 75% of the solid plate.’ 

In triple-riveted double-strapped butt-seams for plates from 14 in. to % in. 
thick, the efficiency ranges from 88% to 86% of the solid plate. 

In high-pressure boilers the holes are required to be drilled in place; that 
is, all holes may be punched }) in. less than full size, then the courses are 
rolled up, tube-heads and joint-covering plates: bolted to courses, with all 
holes together perfectly fair. Then the rivet-holes are drilled to full size, 
and when completed the plates are taken apart and the burr removed. 

The rule for the bursting-pressure of cylindrical boiler-shells is the follow- 
ing: Multiply the ultimate tensile strength of the weakest plate in the shell 
by its thickness in inches and by the efficiency of the joint, and divide result 
by the semi-diameter of shell; the quotient is the bursting-pressure per 
square inch. This pressure divided by the. factor 5 gives the allowable 
working pressure. 


BOILER FEEDING. 


Gravity Boiler-feeders.—If a closed tank be placed above the 
level of the water in a boiler and the tank be filled or partly filled with 
water, then on shutting off the supply to the tank, admitting steam from 
the-boiler to the upper part of the tank, so as torequalize the steam-pressure 
in the boiler and in the tank, and opening a valve in a pipe leading from the 
tank to the boiler the water will run into the boiler. An apparatus. of this 
kind may be made to work with practically perfect efficiency as a boiler- 
feeder, as an injector does, when the feed-supply is at ordinary atmospheric 
temperature, since after the tank is emptied of water and the valves in the 
pipes connecting it with the boiler are closed the condensation of the steam 
remaining in the tank will create a vacuum which will lift a fresh supply of 
water into the tank. The only loss of energy inthe cycle of operations is 
the radiation from the tank and pipes, which may be made very small by 
proper covering. 

When the feed-water supply is hot, such as the return water from a heat- 
ing system, the gravity apparatus may be made to work by having two © 
receivers, one at a low level, which receives the returns or other feed-supply, 
and the other at a point above the boilers. A partial vacuum'being created 
in the upper tank, steam-pressure is applied above the water in the lower 
tank by which it is elevated into. the upper. The operation of such a 
machine may be made automatic by suitable arrangement of valves.. (See ° 
circular of the Scott Boiler Feeder, made by the Q. & C. Co., Chicago.) 


FEED-WATER HEATERS. oi 


Capacity of Feed=-water Heaters.—The following extract from 
a letter by W. R. Billings, treasurer of the Taunton Locomotive Manufactur- 
ng Co., builders of the Wainwright feed-water heater, to Engineering Record, _ 
February, 1898, is of interest in showing the relation of the heating surface 
of a heater to the work done by it: gate 

‘* Closed feed- water heaters are seldom provided with sufficient surface to 
raise the feed temperature to more than 200°. The rate of heat trans- 


1084 APPENDIX. 


mission may be measured by the number of British thermal units which 
pass through a square foot of tubular surface in one hour for each degree 
of difference in temperature between the water and the steam. The diffi- 
culties which attend experiments in this direction can only be appreciated 
by those who have attempted to make such experiments, Certain results 
have been reached, however, which point to what appears to be a reasonable 
conclusion. Oneset of experiments made quite recently gave certain results 
which may be set forth in the table herewith. 


DOH sia cue scatas see 0 Oe L. Wini) LRansmitbedes sin = Tone 
rie sims ibe hia Es is Re Roars vara eevee ia = pours by one sq. Ao 
na era- Pear eateh tran aot of surface for eac 
tures of water and | 11° SD. sack tee td 5 SS degree of average 
steam ahs es SA SHAG a pieewelico Maa difference in temper- 
Llbe ed de eicascre ae ngs 100 i fy), 4 J eebUeee, 


‘*In other words, when the water was brought to within 5° of the temper- 
ature of the heating medium, heat was transmitted through the tubes at the 
rate of 67 B.T.U. per square foot for each degree of difference in temperature 
in one hour. When the amount of water flowing through the heater was so 
largely increased as to make it impossible to get the water any nearer than 
within 18° of the temperature of the steam, the heat was transmitted at the 
rate of 139 B.T.U. per sq. ft. of surface for each degree of difference in 
temperature in one hour. Note here that even with the rate of transmission 
as low as 67 B.T.U. the water was still 5° from the temperature of the 
steam. At what rate would the heat have been transmitted if the water 
could have been brought to within 2° of the temperature of the steam, or to 
210° when the:steam is at 212° ? 

‘‘Wor commercial purposes feed-water heaters are given a H.P.rating which 
allows about one-third of a square foot of surface per H.P.—a boiler H.P. 
being 30 lbs. of water per hour.. If the figures given in the table above are 
accepted as substantially correct, a heater which is to raise 3000 lbs. of water 
per hour from 60° to 207°, using exhaust steam at 212° as.a heating medium, 
should have nearly 84 sq. ft. of heating surface—that is, a 100 H.P. feed-water 
heater which is to maintain a constant temperature of not less than 207°, 
with water flowing through it at the rate of 3000 lbs. per hour, should have 
nearly a square foot of surface per H.P. That feed-water heaters do not 
carry this amount of heating surface is well known.” 


THE STEA™M-ENGINE. 


Current Practice in Engine Proportions, 189% (Compare 
pages 792 to 817.)—A paper with this title by Prof John H. Barr, in Trans. 
A.5. M. E.. xviii. 737, gives the results of an examination of the proportions of 
parts of a great number of single-cylinder engines made by different builders. 
The engines classed as low speed (L. S.) are Corliss or other long-stroke 
engines usually making not more than 100 or 125 revs. per min. Those 
classed as high speed (H. S.) have a stroke generally of 1 to 114 diameters 
and a speed of 200 to 800 revs. per min. The results are expressed in for- 
ee of rational form with empirical coefficients, and are here abridged as 

ollows: 

Thickness of Shell, L. S. only.—t = CD+ B; D=diam. of piston in in.; 
B= 0.8 in.; C varies from 0.04 to 0.06, mean = 0.05. 

Flanges and Cylinder-heads.—1 to 1.5 times thickness of shell. mean 1.2. 

Cylinder-head Studs.—No studs less than 34 in. nor greater than 13¢ in. 
diam. Least number, &, for 10in diam. Average number=0.7D. Average 
diam. = D/40 + in. 

Ports and Pipes.—a = area of port (or pipe) in sq. in.; A = area of piston, 
sq. in.; V = mean piston-speed, ft. per min.; a= AV/C, in which C= mean 
velocity of steam through the port or pipe in ft. per min. 

Ports, H. S. (same ports for steam as for exhaust).—C = 4500 to 6500, mean 
5500. ver ordinary piston-speed of 600 ft. per min. a= KA; K = .09 to .138, 
mean .il. 

Steam-ports, L. 8.—C = 5000 to 9000, mean 6800; K = .08 to .10, mean .09. 

Exhaust-ports, L. S.—C = 4000 to 7000, mean 5500; K = .10 to .125, mean .11. 

Steam-pipes, H. S.—C = 5800 to 7000, mean 6500. If d= diam. of pipe and 
D= diam. of piston, d = .29D to .82D, mean .30D. 

Steam-pipes, L. S.—C = 5000 to 8000, mean 6000: d = .27 to .85D, mean .32D. 

Exhaust-pipes, H. 8.—C = 2500 to 5500, mean 4400; d = .83 to .50D, mean 37D. 

Exhaust-pipes, L. S.—C = 2800 to 4700, mean 3800; d = .385 to .45D, mean .40D, 


LOCOMOTIVES. 1085 


Face of Pistons.—F = face; D= diameter. F’'= CD. H.S.: C=.30to .60 
mean .46. L.S.: C= .25 to .45, mean .32. 
Piston-rods.—_d = diam. of rod; D= diam. of piston; L = stroke, in.; 


d=CVDL. H.S.: C = .12 to 175, mean .145. L.8.: C= .10 to 13, mean .11, 
Connecting-rods. iaEy 8: (generally 6 cranks long, rectangular section): 
b = breadth; h = height of section; L, = length of connecting-rod; D= diam. 


of piston;b = C VDI; C= .045 to .07, mean .057; h = Kb; K = 2.2 to 4, mean 


els Ae (generally 5 cranks long, circular sections sont C= .082 to),105, 
mean .09% 

Cross-head Slides.—Maximum pressure in lbs. per sq. in. of shoe, due to 
the vertical component of the force on the connecting-rod. H.S.: 10.5 to 38, 
mean 27. L.S : 29 to 38, mean 40. 

Cross-head Pins.—l = ‘length; d = diam.; projected area = a = dl = CA; 
A= area of piston; C= Kas H. Sa 06 to .11, mean .08; K = 1 toi: 
mean 1.25. L.S : O = .054 to .10, mean .07; K = 1to 1.5, mean 1.3. 

Crank-pin. 2 pe horse-power of engine; L= length of str oke; 1 = length 
of pin; l= CX HP/L+ B; d= diam. of pin; A = area of piston; dl = KA. 
H.S.: C= .18 to .46, mean .380; B = 2.5in.; K = .17 to .44, mean .24. L.S.: 
C= “4 to .8, mean 6; By=ane 1 Ks = 065 to .115, mean .09. 


Crank-shaft Main Journal.—d = CWHP +N: N; d= diam.;1= length; N= 
revs. per min.; projected area = MA; A = area ‘of piston. "HLS.: C = 6.5 to 
8.5, mean 7.3; ee 2 to 3, mean 2.2: M= .37 to .70, mean .46. L. S.: C=6to 8, 
mean 6.8; K=1.7 to 2.1, mean 1,9; M = .46 to 64, mean .56, 

Piston- ‘speed.— —H. §.: 530 to 660, mean 600; L. S.: 500 to 850, mean 600, 

Weight of Recipr ocating Parts (piston, piston- -rod, cross-head, and cne- 
half of connecting- rod).—W = CD? + LN?; D= diam. of piston; L =len gth 
1860, tae in.; N=revs per min. H. 8S. only: C = 1,200,000 to 2, 300, 000, mean 
1,860,000 

Belt-surface per 1.H.P.—S = CHP+ B; S= product of width of belt in 
feet by velocity of beltin ft. per min. H. S.: C= 21 to 40 mean 28; B = 1800. 
ors C. Xe Ps C30 to 42, mean — 35. 

Fly- wheel (H.S. only). aaa of rim in lbs.: W= C X HP ~+ D,?N*;D, = 
diam. of wheel in in.; C= 65 x 1019 to 2 x f0!2 mean = 12 X 1021, or 
1,200, 000,000,000. 

Weight of Engine per I.H.P. in lIbs., including fly-wheel.—_W = C xX H.P. 
H. §.: C = 100 to 1385, mean 115, L.§.: C = 185 to 240, mean 175. 

Work of Steam-turbines, (See p.791.)—A 300-H.P. De Laval steam- 
turbine at the 12th Street station of the Edison Electric Illuminating Co. in 
New York City in April, 1896, showed on a test a steam-consumption of 
19.275 lbs. of steam per electrical H.P. per hour, equivalent to 17.348 lbs. per 
brake H.P., assuming an efficiency of the. dynamo of 90%. The steam- 
pressure was 145 lbs. gauge and the vacuum 26in. It drove two 100-K.W. 
dynamos. The turbine-disk was 29.5 in. diameter and its speed 9000 revs. 
per min. The dynamos were geared down to 750 revs. The total equip- 
ment, including turbine, gearing, and dynamos, occupied a space 1% ft. 3 in. 
long, 6 ft. 5 in. wide, and 4 ft. 3in. high. 

The “ Turbinia,’’ a torpedo-boat 100 ft. long, 9 ft. beam, and 4414 tons 
displacement, was driven at 31 knots per hour by a Parsons steam-turbine 
in 1897, developing a calculated I.H.P. of 1576 and a thrust H.P. of 946, the 
steam- pressure at the engine being 130 1bs. and at the boilers 200 Ibs. The 
vacuum was 13% Ibs. The revolutions averaged 2100 per minute. The 
calculated steam-consumption was 15.86 lbs. per I.H.P. per hour. On 
another trial the ‘* Turbinia ’’ developed a speed of 3234 knots. 


Relative Cost of Different Sizes of Steam-engines, 
(From catalogue of the Buckeye Engine Co., Part I1]1.) 





i 100 


125] 150 | 200 | 250 | 300 
15 |141¢11314| 13 |1234 


600 | 700 
13%4| 14 


800 


350 | 400 | 500 
15 


Horse-power . | 50 
12. Did: wes 8 


Cost per H.P, 8 20 


























— 


1086. ° APPENDIX. 


GEARING. 


Efficiency of Worm Gearing. (See also page 898.)—Worm gear- 
ing as a means of transmitting power, has until recently, generally been. 
looked upon with suspicion, its efficiency being considered necessarily low 
and its life short. Recent experience, however, indicates that when prop- 
erly proportioned it. is both durable and reasonably efficient. Mr. F. A. 
Halsey discusses the subject in Am. Machinist, Jan.13 and 20, 1898. He 
oe two formulas for the efficiency of worm gearing due to Prof. John 

. Barr: 
tana (1 — f tan a) (1) zat a(1—/f tan a) 

tan asf noi t aT tana-+ ef 
in which F = efficiency; a = angle of thread, being angle between thread - 
and a line perpendicular to the axis of the worm; f = coefficient of friction. 


Kq. (1) applies to the worm thread only, while (2) applies to the worm and 
step combined, on the assumption that the mean friction radius of the two 
is equal. Eq. (1) gives a maximum for EZ when tana = /1-+ P= f i. i @ 
and eq. (2)a maximum when tana = 72-4+.4f2 — 2f....(4) Using a value 
.05 for f gives a value for a in (8) of 43° 34’ and in (4) a value of 52° 49’. 

On plotting equations (1) and (2) the curves show the striking influence of 
the pitch-angle upon the efficiency, and since the lost work is expended in 
friction and wear, it is plain why worms of low angle should be short-lived 
and those of high angle long-lived. The following table is taken from Mr. 
Halsey’s plotted curves: 


k= 





approx., ... (2) 








RELATION BETWEEN THREAD-ANGLE SPEED AND EFFICIENCY OF WORM GEARS. 


Angle of Thread. 





rafaecity Oak bp See SP Veber ge on: piles = oe ae oe ee ee) ee ee Oe 
itch-line, 
tSiaabes 5 | 10 | 20 | 30 | 40 | 45 
minute, iglesia 1 Sead’: Manse Ped cd su EL Sa Ci hd 
Efficiency. 
3 35 52 66 73 7 77 
5 40 56 69 76 79 80 
10 47 62 7 79 82 82 
20 52 67 78 83 85 86 
40 60 74 83 87 88 88 
100 70 82 88 91 91 91 
200 76 85 91 92 92 92 


The experiments of Mr. Wilfred Lewis on worms show a very satisfac- 
tory correspondence with the theory, Mr. Halsey gives a collection of data 
comprising 16 worms doing heavy duty and having pitch-angles ranging 
between 4° 30’ and 45°, which show that every worm having an angle above 
12° 30’ was successful in regard to durability, and every worm below 9° 
was unsuccessful, the overlapping region being occupied by worms some of 
which were successful and some unsuccessful. In several cases worms of 
one pitch-angle had been replaced by worms of a diffcrent angle, an increase 
in the angle leading in every case to better results and a decrease to poorer 
results. He concludes with the following table from experiments by Mr. 
James Christie, of the Pencoyd Iron Works, and gives data connecting the 
load upon the teeth with the pitch-line velocity of the worm: 


LIMITING SPEEDS AND PRESSURES OF WORM GEARING. 


: Double- Double- 
Single-thread thread thread 
Worm 1” Pitch, | Worm 2’ Worm 2}/7 
2% Pitch Diam. Pitch, 2% Pitch, 44 
Pitch Diam. | Piteh Diam. 





Revolutions per minute........ 128) 201) 272) 425] 128) 201] 272) 201] 272] 425 


Velocity at pitch-line in feet 
Or, PUVMMILO 6. «6 ni8 ge oh ees 96] 150) 205) 820] 96} 150) 205) 235] 319) 498 


Limiting pressure in pounds... |1700/13800)1100| 700)1100)1100/1100|1100} 700} 400 








APPROXIMATE HYDRAULIC FORMULA, 1087 


APPROXIMATE HYDRAULIO FORMULE. 
(The Lombard Governor Co., Boston, Mass.) 


Head (H) in feet. Pressure (P) in lbs. per sq. in. Diameter (D) in feet. 
Area (4) in sq. ft. Quantity (Q) in cubic ft. per second. Time (7')inseconds. 


Spouting velocity = 8.02 //H. 


Time (7,) to acquire spouting velocity in a vertical pipe, or (7) in a pipe 
on an angle (6) from horizontal: 


T,=8.02 YH + 82.17, T, = 8.02 H+ 32.17 sin 0. 


Head (#1) or pressure (P) which will vent any quantity (Q) through a 
round orifice of any diameter (D) or area (A): 


H = Q?+14.1D*, H= Q? + 23.75.42: 
P= Q? + 34.1D4, P= Q? + 55.342, 
Quantity (Q) discharged through a round orifice of any diameter (D) or’ 
area (A) under any pressure (P) or under any head (H): 
(Oe YV Px 55.3 x A2, O= WV Px 84.1x D4; 
Q = VHx23.15x 42, Q= WHxi4.71x Di. 
Diameter (D) or area (A) of a round orifice to vent any quantity (Q) under 
any head (H) or under any pressure (FP): 
D= VQ+38VH, D= VQ+58YP; 
A= Q+4.89VH, A=Q+7.35 VP. 


Time (7) of emptying a vessel of any area (4) through an orifice of any 
area (a) anywhere in its side: 


T= 4164 VH +a. 


Time (T) of lowering a water level from (H) to (h)in a tank through an 
orifice of any area(«t)in its side. Area of tank is (4). 


T = 0.416A\ WH - Vr) +a. 


Kinetic energy (K) or foot-pounds in water in a round pipe of any diameter 
(D) when moving at velocity (V): 


KO xe eee. 


Time-average-pressure (4.P.) ina pipe of any length (L) with water mov- 
ing at any velocity (V)° 
A.P, = 0.13824LV + T. 


Note.—This must not be confused with water-hammer pressure, which is 
always many times greater than 4.P. and for which no simple formula may 
be written. : é 

Area (a) of an orifice to empty a tank of any area (A) in any time (7) from 


any head (H): og 
a= 7T-+-0.409A WH. 
Area (a) of an orifice to lower water in a tank of area (4) from head (H) to 
(i) in time (T): “ig ? 
a = T+ 0.409x Ax( YH Vh) 


\ 


1088 APPENDIX, 


SPECIFICATIONS FORK TIN AND TERNE PLATE. 
(Penna. R. R. Co., 1902.) 


Each sheet must (1) be cut as nearly exact to size ordered as possible, 
(2) must be rectangular and flat and free from flaws, (3) must deuble- 
seam successfully under all circumstances, (4) must show a smooth edge 
with no sign of fracture when bent through an angle of 180° and flattened 
down with a wooden mallet, (5) must be so nearly like every cther sheet in 
the shipment, in thickness, uniformity, and amount of coating, that no difti- 
culty will arise in the shops due to varying thickness of sheets, and (6) must 
correspond for the different grades to the figures in the following table : 





: No. 1 No. 2 
Kind of Coating. ake ee Terne Plate. | Terne Plate. 
ure iim. 1 Tin, 34 Lead.|t ‘Tin, 34 Lead. 
Amt. of coating per sq. ft..... 0.0182 lb. 0.0364 Jb. 0.0182 lb. 
Grade IC. ...weight persq.ft.| 0.49 0.51 0.49 
Cited nd star «ices ex itn: 0.62 0.64 0.62 
12 hus B.@. Ce tera pert hiy 0.71 0.73 0.71 
oii 8 8.0 GE arty ge A 0.81 0.83 0.81 
AE Ew D.O.@:@. dae. ta 0.91 0.93 0.91 


LIST OF AUVHORITIES QUOTED IN THIS BOOK. 


When a name is quoted but once or a few times only, the page or pages 

ere given. The names of leading writers of text-books, who are quoted fre- 
uently, have the word ‘‘ various” affixed in place of the page-number, 
he list is somewhat incomplete both as to names and page numbers. 


Abel, F. A., 642 Buel, Richard H., 606, 834 
Abendroth & Root Mfg. Co., 197, 198 | Buffalo Forge Co., 519, 529 
American Screw Co., 209 Builders’ Iron Foundry, 374 
Achard, Arthur, 886, 919 Burr, Wm. A., 565 

Addy, George, 957 Burr, Wm. H., 247, 259, 290, 381 
Addyston Pipe and Steel Co., 187,188 | . 

Alden, G. I., 979 Calvert, F. Crace, 886 

Alexander, J. S., 629 Calvert & Johnson, 469 

Allen, Kenneth, 295 Campbell, H. H., 398. 459, 650 
Allen, Leicester, 582 Campredon, Louis, 403 

Andrews, Thomas, 384 Carnegie Steel Co., 177, 272. 277, 391 
Ansonia Brass and Copper Co., 327 Carpenter, R. C., 454, 615, 718, ete. 
Arnold, Horace L., 959 Chadwick Lead Works, 201, 615 
Ashcroft Mfg. Co., 752, 775 Chamberlain, P. M., 474 
Atkinson, J. J., 532 Chance. H. M., 631 


Chandler, Chas. F., 552 
Chapman Valve Mfg. Co., 198 
Babcock, G. H., 524, 933 Chauvenet, S. H., 370 
Babcock & Wilcox Co., 538, 636 Chase, Chas. P., 312 
Baermann, P. H., 188 Chevandier, Eugene, 640 
Bagshaw, Walter, 952 Christie, James, 394 
Bailey, W. H., 943 Church, Irving P., 415 
Baker, Sir Benjamin, 289, 247, 402 Church, Wm. Lee, 784, 1050 
Balch, S. W., 898 Clapp, Geo. H., 897, 403, 551 


oe 


Baldwin, Wm. J., 541 Clark, Daniel Kinnear, various 
Ball, Frank H., 751 Clarke, Edwin, 740 

Barlow, W. H., 384 Claudel, 455 

Barlow, Prof., 288 Clay, F. W., 291 

Barnaby, S. W., 1013 Clerk, Dugald, 847 

Barnes, D. L., 631, 861, 868 Cloud, John W., 351 

Barrus, Geo. H., 636 Codman, J. E., 193 

Bauer, Chas. A., 207 Coffey, B. H., 810 
Bauschinger, Prof., 239 Coffin, Freeman C., 292 
Bazin, M., 563, 587 Coggswell, W. B., 554 
Beardslee, L. A.. 238, 377 Cole, Romaine C,, 829 
Beaumont, W. W., 979 Coleman, J. J., 470 

Becuel, L. A., 644 Cooper, John H., 876, 900 
Begtrup, J., 348 Cooper, Theodore, 262, 263, 359 
Bennett, P. D., 354 Cotterill and Slade, 432, 974 
Bernard, M. & E., 830 Cowles, Eugene H., 329, 331 
Birkinbine, John, 605 ; Cox, A. J., 290 

Bjorling, P., 676 Cox, E. T., 629 

Blaine, R. G., 616, 1089 Cox, William, 575 

Blauvelt, W. H., 689, 649 Coxe, Eckley B., 632 
Blechynden, A., 1015 Craddock, Thomas, 478 
Bodmer, G. R., 753 Cramp, E. S., 405 

Bolland, Simpson, 946 Crimp, Santo, 564 

Booth, Wm. H., 926 Crocker, F. B., 1070 

Box, Thomas, 475 Cummins, Wm. Russell, 772 


Briggs, Robert, 194, 478, 540, 672 

British Board of Trade, 264, 266, 700 | Daelen, R. M., 617 
Brown, A. G., 723, 724 Dagger, John H. J., 829 
Brown, E, H., 888 Daniel, Wm., 492 
Brown & Sharpe Mfg. Co., 219, 890 D’Arcy, 563 


Browne, Ross E., 597 Davenport, R. W., 680 — 
Brush, Chas. B., 566 Day, R. E., 1030 
Bucxle, W., 634 Dean, F. W., 605, 680 


1089 


1090 


Decceur, P., 800 

DeMeritens, A., 386 

Denton, James E., ats %61, 781, 932 
Dinsmore, R. E 

Dix, Walter S. a 308" 

Dodge Manufacturing Co., 344 
Donald,, J. T., 235 

Donkin,, B., Jr., 491, 783 
Dudley, Chas. B., 326, 333 
Dudley, P. H., 401, 622 
Dudley, W. D., 167 

Dulong, M., 458, 476 

Dunbar, J. H., 796 

Durand, Prof., 56 
Dwelshauvers-Dery, 662 


Egleston, Thomas, 235, 647 
Emery, Chas. Ep » 608, 613, 820 
Engelhardt, F. E., 

Ellis and Howland, Or? 
English, Thos:, 953. 

Ericsson, John, 286 
Eytelwein, 564 


Fairbairn, Sir Wm., 240, 264, 808, 254 
Fairley, W., 531, 533 
Falkenau, ‘A., 509 

Fanning, J. T., 564, 579 
Favre and Silbermann, 621 
Felton, C. E., 

Fernow, B. E., 610 

Field, C. J., 30, 937 

Fitts, James H., 844 
Flather, J. J., 961, 96. 
Flynn, P. J., 463, 559 
Foley, Nelson, 700 
Forbes, Prof., 1033 
Forney, M. N., 855 
Forsyth, Wm., 630 

Foster, R. J., 651 

Francis, J. B., 586, “39, 867 
Frazer, Persifor, 624 
Freeman, J. R., 581, 584 
Frith, A. J., 874 

Fulton, John, 637 


Ganguillet & Rutten, 565 
Gantt, H. L., 406 

Garrison, F. “Ea, 826, 331, 409 
Garvin Machine » Co., 9565 
Gause, F. T., 500 

Gay, Paulin, 966 

Gill, J. P., 657 

Gilmore, E. »., 241 
G‘aisher, 483 

Glasgow, A A. G., 654 
Goodman, John, 934 
Gordon, F. W., 689, 740 
Gordon, 247 
Goss, W. F. M., 863 
Graff, Frederick, 885 
Graham, 'W., 95 50° 
Grant, Georgé B., 898 
Grant, J.J., 960 
Grashof, Dr., 284 

Gray, J. McFarlane, 661 
Gray, J. M., 958 

Greene, D. M.. 567 


LIST OF AUTHORITIES, 


Greig and nyt 868 
Grosseteste, W., 715 
Gruner, L., 623 


Hadfield, R. A., 381, 409 
Halpin, Druitt, “89, 854 
Halsey, Fred’k A., 490, 817 
Harkness, Wm., 900 
Harrison, W. He 939 
Hartig, J., 961 

Hartman, "John M., 364 
Hartnell, Wilson, 348, 818, 838 
Hasson, W.F. C., 104 iY 
Hawksley, T., 485, 513, 564, 
Hazen, H. Allen, 494 
Henderson, G. R., 847%, 854 
Henthorn, J. T., 965 
Hering, Carl, 1045 
Herschel, Clemens, 583. 
Hewitt, Gc. C., 630 
Hewitt, Wm.. 917 
Hildenbrand, Wm., 913 
Hill, Jobn Ww. 17 

Hiscox, G. D., 968 
Hoadley, John Ce 451, 688 
Hobart, J. J., 962 
Hodgkinson, 246 

Holley, Alexander.L., 377 
Honey, F. R., 47, 52 
Hoopes & Townsend, 210 
Houston, Edwin J., 1061 
Houston & Kennelly, 1058 
Howard, James E., 242, 382, 385 
Howden, James, 714 
Howe, Henry M., $i, Oval 451, 516 
Howe, Malverd A., 
Howland, A. H; ‘ie 
Hudson, John G., 465 
Hughes, D - B., 396 
Hughes, H. W. , 909 
Hughes, Thos. E., 917 
Humphreys, Alex. C., 652 
Hunsicker, Millard, 397 
Hunt, Alfred E., 285, 317, 392, 553 
Hunt, Chas. W’., 340, 922 
Huston, Charles, 383 
Hutton, Dr., 64 
Huyghens, 58 


Ingersoll-Sergeant Drill Co., 503 
Isherwood, Benj. F., 472 
Jacobus, D. S., 511, 689, 726, 780 
Johnson, J. B., 309, 314 

Johnson, W. B., 475 

Johnson, Wise ors 290 

Jones, Horace K. 1) OOt 

Jones & Lamson Machine Co., 954 
Jones & Laughlins, 867, 885, 


Keep, W. J., 365, 951 

Kennedy, A A.B. Was 855, 525, 764 
Kernot, Prof. 494 

Kerr, Walter C., 781 

Kiersted, W.. 292 

Kimball, ay P., 498, 682, 637 
Kinealy, d. H., 587 ' 


List OF AUTHORITIES. 


Kirk, A. C., 708 
Kirk, Dr., 1004 
Kirkaldy, David, 296 


Kopp , 472 
Pia, Ei 578 
Kutter, 559 


Landreth, O: H., 712 

Langley, J. W., 409, 410, 412 
Lanza, Gaetano, 310, 369, 864, 972 
La Rue, Benj. F., 248 

Leavitt, E. D., 788 

Le Chatelier, M., 452 

Le Conte, J. fe 565 

Ledoux. M., 

Leonard, H Ht Ward, 1027 
Leonard, Ss. Hk 686 

Lewis, Fred. He 186, 189, 379 
Lewis, I. N., 

Lewis, Wilfred, 352, 862, 878, 899 
Linde, G., 989 

Lindenthal, Gustav, 385 

Lloyd’s Register, 264, 266, 700 
Loss, H. V., 306 

Love, E G., 656 

Lovett, T. D., 256 

Lyne, Lewis F., 718 


McBride, James, 974 
MacCord, C. W., 898 
Macdonald, W. R., 956 
Macgovern, E. in 545 
Mackay, W. M., 542, 544 
Mahler, M., 333 

Main, Chas. T., 590, 780, 790 
Mannesmann, Las 332 
Manning, Chas. H., 675, 823 
Marks, Win. D., #93, 811 
Master Car Builders’ Assoc., 876 
Mattes, W. F., 399 
Matthiessen, 1029 

Mayer, Alfred M., 468 
Mehrtens, G. Gs 395, 405 
Meier, E. D., 6 88 

Meissner, C. A., oe 

Melville, Geo. W., 674 
Mendenhall, T. a, 23 
Merriman, Mansfield, 241, 260, 283 
Metcalf, William, 240, 412 
Meyer, J. G. A., 795, 856 
Meystre, F. J.. 472 

Miller, Metcalf & Parkin, 412 
Miller, T. Spencer, 344, 927 
Mitchell, A A. E., 855, (B08 
Molesworth, Sir G.'L 3 062, 
Molyneux and Wood, "736 
Moore, Gideon E., 653 
Morin, 435, 930, 933 

Morison, Geo. §.. 381, 393 
Morrell, T. AUR 

Morris, Tasker y Om 195, 196 
Mumford, E. R., 1 005 
Murgue, Daniel, 521 


Nagle, A. F., 292, 606, 878 

Napier, 47+, 669 

Nason Mfg. Co., 478, 542 

National Pipe Bending Co., 198 





1091 


Nau, J. B., 367, 409 
Newber! ‘y, J. B.. 624 
Newcomb, Simon, 432 = 
New Jersey Steel’& Iron Co., 253, 810 
Newton, Sir Isaac, 475 

Nichol, B. C., 473 

N ichols, 285 

Norris, R. Van A., 521 
Norwalk Iron Works Co., 488, 504 
Nystrom, John W., 265 


Ordway, Prof., 470 


Paret, T. Dunkin, 967 
Parker, W.., 354 
Parsons, H. de B. . 302 
Passburg, Emil, 466 
Pattinson, John, 629 
Peclet, M., 471, 478, 731 


Pelton Water Wheel Co., 191, 574, 585 


Pence, W. D., 294 ' 
Pencoyd Iron Wor ks, 179, 282, 868 
Pennell, Arthur, 555 

Pennsylvania R. R. Co., 307, 275, 399 
Philadelphia Soeeeen ing Works, 526 
Philbrick, P. H., 446 

Phillips, W. B., 629 

Phoenix Bridge Co., 263 

Phoenix Iron ae 181, 25? 

Pierce, C.S., 

Pierce, H. M. “41 

Pittsburg Testing Laboratory, 248 
Platt, John, 617 

Pocock, F. ‘A, 505 

Porter, Chas. T., 662, 787, 820 
Potter, E. C., 646 

Pottsville Iron & Steel Co., 250 
Pouillet, 455 

Pourcel, Alexandre, 404 

Poupardin, M., 687 

Powell, A. M., 975 

Pratt & Whitney Co., 892, 92 

Price, C. S., 638 

Prony, 564 

Pryibil, P., 97? 


Quereau, C. H., 858, 862 


| Ramsey, Erskine, 638 


Rand Drill Co., 490, 505 
Randolph & Clowes, 198 
Rankine, W. J. M., various 
Ransome, Ernest Li. 241 
Raymond, R. W., 631, 650 
Reese, Jacob, 966 

Regnault, M., various 
Reichhelm, E. P., 651 
Rennie, John, 928 

Reuleaux, various 

Richards, Frank, 488, 491, 499 
Richards, John, 965, 976 
Richards, Windsor, 404 
Riedler, Prof., 507 

Rites, F’. M., 783, 818 
Roberts-Austen, Prof., 451 
Robinson, S. W., 583 
Rockwood, G. I., 781 

John A. Roebling’s Sons’ Co., 214, 921 


1092 


Roelker, C. R., 268 
Roney, W. R., es 

Roots, P. H. & F. M., 526 
Rose, ‘Joshua, 414, 868, 970 
Rothwell, Terme ety 

Rowland, Prof., 6 
Royce, Fred. P., 1043 
Rudiger, E. A., 671 
Russell, S. Bent, 567 
Rust and Coolidge, 290 


Sabin, A. H., 387 

Sadler. S. P.. 639 

Saint Venant, 282 

Salom, P. G., 406, 1056 
Sandberg, C. P., 384 
Saunders, J. L., 544 
Saunders, W. L., 505 
-Scheffler, F. A., 681 
Schroter, Prof., 788 
Schutte, L., & Co., 527 
Seaton, various 

Sellers, Coleman, 890, 953, 975 
Sellers, Wm., 204 
Sharpless, S. Pie 311, 639 
Shelton, F. H., 653 
Shock, W. H., 307 
Simpson, 56 

Sinclair, Angus, 863 
Sloane, T. O’Connor, 1027 
Smeaton, Wm., 493 
Smith, Chas. Aut 537, 874 
Smith, C. Shaler, 256, 865 
Smith, Hamilton, Jr., 556 
Smith, Jesse M., 1050 
Smith, J. Bucknall, 225, 808 
Smith, Oberlin, 865, 973 
Smith: R. H., 962 

Smith, Scott ie 874 
Snell, "Henry He B14 
Stahl, Albert W., 
Stanwood, re Be "soo, 809, 813, 818 
Stead, J. E 

Stearns, Bees 465 

Stein and Schwarz, 410 
Stephens, B. F., 292 
Stillman, Thos, B., 944 
Stockalper, E.. 490 
Stromeyer, C. E., 395 
Struthers, Joseph, pk 
Sturtevant, ue Co., 487, 578 
Stut, J.C. H 

Styffe, Knut, "383 

Suplee, H. re 769, 7¢2 
Suter, Geo. A. 524 
Sweet, John E,, 826 


Tabor, Harris, 751 

Tatham & Bros., 201 

"Taylor, Fred. W., 880 
Taylor, W. J., 646 

Theiss, Emil, 818 

Thomas, J. Ww. , 369 
Thompson, Silvanus P., 1064, 1066 
Thomson, Elihu, 1052 
Thomson, Sir Wm.., 461, 1039 
Thurston, R. H., various 
Tilghman, B. F., 96 
Tompkins, C. R., 336 


LIST OF AUTHORITIES, 


Torrance, H. C., 401 

Torrey, Joseph, 582, 820 

Tower, Beauchamp, 931, 934 
Towne, Henry R.., 876, 907, 911 
Townsend, David, 93° 
Trautwine, A On 59, 118, 311, 482 
Trautwine, Ji C., , 255 
Trenton Iron Co., 216, 223, 230, 915 
Tribe, James, 765 

Trotz, E , 453 

Trowbridge, Jokn, 467 
Trowbridge, W. P., 478, 518, 733 
Tuit, J. E., 616 

Tweddell, R. H., 619 

Tyler, A. i, 940 


Uchatius, Gen’l, 321 

Unwin, W. Cawthor Ts various 
Urquhart, Thos., 645 

U.S. Testing Board, 308 


Vacuum Oil Co., 943 
Vair, G. O., 950 

Violette, M . 640, 642 
Vladomiroff, L., 316 


Wade, Major, eh 374 

Wailes, J. W.. 

Walker Mfg. bon * 905 

Wallis, Philip, 858 

Warren Foundry & Mach. Co., 18% 
Weaver, W. D.. 1043 

Webber, Samuel, 591, 963 
Webber, W. O., 608 

Webster, W. R., 389 

Weidemann & Franz, 469 
Weightman, W. H., 762 
Weisbach, Dr. Julius, various 
Wellington, A. M., 290, 928, 985 
West, Chas. D., 916 

West, Thomas D., 328 
Westinghouse & Galton, 928 
Westinghouse El. & Mfg. Co., 1048 
Weston, Edward, 1029 
Whitham, Jay M., 472, 769, 792, 840 
Whitney, A. J., 389 

Willett, J. R., 538, 540 
Williamson, Prof., 58 

Wilson, Robert, 284 

Wheeler, H. A., 908 

White, Chas. r., T14 

White, Maunsel, 408 

Wohler, 288, 240 

Wolcott, F. ’P., 949 

Wolff, Alfred R , 494, 517, 528, 588 
Wood, De Volson, various. 
Wood, H. A 

Wood. M. P.. ” 386, 389 
Woodbury, 0. J. H.. 537, 931 
Wootten. J. E., 

Wright, C. R. ane 831 
Wright, A. W., 289 


Yarrow, A. F., 710 
Yarrow & Co., 307 
Yates, J. A.. 287 


Zahner, Robert, 490 
Zeuner, 827 


INDEX. 


abb-alt 


Abbreviations, 1 
Abscissas, 69 
Abrasion of manganese steel, 407 
Abrasive processes, 965-967 
Absolute temperature, 461 
zero, 461 
Absorption of gases, 480 
of water by brick, 312 
refrigerating-machines, 984 
Accelerated motion, 427 
Acceleration, definition of, 423 
force of, 427 
work of, 430 
Accumulators, electric, 1045-1048 
Adiabatic compression of air, 499 
curve, 742 
expansion of air, 501 
expansion in ‘compressed air- 
engines, 501la 
expansion of steam, 742 
Adiabatically compressed air, mean 
effective pressures, table, 5016 
fee sere metal, composition of, 
2 
Admittance of alternating cur- 
rents, 1063 
Aiken intensifier, 619 
Air, 481-527 
and vapor mixture, weight of, 
484 
binds in pipes, 579 
carbonic acid allowable i in, 529 
compressed, 498-511 (see Com- 
pressed air) 
compressors, effect of 
temperatures, 506 
compressors, high altitude, table 
of, 503 
compressors, tables, 503-505 
cooling of, 531 
density and pressure, 481, 482 
flow of, in pipes, 485, 489 
flow of, in ventilating ducts, 530 
flow of ‘through orifices, 484, 518 
friction of, in underground pas- 
sages, 531 
head of, due to temperature dif- 
ferences, 533 
heating of, by compression, 498 
horse-power required to com- 
press, 501 
loss of pressure of in pipes, 487; 
tables, 488-490 
manometer, 481 
properties of, 481 
pump for condenser, 841 


intake 


Air, specific heat of, 458, 484 
lift pump, 614 
pyrometer, 453 
thermometer, 454 
velocity of, in pipes, by anemom- 
eter, 491 f 
volumes, densities, and pressures 
(table), 481 
volume transmitted in pipes, 864 
weight of, 165, 481; table, 484 
Alcohol, compressibility of, 164 
Alden absorption dynamometer, 


979 
Algebra, 33-36 
Algebraic symbols, 1 
Alligation, 10 
Alloys, 319-338 
aluminum, 328 
aluminum, tests of, 330 
aluminum- antimony, 331 
aluminum-copper, 329 
aluminum -copper-tin, 330 
aluminum-silicon-iron, 330 
aluminum-tin, 330 
aluminum-tungsten, 330 
aluminum-zine, 330 
antimony, 336 
bearing metal, 333 
bismuth, 332 
caution as to strength of, 329 
See ga of, in brass foundries, 
3 
composition by mixture and by 
analysis, 323 
copper-manganese, 331 
copper-tin, 319, 320 
copper-tin-lead, 326 
copper-tin-zinc, 322, 325 
copper- -zinc, 321 
copper-zine-iron, 326 
fusible, 333 
Japanese, 326 
liquation of metals in, 323 
nickel, 332 
variation in strength of, 323 
white metal, 336 
** Alloy” steels, 407-410 
Alternating currents, 1061-1078 
admittance, 1063 
average, maximum, and effective, 
values, 1061. 
calculation of circuits, 1072 
capacity, 1062 
capacity of conductors, 1067 
converters, 1071 
delta connection, 1069 


1093 


1094 alt-—bai 


Alternating currents, frequency, 
1061 
generators for, 1070 
impedance, 1063 
impedance polygons, 1064-1066 
inductance, 1062 
induction motor, 1072, 1077 
measurement of power in poly- 
phase circuits, 1069 
Ohm’s law applied to, 1064 
power factor, 1062 
reactance, 1063 
single and polyphase, 1068 
skin effect, 1063 
synchronous motors, 1071, 1076 
transformers, 1070 
Y connection, 1069 
Altitude by barometer, 483 
Aluminum, 167, 317 
alloys, 319, 598 (see Alloys) 
alloys, tests of, 330 
brass, 329 
. bronze, 328 
bronze wire, 225 
electrical conductivity of 1028 
solder, 31 
steel, 409 
strength of, 318 
wire, 225 
American base-box system, 182 
Ammonia-absorption refrigerating - 
machine, 984, 987: test of, 997 
Ammonia-compression refrigerating- 
machines, 983, 986; test of, 
999 
Ammonia gas. properties of, 992 
monia liquid, density of, 992 
specific heat of, 992 
Ampere, 1024 
Analyses, asbestos, 235 
of boiler scale, 552 
of boiler water, 553, 554 
of cast iron, 371-374 
of coals, 624-632 
of coal, sampling for, 632 
crucible steel, 411 
fire-clay, 234 
gas, 651 
gases of combustion, 622 
magnesite, 235 
Analytical geometry, 69-71 
Anchor forgings, strength of, 297 
Anemometer, 491 


Angle, economical, of framed struc- | 


tures, 447 
of repose of building material, 
929 
Angles, Carnegie bulb, properties | 
of, table, 278 
Carnegie steel, properties of, 
table, 279a 


a steel, weights and sizes, 
179 


trigonometrical properties of, 66 
plotting without protractor, 52 
problems in, 37, 38 

Angular velocity, 425 

Animal power 433~435 





INDEX. 


Annealing, effect on conductivity, 


effect on steel, 392, 412 
influence of on magnetic capac. 
ity of steel, 396 
non-oxidizing process of, 389 
of steel, 394, 413 
of steel forgings, 396 
of structural steel, 394 
Annuities, 15-17 
Annular gearing, 898 
Anthracite, classification of, 624 
composition of, 624 
sizes of, 632 
space occupied by, 625 
Anthracite-gas, 647 
Anti-friction curve, 50, 939 
metals, 932 
Antimony, properties of, 167 
in alloys, 331, 336 
Apothecaries’ measure and weight, 
18, 19 
Are, circular, 57 
circular, Huyghen’s approxima- 
tion of length of, 58; table, 114 
circular, relations of, 58 
Arc-lights, electric, 1041 
Arches, corrugated, 181 
flooring, 281 
tie-rods for, 281 
oasis a circles 1- 1000, table, 103~ 


of circles 2-100, table advanc- 
ing by $+. 108-112 
of geometrical solids, 61-63 
of geometrical plane figures , 
54-60 
of irregular figures, 55, 56 
of sphere, 61 
of sphere, table, 118 
Arithmetic, 2-32 
Arithmetical progression, 11 
Armature-circuit, e.m.f. of, 1056 
Armature. torque of, 1056 
Asbestos, 235 
Asphaltum coating for iron, 387 
Asses, work of, 435 
Asymptotes of hyperbola, 71 
EM een equivalent pressures 
of, : 
pressure of, 481, 482 
moisture in. 483 
Atomic weights (table) 163 
Authorities, list of, 1089 
Avogadro’s law of LG 479 
Avoirdupois weight, 1 
Axles, railroad, effect of cold. 384 
steel, specifications for, 397 
steel, strength of, 299 
Automatic cut-off engines 753 


Babbitt metal. 336, 337 

Babeock & Wilcox boilers, 
with various coals, 636 

Bagasse as fuel, 643 

Balances, to weigh on incorrect, 19 

Ball-bearings, 940 

Balls, hollow copper, 289 


tests 


INDEX. 


Bands and belts, theory of, 876: 
for carrying grain, 912d 
Bars, eye, tests of, 304 
iron, flat, commercial sizes of, 
table, 170 
iron, various shapes, 
cial sizes of, 171 
Lowmoor iron, strength of, 297 
steel, effect of ‘nicking, 402 
Eeiered iron, tensile strength of, 
ayes , Gilmore’s experiments on, 
various, weights of, 169 
wrought. iron, compression tests 
of, 304 
; wrought iron, weight of, table, 171 
Barometer, leveling with, 482 
to find altitude by, 483 
Barometric readings for various 
altitudes, 482 
Barrels, to find volume of, 64 
number of, in tanks, 126 
Buss apnea steel, strength of, 


commer- 


Batteries, storage, 1045-1048 
Baume’s hydrometer, 165 
Bazin’s experiments on weirs, 587 
formule, flow of water, 563 
Beams, deck, properties. of Carne- 
gie, table, 2 
formule for flexure of, 267 
formule for transverse strength 
of, 268 
special, coefficients for loads on, 


steel, formule for safe loads on, 


265 

variously loaded, 271 

yellow pine, safe loads on, 1023, 
0 


Beardslee’s tests on elevation of 
elastic limit, 238 
Bearings, allowable pressure on, 
935-937 
ball, 940 
cast-iron, 933 
for steam turbines, 941 
high speed, 941 
_ oil pressure in, 937 
overheating of, 938 
pivot, 939 
roller, 940 
steam -engine ,.811-813 
Bearing-metal alloys, 333 
Bearing-metals, anti-friction, 932 
composition of, 326 
Bearing pressure on rivets, 355 
Bed-plates of steam-engines, 817 
Bell-metal, composition of, 325 
Belt conveyors, 912d 
dressings. 887 
Belts. arrangement of, 885 
eare of, 886 
cement for leather or cloth, 887 
centrifugal tension of, 876 
endless, 886 
evil of tight, 885 


ban-boi 


Belts, lacing of, 883 

length of, 884 

open and crossed, 874, 884 
' quarter twist, 883 

sag of, 885 
Belting, 876-887 

formule, 877 

friction of, 876 

horse-power of, 877-880 

notes on, 882 

practice, 877 

rubber, 887 

strength of, 302, 886 

tables, 877, 878 

Taylor’s rules, 880-882 

theory of, 876 

width for given H.P., 879 
Benge curvature of wire rope, 
Bends, effects of on flow of water 

in pipes, 578 


in pipes, 488, 672; table, 199 
Bent lever, 436 
Bessemer converter, temperature 


determinations in, 452 
steel (see Steel, Bess semer) 
Bessemerized cast iron, 375 
Bevel wheels, 898 
Billets, steel, specifications for, 401 
Bins, coal- storage, 912a 
Binomial, any power of, 33 
theorem, 36 
Birmingham gauge, 28 
Bismuth, properties of, 167 
alloys, 332 
Bituminous coal (see Coals) 
Blast-furnaces, consumption of 
charcoal in, 641 
steam-boilers for, 689 
temperature determinations in, 


Blocks or pulleys, 438 
efficiency of, table, 907 
strength of, 906 

Blooms, steel, weight of, 


176 
Blow, force of, 430 
Blowers, 511-52 6 
ae comparative efficiency, 
blast-pipe diameters for, 520 
eapacity of, 517, 1081 
experiments with. 514 
for cupolas, 519, 950 
pressure, 950 
rotary, table of, 526 
steam-jet, 527 
velocity due to pressure, 514 
Sahl -engines, dimensions of, 


table, 


Blue Si an effect on steel, 395 
Board measure. 20 
Bodies, falling, laws of, 424 
Boiler compounds, 717 
explosions, 720 
feed-pumps, 605, 726 
furnaces, height cf, 711 
furnaces, use of steam in, 650 


1096 


boi-cal 


Boiler heads, 706 
heads, strength of, 284, 286 
heads, wrought-iron, 285 
heating-surface for steam heat- 
ing, 538 
scale, analyses of, 552 
tubes, area of, table, 197 
tubes, dimensions of, table, 196 
tubes, expanded, holding power 
of, 307 
Boilers, horse-power, 677 
for steam heating, 538 
incrustation of, 550 
locomotive, 855 
marine, 1015 h 
plate, strength of, at high tem- 
peratures, 383 ‘ 
steam, 677-731 (see Steam-boiler) 
Boiling, resistance to, 463 
Boiling-point of water, 550 
Boiling-points of substances, 455 
Bolts and nuts, 209, 211 
effect of initial strain in, 292 
holding power of in white pine, 
290, 291 
quate -head, table of weights of, 
ak 


strength of, table, 292 
taper, 972 
track, weight of, 210 - 
variation in size of iron for, 206 
Bomb calorimeter, 634 
Braces, diagonal, ‘with tie, stresses 
in, 
Brackets, 
252 
Brake, Prony, 978 
Brass, composition of rolled, 203 
alloys, 325 
plates and bars, weight of, table, 
202, 203 
tube, seamless, table, 198-200 
wire. weight of, table, 202 
Brazing of aluminum bronze, 328 
metal, composition of, 325 
solder, composition of, 325 
es absorption of water by, 


312 
for floors, 281 
kiln, temperatures in, 452 
specific gravity of. 165 
strength of. 302. 312 
weight of, 165, 312 
Bricks. fire, number required for 
various circles, table, 234 
fire, sizes and shapes of, 233 
Bricks magnesia, 235 
Brickwork, measure of, 169 
weight of, 169 
Bridge iron, durability of, 385 
links, steel, strength of, 298 
members, strains in, 262-264 
Memphis, proportions of mate- 
rial, 381 
Memphis. tests of steel in, 393 
trusses, 442 
Brine, boiling of, 463 
properties of, 464, 994 


cast-iron, strength of, 


Briquettes, coal, 632 
British thermal unit (B.T.U.), 455. 
660 


Britannia metal, 
336 
Bronze, 
328 


composition of, 


aluminum, strength of, 
ancient, composition of, 323 
deoxidized, composition of, 327 
Gurley’s, composition of, 325 
manganese. 331 

phosphor. 327 

strength of, 300, 319, 321 

Tobin, 325, 326 


dagen gti sizes and weights of. 
Suerte construction of, 1019- 


fire-proof. 1020 
heating and ventilation of, 534 
transmission of heat through 
walls of, 478 
walls of, 1019 
Building-laws, New York City, 
1019-1021 
on columns, New York, 252 
1019 


on columns, Boston, 252 

on columns, Chicago 2527255 

on structural materials, Chicago 
381 


Building-materials, angle of repos’ 
of, 929 ; 
coefficients of friction of, 929 
sizes and weights. 169. 184 
Bulb angles, properties of Carne 
gie steel, table, 278 
Bulkheads, plating ‘and framing fo1 
table, 287 
Buoyancy, 550 
Burr truss, stresses in, 443 
Bushel of coal, 638 
of coke, 638 
Bush- metal, composition of, 325 
Butt- joints, riveted, 358 
veblesy chain, wrought-iron, 308 
flexible steel wire, 223 
sizes, weight, and strength, 230 
lead-incased power, 
weights, 2 
suspension-bridge. 230 
Cable-ways, suspension. 915 
Cadmium, properties of, 167 
Calculus, 72-79 
Calcium chloride in refrigerating- 
machines, 994 
Calorie engines, 851 
Calorie, definition of, 455 
Co for coal, Mahler bomb, 
steam, 728-731 
steam, coil, 729 
steam, separating, 730 
steam, throttling 729 
Calorimeiric tests of coal, 636 


sizes and 


INDEX. 


Cam, 438 
Canals, irrigation, 564 
speed of vessels on, 1008 
Candle-power of electric lights, 1042 
of gas lights, 
Canvas, strength Ay 302 
Cap-screws, table of standard, 208 
Capacity, electrical, 1062 
electrical, of conductors, 1067 
Car- heating by steam, 538 
Car-journals, friction of, 937 
Cars, steel plate for, 401 
Car-wheels, east iron for, 375 
Carbon, burning out of steel, 402 
effect. of, on strength of steel, 389 
gas, 646 
Carbonic acid allowable in air, 529 
Carnegie steel sections, properties 
of, 272-280 
steel sections, weights and sizes, 
177,178 
’ Carriages, resistance of, on roads, 
435 


Carriers,, bucket, 912a 
Casks, volume of, 64 
Cast copper, strength of, 300, 319 
Cast iron, 365-376 
analyses of, 371-374 
bad, 375 
bearings, 933 
Bessemerized, 375 
chemistry of, 370-374 
columns, eccentric loading of, 254 
columns, strength of, 250-253 
columns, tests of, 250, 251 
columns, weight of, table, 185 
compressive strength of, 245 
corrosion of, 386 
durability of, 385 
influence of phosphorus, sulphur, 
etc., 365-368, 370 
malleable, 375 
mixture of, with steel, 375 
pipe, 185-190 (see Pipe, cast- 
iron) 
pipe-fittings, sizes and weights, 187 
relation of chemical composition 
to fracture, 370 
shrinkage of, 368 
specific gravity of, 374 
specifications for, 374 
strength of, 296, '370-374 
strength in relation to silicon 
and cross-section, 369 
tests of, 369 
variation of density and tenac- 
ity, 374 
Castings, iron, apenbe of, 373 
iron, strength of, 297 
malleable, rules for use of, 376 
shrinkage of, 951 
steel, 405 
steel, specifications for, 397, 406 
steel, strength of, 299 
weight of, from pattern, 952 
Catenary, to plot, 51, 52 
Cy as a preservative coating, 


109% 


cam-chi 


Cement for leather belts, 887 
mortar, strength of, 313 
Portland, strength of, 302 
specific gravity of, 166 
weight of, 166, 170 

Center of gravity, 418 
of gravity of regular figures, 419 
of gyration, 420 
of oscillation, 421 
of percussion, A22 

Centigrade thermometer scale, 448 
-Fahrenheit conversion table, 449 

Centrifugal discharge elevators, 912a 
fans (see Fans, centrifugal) 
force, 423 
force in fly-wheels, 820 
pumps, 607-609 (see 

centrifugal) 

- tension of belts, 876 
C.G.S. system of measurement, 1024 
Chains, crane, sizes, weights, and 

properties, 232 
link-belting, 9126 
monobar, 9126 
pin, 912c 
roller, 912c 
specifications for, 307 
strength of, table, 307, 339 
tests of, table, 307 

Chain-blocks, efficiency of, 907 

Chain-cables, proving tests of, 308 
weight and strength of, 340 

Chalk, strength of, 312 

Change gears for lathes, 955, 956 

Channels, Carnegie steel, properties 

of, table, 277 
open, velocity of water in, 564 
strength of, 297 
weights and sizes, 178-180 

Charcoal, 640-642 
absorption of gases and water by, 


64 
bushel of, 170 
composition of, 642 
consumption of, 
naces, 641 
pig iron, 365, 374 
results of different methods of 
making, 641 
weight per cubic foot, 170 
Chemical elements, table, 163 
symbols, 163 
Chemistry of foundrv irons, 370-374 
Chezy’s formula for flow of water, 558 
Chimneys, 731-741 
draught, power of, 733 
draught, theorv, 731 
effect of flues on draught, 734 
for ventilating, 533 
height of, 734 
height of water column due ta 
unbalanced pressure in, 732 
lightning protection of, 736 
rate of combustion due to, 732 
sheet-iron, 741 
size of, 734 
size of, table, 735 
stability of, 738 


Pumps, 


in blast-fur- 


1098 


chi-col 


Chimneys, steel, 740 

steel, foundations for, 741 
tall brick, 737 

Rees of air in, 733 

weak, 73 
Chord of Ree 58 
Chords of trusses, strains in, 445 
Chrome steel, 4 
Circle, 57-59 

area of, 57 

area of, 1-1000, table, 103-107 


area of, @z-100, advancing by #4, | 


table, 108-112 
equations of, 70 
length of are of, 57 
length of are of, Huyghen’s ap- 
proximation, 58 
length of Pein of, 58 
problems, 39, 4 
properties of, 57 
relations of arc, chord, etc., of, 58 
relations of, to equal, inscribed, 
and circumscribed square, 59 
sectors and segments of, 59 
Circuits, electric, e.m.f. in, 1030 
electric, polyphase, 1068 (see 
Alternating currents) 
electric, power of, 1031 
Circuit, magnetic, 1051 
Circular ares, lengths of, 57 


ares, lengths of, tables, 114, 115 


functions, calculus, 78 

inch, 18 

measure, 20 

mil, 18 

mil wire gauge, 30 

mil wire gauge, table, 29 

pitch, 888 

ring, 59 

segments, table of areas of, 116 
Circumferences of circles, —1000, 

table, 103-107 
of scireles, oe fear polig: advanc- 


ing by 4, 108-11 
of riplee, 1 inch to “33 feet, table, 
1 


Cisterns, capacities of, 121, 126 
Classification of iron and steel, 364 
Clay, cubic feet per ton, 170 
fire, analysis of Mt. Savage, 233 
Clearance in steam-engines, 751,792 
Coal, analyses of, 624-632 
anthracite, sizes of , 632 
bituminous, classification of, 623 
calorimeteric tests of, 636 
classification of, 623-624 
conveyors, 912a 
cost of, for steam power, 789 
DuLong’ s formula for heating, 
value of, 633 
evaporative power of, 636 
foreign, analysis of, 631 
furnaces for different, 635 
heating value of, 633, 634 
handling machinery, 912-912d 
hoisting by rope, 343 
products of distillation of, 639, 651 
telative value of, 633-637 


INDEX. 


Coal, sampling of, for analysis, 632 
semi-bituminous, composition of, 
625, 626 : 
space occupied by anthracite, 625 
storage bins, 912a 
vs. oil as fuel, 646 
washing, 638 
weathering ot, 637 
weight of, 170, 638 ©» 
Welsh, analysis of, 632 
Coal-gas, composition of, 652 
manufacture of, 651 
Coatings, preservative, 387-389 
rustless, for iron and steel, 388 
Coefficients of expansion, 460 
of expansion of iron and steel, 385 
Coefficient of elasticity, 237, 314 
of fineness, 1002 
of friction, definition, 928 
of friction, tables, 929, 930 
of friction of journals, 930, 932 
of friction, rolling, 929 
of performance of ships, 1003 
of propellers, 1011 
of transverse strength, 267 
of water lines, 1002 
for loads on special beams, 270 
Coils, electric, heating of, 1032 
Coil pipe, table, 199 
Coke, analyses of, 637 
making of hard, 638 
ovens, generation of steam from 
waste heat of, 638 
by-products of manufacture, 638, 


639 
weight of. 170, 638 
Coking, experiments in, 637. 
Cold-chisels, form of, 955 
Cold, effect of,on railroad axles, 384 - 
effect of, on strength of iron and 
steel, 383 
drawing, effect of, on steel, 305 
drawn steel, tests of, 305 
rolled steel, tests of, 305 
rolling, effect of, on steel, 393 
saw, 966 
Collapse of corrugated furnaces, 266 
resistance of hollow cylinders to, 
264-266 sy. 
Color determination of tempera- 
ture, 454 
scale for steel tempering, 414. 
Columns, built, 256 
cast-iron, strength of, 250 
cast-iron, tests of, 250, 251 
cast-iron, weight of, table, 185 
eccentric, loading of, 254 
Gordon’s formula for, 247 
Hodgkinson’s formula for, 246 
Fee permissible stress in, 
2 


Merriman’s formuls for, ‘260 

mill, 1022 

Phoenix, dimensions of, 257-259 

steel, Merriman’s tables for, 261 

strength of, 246, 247 

strength of, by New York build- 
ing laws, 1019 


INDEX, 


Columns, wrought-iron, built, 257 
wrought -iron, Merriman's table 
of, 260 
wrought-iron, tests of, 305 
wrought-iron, ultimate strength 
of, table, 25 
Combination, 10 
Combined stresses, 282, 283 
Combustion, analyses of gases of ,622 
heat of, 456, 621 
of fuels, 621 
of gases, rise of temperature in, 623 
rate of, due to chimneys, 732 
theory of, 620 
Composition of forces, 415 
Compound engines, 761-768 (see 
Steam-engines, compound) 
interest, 14 
locomotives, 862, 863 
numbers, 5 
proportion, 6 
shapes, steel, 248 
units of weights and measures, 27 
Compressed-air, 488, 498-511 
adiabatic and isothermal com- 
pression, 499 
adiabatic expansion and com- 
pression, tables, 502 
compound compression, 5015 
eranes, 912 
diagrams, 5016 
drills driven by, 506 : f 
engines, adiabatic expansion in, 
501 a 
engines, efficiency, 596 
for motors, effect of heating, 507 
flow of, in pipes, 489 
formule, 501 
heating of, 498 
hoisting engines, 5056 
horse-power required to compress 
air, 5CO 
losses due to heating, 500 
loss of energy in, 49 


machines, air required to run, 
505a 

mean effective pressures of 
adiabatically compressed air, 
table, 5016 

mean effective pressures, com- 
pound compression, table, 
5016 

mean effective pressures, tables, 
502, 503 

mine pumps, 511 

motors, 507 


Popp system, 507 

practical applications of, 505b 

pumping with, 505a 

reheating of, 506 

shop operation by, 509 

tramways, 510. 511 

transmission, 488 

transmission, efficiencies of, 508 

volumes, mean_ pressures per 
stroke, etc., table, 499 

work of adiabatic compression, 





col-con. 1099 

Compressed steel, 410 
Compression, adiabatic, formule 
for, 501 ; 


adiabatic, tables, 502 
and flexure combined, 282. 
and shear combined, 282 
and torsion combined, 283 
in steam-engines, 751 
members in structures, 
strains in, 280 
Compressive strength, 244-246 
strengths of woods, 311 - 
strength of iron bars. 304 
tests, specimens for, 245° 
Compressors, air, 503- 505 
air, Eee Sy of intake temperature, 
Condensers, 839-846 
_air-pump for, 841 
circulating pump for, 843 . 
continuous use of cooling water 
in, 844. 
cooling towers for, 844 
cooling water required, 841 
ejector, 840. 
evaporative surface, 844 
increase of power due to, 846 
jet, 839 
surface, 840 
EUey and tube plates of, 840, 
tubes, heat transmission in, 472 
Conduction of heat, 468 
of heat, external, 469 
of heat, internal, 468 
Conductiv ity, electric, of steel, 403 
electrical, of metals, 1028 


unit 


Conductors, electrical, heating of, 
1031 
electrical, in series or parallel, 


resistance of, 1030 
Conduit, water, efficiency of, 589 
Cone, measures of, 61 
pulleys, 874 
Conic sections. 71 
Goanegiingreds, steam-engine, 799, 


tapered, 801 
Conoid, parabolic, 63 
Conservation of energy, 432 
Construction of buildings, 1019- 
Convection, loss of heat due to, 476 
of heat, 469 
of heat, Dulong’s law of, table 
of factors for, 477 
Conversion table, Centigrade-lah- 
renheit, 449 
tables, metric, 23-26 
Converter, Bessemer, temperature 
determinations in, 452 
Converters, electric, 1071 
Conveying ‘of coal in mines, 913, 914 
Conveyors, belt, 912d 
eable-hoist, 915 
coal, 912a 
horse-power required for, 912c 
screw, 912d 


1100 


coo-cyl 


Cooling of air for ventilation, 531 
towers for condensers, 844 
Co-ordinate axes, 69 
Copper, 167 
ball pyrometer, 451 
cast, strength of, 300, 319 
drawn, strength of, 300 
balls, hollow, 289 
manganese alloys, 331 
nicke! alloy, 332 
plates, strength of, 300 
plates, weight of, table, 202 
round bolt, weight of, table, 203 
Se of, at high temperatures, 


tin alloys, 320 

tin alloys, properties and compo- 
sition of, 319 

tin-aluminum alloys, 330 

tin-zine alloys, properties and 
composition, 322, 323 

tubing, weight of, table, 200 

weight required in different sys- 
tems of transmission, 1075 

wire, table of dimensions, weight, 
and resistance of 202, 218- 
220, 1034 

wire, ‘cost of, for long-distance 
transmission, 1036, 1040 

zinc alloys, strength of, 323 

zinc alloys, table of composition 
and properties, 321 

zinc-iron alloys, 326 

Cordage, technical terms relating 


to, 341 
weight of, table, 906 
Cork, properties of, 316 
Corn, weight of, 170 
Corrosion of i iron, 386 
of ca ipa 386, 552, 716- 


Corrosive agents in atmosphere 386 
Corrugated arches, 1 
furnaces, 266, 702, 709 
iron, sizes and weights, 181 
plates, properties of Carnegie 
steel, table, 274 
Eke of an angle,65; table, 159- 
62 
Cosine of an angle, 65; table, 159- 
2 


Cost of coal for steam-power, 789 
of steam-power, 790 
Cotangent of an angle, 65; 
159-162 
Cotton ropes. strength of, 301 
Couloumb, 1024 
Counterbalancing 
gines, 909 
of locomotives, 864 
of steam-engines, 788 
Se poles system of hoisting, 
1 


Couples, 418 

Coverings for steam-pipe, tests of, 
470, 471 

sie of angles, table, 159- 


table, 


of hoisting-en- 





INDEX. 


Cox’s formula for loss of head 
575 
Crane os: 232 
Cranes, 911 
classification of, 911 
compressed air, 912 
electric, 912 
jib, 912 
stresses in, 440 
travelling, 912 
guyed, stresses in, 444 
simple, stresses in, 440 
Cranks, steam-engine, 805 
Crank Kept steam-engine, table, 
83 


pins, steam-engine, 801-804 
pins, steel, specifications for, 401 
shafts, steam-engine, 813-815 
shaft, steam-engine, torsion and 
flexure of, 814 
Cross-head gui ides, 798 
pin, 804 
Crucible steel, 410-414 (see Steel, 
crucible) 
Crushing strength of masonry mate- 
rials, 312 
Cubature, 75 
Cubes of numbers, table, 86-101 
of decimals, table, 101 
Cube root, 8 
roots, table of, 86-101 
Cubic feet per gallon, table, 122 
measure, 18 
Cupcla practice, 946-950 
result of increased driving, 949 
Cupolas, blast-pipes in, 520 
blast-pressure in, 948 
blowers for, 519, 950 
charges for, 946-947 
charges in stove foundries, 949 
dimensions of, 947 
loss in melting iron in, 950 
slag in, 948 
Currents, electric (see Electric cur-' 
rents) 
Current motors, 589 
Cutting speeds. of machine tools, 
953; table, 954 
stone with wire, 966 
Cycloid, construction of, 49 
differential equations of” 79 
differential measure of, 60 
integration of, 79 
Cycloidal gear-teeth, 892 
Cylinder condensation 
engines, 752, 753 
Cylinder, measures of, 61 
Cylinders, hollow, limit of thickness, 


in steam- 


288 
hollow, resistance of, to collapse, 
264-266 


hollow, under tension, 287, 289 

hydraulic, thickness of, 617 

hydraulic press, thickness of, 
288 

locomotive, 854 

steam-engine (see Steam-engines) 


table of capacities of, 120 


INDEX. 


Cylindrical ring, 62 
Cyppdre alanis capacities of, table, 
121 


eS a law of gaseous pressures, 

48 

Dam, stability of, 417 

D’Arcy’s formula, flow of water, 
5 


63 
formula, table from, of flow of 
water in pipes, 569-572 
Decimals, 3 
squares Sal cubes of, 101 
Decimal equivalents of fractions, 3 
ene of feet and inches, 
112 


gauge, 32 
eee aa weights and _= sizes, 
properties of Carnegie steel, 278 
Delta connection for alternating 

currents, 1069 
metal, 225, 326 
Denominate numbers, 5 
Deoxidized bronze, 327 
Derrick, stresses in, 441 
Diagonals, formule for strains in, 
444 
Diametral pitch, 888 
Differential gearing, 898 
calculus, 72-79 
of algebraic function, 72 
of exponential function, 77 
partial, 73 
coefficient, 73; sign of, 76 
second, third, ‘ete. 5 the 
pulley, 439 
screw, 439; efficiency of, 974 
windlass, 439 
Differentiation, formule for, 73 
Discount, 13 
Disk fans (see Fans, disk) 
Displacement of ships, 1001, 1008 
Distillation of coal, 639 
Distiller for marine work, 847 
Domes on steam-boilers, 711 
Draught power of chimneys, 732 
theory of chimneys, 731 
Drawing-press, blanks for, 973 
seg, centrifugal pump as a, 
6 
Dressings, belt, 887 
Drift bolts, resistance of, in timber, 


9 
Drill gauge, table, 29 " 
Dee horse-power required by, 


Drills, rock, air required for, 505a 
rock, requirements of air-driven, 
506 


twist, speed of, 957 
tap, 970, 971; sizes of, 208 
Drilling holes, speed of, 956 
machines, electric, 956 
Drop im electric circuits, 1029-1031 
press, pressures attainable by, 


Drums for hoisting-ropes, 917 


1101 


ecyl-eila 


Dry measure, 18 
Drying and evaporation, 462-467 
in a vacuum, 466 
Ducts, cold-air, for steam-heating, 
5 


Ductility of metals, table, 169 
Dulong’s formula for heating value 


of coal, 633 

ue of convection, table of factors 
or, 

law of radiation, table of factors 
for, 476 


Durability of iron, 385, 386 
Durand’s rule for areas, 56 
Dust explosions, 642 

fuel, 642 
Duty, measure of, 27 

of pumping-engine, 610. 

- trials of pumping-engines, 609- 

612 
1055- 


Dynamo-electric machines, 


machines, classification of, 1055 


machines, design of, 1058- 
1060 
machines, e.m.f. of armature cir- 
cuit, 1056 

machines, moving force oi, 
1055 

machines, strength of field, 
1057 

machines, torque of armature, 
1056 

machines, types of, 1055 

machines, tables of, 1074-1077 


Dynamometers, 978-980 
Alden absorption, 979 
Prony brake, 978 
traction, 978 
transmission, 980 

Dyne, definition of, 415 


Earth, cubic feet per ton, 170 
Economical angle of framed struc- 
tures, 447 
Eccentrics, steam-engine, 816 
Economizers, fuel, 715 
Edison wire gauge, 30; table, 29 
Efficiency of a machine, 432 
of compressed-air engines, 506 
of pereseed a transmission, 
508 


of electric transmission, 1038 

of fans, 516, 520, 525, 526 

of fans and chimneys for ventila. 

tion, 533 

of injector, 726 

of pumps, 604, 608 

of riveted joints, 359, 362 

of screws. 974 

of steam-boilers, 683, 689 

of steam-engines, 749, 775 
Effort, definition of, 429 
Ejector condensers, 840 
Elastic-limit, 236-239 

apparent, 237 

Bauschinger’s definition of, 239 

elevation of, 238 


ela—-exh 


1102 


Elastic-limit of wire rope, 917 
relation of to endurance, 238 
Wohler’s experiments on, 238 

Elastic resilience, 270 
resistance to torsion, 282 

Elasticity, coefiicient of, 237 
modulus of, 237 
moda of, of various materials, 

eee conductivity of steel, 

Electrical engineering, 1024-1077 
alternating currents, 1061-1077 
direct currents, 1024-1060 

Eee. horse-power, 1031; table, 


machines, tables of, 1074-1077 
resistance, 1027-1032 
symbols, 1078 _ 
Electricity, standards of measure- 
ment, 1024 
systems of Cet wae 1041 
units used in, 1024. 
Electric circuits (see Circuits, elec- 
tric ) 
currents, alternating, 1061-1072 
(see Alternating currents) 
currents, direct, 1024-1060 
current, direction of, 1054 
currents, heating due to, 1031 
current required to fuse wires, 
1032 
currents, short 
036 
heaters, 546, 1044 
light stations, economy of en- 
gines in, 785 
lighting, 1041-1043 
motors, alternating current, 1071, 
1077 
motors, direct current, 1055, 1074 
-1076 
railways, 1041 
storage-batteries, 1045-1048 
transmission, 1033-1041 (see 
Transmission, electric) 
wires (see Wires, electric) 
welding, 1046 
Electro-chemical equivalents, 1049 
Electro-magnets, 1050-1054 
polarity of, 1054 
strength of, 1053 
winding for, 1053 | 
Electron aane eS measurements, 
105 


Electrolysis, 1048 

Elements, chemical, table, 163 
of machines, 435-440 

Elevators, coal, 912a 

Ellipse, construction of, 46, 47 
equations of, 70 
measures of, 59, 60 

Ellipsoid, 63 

Elongation, measurement of, 243 

E.M.F. of electric circuits, 1030 
of armature circuit, 1056 

Emery, grades of, 968 ; 
wheels, speed and selection of, 967 


circuiting of, 


INDEX. 


Emery-wheels. strains in, 969 
Hondas rope system of haulage, 


screw 440 
Endurance of materials, relation of 
to elastic limit 238 
Energy, conservation of, 432 
definition of, 429 
measure of, 429 
of ree. il of guns, 431 
sources of, 432 


Engines, blowing, 526 


compressed air, 
506 

fire, capacities of, 580 

gas, 847-850 (see Gas-enginesy 

gasoline, 850 

hoisting, 908 

hot-air, 850 

hydraulic, 619 

marine, 1017-1019 

marine, steam and exhaust open- 
ings, sizes of, 674 

ae ra: steam- -pipes for, 674, 
1 

naphtha, 850 

petroleum, 850 

petroleum, tests of, 851 

pumping, 609-612 (see Pumping- 


efficiency of, 


engines) 
steam, 742-847 (see Steam-en- 
gines) 
winding, 909 
Hngine: plane 


913 

Epicycloid, 50 
Equation of payments, 14 

of pipes, 491 
Equations, algebraic, 34, 35 

of circle, 70 

of ellipse, 70 

of hyperbola, GL 

of parabola, 70 

quadratic, 35 

referred to co-ordinate axes, 69 
Equilibrium of forces, 418 
Bevelen orifice, mine ventilation, 


wire-rope haulage, 


Equivalents, electro-chemical, 1049 
Erosion of soils, 565 
Ether, compressibility of, 164 
Evaporation, 462-467 
by exhaust steam, 465 
by multiple system, 463 
factors of, 6956-699 
in salt manufacture, 463 
of sugar solutions, 465 
of water from reservoirs and 
channels, 463 
latent heat of, 462 
total heat of, 462 
unit of, 677 
Evaporator, for marine work, 847, 
1016 
Evolution, 7 
Exhaust-steam, 


evaporation by; 
465 | 
for heating, 780 


INDEX. 


Exhauster, steam-jet, 527 
Expansion, adiabatic, formule for, 
501; tables, 502 
by heat, 459 
coefficients of, 460 
of iron and steel, 385 
of liquids, 461 
of solids by heat, 460 
of steam, 742 
of steam, actual ratios of, 750 
of timber, 311 
of water, 547 
Explosions, dust, 642 
ere energy of steam-boilers, 


Exponents, theory of, 36 

Exponential function, 
Bralwiad 

Eye bars, tests of, 304 


differential 


Factors of evaporation. 695b-699 
Factor of safety, 314 
in steam-boilers, 700 
Fahrenheit- Centigrade 
table, 449 
Failures of stand-pipes, 294 
of steel, 403 
Fairbairn’s experiments on riveted 
joints, 354 
Faliing bodies, graphic representa- 
tion, 425 
bodies, laws of, 424 
Fans and blowers, 511-526 
capacity of, 517, 1083 
comparative efficiencies, 516 
Fans, best proportions of, 512 
centrifugal, 511, 518-523 
disk, 524-526 
efficiency of, 520, 533 
experiments on, 515, 516, 522 
for cupolas and forges, 519 
influence of speed of, 523 
influence of spiral casings on, 
523 
pressure due to velocity of, 513 
pet gk of air delivered by, 
Farad, definition and value of, 
1024 


conversion 


Feed-pump (see Pumps) 
F counts cold, strains caused by, 
2 
water heaters, 727, 1083 
water heaters, marine practice, 
1016 
water, saving due to heating, 
Teas 
water, purification of, 554 
Feed-wire, stranded, table of sizes 
and weights, 222 
Fibre-graphite lubricant, 945 
Fifth roots and powers of numbers, 
102 


Fineness, coefficient of, 1002 

Finishing temperature, effect of in 
steel rolling, 392 

Fink roof-truss, 446 

Fire, temperature of, 622 


exh-fio 


1108 


Lady arches in locomotives, 
Fire-brick, number required for 
various circles, table, 234 
sizes and shapes of, 233 

weight of, 233 
Die Feed analysis of Mt. Savage, 
pyrometer, 453 
Fire-engines, capacities of, 580 
Fire-proof buildings, 1020 
Fire-streams, 579-581 
discharge from nozzles at differ- 
ent pressures, 579 
sige of increased hose-length, 
friction loss in hose, 580 
pressure required for given length 
of, table, 581 
Fireless locomotive, 866 
Fits, forcing and shrinkage, 973 
Fittings, cast-iron pipe, sizes and 
weights, table, 187 
Flagging, strength ‘of, 313 
mae for cast-iron pipe, table, 


pipe, standard, table, 192 
pipe, extra, heavy, table, 193 
oe plates in steam-boilers, 701, 


plates, strength of, 283 
ie iron, weight of, table, 172, 


Flexure of beams, formule for, 267 
and compression combined, 282 
and tension combined, 282 
and torsion combined, 283 

ee equation for flow of air, 


Flight conveyors, 912a 
Flights, sizes and weights of, 912c 
Floors, ‘loads on, 281 
maximum load on, 1021 
strength of, 1019, 1021 
Flooring material, 281 
Flow of air in pipes, 485 
of air through orifices, 484, 518 
of compressed air, 489 
of gases, 480 
of gas in pipes, 657-659 
of gas in pipes, tables, 658 
of metals, 973 
of steam, 
672 
of steam, in pipes, 669-671 
of steam, loss of pressure due te 
friction, 671 
of steam, loss of pressure due ta 
radiation, 671 
of steam, Napier’s rule, 669 
of steam, resistance of bends 
valves, etc., 672 
of steam, tables of, 668, 6 
of steam, through a nozzle, 668 
of water, 555-588 
of water, Bazin’s formule, 563 
of water, Chezy’s formula, 558 
of water, D’Arcy’s formula, 563 


capacities of pipes, 


1104 


filo-fue 


Flow of water, experiments on, 566- 


of water, fall per mile and slope, 
table, 558 
of water, Flynn’s formula, 562 
of 1039" formulz for, 557-564, 
1089 


of water in pipes, 557 

of water in pipes at uniform 
velocity, table, 572 

of water in cast-iron pipe, 566 

of water in house-service pipes, 
table, 578 

of water in 20” pipe, 566 

of water in pipes, table from 
D’Arcy’s formula, 569-572 

of water in pipes, tables from 
Kutter’s formula, 568, 569 

of water, Kutter’s formula, 559 

of water, Molesworth’s formula, 
562 

of water, old formuls for, 564 

of water over weirs, 555, 586 


of water, “r for pipes and con- 
duits, table, 559 
of water through orifices, 555, 


584 
Flowing water, horse-power of 589 
water, measurement of, 582 
Flues, collapsing pressure ‘of, 265 
corrugated, British Aaa 266, 702 
corrugated, U.S. rules, 709 
(see also Tubes and Boilers) 
Flywheels, steam-engine, 817-824 
(see Steam-engines) 

Foaming or priming of steam- 
boilers, 552, 718 | f 
Foot and inches, decimal equiva- 

lents of, table, 112 
Foot-pound, unit of work, 428 
Force, centrifugal, 423 

definitions of, 415 
expression of, 429 
graphic representation of, 415 
moment of, 4 
of do ht 427 
of a blow, 430 
of wind, 492 
units of, 415 
Forces, composition of, 415 
equilibrium of, 418 
parallel, 417 
parallelogram of, 416 
parallelopipedon’ of, 416 
polygon of, 416 
resolution of , 415 
se draught in steam-boilers, 
14 


draught, marine practice, 1015 . 
Forcing and shrinking fits, 973 
Forges, fans for, 519 
Forging, heating of steel for, 413 

hydraulic, 618, 620 

of tool steel, 413 
Forgings, strength of, 297 

steel, annealing of, 396 
Foundry iron, analyses of, 371-374 

irons, chemistry of, 370 


INDEX. 


Foundry irons, grades of, 372 
ladles, dimensions of, 953 
practice, 946-953 
practice, moulding-sand, 952 
percger shrinkage of castings, 
practice, use of softeners, 950 

Fractions, 2 
product of, in decimals, 4 

Frames, steam-engine, 817 

Ae structures, stresses in, 440— 

Framing, for bulkheads, table, 287 
for tanks, 287 

Francis’s formule for weirs, 586 

Freezing-point of water, 550 

French measures and weights, 21-26 
thermal unit, 455 

Frequency of alternating currents, 


Friction and lubrication, 928-945 
brakes, capacity of, 980 
ecefficient of, definition, 928 
coefficient of, tables, 929, 930 
fluid, laws of, 929 
gearing, 905 
laws of, of lubricated journals, 

934 
moment of, 938 
Morin’s laws of, 933 
of air in mine passages, 531 
of car-journals, 937 
of lubricated journals, 931 
of ae under steam pressure, 


of motion, 929 
of pivot bearings, 939 
of rest, 928 
of solids, 928 
of steam - -engines, 941 
of steel tires on rails, 928 
rolling, 928, 929 
unlubricated, law of, 928 
work of, 938 
rollers, 940 
Frictional heads, flow of water, 577 
Frustum, of pyramid, 61 
of cone, 61 
of parabolic conoid, 64 
of spheroid, 63 
of spindle, 63 
Fuel, 620-651 
bagasse, 643 
charcoal, 640-642 (see Charcoal) 
coke, 637-639 (see Coke) 
combustion of, 620 
dust, 642 
economizers, 715 
for cupolas, 948 
gas, 646, 1082 (see Gas) 
gas for small furnaces, 651 
heat of combustion of, 621 
peat, 643 
petroleum, 645 
pressed, 632 
sawdust, 643 
straw, 643 
solid, classification of, 623 


INDEX. 


puel. wet tan-bark, 643 
theory of combustion of, 620 
turf, 643 
weight of, 170 
wood, 639. 640 
Functions, trigonometrical, of half 
an angle, 67 
of Te and difference of angles, 
6 
ot twice an angle, 67 
tables of, 159-162 
Furnaces, blast, temperature deter- 
minations in, 452 
corrugated, 266, 709 
down draught, 635, Mle 
for different coals, 635 
gas-fuel for, 651 
industrial, temperatures in, 451 
open- -hearth, temperature deter- 
minations in, 452 
steam-boiler, formule for, 702 
steam-boiler (see Boiler-furnaces) 
Fusible alloys, 333 
plugs in boilers, 710 
Fusibility of metals, 167 
Fusing-disk, 966 
F Using rember atlizes of substances, 


Fusion, latent heat of, 461 
of electric wires, 1032 


g, value of, 424 
Gallons per cubic foot, table, 122 
Galvanic action, corrosion by, 386 
Galvanized wire rope, 228 
Gas, ammonia, 992, 993 
analyses by volume and weight, 
651 


anthracite, 647 
bituminous, 64:7 


carbon, 646 

coal, 651 

fired steam-boilers, 714 

flow of in pipes, 657-659 (see 


Flow of gas) 
fuel, 646-651, 1082 
fuel, cost of, 651 
fuel for small furnaces, 651 


illuminating, 651-659 (cee Illu- | 


minating-gas) 
natural, 649 
producer, 649 
producer, combustion of, 650 
producer, from ton of coal, 649 
sulphur-dioxide, 992 
water, 648, 652-657 (see Water- 
gas) 
and vapor mixtures, laws of, 


80 
Gas-engines, 847-850 
combustion of gas in Otto, 849 
efficiency of, 848 
pressures developed i in, 849 
temperatures developed i in, 849 
tests of, 848 
use of carburetted air in, 849 
Gas-pipe, cast-iron, weight ‘of” table, 
188 


1105 


fue-geo 


Gas-producers. use of steam in, 650 
Gases, absorption of, 480 
Avogadro’s law of, 479 
combustion of, rise of tempera- 
ture in, 623 
densities of, 479 
expansion of, 479 
expansion of by heat, table, 459 
flow of, 480 
heat of combustion of, 456 
law of Charles, 479 
Mariotte’s law of, 479 
of combustion, analyses of, 622 
physical properties of, 479 
specific heats of, 458 
weight and specific gravity of, 
table, 165 
WRse, use of, under boilers, 689, 
690 
Gasoline-engines, 850 
Gauges, limit, for serew threads, 205 
limit, for screw threads, table, 206 
Gauge, wire, 28-30 
sheet metal, 28, 30-32 
Stub’s wire, 29 
decimal, 32 
Gauss, definition and value of, 1052 


Gear, reversing, 816 


worm, 440 

wheels, calculation of speed of, 
891 

wheels, formule for dimensions 
of, 890 


wheels, milling cutters fon, 892 
wheels, proportions of, 8 
Gearing; annular, 898 
bevel, 898 
chordal pitch, 889 
comparison of formule, 902, 903 
cycloidal teeth, 892 
differential, 899 
efficiency of, 899 
forms of teeth, 892-899 
formule for dimensions of, 890 
friction, 905 
involute teeth, 894 
pitch, pitch- circle, etc , 887 
pitch diameters for 1-inch circular 
pitch, 889 
proportions of teeth, 889-891 
racks, 895 
relation of diametral and circular 
pitch, 888 
speed of, oe 
spiral, 897 
strength of, 900-905 
stepped, 897 
toothed-wheel, 439, 887-906 
twisted, 897 
worm, 897, 1086 
Gears, lathe, for screw-cutting, 955 
Generators, electric, 1055-1060, 
1074-1077 
alternating current, 1070, 1077 
(see Dynamo electric machines) 
Geometrical progression, 11 
problems, 37-52 
propositions, 53 


ger-hea 


1106 


German silver, 300, 332 
silver, conductivity of, 1028 
Gilbert, ‘definition and value of , 1050 
Girders, allowed stresses in ‘plate 
and lattice, 264 
building, New York building 
laws, 1020 
iron-plate, strength of, 297 
steam-boiler, rules for, 703 
Warren, stresses in, 445 
Glass, skylight, sizes and weights, 
184 


strength of, 308 
properties of, 167 
Gold-melting, temperature deter- 
minations, 452 
Gold-ore, cubic feet per ton, 170 
Gordon’s formula for columns, 247 
Governors, steam-engine, 836-839 
Grade line, hydraulic, 578 
Grain elevators, 912d 
weight of, 170 
Granite, strength of, 302, 312 
Graphite, lubricant, 945 
paint, 387 
Grate surface in locomotives, 856 
surface of a steam-boiler, 680 
Gravel, cubic feet per ton, 170 
Gravity, acceleration due to, 424 
center of, 418 
discharge elevators, 912a 


specific, 163-165 (see Specific 
gravity) 
Greatest common measure or divi- 
sor, 2 


Greek letters, 1 

Green’s fuel economizer, 715 

Greenhouses, hot-water, heating of, 
542 


steam-heating of, 541 
Grinder, horse-power required to 
run, 963 
Grindstones, speed of, 968, 969 
strains in, 968 
varieties of , 970 
Gurley’s bronze, composition of, 325 
Gun-bronze, variation in strengéh 
of, 321 
Guns, energy of recoil of, se 
formula for thickness of, 2 
Gun-metal neni astabo ction of, 
325 


Guy-ropes for stand-pipes, 293 
Guy-wires, table of sizes, weights, 
and strength of, 223 
Gyration, center of, 420 
table of radii of, 421 
radius of, 247, 249 


Hammering, effect of, on steel, 412 

Hardening of steel, 393, 4 

Hardness of copper-tin alloys, 320 
of water, 553 

Haulage, wire-rope, 912d-916 
bari: it endless rope system, 


wire-rope, engine-plane, 913 
wire-rope, inclined plane, 913 


INDEX. 


Haulage , Wire-rope, tail-rope system, 
913 


wire-rope, tramway, 914 
Hauling capacity of locomotives, 
853 


Hawley down-draught furnace, 712 
Hawsers, flexible steel wire, 223 
Hawser, ‘hemp, weight of, 223 
manila, weight Ofg228 
steel, weight of, 223 
steel, table of sizes and proper- 
ties, 229 
table of comparative strength of 
see hemp, manila, and chain, 
23 
Head, frictional, in cast-iron pipe, 
table, 577 
loss of, 573-579 (see Loss of head) 
of air, due to temperature differ- 
ences, 533 
of water, 557 
of water, comparison of, with 
various units, 548 
of water, value in pounds per 
square ‘inch, table, 189, 190 
Heads of boilers, 706 
of boilers, unbraced wrought - 
iron, strength of, 285 
Heat, 448-480 
conducting power of metals, 469 
conduction of, 468 
convection of, 469 
effect of, on grain of steel, 412 
expansion due to, 459 
eager by electric current, 


latent, 461 (see Latent heat) 

loss by convection, 476 

mechanical equivalent of, 456 

of combustion, 45 

of combustion of fuels, 621 

quantitative measurement of, 455 

Were. power of substances, 
6 


radiation of, 467 
Ft of various substances, 
4 


ily 5 power of substances, 
8 
resistance of metals, 468 
specific, 457-459 (see 
heat) 
steam, storing of, 789 
transmission of, from steam to 
water, 472, 473 
transmission of, in 
tubes, 473 
transmission of, through building 
walls, ete., 478, 534 
transmission of, through plates, 
471-475 
transmission power of various 
substances, 478 
treatment of crucible steel, 411 
unit of, 455, 660 
units per pound of water, 548 
Heaters, electric, 1044 
feed-water, 727, 1083 


Specific 


condenser 


INDEX. 


Heating and Ventilation, 528-546 
blower system, 545, 1081 
boiler-heating surface, 538 
computation of radiating surface, 

536 
heating value of radiators, 534 
heating surface, indirect, 537 
hot-water heating, 542-544 (see 
Hot-water heating) 
overhead steam-pipes, 537 
steam-heating, 534-541 
Steam-heating) 
transmission of heat through 
building walls, 534 

Heating a building to 70°, 545 
by electricity, 546, 1044 
by exhaust steam, 780 
of electrical conductors, 1031 
of greenhouses, 541, 542 
of large buildings, 534 
of steel for forging, 413 
of tool steel, 412 
surface of steam-boiler, 678; meas- 

urement of, 679 
value of coals, 634, 635 
value of wood, 639 - 
Height, table of, corresponding to 
a given velocity, 425 
Heine boiler, test of, with different 
coals, 688 . 
ee springs, capacity of, 349, 


(see 


springs for locomotives, 353 
steel springs, 347 
Helix, 60 
Hemp ropes, strength of, 301 
rope, table of strength and 
weight of, 340 
rope, table of strength of, 338 
Apaatk flat, table of strength of, 
33 
Henry, definition and value of, 1024 
Hobson’s hot-blast pyrometer, 453 
Hodgkinson’s formula for columns, 


- 246 
Hoisting, 906-916 

by hydraulic pressure, 617 

coal, 343 | 

counterpoise system 910 

cranes, 911 (see Cranes) 

effect of slack rope, 908 

endless rope system, 910 

engines, 908 

engines, compressed-air, 505b 

engines, counterbalancing of, 909 

horse-power required for, 907 

Koepe system, 910 

limit of depth for, 908 

loaded wagon system, 910 

pneumatic, 909 

rope, 340 

rope, iron, or steel, dimensions, 
strength and properties, table, 
226 . 

ropes, stresses In, 
planes, 915 

rope, sizes and strength of, 343, 
906 


on inclined 


hea-hyd 1107 


Hoisting rope, tension required to 
prevent slipping, 916 
suspensicn cableways, 915 
tapering ropes, 910, 916 
Holding power of bolts in white 
pine, 291 
power of expanded boiler-tubes, 


power of lag-screws, 290 

power of nails in woods, 291 

power of spikes, 289 

power of wood screws, 290 
Hollow cylinders, resistance of, to 

collapse, 264-266 

shafts, torsional strength of, 282 
Hooks, proportions of, 907 
Horse-gin, 434 
Horse, work of, 434 
Horse-power constants of steam- 

engines, 757 

cost of, 590 

definition of, 27, 429 

electrical, 1031 

electrical, table of, 1039 

hours, definition of, 429 

nominal, definition of, 756 

of fans, 516 

of flowing water, 589 

of locomotive boilers, 679 

of marine boilers, 679 

of a steam-boiler, 677 

of a steam-boiler, builders’ rating, 


of Mepitah done 755-761 

of windmills, 4 

required to eae air, 500 
Hose, fire, friction losses in, 580 
Hot-air engines, 850 
apices pyrometer, 


Hot boxes, 938 
water heating, 542-544 
water heating. arrangement of 
mains, 544 
water heating, computation of 
? radiating surface, 543 
water heating, indirect, 544 
whe heating of greenhouses, 
water heating, rules for, 544 
Barre heating, sizes of pipes for, 
water heating, velocity of flow, 
542 


Hobson’s, 


House-service pipes, flow of water 
| in, table, 578 
Howe truss, stresses in, 445 
Humidity, relative, table of, 483 
Hydraulics, 555- 588 (see Flow of 
water) 
Byd apparatus, efficiency of, 


cylinders, thickness of, 617 
engine, 619 

forging, 618, 620 

formule, 557-564, 1087 
grade-line, 578 

machinery, friction of, 616 


1108 hyd-iro 


Hydraulic pipe, 191 
power in London, 617 
ies thickness of cylinders for, 
presses in iron works, 617 
pressure, hoisting by, 617 
pressure transmission, 616-620 
Pee transmission, energy of, 


pressure transmission, speed of 
Mee’ through pipesand valves, 
6 
ram, 614, 615 
riveting machines, 618 
Hydrometer, 165 
Hivaroinee dry and wet bulb, 
Hyperbola, asymptotes of, 71 
construction of, 49 
equations of, 71 
curve on indicator diagrams, 759 
Hyperbolic logarithms, tables of, 
156-158 


Hypocycloid, 50 


I beams (see Beams) 
Ice, properties of, 550 
making machines, 981-1001 (see 
Refrigerating machines) 
manufacture, 999 
melting effect, 983 
Tiluminating-gas, 651-659 
calorific equivalents of constitu- 
ents, 654 
coal-gas, 651 
fuel value of, 656 
space required for plants, 656 
water-gas, 652 
Impact, 431 
Impedance, 1063 
polygons, 1064-1066 
Impurities of water, 551 
Incandescent lamp, 1042 
Inches and fractions as decimals of 
a foot, table, 112 
Inclined-plane, 437 
motion on, 428 
stresses in hoisting-ropes on, 915 
plane, wire-rope haulage, 913 
Incrustation and scale, 551, 716 
India-rubber, vulcanized, tests of, 
316 
Indicated horse-power, 755 
Indicators, steam-engine, 754-761 
(see Steam-engines) | 
Indicator tests of locomotives, 863 
Indirect heating surface, 537 
Inductance, 1062 
of lines and circuits, 1066 
Ynduction motors, 1072 
Inertia, definition of, 415 
moment of, 247, 419 
Ingots, steel, segregation in, 404 
Iniector, efficiency of, 726 
equation of, 725 c 
Snoxidizable surfaces, production of, 


Inspection of steam-boilers, 720 


INDEX. 


Insulation, Underwriters’, 1033 
Insulators, electrical value of, 1028 
Integrals, 73 
table of, 78, 79 
Integration, 74 
Intensifier, hydraulic, 619 
Interest, 13 
compound, 14 
Interpolation, formula for, 1080 
Involute, 52 
gear-teeth, 894 
gear-teeth, approximation of, 896 
Involution,6 — 
Tridium, properties of, 167 
Iron and steel, 167, 364-389 
and steel boiler-plate, 382 
and steel, classification of, 364 
and steel, effect of cold on 
strength of, 383 
and steel in structures, formule 
for unit strains in, 379 
and steel, inoxidizable surface 
for, 388 
Bnd et latent heat of fusion of, 


and steel, manganese plating of, 
389 j 


and steel, Pennsylvania Rail- 
road specifications for, 378 

and steel, preservative coatings 
for, 387 

and preees rustless coatings for, 


and steel, specific heat of, 459 

and steel, tensile strength at high 
temperatures, 382 

bars (see Bars) 

bridges, durability of, 385 

cast, 365-376 (see Cast iron) 

coefficients of expansion of, 385 

color of, at various tempera- 
tures, 455 

copper-zine alloys, 326 

corrosion of, 386 

corrugated, sizes and weights, 181 

durability of, 385, 386 

flat-rolled, weight of, 172, 173 

for stay-bolts, 379 

for U. S. standard bolts, varia- 
tion in size of, 206 

foundry, analyses of, 371-374 

foundry, chemistry of, 370-374 

malleable, 375, 376 (see Malleable 
iron) 

pig (see Pig iron) | 

plates, approximating weight of, 


plate, weight of, table, 174, 175 

rivet, shearing resistance of, 363 

rope, table of strength of, 338 

rope, flat, table of strength of, 
339 

shearing strength of, 306 

sheets, weight of, 32, 174 

silicon-aluminum alloys, 330 

tubes, collapsing pressure of, 265 

wrought, 377-379 (see Wrought 


iron) 


INDEX. 


Irregular figure, area of, 55, 56 
solid, volume of, 64 

Irrigation canals, 564 

Isothermal compression of air, 499 
expansion of steam, 742 


Japanese alloys, composition of, 326 
Jet-condensers, 839 
Jet propulsion of ships, 1014 
Jet, reaction of, 1015 
Jets, water, 579 
Joints, riveted, 354-363 (see Riv- 
eted joints) 

Joists, contents of, 21 
Joule, definition and value of, 1024 
Joule’s equivalent, 456 
Journal-bearings, 930-939 

cast-iron, 933 

of engines, 810-815 
Journals, coefficients of friction of, 


930 
lubricated, friction of, 931, 932, 
934, 935, 937 


Kelvin’s rule for electric transmis- 
sion, 1036 

Kerosene for scale in boilers, 718 
Keys, dimensions of, 977 

for machine tools, 976 

for shafting, sizes of, 976 

holding power of, 978 

sizes of, for mill-gearing, 975 
Kinetic energy, 429 
King-post truss, stresses in, 442 


Kirkaldy’s tests on strength of 
materials, 296-303 
Knots, 344 


Knot or nautical mile, 17 
Koepe system of hoisting, 910 
Krupp steel tires and axles, 298, 299 
Kutter’s formula, flow of water, 559 
formula, table from, of flow of 
water in pipes, 568, 569 


Ladles, foundry, dimensions of, 953 
Lag-screws, holding power of, 290 
Lacing of belts, 883 
Lamps, arc, 1041 
Lamps, incandescent electric, 1042 
life of, 1042 
specifications for, 1043 
Lamps, Nernst, 1043 
Lap-joints, riveted, 358 
Land measure, 17 
‘“‘Lang Lay” rope, 229 
Lap and lead in slide valves, 824-835 
Latent heat of ammonia, 992 
heat of evaporation, 462 
heat of fusion of iron and steel, 
459 
heats of fusion of various sub- 
stances, 461 
Lathe, change- -gears tee 956 
cutting speed of, 9 
horse-power to ahs “061-963 
rules for screw-cutting gears, 955 
setting taper in, 956 
tools, forms of, 955 


1109 


irr—loc 


Lattice girders, allowed stresses in, 


264 
Law of Charles, 479 
Laws of falling bodies, 424 
of motion, 415 
Lead, properties of, 167 
Pipe. Mit iat and sizes of, table, 
2 


pipe, tin-lined, sizes and weights, 
table, 201 
sheet, weight of, 200 
and tin tubing, 200 . 
waste-pipe, weights and sizes of 
200 
Leakage of steam in engines, 761 
Least common multiple, 2 
Leather, strength of, 302 
Le Chatelier’s pyrometer, 451 
Levelling by barometer, 482 
by boiling water, 482 
Lever, 435 
bent, 436 
Lighting, electric, 1041-1043 
eee protection of chimneys, 


Lignites, analysis of, 631 
Lime, weight of, 170 
and cement mortar, strength of, 
313 
Limestone, strength of, 312, 313 
Limit, elastic, 236-239 
gauges for screw-threads, 206 
Lines of force, 1050 
Links, steam-engine, size of, 815 ' 
steel bridge, strength of, 298 
Link-belting, sizes and weights, 9126 
ee age oa steam-engine, 834—- 
8 


Lintels in buildings, 1020 
Liquation of metals in alloys, 323 
Liquid measure, 18 
Liquids, expansion of, 461 
specific gravity of, 164 
specific heats of, 457, 458 
Locomotives, 851-866 
boiler pressure, 859 
boilers, size of, 855 
compounding of, 863 
counterbalancing of, 864 
cylinders, 854 
dimensions of, 859b-862 
drivers, sizes of, 859 
effect of speed on cylinder pres« 
sure, 859 
efficiency of, 854 
exhaust-nozzles, 856 
fire-brick arches in, 857 
fireless, 866 
forgings, strength of, 297 
formula for curves, 859a 
free-steaming, 855 
fuel waste of, 863 
grate surface of, 856 
hauling capacity of, 853 
horse-power of, 855 
indicator tests of, 863 
light, 865 
link motion, 859a 


1110 


loc-mea 


Locomotives, narrow-gauge, 865 
oil consumption of, 943 
performance of high-speed, 859a 
petroleum-burning, 865 
safe load on tires, 865 
smoke-stacks, 856 
speed of, 859a 
steam distribution of, 858 
steam-ports, size of, 859 
testing apparatus, 863 
tractive power of, 853, 857 
types of, 858 
valve travel, 859 
water consumption of, 862 
weight of, 857 
Wootten, 855 
Logarithms, 77 
hyperbolic, tables of, 156-158 
tables of, 129-156 
use of, 127-129 
Logarithmic curve, 71 
sines, etc., 162 
Logs, area of water required to 
store, 232 
weight of, 232 
Long measure, 17 
measure, French, 21 
Loops of force, 1050 
Loop, steam, 676 
Loss of head, 573-579 
of head, Cox’s formula, 575 
of head, in cast-iron pipe, tables, 
574, 575 
of head in riveted steel pipes, 574 
Low strength of steel, 392 
Lowmoor iron bars, strength of, 297 
Lubrication, 942-945 
Lubricants, examination of oil, 943 
measurement of durability, 942 
oil, specifications for, 944 
qualifications of good, 942 
relative value of, 942 
soda mixture, 945 
solid, 945 
specifications for petroleum, 943 
Lumber, weight of, 232 


Machines, dynamo-electric, 1055- 
1060 (see Dynamo-electric 
machines) 


Machines, efficiency of, 432 
elements of, 435-440 
Machine screws, table of propor- 
tions of, 209 
screws, taps for, 970 
shop, 953-978 
mee horse-power required in, 


tools, keys for, 976 
tools, power required for, 960-965 
tools, proportioning of, 975 
tools, soda mixture for, 945 
Machinery, coal-handling, 912—912d 
horse-power required to run, 964 
Maclaurin’s theorem, 76 
Magnesia bricks, 235 
Magnesium, properties of, 168 
Magnetic balance, 396 


INDEX. 


Magnetic capacity of iron, effect of 
annealing, 396 
circuit, 1051; units of, 1050 
field, strength of, 1057 
Magneto-motive force, 1050, 1051 
Magnets, electro-, 1050-1054. 
Magnolia metal, composition of, 
334 
Mahler’s calorimeter, 634 
Main-rods, steel, specifications for, 


4 
Malleable castings, rules for use of, 
76 


iron, 375 
iron, strength of, 376 
Malleability of metals, table, 169 
Man-wheel, 434 
Man, work of, tables, 433 
Mandrels, standard, 972 
Manganese, properties of, 168 
bronze, 331 
copper alloys, 331 
effect of on steel, 389 
effect of on cast iron, 367 
plating of iron, 389 
steel, 407 
Manila rope, 340; weight 
strength of, 304, 544 
Mannesmann tubes, strength of, 
2 


and 


Manometer, air, 481 
Marble, strength of, 302 
Marine Engineering, 1001-1019 (see 
Ships and Steam-engines) 
Marine boilers, 1015 
engines, comparison of old and 
modern, 1017 
engines, three-stage, 
pansion, 1017-1019 
Marriotte’s law of gases, 479, 742 
Masonry, crushing strength of, 312 
materials, weight and _ specific 
gravity of, 166 
Mass, definition of, 427 
expression of, 429 
Materials, 163-235 
strength of, 236-346 
strength of, . Kirkaldy’s 
296-303 
mice stresses permissible in, 
8 


triple-ex- 


tests, 


various, weights of, 169; table, 166 
Maxima and minima, 76 
without calculus, 1080 
Maxwcts definition and value of, 
D 


Mean effective pressures of adia- 
batically compressed air, 5016 
effective pressure of compressed 
air, table, 502, 503 
Measurements, miner’s inch, 585 
Measurement of air velocity, 491 
of elongation. 243 
of flowing water, 582-588 
of vessels, 1001 
weir-dam, 586 
Measures, apothecaries, 18, 19 
board, 20 


INDEX. 


Measures, circular, 20 


nautical, 17 
of work, power, and duty, 27 
old land, 1 
shipping, 19 
solid or cubic, 18 
square, 1 
surface, 18 
time, 20 
timber, 20 
Measures and weights, metric sys- 
tem, 21—26 
Mechanics, 415-447 
Mechanical equivalent of heat, 456 
powers, 435 
stokers, 711 
ne bree compressed-air tramway, 
5 


Melting-points of substances, 455 
Members, bridge, strains allowed i in, 
262-264 
Memphis bridge, tests of steel in, 393 
bridge, proportions of materials 
in, 381 
Mensuration, 54-64 
Mercurial thermometer 448 
Mercury-bath pivot, 940 
Mercury, compressibility of, 164 
properties of, 168 
Merriman’s formula for columns, 260 
Mesuré and Nouel’s pyrometric tele- 
scope, 453 
Metacentre, definition of, 550 
Metaline lubricant, 945 
Metals, anti-friction, 932 
coefficients of expansion of, 460 
coefficients of friction of, 930 
electrical conductivity of, 1028 
flow of, 973 
heat-conducting pee of, 469 
life of under shocks, 2 
properties of, 167- 60° 
resistance overcome in cutting of, 
960 
specific heats of, 453 
specific gravity of, 164 
weight of, 164 
table of ductility, infusibility, 
malleability, and tenacity, 169 
tenacity of, at various tempera- 
tures, 382-384 
Meter, Venturi, 583 
Meters, water delivered through, 579 
Metric conversion, tables, 23-26 
measures and weights, 21, 22 
screw-threads, cutting of, 956 
Mil, circular, 18, 29 30 
Mile-ohm, weight of wire per, 217 
Mill columns, 1022 
ower, value of, 589 
Milling cutters for gear-wheels, 892 
cutters inserted teeth, 960 
cutters, number of teeth i in, 958 
cutters, pitch of teeth, 957 
cutters, spiral, 960 


1111 


mea=nic 


- 


Milling cutters, steel for, 957 
ete: | cutting speed of, 958- 
machines, feed of, 959, 960 
machines, high results with, 959 
machine vs. planer, 960 

Miner’s inch, 18 
inch measurements, 585 

Mines, centrifugal fans for, 521 

Mine fans, experiments on, 522 
ventilation 531 
ventilation, equivalent orifice, 533 

Modulus of elasticity, 237 
of Age of various materials, 
of resistance, 247 
of rupture 267 

Moisture in atmosphere, 483 
in steam, determination of, 728- 

olor: formula, flow of water, 

Moments, method of, for determin- 

ing stresses, 445 

Moment of a couple, 418 
of a force, 416 
of friction, 938 
of inertia, 247, 419 
of inertia of structural shapes, 

248, 249 
statical, A417 

Momentum, 428 , 

Monobar, 912 

Morin’s laws of friction, 933 

Mortar, strength of, 313 

Motion, accelerated, eat for, 

2 
friction of, 929 
Newton’s laws of, 415 
on inclined planes, 428 
perpetual, 432 
retarded, 424 
Motors, alternating-current, 1071, 


compressed-air, 507 
electric, direct- current, 1055, 
1074-1076 

water-current, 589 
Moulding-sand, 952 
Moving strut, 436 
Mule, work of, 435 
Multiphase electric currents, 1068 
Muntz metal composition of, 325 
Multiple system of evaporation 463 
Mushet steel, 409 


Nails, cut vs. wire, 290 
cut, table of sizes and weights, 213 
wire, table of, sizes and weights, 
214, 215 
Nail- holding power of wood, 291 
Naphtha engines, 850 
Napier’s rule for flow of steam, 669 
Natural gas, 649 
Nautical measure, 17 
mile, 17 
Newton’s laws of motion, 415 
Nickel-copper alloys, 332 


1112 


nic-pip 


Nickel, properties of, 168 
steel, 4 
steel, tests of, 408 
Nozzles for measuring discharge of 
pumping-engines, 584 


Oats, weight of, 170 
Ocean waves, power of, 599 
Derseaes definition and value of, 


Ohm, definition and value of, 1024 
Ohm’s law, 1029 
law, applied. to alternating cur- 
rents, 1064 
law, applied to parallel circuits, 


law. applied to series circuits, 
1029 


Oil, amount needed for engines, 
943 
as fuel, 646 
fire-test of, 944 
lubricating, 942-945 (see Lubri- 
cants 
paraffine, 944 
well, 944 
pressure in bearings, 937 
tempering of steel forgings, 396 
vs. coal as fuel, 646 
Open-hearth furnace, temperature 
determinations in, 452 
steel (see Steel, open-hearth) 
Ordinates and abscissas, 69 
Ores, weight of, 170 
Orifice, equivalent, in mine ventila- 
tion, 533 
flow of air through, 484, 518 
flow of water through, 555 
rectangular, flow of 
through, table, 584 
Oscillation, center of, 421 
radius of, 421 
Overhead steam-pipe radiators, 537 
Ox, work of, 435 
Oxygen, effect of, on strength of 
steel, 391 


water 


xz, value and relations of, 57 
Packing-rings of engines, 796 
Paddle-wheels, 1013, 1014 
Paint, 387 
qualities of, 388 
quantity of, for a given surface, 
388 


Parabola, area of, by calculus, 74 
construction of, 48 
equations of, 70 

Parabolic, conoid, 63 
spindle, 64 

Parallel rods, steel, 

for, 401 
forces, 417 

Parallelogram, area of, 54 
definition of, 54 
of forces, 416 
of velocities, 426 

Parallelopipedon of forces, 416 

Parentheses in algebra, 34 


specifications 


INDEX, 


Partial differential coefficient, 78 
payments, 15 
Payments, equation of, 14 
Peat, 643 
Pelton water-wheel, 597, 1081 
tables of, 598, 599 
Pencoyd shapes, weights and sizes, 
ies Wiss 
Pendulum, 422 
conical, 423 
Percussion, center of, 422 
Perfect discharge elevators, 912a 
Perforated plates, excess of strength 
of, 359 
plates, strength of, 354 
Permeability, magnetic, 1051 
table, 1052 
Permutation, 10 
Perpetual motion, 432 
Rete as a metallurgical fuel, 
burning locomotives, 865 
cost of, as fuel, 646 
engines, 850 
Lima, 645 
products of distillation of, 645 
products, specifications for, 944 
value of, as fuel, 645 
Pewter, composition Of 336 
Phoenix columns, dimensions of, 
257-259 
Phosphorus, 
iron, 366 
influence of, on steel, 389 
Phosphor-bronze, composition of, 
325, 334 
specifications for, 327 
springs, 352 
strength of, 327 
Pictet fluid, 982 
ice-machine, 985 
Piezometer, 582 
Pig iron, analysis of, 371 
chemistry of, 370 
charcoal, strength of, 374 
distribution of silicon i in, 369 
grading of, 365 
influence of silicon, etc., on, 365 
tests of, 369 
Pillars, strength of, 246 
Pins, taper, 972 
Pine, strength of, 309 
Pipes, air-bound, 579 
bent, table of, 199 
block-tin, weights and sizes of, 
table, 200 
capacity of, 573 
cast-iron, 185-190 
cast-iron, gas, weight of, 188 
cast-iron, safe pressures for, ta- 
bles, 189, 190 
cast-iron, thickness of, for various 
heads, 188, 189 
cast - iron water, 
strength of, 251 
cast-iron, weight of, 185, 188 
cast - iron, weight of 12-foot 
lengths, 186 


influence of, on cast 


transverse 


INDEX. 


Pipes, coiled, table of, 199 

effects of bends in, 488, 578, 672 

equation of, 491 

fittings, cast-iron, 
weights, 187 

fittings, spiral-riveted, table, 198 

Dab e for cast-iron pipe, table, 

flanges, extra heavy, table, 193 

flanges, table of standard, 192 

flow of air in, 485, 489 

flow of gas in, 657 

flow of steam in, 669-673 

flow of water in, 557, 566-572 

for steam-heating, 540 

house-service, flow of water in, 
table, 578 

lead, safe heads for, 201 

lead, tin-lined, sizes and weights, 
table, 201 

mec age and sizes of, table, 


sizes and 


loss of air-pressure in,487; tables, 
488, 489, 490 

loss of head in, 573-579 (see Loss 
of head 

ey of water discharged by, 


riveted hydraulic, weights and 
_ safe heads, table, 191 
EvecediKp dimensions of, table, 


riveted, safe pressures in, 707 

riveted-steel water, 295 

spiral riveted, table of, 198 

Steam (see Steam-pipes) 

table of capacities of, 120 

threads on, 195 

wrought-iron, standard, table of 
dimensions, 194. 

volume of air transmitted in, 
table, 486 

water, relation of diameter to 
capacity, 566 

Fao coeaaey radiation through, 


Pistons, steam-engine, 795 
Piston-rings, steam-engine, 796 
Piston-rods, steam-engine, 796-798 
Piston-valves, steam-engine, 834, 
1016 
Pitch, diametral, 888 
of gearing, 887 
of rivets, 357-359 
of screw propellers, 1012 
Pitot tube gauge, 583 
Pivot-bearings, 939 
Pivot-bearing, mercury bath, 940 
Plane, inclined, 487 (see Inclined 
plane) 
surfaces, mensuration of, 54 
Planers, cutting speed of, 953 
Planer, heavy work on, 960 
horse- -power required to run, 963 
tools, forms of, 955 
vs. milling- machine, 960 
Plates, acid-pickled, heat transmis- 
sion through, 474 


ee 


1113 


pip-pou 


Plates, areas of, in square feet, table, 


123 

boiler, strength of, at high tem- 
peratures, 383 

* brass, weight of, table, 202 


corrugated- steel, properties of, 
table, 274 

Carnegie trough, properties of, 
table, 274 


circular, strength of, 283 

copper, weight of, table, 202 

copper, strength of, 300 

flat, cast-iron, strength of, 286 

flat, for steam- boilers, rules for, 
701, 706, 709 

iron, ‘approximating weight of, 


iron, weight of, table, 175 

of different materials, table for 
calculating weights of, 169 

stayed, strength of, 2 

for stand- -pipes, 293 

perforated, strength of, 353, 360 

punched, loss of strength i in, 354 

steel boiler, specifications for, on 

steel, corrections for size of, 
tests, 380 

nee for cars, specifications for, 
401 

steel, specifications for, 400, 401 

steel, tests of, 297, 390 

strength of flat, 283-286 

strength of flat unstayed, 284 

transmission of heat through, 471 

transmission of heat through, air 
to water, 474 

transmission of heat through 
steam to air, 475 i 

Plate-girders, allowed stresses in, 

264 


girder, strength of, 297 
Plating for bulkheads, table, 287 
steel, stresses in, due to water- 
pressure, 287 
for tanks, table, 287 
Platinum, properties of, 168 
wire, 295 
Plugs, fusible, in steam-boilers, 710 
Pneumatic hoisting, 909 
Polarity of ae: magnets, 1054 
Polyedron, 6 
Polygon, area of, 55 
construction o1, 42, 43 
definition of, 55 
table of, 44, 55 
Polygons, ‘impedance, 1064-1066 
of forces, 416 
Polyphase circuits, 1068 
Popp system of compressed air, 


507 
Population of the United States, 12 
Port opening in steam-engines, 828 
Portland cement strength of, 302 
Postal transmission, pneumatic, 509 
Potential energy, 429 


Pound-calorie, definition of, 455 


Pouse Ce square inch, equivalenta 
ot, 


ve 


1114 


pow-rad 


Powell’s screw-thread. 975 
Power, animal, 433 
definition of, 429 
5 of alternating currents, 
1 
hydraulic, in London. 617 
measure of, 27 
of electric circuits. 1031 
of a waterfall, 588 
of ocean waves, 599 
unit of. 429 
Powers of numbers. tables, 7, 86- 
102 


of numbers, algebraic, 33 
Pratt truss, stresses in, 443 
Preservative coatings, 387-389 __ 
Press, hydraulic, thickness of cylin- 
ders for, 288 
Pressed fuel, 632 
Eresesry hydraulic, in iron works, 
6 ; 
punches, etc., 972 
Pressure, collapsing. of flues, 265 
collapsing, of hollow cylinders, 264 
Priming, or Jae Sprott of steam- 
boilers, 552, 718 
Prism, 60 
Prismoid, 61 
rectangular, 61 
Prismoidal formula, 62 
Problems, geometrical, 37-52 
in circles, 39, 40 
in lines and angles, 37, 38 
in polygons, 42 
in triangles, 41 
Producers, gas, use of steam in, 650 
Producer-gas, 646-651 (see Gas) 
Progression, arithmetical and geo- 
metrical, 11 
Prony brake, 978 
Propeller, screw, 1010-1013 (see 
Screw-propeller 
shafts, strength of, 299 
Proportion, 5 
compound, 6 
Pulleys, 873-875 
arrangement of, 874 
arms of, 820 
cone, 874 
convexity of, 874 
differential, 439 
for rope-driving, 925 
or blocks, 438 
proportions of, 873 
speed of, 884, 891 
Pulsometer, 612 
tests of, 613 
Pumps and pumping-engines, 601- 
614 


air, for condensers, 841 

air-lift, 614 

boiler-feed, 605 

boiler-feed, efficiency of, 726 

centrifugal, 606-609 

centrifugal, as suction-dredge, 609 

centrifugal, efficiency of, 608 
centrifugal, relation of height of 

lift to velocity, 606 


INDEX 


Pumps. centrifugal, sizes of, 607 
centrifugal tests of 609 
circulating. for condensers. 843 
compressed-air mine, 511 
depth of suction of. 602 ~ 
direct-acting, efficiency of, 604 
direct-acting , proportions of steam 

cylinder, 602 
duplex steam. sizes of, 604 
feed for marine engines, 843 
horse-power of, 601 
jet, 614 
leakage test of, 611 
lift’, water raised by, 602 
piston speed of, 605 
single steam, sizes of, 603 
eared of water in passages of, 602, 
suction of, with hot water 602 
theoretical capacity of, 601 
vacuum, 612 

Pump-valves, 606 

Pumping by compressed air. 505a 

Pe engines, duty trials of, 


economy of, 782 
table of data and results of duty 
trials of, 611 
triple-expansion, 782 
use of nozzles to measure dis- 
charge of, 584 
Punches, clearance of, 972 
spiral, 972 
Punched plates, strength of, 354 
Punching, effect of, on structural 
steel, 394 
and drilling of steel, 395 
Purification of water, 554 
Pyramid, 60 
frustum of, 61 
Pyrometer, air, Wiborg’s, 453 
copper-ball, 451 
fire-clay, Seger’s, 453 
Hobson’s hot-blast, 453 
Le Chatelier’s, 451 
principles of, 448 
thermo-electric, 451 
Uehling-Steinbart, 453 
Pyrometric telescope, 453 
Pyrometry, 448-455 


Quadratic equations, 35 
Quadrature of plane figures, 74 

of surfaces of revolution, 75 
Quadrilateral, definition of, 54 

area of, 54 

area of, inscribed in circle, 54 
Quadruple-expansion engines 772 
el res measurement of heat, 


Quarter-twist belt, 883 

Quartz, cubic feet per ton, 170 

Queen-post truss, stresses in, 442 
inverted, stresses in, 443 


Rack, gearing, 895 
Radiating power of substances, 468 


INDEX, 


Radiating surface, computation of, 
for hot-water heating, 543 
surface, computation of, ior 
steam heat, 536 
Radiation of heat, 467 
of various substances, 475 
table of factors for Dulong’s laws 
of, 476 
Radiators, experiments with, 545 
heating value of, 477, 534 
overhead steam-pipe, 537 
Radius of curvature of wire rope, 922 
of gyration, 247, 420 
of gyration, graphical method for 
finding, 248 
of gyration of structural shapes, 
4 


249 
of oscillation, 421 
Rails, size of bolts for splicing 210 
size of spikes for, 212 
steel, maximum safe load on, 865 
steel, specifications for, 398 
steel, strength of, 298 
Railroad axles, 384 
trains, resistance of, 851 
trains, speed of, 859 
Railways, electric, 1041 
narrow-gauge, 865 : 
Railway, street, compressed-air, 
510, 511 
Ram, hydraulic, 614 
Ratio 5 
Reactance of alternating eurrents, 
1063 


Reamers, taper, 972 
Réaumer thermometer-scale, 448 
Recalescence of steel, 402 
Receiver-space in engines, 766 
Reciprocals of numbers, tables of, 
80-85 
use of, 85 
Rectangle definition of, 54 
value of diagonal of, 54 
Red lead as a preservative, 387 
Reduction, ascending and descend- 
ing, 5 
Rectangular prismoid, 61 
Reese’s fusing disk, 966 
Reflecting power of substances, 468 
Refrigerating-machines air-ma- 
chines, 983 
ammonia-absorption, 984, 987 
ammonia-compression, 983, 986 
eylinder-heating, 997 
ether-machines, 983 
heat-balance, 990 
ice-melting effect, 983 
liquids for, pressures and boiling- 
points, 982 
operations of, 981 
pipe-coils ior, 985 
pertormances of, 994-997 
properties of brine, 994 
properties of vapor, 993 
relative efficiency of, 988 
relative performance of ammonia- 
compression and _ absorption 
machines, 983 


1115 


rad-riv 


Refrigerating-machines, sulphur-di- 
oxide machine, 985 
temperature range, 991 
tests of, 990-992 
using water vapor, 988 
Refrigeration, 981-1001 
means of applying the cold, 999 
Registers for steam-heating, 539 
Hespoulse experiments on steam, 
Reluctance, magnetic, 1050, 1051 
Reservoirs, evaporation of water 
in, 463 
Resilience, 238 
elastic, 270 
Resistance, elastic, to torsion, 282 
electrical, 1027-1032 
electrical, effect of annealing, 
1029 


electrical, effect of temperature, 
"1029 

electrical, in circuits, 1029-1031 
electrical, internal, 1031 
electrical, standard of, 1029 

ele te of copper wire, 1029, 


electrical, of steel, 403 
elevation of ultimate, 238 
of metals to repeated 


238 
modulus of, 247 
of ships, 1002 
of trains, 851 
work of, of a material, 238 
Resolution of forces, 415 
Reversing-gear for steam-engines, 
dimensions of, 813 
Retarded motion, 424 
Tippee definition and area of, 


shocks, 


5 
ae definition and area of, 


Rivet-iron and -steel, shearing re- 
sistance of, 363 
Rivets, bearing pressure on, 356 
cenerhent, for boilers, weight. of, 
21% A 
diameters of, table, 360 
in steam-boilers, rules for, 700 
pitch of, 359 
pressure required to drive, 1080 
rules for strength of, 360 
steel, specifications for, 401 
Riveting. efficiency of different 
methods, 355 
hand, strength of, 355 
hydraulic, strength of, 355 
machines, hydraulic, 618 
of structural steel, 394 
pressure required for, 362 
Riveted iron pipe, dimensions of, 
table, 197 
joints, 299, 354-363 
joints, drilled vs. punched holes 


joints, efficiencies of, 359, 361 
joints, notes on, 356 
joints, proportions of, 358, 359 


1116 


riv-sel 


Riveted joints. single-riveted lap, 


357 

joints, Lanes pineaeth of 
double-riveted, 

joints, tests of aa ible eiveted 


lap and butt, 360 
joints, tests of, ‘table, 303 
pipe, flow of water in, 574 
pipe, weight of iron for, 197 
Roads, resistance of carriages on, 
435 
Rock-drills, air required for, 505a 
requirements of air-driven, 506 
Rods of different materials, table 
for calculating weights of, 
169 
Roof-truss, stresses in, 446 
Roofs, safe loads on, 184, 281 
strength of, 1019 
Roofing materials, 181-184 
materials, weight of 
184 
Roller-bearings, 940 
Rolling of steel effect of finishing 
temperature, 392 
Ropes and cables, 338-346 
eable-traction, 226 
charcoal-wire, 228 
Gagton and hemp, strength of, 
for coal-hoisting, 343 
hemp and wire, table of, working 
loads for, 339 
hemp, table of, strength and 
weight of, 340 
hoisting (see Hoisting-rope) 
**Lang Lay,’’ 229 
locked-wire, 231 
manila, 340 
eee weight and strength of, 
44 


various, 


splicing of, 341 
steel flat, ‘table of sizes, weight, 
and strength, 229 
steel-wire hawsers, 229 
stevedore, 340 
table of, strength of iron, steel, 
and hemp, 338 
table of rength of flat iron, 
steel, and hemp, 339 
technical terms relating to, 341 
transmission, 340 
wire (see Wire-rope) 
Rope-driving, 922-927 
English practice, 926 
horse-power of, 924 
pulleys for, 925 
sag of rope, 925 
tension of rope, 925 
various speeds of, 924 
weight of rope, 928 
Rotary blowers, 526 
steam-engines, 791 
Rotation. accelerated, work of, 


Ee belting, 887 
vulcanized, tests of, 316 
Rule of three, 6 


. Screws, 


INDEX. 


Rupture, modulus of, 267 
Rustless coatings for iron, 388 


Safety, facturc of, 314 

valves for steam-boilers, 
724 

Salt brine, properties of, 464 
manufacture, evaporation in, 463 
solubility of, 464 
solution, specific heat of, 458 
weight of, 

Sand-blast, 066 

Sand, cubic feet per ton, 170 
moulding, 952 

Sandstone, strength of, 312 

Saturation point of vapors, 480 

Sawdust as fuel, 643 

Sawing metal, 966 

Scale, boiler, 716 
boiler, analyses of, 552 

Scales, thermometer, comparison 

of, 448; table, 449 
Scantling, table of contents of, 21 
Boni e anti-friction curve, 50 
3 


Screw, 60 
bolts, efficiency of, 974 
conveyors, 912d 
differential, 439 
differential, efficiency of, 974 
efficiency of, 974 
(element of machine), 437 
propeller, 1010-1013 
propeller, coefficients of, 1011 
propeller, efficiency of, 1012 
propeller, slip of, 1012 
eap, table of 


721~ 


standard, 
208 
lag, holding power of, 290 
machine, proportions of, 209 
machine, taps for, 970 
set, table of standard, 208 
threads, 204—207 
threads, English standard,. 205 
threads, limit gauges for, 206 
threads, metric. cutting of, 956 
thread, Powell’s, 975 
threads, Sellers. 204 
threads, standard for taps, 207 
threads, U. S. standard, 204 
threads, U. S. standard, table of 
pitches. 204 
threads, U. S. standard, table of 
proportions of, 205 
threads, Whitworth, table, 205 
wood, holding power of, 290 
Sea- water, freezing-point of, 550 
Secant of an angle, 65 
table of, 159-162 
Sector of circle, 59 
Sediment in steam-boilers, 717 
Seger’s fire-clay pyrometer, 453 
Segment of circle, 59 
Seema circular, table of areas of, 
1 


Segregation in steel ingots, 404 
Self-inductance of lines and gir- 
cuits, 1066 


INDEX. 


Separators, steam, 72 
Set-screws, holding power of, 977 
standard, table of, 208 
Sewers, grade of, 566 
Shaft-bearings, 810 
Shaft-governors, 838 
Shafts, hollow, 871 
see torsional strength of, 282, 
steam-engine, 806-813 
sect propeller, strength of, 299, 


815 
Shafting, 867-872 
deflection of, 868 
formule for, 867 
Lee transmitted by, 869- 
8 
horse-power to drive, 963 
laying out, 871, 872 
keys for, 975 
Shaku-do, Japanese alloy, 326 
Shapes of test specimens, 243 


structural, properties of, 272-280 


Shear and compression combined, 
282 


and tension combined, 282 
poles. stresses in, 442 
Shearing, effect of, on structural 
steel, 394 
resistance of rivets, 363 
unit strains of, 379 
strength of iron and steel, 306 
strength of woods, table, 312 
Sheaves, wire-rope, 917, 919 
Shells of steam-boilers, material 
for, 700 
spherical, strength of, 286 
Shell-plate formulze for steam-boil- 
ers, 701 
Sheet brass, weight of, 203 
copper, weight of, 202 
metal, strength of, 300 
metal, weight of, by decimal 
gauge, 32 , 
Sheets, iron and steel, weight of, 


174 
Shibu-ichi, Japanese alloy, 326 
Shingles, weights and areas of, 183 
Ships, coefficient of fineness of, 1002 
coefficient of performance, 1003 
coefficient of water-lines, 1002 
displacement of, 1001, 1009 
horse-power of, 1009 


horse-power for given speeds, 
1006 

horse-power of, from wetted sur- 
face, 1005 


jet propulsion of, 1014 

resistance of, 1002 

resistance of, per horse-power 

1006 

rules for measuring, 1001 

rules for tonnage, 1001 

speed in canals, 1008 

trials of, 1007, 1008 

twin-screw, 1017 

wetted surface of, 1005 
Shipping measure, 19, 1001 


1117 


sep-sol 


Shocks, resistance of metals to re- 
peated, 240 
stresses produced by, 241 
pass ete Bde by compressed air, 


Short circuits, electric, 1036 
Shee clan standard, sizes of, 


Shrinkage fits, 973 
of cast iron, 368 
of castings, 951 
Signs, arithmetical, 1 
Sign of differential coefficients, 76 
of trigonometrical functions, 66 
Silicon-aluminum-iron alloys, 330 
Silicon-bronze, 328 
Silicon-bronze wire, 225, 327 
ae of, in pig iron, 


influence of, on cast iron, 365, 370 
influence of, on steel, 389 
relation of, to strength of cast 
iron, 369, 370 
Silver-melting, temperature deter- 
minations, 452 
Silver, properties of, 168 
ore, cubic feet per ton, 170 
Simplex gas-engine, test of, 848 
Smokestack guys, 223 
Simpson’s rule, 56 
Sine of an angle, 65 
tables of, 159-162 
Single-phase circuits, 1068 
Sinking-funds, 17 
Siphon, 581, 582 
Skin effect of alternating currents, 


1065 
Skylight glass, sizes and weights, 184 
Slag in cupolas, 948 
in wrought iron, 377 
Cea roofing, dimensions and areas, 


roofing, weight of, 183 
Slide-valves, steam-engine, 824-835 
(see Steam-engines) 
Slope, table of, and fall in feet per 
mile, 558 
Smoke prevention, 712-714 
Smoke-stacks, locomotive, 856 
sheet-iron, 741 
Snow, weight of, 184, 281, 550 
Soapstone lubricant, 945 
strength of, 312 : 
Soda mixture for machine tools, 


Softeners in foundry practice, 950 

Softening of water, 554 

Soils, resistance of, to erosion, 565 

Solder, brazing, composition of, 325 
for aluminum, 319 

Solders, composition of various, 


Soldering aluminum bronze, 329 
Solid bodies, mensuration of, 60-64 
measure, 18 
of revolution, 62 
Solubility of common salt, 463 
of sulphate of lime, 463 


1118 


sou-sta 


Sources of energy, 432 
Specific gravity, 163-165 
gravity and Baume’s hydrom- 
, eter compared, table, 165 
gravity of brine, 464, 994 
gravity of cast iron, 374 - 
gravity of copper-tin alloys, 320 
gravity of copper-tin-zinc alloys, 
323 
gravity of gases, 166 
gravity of ice, 550 
gravity of metals, table, 164 
gravity of liquids, table, 164 
gravity of steel, 403 
gravity of stones, brick, etc., 166 
Specific heat, 457-459 
heat, determination of, 457 
heat of air, 484 
heat of ammonia, 992 
heats of gases, 458 
heat of ice, 550 
heat of iron and steel, 459 
heat of liquids, 457 
heats of metals, 458 
heat of saturated steam, 660 
heat of superheated steam, 661 
heat of water, 550 
heats of solids, 457, 458 
heat of woods, 458 
Specifications for boiler-plate, 399 
for car-wheel iron, 375 
for cast iron, 374 
for chains, 307 
for elliptical steel springs, 352 
for helical steel springs, 353 
for incandescent lamps, 1043 
for oils, 945 
for petroleum lubricants, 943 
for phosphor-bronze, 327 
for spring steel, 401 
for steel axles, 397 
for steel billets, 401 
for steel castings, 397, 406 
for steel crank-pims, 401 
for steel forgings, 397 
for steel main-rods, 401 
for steel parallel rods, 401 
for steel rails, 398 
for steel rivets, 399, 401 
for steel splice-bars, 398 
for steel tires, 398 
for steel in Memphis bridge, 382 
for structural steel, 400 ’ 
for structural steel for bridges, 
399 
for Serur aaa steel for buildings, 
398 
for structural steel for ships, 399 
for tin and terne-plate, 1088 
for wrought iron, 378, 379 
Speed of cutting-tools, 953, 954 
of vessels, 1006-1009 
Sphere, measures of, 61 
Spheres of different materials, table 
for calculating weight of, 169 
table of volumes and areas, 118 
Spherical segment, area and vol- 
ume of, 2 


INDEX. 


Spherical polygon area of 61 
triangle area and volume of, 61 
zone, area and volume of 62 
shells. strength of, 286 
shell, thickness of, to resist a 

given pressure, 286 
Spheroid, 63 i 
Spey boat, sizes and weights of, 
212 
holding power of, 289 
street-railway, 21 
track, 212 
wire 213 
wrought, 213 

Spindle, surface and volume of, 63 

Spiral. 50, 60 
conical, 60 
construction of, 50 
plane, 60 
gears, 897 

Spiral-riveted pipe, table of, 198 
riveted pipe-fittings, table, 198 

Splice-bars, steel, specifications for, 

398 

Splicing of ropes, 341 
of wire rope, 346 

Spring steel, strength of, 299 

Springs, 347-353 
elliptical, 347 
elliptical, sizes of, 352 
elliptical, specifications for, 352 
for engine-governors, 838 
helical, 347 
helical, formule for deflection and 

strength, 348 
helical, specifications for, 353 
helical, steel, table of capacity 
and deflection, 347, 353 
laminated steel. 347 | 
locomotive, specifications for, 400 
phosphor-bronze, 352 
sermi-elliptical, 347 
to resist torsion, 352 

Spruce, strength of, 310 

Spur gears, machine-cut, 905 

Square, definition of, 54 
measure, 18 
root, 8 
roots, tables of, 86-101 
value of diagonal of, 54 

Squares of numbers, table, 86-101 
of decimals, table, 101 

St. Gothard tunnel, loss of pressure 

in air-pipe mains in, 490 

Stability, 417 
of a dam, 417 

Stand-pipes, 292-295 
failures of, 294 
guy-ropes for, 293 
heights of, to resist wind-pres- 

sure, 293 
heights of, for various diameters 
and plates, table, 294 
thickness of bottom plates, 295 
thickness of plates in, 293 
wind strain on, 293 
Stand-pipe at Yonkers, N. Y., 295 
Statical moment, 416, 417 


INDEX. 


Stay-bolt iron, 379 

Stayed surfaces, strength of, 286 

Stays, steam-boiler, loads on, 703 
steam-boiler, material for, 703 

Stay-bolts in steam-boilers, 710 

Steam, 659-676 


determining moisture in, 728- 
731 


dry, definition, 659 

dry, identification of, 730 

expansion of, 742, 743 

flow of, 668-674 (see Flow of 
steam ) 

gaseous, 661 

generation of, from waste heat of 
coke-ovens, 638 

heat required to generate 1 pound 
of, 660 

latent heat of, 659 

loss of pressure in pipes, 671 

mean pressure of expanded, 743 

moisture in, 728 

properties of, as applied to steam- 
heating, 540 

Regnault’s experiments on, 661 

relative volume of, 660 

saturated, definition, 659 

saturated, density, volume, and 
latent heat of, 660 

saturated, properties of, table, 
663-668 

saturated, specific heat of, 660 

saturated, temperature and pres- 
sure of, 659 

saturated, total heat of, 659 

superheated, definition, 659 

superheated, economy of steam- 
engines with, 783 

superheated, properties of, 661 

superheated, specific heat of, 661 

temperature of, 659 

weight of, per cubic foot, table, 
662 

wet, definition, 659 

work of, in single cylinder, 746- 


753 
Steam-boiler, 677-731 
Steam-boilers, bumped heads, rules 
for, 706 
conditions to secure economy of, 
682 
construction of, 700-711, 1085 
construction of, United States 
merchant-vessel rules, 705-708 
corrosion of, 386, 716-721 
dangerous, 720 
domes on, 711 
down-draught furnace for, 712 
effect of heating air for furnaces 
of, 687 
efficiency of, 683 
explosive energy of, 720 
factors of evaporation, 696-699 
factors of safety of 700 
feed-pumps for, efficiency of, 726 
feed-water heaters for, 727 
feed-water, saving due to heat- 
ing of, 727 


sta—ste + OTTs 


Steam-boilers, flat platesin rules for, 


701, 706, 709 

flues and gas-passages, propor- 
tions of, 680 

foaming or priming of, 552, 718 

for blast-furnaces, 689 

forced combustion in, 714 

fuel economizers, 715 

furnace formule, 702 

furnaces, height of, 711 

fusible plugs in, 710 

gas-fired, 714 

girders, rules for, 703 

grate-surface, 678, 680 

grate-surface, relation to heating 
surface, 682 

gravity feeders, 1083 

heat losses in, 684 

heating-surface in, 678 

heating-surface, relation of. to 
grate-surface, 682 - 

height of chimney for, 735 

high rates of evaporation, 687 

horse-power of, 677 

incrustation of, 716-721 

Injectors on, 725, 726 (see Inject- 

ors) , 

ON of, Philadelphia rules, 


_marine, corrosion of, 719 


maximum efficiency with Cum- 
berland coal, 689 

measure of duty of, 678 

mechanical stokers for, 711 

performance of, 681-685 

plates, ductility of, 705 

plates, tensile strength of, 705 

pressure allowable in, 706-708 

proportions of, 678-681 

proportions of grate-spacing, 681 

proportions of grate-surface, 680 

proportions of heating-surface, 


proportions of grate- and heating- 
surface for given horse-power, 
678 | : 

proportions of, .eating-surface per 
horse-power, 679 

safe working-pressure, 707 

Tiveting, rules for, 700 

safety-valves for, 721-724 

safety-valves, discharge of steam 
through, 724 

safety-valves, formule for, 721 

safety-valves, spring-loaded, 724 

scale in, 716 

scale compounds, 716 

sediment in, 717 

shells, material for, 700 

shell-plate formule, 701 

smoke prevention, 712-714 

stays, loads on, 703 

stays, material for, 703 

stay-bolts in, 710 

strains caused by cold feed-water, 


Wa 
strength of, 700-711 
strength of rivets, 700 


1120 ¢ ste 


Steam-boilers, tannate of soda com- 


pound in, 718 
tests of, 685-699 
tests of, at Centennial Exhibition, 
685 
tests of, hydraulic, 700 
tests, rules for, 690-695b 
tubes, holding power of, 704 
tubes, iron vs. steel, 704 
tubes, material for, 704, 709 
tube plates, rules for, 704 
use of kerosene i in, 718 
use of zinc in, 720 
using waste gases, 689, 690 


Steam-calorimeters, 728-731 
Steam-domes on boilers, 711 
Steam-engines, 742-847 


advantages of compounding, 762 

at Columbian Exposition, 774 

bearings, size of, 810-813 

bed-plates, dimensions of, 817 

capacity of, 748 

clearance in, 751 

compound, 761-768 

compound, best. cylinder ratios, 
768 


compound, calculation of cylin- 
ders of, 768 

compound, combined indicator 
diagrams, 764 

compound, condensing, 788 

compound, cylinder proportions 
in, 765 

compound, economy of, 780 

compound, efficiency of , 784 , 

compound, expansions in two- 
cylinder, 765 

compound, formule for expan- 
sion and work in, 767 

compound, high-speed, 
mances of, 778, 779 

compound, high-speed, sizes of, 
778, 779 : 

compound marine, approximate 
horse-power of, 766 

compound marine, cylinder ra- 
tios of, 766 j 

compound, non-condensing, effi- 
ciency of, 784 } 

compound, pressures in two 
cylinders, 765 

compound, receiver type, 762 

compound, receiver, ideal dia- 
gram, 763 ’ é 

compound, receiver space in, 
766 

compound, steam-jacketed, per- 
formances of, 778 

Sopa ao steam-jacketed, test 
ol, 

compound, Sulzer, water con- 
sumption of, 783 

compound, two vs. three cylin- 
ders, 781 f 

compound, velocity of steam in 
passages of, 772 ‘ 

compound, water consumption 
of, 7 


perfor- 


INDEX. 





Steam-engines, ¢ompound, Wolff 


type, 762 
er Wolff, ideal diagram, 
63 


compression, best periods of, 752 

compression, effect of, 751 

condensers, 839-847 (see Con- 
densers) 

connecting-rods, dimensions of, 
799 Oe 

connecting-rod ends, 800 

Corliss, 773, 780 

cost of, 1085 

counterbalancing of, 788 

cranks, dimensions of, 805 

crank-pins, dimensions of, 801- 
804 

crank- -pins, pressure on, 804 

crank-pins, strength of, "803 

crank- shafts, dimensions of, 813 

crank-shafts for torsion and flex- 
ure, 814 

Sar culds for triple-expansion, 

erank-shafts, three-throw, 815 

crosshead. and crank, relative 
motion of, 831 

crosshead-pin, dimensions of, 804 

cut-off, most economical point 
of, 777 

cylinder condensation, 
ments on, 753 

ere condensation, loss by, 

cylinders, dimensions of, 792 

cylinder-heads, dimensions of , 794. 

eylinder-head bolts, size of, 795 

dimensions of parts of, 7 92-817 - 

eccentrics, dimensions ‘of; 816 

eccentric- tods, dimensions of, 816 

economic performance of, 7 775-791 

economy at. various speeds, 786 

ii iiee effect on, of wet steam, 


experi- 


economy of compound vs. triple- 
expansion, 781 

economy of, in central stations, 

economy of, simple and com- 
pound compared, 780 

wey! under variable loads, 
84 

ee with superheated steam. 
83 


effect of moisture in steam, 781 

ss ated 1-H. Bx of compound, 

estimating I.H.P. of single-cylin- 
der, 755 

efficiency in thermal units. per 
minute, 749 

oreo steam used for heating, 


expansions in, table, 750 

expansive working of steam in, ta« 
ble, 747 

flywheels, 817-824 

flywheels, arms of, 820 


INDEX. 


Steam-engine, flywheels, centrifugal 


force in, 820 
flywheels, diameters of, 821 
flywheels, formule for, 817 
flywheels, thickness of rim of, 823 
flywheels, speed variation in, 817 
flywheels, strains in, 822 
flywheels, weight of, 818, 819 
flywheels, wire-wound, 824 
flywheels, wooden rim, 823 
foundations embedded in air, 789 
frames, dimensions of, 817 
friction of, 941 
governors, fly-ball, 836 
governors, flywheel, 838 
governors, shaft, 838 
governors, springs for, 838 
guides, size of, 798 
high piston speed in, 787 
high-speed Corliss, 787 
ge ro: performances of, 777- 

8 


high-speed, sizes of, 777-780 

horse-power constants, 756-758 

indicated horse-power (I.H.P.) 
of single-cylinder, 755-761 

indicator diagrams, 754 

indicator diagrams, to draw 
clearance line on, 759 

indicator diagrams, to draw ex- 
pansion curve, 759 

indicators, effect of leakage, 761 

indicators, errors of, 756 

indicator rigs, 759 

limitation of speed of, 787 

links, size of, 815 

link motions, 834-836 

mean and terminal pressures, 743 

marine, 1015-1019 

mean effective pressure, calcula- 
tion of, 744 

measures of duty of, 748 

non-condensing, 776, 778, 779 

oil required for, 943 

pipes for, 673 

pistons, clearance of, 792 

pistons, dimensions of, 795 

piston-rings, size of, 796 

piston-rods, fit of, 796 

piston-rods, size of, Dr 

piston-rod guides, size of, 798 

piston-valves, 834 

prevention of vibration in, 789 

progress in, 773 

proportions of, 792-817. 1086 

quadruple expansion, 772, 773 

ratio of expansion of steam, 745 

reversing gear, dimensions of, 


816 
rotary, 791, 792 
shafts, bearings for, 810-813 
shafts, bending resistance of, 808 
shafts, dimensions of, 806-— 813 
shafts, equivalent twisting mo- 
ment of, 808 
shafts, flywheel, 809 
shafts, twisting resistance of, 806 
single- ‘cylinder, economy of, 775 


1121 


ste % 


Steam-engines, single-cyiinder, water 


consumption of, 7 
single-cylinder, high-speed, sizes 
and performances of, 778 
pier an oo crank-angles, table, 


slide-valves, cut-off for various 
lap and travel, table, 831, 
832 

slide-valve, definitions, 824 

slide-valve’ diagrams, Sweet’s, 


slide-valve diagrams, Zeuner’s, 
iZ 


slide-valve, diagram of port. open- 
ing, cut- off, and travel, 833 

slide-valve, effect of changing lap, 
lead, etc., 829 

sg -valve, ‘effect of lap and lead 

slide-valve, lead, 829 

slide-valve, port opening, 828 

slide-valve, ratio of lap to travel, 
829, 831 

slide- valves, relative motion of 
crosshead and crank, 831 

slide-valve, setting of, 834 

small, coal consumption of, 786 

small, water consumption of, 
786 

steam consumption per _ horse- 
power-hour, 750 

steam-jackets, influence of, 787 

superheated steam in, 783 

three-cylinder, 815 

to change speed of, 837 

to put on center, “834 

eat granny “769-772, 1017- 


triple-expansion and compound, 
relative economy, 781 

triple-expansion, crank-shafts for, 
815 

triple-expansion, cylinder pro- 
portions, 769 

triple-expansion, cylinder pro- 
portion formule, 769-771 

triple-expansion, cylinder diame- 
ters, 773 

et aaa eylinder ratios, 

i 


triple-expansion, high-speed, sizes 
and performances of, 779, 
780 
2a reaget SeeT non-condensing, 
779 
triple-expansion, 
cranks in, 772 
triple-expansion, steam-jacketed, 
performances of, 779, 
triple-expansion, Sulzer, water 
consumption of, 783 
triple-expansion, theoretical mean 
effective pressures, 770 
triple-expansion, types of, 771. 
triple-expansion, water consump- 
tion of, 777 
valve-rods, dimensions of, 815 


sequence of 


1122 ste 


Steam-engines, water consumption 


OF 753, 1104 (14, 180,090; (80 
water consumption from indica- 
tor-cards, 7 
work of one pound of steam, 749 
work of steam in single-cylinder, 
746-753 
wrist-pin, dimensions of, 804 


Steam heat, rotate, of, 789 


heating, 534-541 
heating, diameter of supply mains, 
539 


heating, indirect, 537 

heating, indirect, size of registers 
and ducts, 539 

heating of erpeg no usey 541 

heating, pipes for, 540 

heating, properties of steam and 
condensed water, 540 

jackets on engines, "787 

jet blower, 527 

jet exhauster, 527 

jet ventilator, 527 


loop, 676 C3 
-metal, composition of, 325 
pipes, 674-676 


pipes, copper, strength of, 675 
pipes, copper, tests of, 674 

pipes, failures of, 676 

pipes for engines, 673 

pipes for marine engines, 674, 


pipes, riveted-steel, 675 

pipes, uncovered, loss from, 676 
pipes, valves in, 675 

pipes, wire- wound, 675 

pipe coverings, tests of, 471 
power, cost of, 790 

power, cost of coal for, 789 
separators, 728 

turbines, 790 . 

vessels (see Ships) 


Steel, 389-414 


aluminum, 409 : 

analyses and properties of, 389 

and iron, classification of, 364 

annealing of, 412, 413 

axles, specifications for, 397 

axles, strength of, 299 

bars, "effect of nicking, 402 

beams, safe load on, 269 

Bessemer basic, ultimate strength 
of, 390 

eer es range of strength of, 
391, 

billets, ere ae eal for, 401 

blooms, weight of, table, 176 

bridge-links, strength of, 297 

burning carbon out of, 402 

castings, 405 

castings, specifications for, 397, 
406 


castings, strength of, 299 
chrome, 409 

old-drawn, tests of, 305 
cold-rolled, tests of, 305 
color-scale for tempering, 414 
columns, 256-261 


INDEX. 


Steel columns, Merriman’s tables of 


261 

crank-pins, specifications for, 401 

crucible, 410-414 

crucible, analyses of, 411 

erg pie effect of heat treatment, 
411 

ores selection of grades of, 

1 

crucible, specific gravities of, 411 

effect of ‘annealing on grain of, 392 

effect of annealing on magnetic 
capacity, 396 

effect of cold on strength of, 383 

effect of finishing temperature in 
rolling, 392 } 

effect of heat on grain, 412 

eter of oxygen on strength of, 

electrical conductivity of, 403 

eye-bars, test of, 304 

failures of, 403 

fluid- compressed, 410 

for car-axles, specifications, 401 

for rails, specifications, 401 

for milling cutters, 957 

forgings, annealing of, 396 

forgings, oil- tempering of, 396 

forgings, specifications for, 397 

hardening of, 393 

heating of, for forging, 413 

in Memphis bridge, tests of, 393 

ingots, segregation in, 404 

kinds of, for different uses, 397 

life of, under shock, 240 

low strength of, 392. 

main-rods, specifications for, 401 

manganese, 407 

manganese, abrasion of, 407 

mixture of with cast iron, 375 

Mushet, 4 

nickel, 407 

nickel, tests of, 408 

open- “hearth, mange of strength 
of, 391 

open- Ricard pho tty strength 
of, 391 

parallel-rods, specifications, 401 

plates (see Plates, steel) 

rails, specifications for, 398 

rails, strength of, 298 

range of strength in, 391, 392 

recalescence of, 402 

relation between chemical com- 
position and physical charac. 
ter of, 389 

rivet, shearing resistance of 363 

rivet, specifications for, 399 

rivets, specifications for, 401 

rope, table of strength of, 338 

rope. flat, table of strength of 
33 


shearing strength of, 306 

sheets, weight of, 174 

specific gravity of, 403, 411 

specifications for, 397-402 

pee. -bars, specifications for, 
8 


INDEX, 


Steel, spring, strength of, 299 
springs (see Springs, steel) 
strength of, 297-303 
strength of, variation in, 398 
structural, annealing of, 394, 395 
structural. drilling of, 395 
Structural, earliest uses of, 405 
structural, effect of punching 

and shearing, 394 
structural, for bridges, specifica- 
tions of, 399 
structural, for buildings, specifi- 
cations of, 398 
structural, for ships, specifications 
of, 399 
Structural, properties of, 272-280 
structural, punching of, 395 
structural, riveting of, 304 
structural, specifications for, 400 
erage: size and weights, 177- 


structural, treatment of, 394-396 
structural, upsetting of, 394. 
structural, welding of, 394 
struts, 259 
tempering of, 414 
tensile strength of, at high tem- 
peratures, 382 
tensile strength of pure, 392 
tires, specifications for, 398 
tires, strength of, 298 
tool, heating of, 412 
tungsten, 409 
water-pipe, 295 
welding of, 396 
wire gauge, tables, 29 
working of, at blue heat, 395 
working stresses in bridge mem- 
bers, 262 
Stevedore rope, 340 
Stokers, mechanical for 
boilers, 711 
under-feed,712 
Stone-cutting with wire, 966 
Stone, specific gravity of, table, 


16 
weight of, table, 166 
strength of, 302, 312 
Storage-batteries, 1045-1048 
efficiency of, 1048 
Storage of steam heat, 789 
Storms, pressure of wind in, 494 
Stoves,  compressed- air heating, effi- 
ciency of, 507 
Stove foundries, cupola charges in, 
949 
Strain, 236 
Strains, formule for unit, in iron 
and steel in structures, 379 
Straw as fuel, 643 


flow, 584-588 : 
Streams, fire, 579-581 (see Fire- 
streams) 
running, horse-power of, 589 
Strength, compressive, 244-246 
compressive, of woods, 311 
loss of, in punched plates, 353: 


steam- 


measurement of 


- BL2S 


ste-str 


Strength, range of, in steel, sh 392» 
shearing, of iron and steel, 3 ‘ 
shearing, of woods, table, at 
tensile, 242 
tensile, of iron and steel at high 
temperatures, 382 

torsional, 281 

transverse, 266-27 1 

of aluminum, 318 

of Bie gt iy alloys, 328, 

of anchor-forgings, 297 

of basic Bessemer steel, 390 

of belting, 302 

of blocks, 906 

of boiler-heads, 285 

of boiler-plate at high tempera- 
tures, 383 

of bolts, 292 

of brick, 302,012 

of bridge-links, 298 

of bronze, 300, 319-332 

of canvas, 302 

of cast iron, 370, 374 

of cast iron, relation of, to sili- 
con, 369 

of cast- iron columns, 250-254 

of cast-iron water-pipe, 251 

of chains, table, 307 

of chain cables, table, 340 

of castings, 297 

of cement mortar, 313 

of chalk, 312 

of columns, 246, 250-261 

of columns, New York building 
laws, 1019 

of ee at high temperatures, 


of copper plates, 300 

of copper-tin alloys, 320: 

of copper-tin-zine alloys, graphic 
representation, 323 

of copper-zine alloys, 32a 

of cordage, table, 906 

of erank-pins, 803 

of double-riveted seams, calcu- 
lated, 361 

of electro- magnet, 1053 

of flagging, 313 

of flat plates, 283-286 

of floors, 1019, 1021 

of German silver, 300 

of glass, 308 

of granite, 302, 312 

of gun- -bronze, 321 

of hand and hydraulic riveted 
joints, 355 

of iron and steel, effect of cold on, 

3 


of lime-cement mortar, 313 
of limestone, 312, 313 

of locomotive forgings, 297 

of Lowmoor iron bars, 297 

of malleable iron, 367 

of Mannesman tubes, 296 

of marble, 302 

of masonry, 312 

of materials, 236-346 


. 


1124 


str—ten. 


Strength of materials, Kirkaldy’s 
tests, 296-803 
of perforated plates, 353 
of phosphor-bronze, 327 
of Portland cement, 302 
of riveted joints, 299, 354-362 
of roofs, 446, 1019 
of rope, 301, 338, 339 
of sandstone, 312 
of sheet metal, 300 
of silicon-bronze wire, 327 
of soapstone, 312 
of spring steel, 299 
of spruce timber, 310 
of stayed surfaces, 286 
of steam-boilers, 700-711 
of steel axles, 299 
of steel castings, 299 
of aed open-hearth structural, 
1 


of steel propeller-shafts, 299 
of steel rails, 298 
of steel tires, 298 
of stone, 312 
of structural shapes, 272-280 
of timber, 309-312, 1079 
of twisted iron, 241 
of unstayed surfaces, 284 
of yellow pine, 309 
of welds, 300, 308 
of wire, 301, 303 
of wire and hemp rope, 301, 340 
of wrought-iron columns, 255 
tensile, of pure steel, 392 
Stress and strain, 236 
Stress due to temperature, 283 
Stresses allowed in bridge members, 
62-264 
combined, 282 
effect of, 236 
in framed structures, 440-447 
in steel plating due to water 
pressure, 287 
eats i in structural mate- 


rials, 3 
produced by shocks, 241 
Structural shapes, elements of, 
248 


shapes, moment of inertia of, 248, 
273-280 
shapes, properties of, 272-280 
shapes, radius of gyration of, 
DAB uk 
shapes, sizes and weights, 177-180 
steel (see Steel, structural) 
Structures, formul» for unit strains 
in iron and steel in, 379 
Strut, moving, 436 
Struts, steel, formule for, 259 
strength of, 246 
wrought-iron, formule for, 259 
Sugar manufacture, 643 
solutions, concentration of, 465 
Sulphate of lime, solubility of, 464 
Sulphur dioxide and ammonia-gas, 
properties of, 992 
dioxide refrigerating-machine, 985 
influence of, on cast iron, 367, 370; 


j 
i 
{ 





INDEX. 


Sulphur, influence of, on steel, 389 

Sum and difference of angles, func- 
tions of, 66 

Superheated steam, economy of 
steam-engines with, 783 

Surface condensers, 840-844 

Surfaces, unstayed ‘flat, 284 

Suspension cableways, ‘915 

Sweet’s slide-valve diagram, 826 

Symbols, chemical, 163 

electrical, 1078 
Synchronous motor, 1071 


T shapes, properties of ata gin 
steel, table, 279 
Tail-rope system of haulage, 913 
Tanbark as fuel, 643 
Tangent of an angle, 65 
table of 159-162 ’ 
ee plating and framing for, 


capacities of, tables, 121, 125, 


Tannate of soda boiler compound, 


Taps for machine screws, 970 
formule and table for screw- 
threads of, 207 
Tap-drills, sizes of, 208 
table of, 970, 971 
Taper, to set in a lathe, 956 
pins, 972 
Tapered wire rope, 916 
Taylor’s rules for belting, 880-882 
theorem, 76 
Tees, Pencoyd steel, weights and 
sizes, 179 
Teeth of gears, forms of, 892 
of gears, proportions of, 889, 890 
Telegraph-wire, copper, table of 
size weight and resistance of ,221 
joints in, 217 
tests of, table, 217 
Telescope, Mesuré 
pyrometric, 453 
Temperature, absolute, 461 
determination by color, 454 
decor ibe of melting-points, 


of re 622 
rise of, in combustion of gases, 
6 


22 
stress due to, 283 
effect of, on strength, 309, 382 
Tempering. effect of, on steel, 412 
of steel, 414 
oil, of steel forgings. 396 
Tenacity of metals, 169 
of metals at various tempera- 
tures, 309. 382-384 
Tensile strength, 242-244 
strength, increase of, by twist- 
ing, 241 
strength of iron and steel at high 
temperatures, 382 
strength of pure steel, 392 
tests, shapes of specimens for, 
243 


and Nouel’s 


INDEX. 


Tension and flexure, combined, 282 

and shear, combined, 282 
Terne-plate, 182 

specifications for, 1088 
Terra-cotta, weight of, 181 
Test-pieces, comparison of large and 

small, 393 

Tests of aluminum alloys, 330 

of aluminum brass, 329 

of cast iron, 369 

calorimetric, of coal, 636 

compressive, of wrought - iron 

bars, 304 

compressive, specimens for, 245 

tensile, precautions in, 243 

tensile, specimens for, 243 

tensile, table of, 242 

of brick, 312 

of cast-iron columns, 250-254 

of centrifugal pumps, 609 

of chains, table, 307 

of chain cables, 308 

of cold-dzawn steel, 305 

of cold-rolled steel, 305 

of fans, 514, 522, 524 

of gas-engines, 849 

of petroleum-engines, 851 

of hydraulic ram, 615 

of lap and butt riveted joints, 360 

of sone Kirkaldy’s, 296- 


of Pemensteel, 408 

of pine timber, 309 

of pulsometers, 613 

of pumping-engines, 611 

of riveted joints, table, 303 

of steam-boilers, 685-699 

of steam-boilers, rules for, 690- 
95 


of steel eye-bars, 304 
of steel plate, 390 
of steel in Memphis bridge, 393 
of turbine wheels, 596 
of woods, 306 
of wrought-iron columns, 305 
of vulcanized rubber, 316 
Theory of exponents, 36 
Thermal capacity, definition of, 457 
units, 455, 660 
units, comparison of British and 
French, 455 
Thermodynamics, A78 
Thermometers, 448 
Thermometer, air, 454 
scales, comparison of, 448 
scales, comparison of, table, 449 
Threads, pipe, 195 
Three-phase circuits, 1068 
Toothed-wheel gearing, 439, 887- 
906 (see Gearing) 
Tidal-power, utilization of, 600 
Tie-rods for brick arches, 281 
Tiles, weight of, 181 
Timber beams, safe loads, 1023 
expansion of, Slt 
measure, 20 
properties of, table, 310 
resistance of ‘drift-bolts i in, 290 


1125 


ten-tra 


ae oar strength of, 309-312, 


table of contents in feet, 21 ~ 
weight of, table, 310 

Time, measure of, 20 

Tin, properties of, 168 | 
-aluminum alloys, 330 
-copper alloys, 319, 320 
-copper- -aluminum alloys, 330 
-copper-zine alloys, 322, 323 


lined Pipe. sizes and weights, 
table, 2 

pipe, HERES and sizes of, 200 

plate, 182 


plate, specifications for, 1088 
plate, American packages of 
182 
_ plate, comparison of gauges and 
weights, table, 182 
Tires, steel, friction of, on rails, 928 
steel, specifications for, 398 
steel, strength of, 298 
Tobin brofize, analyses and proper- 
ties of, 325, 326 
Toggle- joint, 436 
Tons per mile, equivalent of, 27 
Tonnage of vessels, 19, 1001 
Tools, machine, speed of , 953 
metal-cutting, forms of, 955 
Tool-steel, heating of, 412 
Torque of an armature, 1056 
Torsion and compression 
bined, 283 
and flexure combined, 283 
elastic resistance to, 282 
of shafts, 806 
Torsional strength, 281 
Total heat of evaporation, 462 
Track bolts, 210 
spikes, sizes and weights of, 212 
sera power of locomotives, 853, 
85 
Tractrix, 50 
Trains, railroad, resistance of, 851 
railroad, resistance due to friction, 
939 
railroad, speed of, 859 
Trammels, to describe an ellipse 
with, 46 
Tramway, compressed-air, 510 
Tramways, wire-rope, 914 
Transformers, electric, 1070. 
Transmission, compressed- air, 488 
compressed air, efficiency of , 508 
electric, 1033- 1041 
electric area of wires, 1033 
electric, cost of copper, 1040 
electric, economy of, 1036 
electric, efficiency of, 1038 
electric, systems of, 1041 
electric, weeny of copper for 
1033, 1076 
electric, wire table for, 1037 
hydraulic - pressure, 616-620 (see 
Hydraulic - pressure transmis 
sion ) 
of heat (see Heat) 
pneumatic postal, 509 


come 


1126 tra-ven 
Transmission, rope, 922-927 (see 
_Rope- driving) ; 
wire-rope. 917-922 (see Wire 
rope) 


Transmission-rope, 340 
Transporting power of water, 565 
Triple-expansion engine, 769-772 
(see Steam-engines) 
Transverse strength, 266-271 
strength of beams, formule for, 
268 


strength, coefficient of, 267 
Trapezium, 54. 
Trapezoid, 54 
Trapezoidal rule, 56 
Triangle, mensuration of, 54 
problems 1 in, 41, 
spherical, 61 
trigonometrical solution of, 68 
Trigonometry, 65-68 
Trigonometrical formule, 66, 
functions, relations of, 65 
functions, signs of, 66 
functions, table of natural, 159- 
161 
funetions, table of logarithmic, 
1 


Triple-effect evaporator, 463 
Trough plates, properties of steel, 
table, 274 
Troy weight, 20 
Trusses, Burr, 443 
Fink roof, 446 
Howe, 445 
King-post, 442 
Pratt, 443 
Queen-post, 442 
roof, 446 | 
Warren girder, 445 
Whipple, 443 
Tubes, boiler, table, 196 
boiler, table of areas of, 197 
condenser, 840 
pope poryer of water flowing in, 
of different materials, table for 
calculating weights of, 169 
expanded boiler, holding power 
Oboe sae 
iron, collapsing pressure of, 265 
Mannesmann, strength of, 296 
seamless brass, table, 198 
steam-boiler, holding power of, 
704 
steam-boiler, iron vs. steel, 704 
steam-boiler, material for, 704, 


09 

strength of small, 266 

welded solid-drawn steel, 199 

wrought-iron, extra-strong, 196 
Tube opiate: steam-boiler, rules for, 

vi 

Tubing, brass, weight of, table, 200 

copper, weight of, table, 200 

lead and tin, 200 

zinc, weight. of, table, 200 
Tungsten- aluminum alloys, 330 
Tungsten steel, 409 


INDEX. 


Turbines, steam, 790, 1085 
steam, bearings for, 941 
Turbine wheels, 591-599 
wheels, dimensions of, 597 
wheels, efficiency of, 594 
wheels, Pelton, 597 
wheels, proportions of, 591 
wheels, table, 595 
wheels, tests of, 596 
Turf as fuel, 643 
Turnbuckles, 211 
Turret lathes, cutting-speed of, 954 
Tuyeres for cupolas, 948 
Twin-screw vessels, 1017 
Twist-drill gauge, tables, 29 
Twist-drills, sizes and speeds, 957 
Twisted iron bars, 241 
Two-phase currents, 1068 
Type metal, 336 


Uehling-Steinbart pyrometer, 453 
Unequal arms on balances, 19 
Units, electrical, 1024 
equivalent value of electrical and 
mechanical, 1026 
of the magnetic circuit, 1050 
Unit of evaporation, 677 
of force, 415 
of power, 429 
of heat, 455, 660 
of work, 428 
Unstayed ‘surfaces, strength of, 284 
Upsetting of structural steel, 394 
United States, population of, 12 
standard gauge, sheet- metal, 30 
standard gauge, sheet-metal, ta- 
ble, 31 


Vacuum, drying in, 466 

pumps, 612 
Valve-gears, steam-engine, 824-836 
Valve-rods, steam-engine, 815 

(see Steam- engines) 
Valves, marine-engine, 1016 
ump, 606. 

In steam-pipes, 675 
Vapors, saturation-point of, 480 
Vapor water, weight. of, 484. 

and gas mixtures, laws of, 480 

for refrigerating-machines, 982 
Varnish, 387 
Velocity, angular, 425 

definition of, 423 

expression of, 429 

linear, of a turning body, 425 

measure of, 2 

of a in pipes by anemometer, 

parallelogram of, 426 

table of height corresponding toa 

given acquired 425 

of water in cast-iron pipe, 567 

of water in open channels, 564 
Ventilating fans, 517-525 

ducts, flow of airin, 530 
Ventilation, 528-546 

air-cooling for, 531 

blower system, 545 


INDEX. 


Ventilation, efficiency of fans and 
chimneys, 533 
head of air, 533 
of large buildings, 534 
of mines, 531 
Ventilators, centrifugal, for mines, 
521 


Ventilator, steam-jet, 527 

Venturi meter, 583 

Versed sine of an angle, 65 
sine, relations of, in circle, 58 

Verticals, formule for strains in, 

444 

Vertical high-speed engines, 777 

Vessels (see Ships) 

Vibration of steam- -engines, 789 

Vis-viva, 428 

Volt, 1024 

Vulcanized rubber, tests of, 316 


Walls of buildings, 1019 
Warehouse floors, 1019 
Warren girders, stresses in, 445 
Washers, sizes and weights of, 212 
Washing of coal, 638 
Water, 547-555 
abrading power of, 565 
analyses of, 553, 554 
boiling- point of, 550 
boiling-point at various baro- 
metric pressures, 483 J 
comparison of head, in feet, with 
various units, 548 
compressibility of, 164, 551 
consumption of locomotives, 862 
consumption of steam-engines, 
753,776, 777, 783, 785 
erosion by flowing, 565 


evaporation of. in reservoirs and 


channels. 463 

expansion of, 547 

fall, efficiency of. 588 

fall. power of, 588 

flow of. 555-588 (see Flow of 
water) 

flowing in tube, horse-power of, 
589 


flowing measurement of, 582- 
588 


freezing-point of, 550 

hardness of, 553 

head of, 557 

head of, equivalent to pounds per 
square inch table. 5 

heat-units per pound, yer 

horse-power rere? to raise, 601 

impurities of. 5 

jets, 579 

meters 579 

power 588-620 

power plants, high-pressure, 1081 

power, value of, 

pressure due to weight of, 549 

pressure of one inch, 27. 549 

pressure of one foot 27, 549 

price of 5 

pumping by compressed air, 505a 

purification of 554 


ven-win . LIZ, 


Water, 

pipes, 573 

relation of diameter of pipe to 
capacity, 566 

softening of, 554 

specific heat of, 550 

transporting power of, 565 

ree of, in cast-iron pipe, 


quantity discharged from 


Natta of, in open channels, 
weight of, 27, 547, 548 

gas, 648 

gas, analyses of, 653 

gas, manufacture of, 652 

gas plant, efficiency of, 654 


gas plant, space required for, 
656 


lines, coefficient of, 1002 
pipes, riveted- steel, 295 
pipe, cast-iron, transverse 
strength of, 251 
pipe, cast-iron, weight of, 188 
tower (see Stand- pipe) 
vapor and air mixture, weight 
of, 484 
vapor, weight of, table, 484 
wheel, 591-599 
wheel, Pelton, 597, 1081 
wheels, power of, 1082 
Watt, definition and value of, 1024 
Waves, ocean. power of, 599 
Weathering of coal, 637 
Wedge, 437 
volume of, 61 
Weighing on incorrect balance, 19 
Weights and measures, 17-27 
and measures, Metric, 22-26 
Weight and pressure per unit area, 
Metric equivalents of, 27 
of materials, 164-166 (see also 
material in question) 
Weir-dam measurement, 586 
Weirs, flow of water over, 555, 586 
Bazin’s experiments. 587 
Weir formule, Francis’s, 586 
table, 587, 588 
Welding. electric 1044 
of steel, 394, 396 
Welds, strength of, 300. 308 
Wetted surface of ships, 1005 
Wheat, weight of, 170 
Wheel and axle, 439 
Wheels emery, 967-970 hice Emery 
wheels) 
polishing, speed of, 968 
turbine, 591-599 (see Turbine 
wheels) 
Whipple truss, stresses in, 443 
White-metal alloys. 336 
composition of, 335 
Whitworth process of fluid com- 
pressed steel, 410 
Wiborg’s air-pyrometer. 453 
Wind, 492-494 
force of, 492 
pressure of, in storms. 494 
strain on stand-pipes. 293 


1128 win-wro INDEX. 


Windlass, differential, 439 Wire rope haulage, 912-916 (see 
Windmills, 494-498 Haulage) 
capacity of 496 ropes, tapered, 916 


cost of, 498 

. economy of, 497 
efficiency of, 494 
horse-power of, 497 


Winding-engines, 909 


Wire, aluminum, properties of, 225 
aluminum bronze, properties of, 
225 
brass, properties of, 225 
brass, weight of, table, 202 
copper, properties of, 225 
delta-metal, properties of, 225 
copper, rules for resistance of , 222 
copper, specifications for, 225 
copper telegraph, size, weight, 
and resistance of table, 221 
copper, weight of, table, 202 
electric, carrying capacity of , 1033 
electric, fusion of, 1032 
electric, heating is 1032 
electric, insulation ‘of, 1033 
electric, table, 1034-1035 
galvanized i iron, specifications for, 
224 
galvanized iron, for telegraph and 
telephone lines, 217 
galvanized steel strand, 223 
gauges, tables, 29 
insulated copper, 221 
iron, 216 
nails, VPA Ws We 2 Ess 
phosphor- bronze, strength of, 327 
piano, size and strength of, 224 
plough-steel, 224 : 
phosphor-bronze, properties of, 
platinum, properties of, 225 
silicon bronze, =roperties of, 225 
silicon bronze, strength of, 327 
stranded feed, table of sizes and 
weights, 229 
strength of, 216, 301, 303 
telegraph, joints in, 217 
telegraph, tests of, table, 217 
beloe neu weight per mile- ohm, 


wound flywheels, 824 

ropes, 226-231 

rope, bending curvature, 921 

rope, bending stress of, 918 

rope, care of, 231 

Tope, elastic limit of, table, 917 

rope for guys and rigging, 228 

rope for transmission, dimensions, 
strength, and properties, 227 

rope, galvanized steel, dimen- 
sions, strength, and. proper- 
ties, 229 

rope, locked, 231 

rope, plough- steel, 227, 228 

rope, radius of curvature of, 922 

rope, sheaves for, 917, 919 

rope, splicing of, 346 

Tope, strength and aight @ligest One. 


rope tramways, 914 

rope transmission, 917-921 \ 

rope transmission, deflection of 
rope; 20 > ps 

rope transmission, horse-power 
transmitted, 919 

rope transmission, inclined, 921 

rope mS StOn limits of span, 

es eect oboe , long-distance, 

rope, use of, 231 

TANS SOM Dene ade u 1034, 1035- 


Wiring-tables, 1037 
Wohler’s experiments, on strength 
of materials, 238 
Wood as a fuel, 639, 640 
composition of, 640 
compressive strengths of, 311 
expansion of, 3 
heat see Ho expel water 
from, 640 
heating value of, 639 
holding power of bolts in, 291 
nail-holding power of, 291 
screws, holding power of, 290 
specific gravity of, table, 165 
weight of, table, 165 
strength of, 302, 309-312, 1079 
tests of, 306 
weight of, per cord, 232 
Woods, shearing strength of various 
table, ole 
specific heats of, 458 
weight of various, table, 310 
Wooden flywheels, 823, 824 
Woodstone, properties of” 316 
Woolf compound engines, 762 
Wootten’s locomotive, 855 
Work, definition of, 27, 428 
expression of, 429 
measure of, 27 
of acceleration, 430 
of accelerated rotation, 430 
of adiabatic compression, 501 
of friction, 938 
of a horse, 434 
of a man, 433 
rate of, 27 
unit of, 27, 428 
World’s Fair buildings, specifica- 
tions of wrought iron for, 379 
Worm-gear, 440 
Worm-gearing, 897, 1086 
Wrist-pins, steam-engine, 804 
Wrought iron, 377-379 
iron bars, compression tests of , 304 
iron built columns, 25 
iron columns, tests of, 305 
iron chain cables, 308° 
iron columns, Merriman’s table 
for, 260 
iron, influence of chemical com- 
position on properties of, 377 


INDEX, wro-zon 1129 


Wrought iron, influence of rolling on, Zero, absolute, 461 
Sit Zeuner’s slide-valve diagram, 827 


iron pipe, standard, table of 
dimensions, 194 

iron, slag in, 377 

iron, specifications for, 378 

iron, strength of, 245, 297, 300, 
304, 378 

iron, strength of, at high temper- 
atures, 383 

"aa extra-strong, table, 
1 


Xylolith, properties of, 316 


Y connection for alternating cur- 
rents, 1068 
-Yield-point, 237 
determination of, 237 


Z bars, Carnegie steel, properties of, 
table, 280 | 
weights and sizes, 178 


Zine, properties of, 1 


aluminum alloys, Ba 

-copper alloys, strength of, 323 

-copper alloys, table of composi- 
tion and properties, 321 

-copper-iron alloys, 326 

-copper-tin alloys, specific gravi- 
ties of , 323 

-copper- -tin alloys, table of proper- 
ties and composition, 322 

-copper-tin alloys, variation in 
strength of, graphic representa- 
tion, 323 

-copper-tin cede variation in 
strength of, 324 

tubing, weight of, table, 200 

use of, in boilers, 720 


Zone, spherical, 62 


of spheroid, 63 
of spindle, 63 


r> ye at 

cre » wa 
: +% we Gr: 

t tartig yeurgatly Poe me 


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ALPHABETICAL INDEX TO ADVERTISEMENTS. 


PAGE 
ALPHONS CUSTODIS CHIMNEY CONSTRUCTION COMPANY... 4 
meee tan BING INE) COMPANY ¢ ..f002: «cleus b> bake ce ua bacube 6 
AMERICAN PIPE MANUFACTURING COMPANY.............. 14 
AMERICAN STEEL & WIRE \COMPANY............0c200+00w-« 9 
ANSONIA BRASS AND COPPER COMPANY ............--.ee: 16 
MLAS PORTLAND OMMENT COMPANY | iiss’. oé os aceerdes ssllbuc iy 
PABCOCK el WILCOX OOMPAN V, THEY 2... ce cc oss ode wake 3 
PEM MN LOCOMOLI ME NV ORANG set a. vase ealtiemee odeewouek 2 
MUS TONTR EG LINGCOMPANY 2 agro isceiswe ne4cciehe Fee Siew 12 
BRLOUGIEPOR I" CHIAINGCOMPAN VacTUED oo... oc... cc we dects gee 16 
BROWN HOISTING MACHINERY COMPANY, THE............ 11 
CHAPMAN VALVE MANUFACTURING COMPANY............ 13 
GUESSONTS COUMPANS» GHORGE Virdee. «of. oo iss codaey « oben 10 
GAKVIN MACHINE COMPANS ACH bs Vout cvbis es. bolle eos onal g 15 
GENER RIPE LEOCLRIC COMPANY JTHIC 45, >. t2s...030.2sn eee. 17 
GREEN FUEL ECONOMIZER COMPANY, THE................ 3 
HANCOCK INSPIRATOR COMPANY, THE................0.0-- 2 
KMUEP ET eee COMPS) gee nee ow. So be hee 18 
LIDGERWOOD MANUFACTURING COMPANY................. #4 
LODGE & SHIPLEY MACHINE TOOL COMPANY, THE........ 14 
LUNEENELEIMERAGOUMPEA NNwEliT Ie Sulake... oss as cule 5 
MAURER BOSS ENT? Yami te, uo ae eae 11 
MORSE TWIST DRILL AND MACHINE COMPANY............. 13 
MATIONA Li MCT EL COMPE ARLY ripe amie. las. cca Whos 12 
SATION ATO ReOOMP Alvear ee ee... ac. «ne eee 1 
NORTON COMPAN We ee ven kee 15 
NORWALK IRON WORKS COMPANY, THE..............ec0e- 6 
QUEEN & COMPANY, INCORPORATED. 2.52... dccdeds oh eee 18 
RANDOLPH: CLOW HS WOM Pier a foes be de cee nh, Cee 9 
RIDER-HPRICSSON ENGINES OOMPANY |. 2... sc5c nessa eee i 
ROEBLING’S SONS COMPANY, JOHN A.............0cecceees 8 
SELLERS & COMPANY, WILLIAM, INCORPORATED. ........ 10 
SIMMONS. COMPANY, JOH RIE... <u sa0 0d.) ede; eee 16 
STANDARD STEEL, WOME sCOMPANY.......42,cmeeen «5 cue 2 
TV DER COMPANY, TH sVamieeas... .. 5.6 -.n >. 8 


UNDER-FEED STOKER COMPANY OF AMERICA, THE........ 4 


. Pree 


Co SAAR Beat senate ¥ 
[eee RARULAY ASF oy cata 
oe a OE ES OD ce ee 
i. uso eo yuaiealayes 
> ae ee eeiis TOD: 200 <¥ 
Sy olleg weeqiet + /EARO We GNOMES LEE 
‘i anpe ta. Weary CA ees ART Re 
red <p vee VAT: coy . 
¥ a See ‘Tike LHSY OAM 1% 
S se i et? uae ie sie ever Wid aie TREN, 
es § Lise. oedht Oe RAIL. ae 
ie eee KOR EY 
ue. ie fips aati es Sia 75 
LAS UkOG PODS SADE LS 9 | 
“R0T 3 VAAL): OOP ASE 
na oi Dita. RONG BR See 
MOD Bates Wan Yak 
ie “COC AEREMADY ae 
Bets is OM nee Bae 


a 





CLASSIFIED INDEX TO ADVERTISEMEN'S. 


BELTING AND Hose. PAGE 

Boston: Belting. Comet acseeeet ee eye Cah Me kaka tee oeb ale eM sey tteserra 12 
Borer LuBESss Nationale babe: Come acer tere. we ee clot talclers 1 
Bor1teR Tuses (Brass). Randolph-Clowes Co............es0e0. sere SO 
BorLers, STEAM, 

Babcock id Wileox:Co., CHG ces acne cote swielete sions ota anton a 3 
Brass Rops, SHEETS, TUBES, WIRE, ETC. 

Ansonia) Brass+and (Copper Costs xteaien ce kcictatais cheer eb aie te 16 

Randolph-ClawesiiCoy Sees ee seach aes wehbe eee 9 
CEMENT, AMERICAN PorTLAND. Atlas Portland Cement Co......... 17 
CHAIN. - Bridgeport-Chaiw Co: je TAG aces ores) tee on oe tee ae 16 
Cuimneys. Alphons Custodis Chimney Construction Co............. 4 
Cuucks, MILLING CuTTeRs, REAMERS, SPRING CuTrrEeRsS, TAPS, ETC. 

Morse Twist Drill and Machine Co. ...........00020cccvccece 13 
CoMPRESSORS—AIR, GAS, ETC. 

Norwalk, Icon] W orkasGos vy Bhs 2 aaah Ae les tea ree 6 
CoNCRETE CONSTRUCTION (REINFORCED). 

Brown Hoisting Machinery Co., The......../..0.02..0.4.000 pe 

Alphons Custodis Chimney Construction Co.................. 4 
CONCRETE REINFORCEMENT—WIRE. American Steel & Wire Co..... 9 
CoprEeR WIRES, CABLES, BARS, SHEETS, TUBES, ETC. 

Ansonia, Brass-and Copper Cou gavin saa we otra foo 5 ok. SRL 16 
CRrUsHERS—ORE, Rock, STONE. . 

Geo., V.. Cresson: COs ci. en leterox her ovis SUNT Mee eo) Chat one: chet ethene ties on eee 10 
DRILLS, POWER AND Hann. 

Norwalk fronaWworks ‘Conf Lhen ses etecerlte sce eeicls Se Wen eee 6 
Dritis, Twist. Morse Twist Drill and Machine Co................. 13 
ELECTRICAL GenERAToRS, Motors, Arc AND INCANDESCENT LAMpPs, 

ETC. 

General Mlectrie:Co., Veber cei s Meerne cals waist fe soe aeaeee eee 17 
EMERY AND CORUNDUM WHEELS. Norton Co...........-.2++eee0% 15 
ENGINEERING RequisitrEs. Lunkenheimer Co., The................ 5 
ENGINEERS AND CONTRACTORS. 

Brown Hoisting Machmery Co;;.The..... 0. ...025 0. 0ce see Oe 1h 
ENGINES. 

American, HngimevCome Sette Ote < MSR hele Zils! Sle bat ede, Salers ee Anan 6 

Rider=HricssOni Engine os. . terc.d sii els,, Sik Woktiens Geloetsteeedas oe f, 
ENGINES, BLOWING. ; 

Lidgerwood MigaCommeuetic. 4.50 s/ainss ss  opgeneena meinaerene tea 7 
Fire Brick, Trues, Suass, Curona Lininas, Cray Rerorts, ETC. 

Maurer & Son! Henson, . . cis.o:s-s els 1010p peteatotsece! «a ene 1l 
FuEL-ECONOMIZERS AND FURNACES. 

Green Fuel Economizer @o., The ....4. ..- sree ae ele eneee Po Bees 

Under-Feed: Stoker Co, of America, The... ..:......: meen ma, + 


CLASSIFIED INDEX [TO ADVERTISEMENTS. 


HotIstine MacHINERY—ELEVaTORS, CONVEYORS, ETC. ae: 
Brown; eloistine: Machimery Co: eine ay. are cee eter Veli 
fulgorwncd Wie COMO er eae eM RUNG CaM tetere 7 

HYDRANTS. Chapman Valve Wiig. Coy oc. cure. . 6 eee ee eaters ee 13 

INSULATED WIRES AND CABLES. 

Ansoniaybrass andioopper Coes... | aan dee ee ee 16 
Locomotives. “Baldwin Locomotive Works ...)...5......2-5.06..4 2 
MecHANICAL STOKERS. Under-Feed Stoker Co. of America, The.... 4 
Matere:): National MeterCo: 2... 60)... 4 4b dae. aE eee 12 


Mitntinc Macuinges, SHAPERS, PLANERS, PuNcHES, RoLus, SHEARS, 
Latues, Macuine Toots, Bouts, ETc. 


Garvin) Machine, Co,,. Fhe-. i008 fs2 berm ain oe) ee as 

Lodge & Shipley Machine Tool Co., The........2........... tet 

Sellers & Co... William’ (Incorporated) cnc)... Gueedhie) ese) ae 10 
MINING AND QUARRYING MACHINERY. 

Brown, Hoisting Machinery Co/, (RheN. af7 a5 ae 1] 

Norwalk Tron. Works Co.; ‘Bhe: wave ceeee see. See 9 
NINING SCREENS... I yler Co., The W 4s! sighed} bee hee eee 8 
PackING—PistTon, VALVE, JOINT. Boston Belting Co.............. ie 
Pipe, WATER AND GAS. 

Amerncan' Pipe Mic. Cone oi... tees cant Ye Seed ee 14 

National Tube @o.vsestadir doa sicieiesich BU ae ROR ere i: 

Simmons Cos) ob tise. ea hee. cise ee ee 16 
Pumpine MAcHINERY. 

National Meter°Cos.:.. 6% ais salegie oe hUpSe Renn okt boar tmenertiemeanes 12 

Rider-Ericsson Engine Co.) 2 mts 5 ahr SE eee ee ores lee Ge 
RuBBER Goops... Boston Belting Coaster) aa eee ee 12 
STEAM SPECIALTIES AND ENGINEERING APPLIANCES. 

Hancock InspiratoriGo.,/ Lheigdi.). vesenia. ) tae Pee oe 2 
STOKERS— AUTOMATIC BidewEoe!l Stoker Co. of America, The...... 4 
SURVEYING InsTRUMENTS. 

Keuffel &. Msser Coy i. coc. on bk CER Oe eee ee 18 

QOuecenss Cos, incorporated © 600.4 «4. ee a eee 18 
Wirps. otandard steel. Works Co... “sa. 12s. eRe Hee aes er 2 
Moon GRINDERS. Norton Co, : 3.7... 055s «ete ae ee ee 5 
VALVES—GAS, WATER, AND STEAM. 


Chapmian ValveiMie:Oo... isc Js oR coat le a fee 1 
Hancock Inspirator Co., The 
Lunkenheimer Co., The. 


o 0 Wael ee. bile os) efiebist. 5 fs fe Fe cei ote hace ohh fepan) donee ie 


3 
2 
5 
WaAtmrR-Suppiy, | Rider-Ericsson Engine Coi%) . 37) sivinc tT fee)... " 
WateR-WorKS, CONTRACTORS FoR. American Pipe Mfg. Co......... 14 
WHEELS. Standard Steel Works on D) 
Wire Cuorn. Tyler Co., The W. 8 
WiRE FOR CONCRETE ae American Steel & Wire Co... 9 
Wire Rope anp TELEGRAPH, TELEPHONE, AND TROLLEY WIRE. 

Ansonia Brass and Copper Co. 

Roebling's'Sons Cos Jonna...» ....) saeeedl Geeta pF 2k Eee 


NATIONAL TUBE COMPANY 


MANUFACTURERS OF 


TUBULAR PRODUCTS 


MERCHANT PIPE for Steam, Gas, and Water 
WROUGHT PIPE, up to 30 inches O.D. 


Special Steel Lap-welded Pipe Fitted with 
Converse Patent Lock Joint and Matheson Joint 


Combining Lightness with Great Strength and Durability 
Kalameined, Asphalted, and Tarred Pipe 


SHELBY 
SEAMLESS STEEL TUBING 


For Boiler Tubes, Cylinders, Automobile Parts 
Bicycle Frames, Trolley Poles, Flagstaffs 
AND OVER 300 DIFFERENT USES 
Seamless Steel Bells Seamless Steel Gongs 


BEICBUN Gore Agen BS yer Gs 


Malleable and Cast-iron Fittings 

Wrought and Malleable Couplings 
Nipples, Long Screws and Followers 
‘* High-Duty-Metal’’ Valves Iron Cocks Iron Body Valves 


“KEWANEE” UNIONS 


‘*Kewanee’’ Valves and ‘‘Kewanee’’ Boiler Couplings 
DRIVE WELL POINTS WELL SUPPLIES 


NATIONAL TUBE COMPANY 
General Offices: FRICK BUILDING, PITTSBURGH, PA. 
DISTRICT SALES OFFICES 


New York Pittsburgh Chicago St. Louis 
Philadelphia Atlanta New Orleans Denver 


San Francisco Portland Seattle Salt Lake City 
1 ; 





BALDWIN LOCOMOTIVE WORKS 


MANUFACTURERS OF 


LOC OMOTIVES 


t of Every Description 
BURNHAM, WILLIAMS & CoO. 
PHILADELPHIA, PA., U.S.A. 
Cable Address: ‘‘Baldwin,’’ Philadelphia. 


STANDARD STEEL WORKS CO. 
HARRISON BLDG., PHILADELPHIA, PA., U. S. A. 
SOLID FORGED ROLLED AND 
STEEL TIRED WHEELS 


mounted on axles fitted with Motor Gears for 
Electric Railway Service. 
LOCOMOTIVE TIRES RAILWAY SPRINGS 


FORGINGS CASTINGS 


THE HANCOCK VALVES 


Made in one grade ONLY 
FOR. ALL KINDS OF SERVICE 


ee OUR GUARANTEE 


“‘We guarantee that each and every 
Hancock Globe, Angle, 60° and Cross 
Valve, with our monogram on it, has 
been tested with 1000 pounds water 
pressure and found tight before 
leaving the works.’’ 























Write for our book of 
*Valves” 


wi Lhe Hancock Inspirator Co. 


85-87-89 Liberty St. 22-24-26 So. Canal St. 
« NEW YORK CHICAGO 





The Babcock & Wilcox Co. 


85 Liberty Street, New York. 


Makers of 


BABCOCK & WILCOX 


Stirling, A. & T. Horizontal, 
Cahall Vertical, 


Water Tube Steam Boilers. 
Steam Superheaters. 
Mechanical Stokers. 


Works: 


Bayonne, New Jersey. Barberton, Ohio. 





GREEN’S FUEL ECONOMIZER 


FOR STEAM BO!LERS. 





ACES.—Heats the feed water to a High Temperature, thus 
Wdetene 5 SAVING IN COAL. 1 


ay ; Can 6 i Pde to any type of pes 
wit. toppage of works. arge volume of water always in reserve a 
eee rare he nt ready for immediate delivery to the boilers. 


Sixteen Prize Medals. 
SOLE MAKERS IN THE UNITED STATES. 


THE GREEN FUEL ECONOMIZER CO. of Matteuwan, B. 2% 
3 


THE JONES STOKER 


The ONLY system of mechanical stoking 
in which the fuel supply and the air supply 
are automatically proportioned to each other 
and to varying loads by the steam pressure. 
THE ADVANTAGES OF SUCH AUTOMATIC 
REGULATION ARE OBVIOUS. ? 


THE 


Under-Feed Stoker Co. of America 
MARQUETTE BUILDING, CHICAGO 














PERFORATED 
RADIAL BRICK. 


REINFORCED 
CONCRETE. 


Main Office: BENNETT BUILDING, NEW YORK. 


BRANCHES: 


CHICAGO, PHILADELPHIA, BOSTON, ATLANTA, CLEVELAND, 
ST. LOUIS, DETROIT, PITTSBURG, KANSAS. 


Catalogue on application. 





Branches: - New York, 66-684 fi ae St; : ondon, 5 E., 29 Cres DoverSt: Chicas (oe Dearborn Sts. 


1B? 





THE NORWALK AIR COMPRESSOR 


OF STANDARD PATTERN 


is built with Tandem 





Compound Air Cylind- 
ers. Corliss Air Valves 
on the intake cylinders 
insure small clearance 
spaces. The Intercooler 
between the cylinders 
saves power by remov- 
| ing the heat of compres- 
sion before the work is 
1 done, not after, and 
the compressing is all 
done by a straight pull 
and push on a continu- 
ous piston’ rod. The 
Compressor is self-con- 

SRE tained; the repair bills 
sare reduced to a minimum, and the machine is €conomical and efficient, 
‘Special machines for high pressures and for liquefying gases. Compound and 
Triple Steam Ends. 





A catalog, explaining its many points of superiority, is sent free to 
business men and engineers who apply to 


THE NORWALK IRON WORKS CO., 


SOUTH NORWALK, CONN. 


AMERICAN-BALL DUPLEX 
COMPOUND ENCINE 


AND 


DIRECT-CONNECTED 
_ GENERATOR. 
, a =n 


The latest develop= 
ment in practical 
steam-engineering. 









The highest econ- 

omy of steam with 

<=the simplest possi- 

z yy —< ble construction. 

-Complete electric and steam equipments fur- 
nished of our own manufacture. 


AMERICAN ENGINE CO., 
New York Qffice-95 Liberky St. Bound Brook, N. J. 


Sa a nl 
HOISTING ENGINES - 


CABLEWAYS, AND CONVEYING DEVICES OF EVERY DESCRIPTION 
of the LIDGERWOOD make 
wept 


are unequalled for adaptation and efficiency. 









Our Hoisting Engines are built to gauge 
on the Duplicate Part System. 
Quick delivery assured. 


we 


a) Over 30,000 in use. 


STEAM AND ELECTRIC 
HOISTS. 


Send for 
Latest Catalogues. 


DOMESTIC WATER-SUPPLY 


Without Depending on the Wind. 


THE “REECO-RIDER” 
AND “ REECO-ERICSSON” 
HOT-AIR PUMPING- 

ENGINES 





















































In use for thirty-five years. 





More than 40,000 sold. 


Specified by the Leading Engie 
neers of the World. 


Catalogue on application to neare: 
est store. ; 


RibsEMGsRON ENGINE Co., 


NEW YORK, BOSTON, PHILADELPHIA, CHICAGO, 
7 re 


Wire Rope, 


MADE AT, 


aS 
Aa , TRENTON, N. J,. 


ADDRESS! 








The Tyler Double 
S Crimped Wire 
Cloth and Screen 


Mining Screens, Rolled Wire Cloth, Rolled Slot 
Screens, Galvanized Wire Cloth, Tinned Wire 
Cloth, Locomotive Stack Netting, Plated Mill 
Screen Cloth, Fourdrinier Wires, Galvan- 
ized Wire Netting, Twilled Wire Cloth, 
Coal Screen Cloth, etc. 
Wire Cloth of every kind, from the coarse meshes of heavy wire, to 


the fine meshes of thread-like wire, made from iron, steel, brass, 
phosphor-bronze or copper, and woven to suit requirement, 


SEND FOR CATALOGUE “M. E." 


THE W. S. TYLER COMPANY 


CLEVELAND, QO. 














gear 
ca Sy geadheeee 





sf et es 
















RANDOLPH-CLOWES CoO.’ 
WATERBURY, CONN. 


BRASS ano COPPER ROLLING MILLS 


AND 


TUBE WORKS. 


SEAMLESS BRASS and COPPER 
TUBES and SHELLS 
Up to 36 Inches Diameter. 

9 


_ 


WM. SELLERS & CO. 


(INCORPORATED), 


PHILADELPHIA, U. S.A. 


HIGH-SPEED TRAVELING AND SWING-CRANES, 
INJECTORS FOR ALL CONDITIONS OF SERVICE. 
GRINDING-MACHINES FOR TOOLS AND DRILLS. 


IMPROVED HYDRAULIC TESTING-MACHINES, 
Under Patents of A. H. Emery. 


TURNTABLES FOR LOCOMOTIVES AND SHOP- 
CARS. . 


IMPROVED LABOR-SAVING MACHINE TOOLS 
For Railway and Machine-shop Equipment. 


SHAFTING IN ALL ITS DETAILS FOR THE ECO- 
NOMICAL TRANSMISSION OF POWER. 


GEO. V. CRESSON CO,, 


Main Office and Works, 
Allegheny Ave. west of Seventeenth St., Philadelphia, Pa. 


New York Office: 141 Liberty St. 





Engineers, Founders, and Machinists. 


Manufacturers of 
POWER TRANSMITTING MACHINERY, 
CRUSHING ROLLS and JAW CRUSHERS, 


= 


Builders of 


SPECIAL MACHINERY TO ORDER. 
10 


d ve ve é : ve 
eto ince ecto incl Fer in ro inclt 


REINFORCED CONCRETE 
CONSTRUCTION 


using a special corrugated iron; attached to buildings in 

the ordinary way and plastered with Portland cement, 

making a light, strong, fire-proof construction for roofs, 
walls, floors, etc. 


THE BROWN HOISTING MACHINERY CO., 


Engineers, Designers, and Builders of 
Hotsting Machinery of Every Description. 


Main Office and Works, CLEVELAND, OHIO. 
Branch Offices, NEW YORK and PITTSBURG. 


ESTABLISHED 1856. 


HENRY MAURER & SON, 


MANUFACTURERS OF 


FIRE BRICK, TILES, SLABS, CUPOLA LININGS, 


Clay Retorts for Gas Works. 


Office, 420 East 23d Street, 


ks, M N. J. 
P. O., Telegeiphe andes R. Station.) N EW YORK. 


11 


RUBBER. GoopDs ; 


FOR ¢ 
RAILWAYS, STEAMSHIPS, MILLS, ‘ 
MINES, SMELTERS, & ALL ¢ 






MECHANICAL PURPOSES. 






\iYEGWZS ~Belting, Hose, Packings, 
— 


Le Rubber Covered Rollers, 


Manufactured by 



































James Bennett Forsyth, Gen. Mer. 
Original Mfrs, Boston, New a0 Bifielo, Chicago, 


Vulcanized 256-260 100-102 175-177 
Rubber Goods, Devonshire St. Reade St. Pearl we Lake St. 


@S eee. ] 2 2 2] @ 


‘ The Trade Mack etc., of Superior Quality 
(IT TT ATA 





THE GREATEST Ct GREATEST 


WATER METER 


RECORD EVER MADE. 


640,000 


Crown, Empire, Nash, Gem 
METERS IN USE. 


National Meter Company, 


New York, Chicago, Boston, Pittsburg, Los Angeles 
12 ; 















Morse Twist Drill & Machine Co. 
New Bedford, Mass., U. S. A. 
MAKERS OF 











ARBORS MANDRELS 
CENTER Keys METAL SLITTING Saws 
CHUCKS MILLs 
COUNTERBORES REAMERS 
COUNTERSINKS SCREW PLATES 
CUTTERS 3 SLEEVES 
Dies SOCKETS 
DRILLS TAPS 
GAUGES TAPER PINS 
i LATHE CENTERS THREADING TOOL 
MACHINES WRENCHES 









aE 


CHAPMAN VALVE MEG. CO, 


WORKS AND MAIN OFFICE: 
INDIAN ORCHARD, MASS. 


BRANCH OFFICES: 





- BOSTON, NEW YORK, PHILADELPHIA, BALTIMORE, 
ALLENTOWN, PA.; CHICAGO, ST. LOUIS, SAN FRAN- 
CISCO, LONDON, ENGLAND; PARIS, FRANCE; AND 

JOHANNESBURG, SOUTH AFRICA. 


MADE IN ALL SIZES AND 
VALVES FOR ALL PURPOSES AND 
PRESSURES. 
CORRESPONDENCE SOLICITED. 
13 


ENGINE 
AND 


TURRET 
LATHES 


WITH 


Patent or 





Cone Pulley 


Headstock 


Sizes 14” to 48” swing. 
THE LODGE AND SHIPLEY MACHINE TOOL CO. 


CINCINNATI, OHIO, U. S. A. 








THE AMERICAN 
PIPE MFG. CO. 


ENGINEERS AND CONTRACTORS FOR 


Water-Works 


————_—_——_————Manufacturers 0of—————_— 


PHIPP’S HYDRAULIC PIPE 


112 NORTH BROAD STREET 
PHILADELPHIA 





A Correct Solution for every Grinding Problem 


IS FOUND IN 


Norton Grinding Wheels 


MADF OF 


ALUNDUM 


the abrasive which possesses the attributes of sharpness, 
right temper and untformity 


Booklet Alundum 465E on Request 


NORTON COMPANY, Worcrsten mass. 


Alundum Plant, Niagara Falls, New York 


NEW YORK OFFICE CHICAGO STORE 
26 Cortland Street, Havemeyer Building 48 South Canal Street 


GARVIN 


Milling Machines, 
Profilers, 

Screw Machines, 
Monitor Lathes, 
=~ LappingMachines, | 
=. We Gang Drill Presses, | 


















7 SRN Cutter Grinders, 
S Hand Lathes, 


NEW DESIGNS. NEW IMPROVEMENTS. 
Write for Catalogue. 


THE GARVIN MACHINE CoO,., 


Spring and Varick Streets, New York City. 


Agents in all Principal Cities. 


15 


THE 


ANSONIA BRASS & COPPER CO. 


MANUFACTURERS OF 


COPPER WIRE AND CABLES 


For Trolley Roads, Electric Lighting Companies, 
Power Transmission Plants, Etc. 


DRAWN COPPER BARS 


For Switchboards, Commutators, Armatures, Etc. 


SOLE MANUFACTURERS 
rT 
TOBIN BRONZE” 
Rods for Yacht Shafting, Bolts, Pump Pistons; also Sheets, Tubes, Etc. 


99 JOHN ST., NEW YORK CITY 





WELDLESS STEEL WIRE CHAIN. 
TWICE THE STRENGTH OF WELDED. 






TRIUMPH PATTERN. 14 sizes. 
Send for results of voluntary tests made by the 
British Scientific Society. 


THE BRIDGEPORT CHAIN CO., Bridgeport, Conn. 
WE MAKE OVER TEN MILES PER DAY. 





xh 


The General Electric Gompany's 


Type M Control 
(Sprague-General Electric System) . 


FOR ELECTRIC TRAINS HAS ‘BEEN ADOPTED “EXCLU= 
SIVELY BY THE NEW YORK UNDERGROUND RAILWAY. - 


(Interborough Rapid Transit Company ) 


4LL ELECTRIC TRAINS ON MANHATTAN ISLAND ARE 
EQUIPPED WITH THE SPRAGUE-GENERAL 
ELECTRIC SYSTEM OF CONTROL. 


General Office: SCHENECTADY, N. Y. 
New York Office: 44 Broad Street. Sales Offices in all large cities 


ATLAS 
PORTLAND 
CEMENT 


Is the Standard American Brand. 








Used by all the leading Engineers and 
Contractors throughout the United States, 
and preferred by the U. S. Government. 


ATLAS PORTLAND CEMENT CO., 


3 BROAD STREET, __ NEW YORK. — 


PYRON IIlililillMitit 


FOR ALL TECHNICAL PURPOSES. 





The Queen Mercurial Pyrometer, for Stack Temper- 
atures, reading to 1ooo° F. 


The Queen Metallic Pyrometer, for Oven Temper- 


atures, reading to 1500° F. 


The Queen-Chatelier Pyrometer, for Furaace Tem. 
peratures, with direct reading scale to 3000° F. 


For a complete list and descriptions of the Pyrometers 
manufactured by us send for our Pyrometer Catalogue. 


QUEEN & CO., Inc. 


N.W. CORNER OF EIGHTH AND ARCH STREETS 
PHILADELPHIA 


KEUFFEL & ESSER CO. 


127 FULTON ST.,N.Y. General Offices and Factories, HOBOKEN, N. J. 
CHICAGO—ST. LOUIS—SAN FRANCISCO 


DRAWING MATERIALS. MATHEMATICAL AND SURVEYING 
INSTRUMENTS. MEASURING TAPES ; 


Our Paragon Drawing Instruments enjoy 
an excellent and wide reputation. They are 
of the most precise workmanship, the finest 
finish, the most practical design, and are made 
in the greatest variety. We also have Key. 
Excelsior and other brands of instruments. 

We carry the largest and most complete 
assortment of Drawing Papers, Tracing Cloths 
ere we appriccsatay and Papers, Blueprint, Blackprint and Brown- 
print Papers, Profile Papers. 

K & BE Measuring Tapes, Steel, Metallic, Linen. 
Most accurate. Best quality. Largest assortment. 

We make the greatest variety of engine-divided 
Slide Rules, and call especial attention toour Patented 
Adjustment, which insures permanent, smooth work- 
ing of the slide. Some of our other well-known cal- 
culating instruments are the Reckoning Machine, 
Fuller’s Slide Rule, Thacher’s Calculating Instrument, 
Spery’s Pocket Calculator, etc. 











Our complete 
(550 page) catalogue oe 
on request 








